May 2012 

NASA/CR–2012-217567 

Nonlinear Motion Cueing Algorithm: Filtering 

at Pilot Station and Development of the 

Nonlinear Optimal Filters for Pitch and Roll 

Kirill B. Zaychik and Frank M. Cardullo 

State University of New York, Binghamton, New York 
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May 2012 

NASA/CR–2012-217567 

Nonlinear Motion Cueing Algorithm: Filtering 

at Pilot Station and Development of the 

Nonlinear Optimal Filters for Pitch and Roll 

Kirill B. Zaychik and Frank M. Cardullo 

State University of New York, Binghamton, New York 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 

The use of trademarks or names of manufacturers in this report is for accurate reporting and does not 

constitute an official endorsement, either expressed or implied, of such products or manufacturers by the 

National Aeronautics and Space Administration. 
i 

I. Abstract 

Telban and Cardullo [1] have developed and successfully implemented the nonlinear optimal motion cueing algorithm at the Visual Motion Simulato r (VMS) at the 

NASA Langley Research Center in 2005. Th e latest version of the non-linear algorithm 

performed filtering of m otion cues in all de grees-of-freedom except for pitch and roll. 

This manuscript describes the development and implementation of the non-linear optimal 

motion cueing algorithm for the pitch and roll degrees of f reedom. Presented results 

indicate improved cues in the specified channels as compared to the original design. 

To further advance motion cueing in general, this manuscript describes 

modifications to the ex isting algorithm, which allow for filtering at the location of the 

pilot’s head as opposed to the centroid of the motion platform. The rational for such 

modification to the curing algorithms is that the location of the pilot’s vestibular system 

must be taken into account as opposed to the off-set of the centroid of the cockpit relative 

to the c enter of rotation alone. Results provided in this report suggest improved 

performance of the motion cueing algorithm. 
 ii

THIS PAGE INTENTIONALLY LEFT BLANK 
II. Contents 

 	
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iv

2.6. newopt4.f........................................................................................................ 55

2.7. nfilr.f............................................................................................................... 59

2.8. nfilp.f .............................................................................................................. 62

2.9. nfilq.f .............................................................................................................. 65

2.10. nfilx.f........................................................................................................... 68

2.11. nfily.f........................................................................................................... 72

2.12. nfilz.f........................................................................................................... 76

2.13. resetc2.f....................................................................................................... 79

2.14. simq.f .......................................................................................................... 83

2.15. state4.f......................................................................................................... 84

2.16. vmult.f......................................................................................................... 91

2.17. winit4.f........................................................................................................ 91

Appendix B. Non-linear optimal algorithm: filtering at platform centroid (original) vs. 

filtering at PS (modified) ................................................................................................ 102

1. Pitch ..................................................................................................................... 102

2. Roll....................................................................................................................... 109

3. Yaw...................................................................................................................... 115

4. Surge .................................................................................................................... 122

5. Sway..................................................................................................................... 128

6. Heave ................................................................................................................... 134

Appendix C. Non-linear optimal algorithm: original vs. augmented ............................. 141

1. Pitch ..................................................................................................................... 141

2. Roll....................................................................................................................... 148

3. Yaw...................................................................................................................... 154

4. Surge .................................................................................................................... 161

5. Sway..................................................................................................................... 168

6. Heave ................................................................................................................... 174

Appendix D. Non-linear optimal algorithm: original applied at PS (filt. @ PS Original) 

vs. augmented (Augmented)........................................................................................... 181

1. Pitch ..................................................................................................................... 181

2. Roll....................................................................................................................... 188

3. Yaw...................................................................................................................... 195

4. Surge .................................................................................................................... 202

5. Sway..................................................................................................................... 209

6. Heave ................................................................................................................... 216

References....................................................................................................................... 223
v

II. List of Tables

Table 3.1. Upper and Lower ball joints coordinates......................................................... 15

Table 3.2. Characteristics of the input signal for each degree of freedom ....................... 18
vi

II. List of Figures

Figure 2.1. Vehicle simulator structure. Adopted from Telban and Cardullo [1] .............. 2

Figure 2.2. Reference frames used in the algorithm and their mutual orientation. Adopted 

from Teban and Cardullo [1] .............................................................................................. 3

Figure 2.3. VMS motion system geometry. Adapted from Telban and Cardullo [1]......... 4

Figure 2.4. Linear Optimal Algorithm Structure. Adopted from Telban and Cardullo [1] 8

Figure 2.5. Optimal Algorithm Implementation for Longitudinal Mode. Adopted from 

Telban and Cardullo [1]...................................................................................................... 9

Figure 2.6. Non-linear Optimal Cueing Algorithm Structure. Adopted from Telban and 

Cardullo [1]....................................................................................................................... 10

Figure 2.7. Nonlinear optimal algorithm implementation. Longitudinal mode. Adopted 

from Telban and Cardullo [1] ........................................................................................... 10

Figure 2.8. Nonlinear Algorithm Implementation with Unity-Gain Pitch Filter. Adopted 

from Telban and Cardullo [1]. .......................................................................................... 11

Figure 3.1. Geometrical interpretation of the 

FrS

reference frame shift from 

OS

(centroid 

of the upper motion platform) to 

OPS

(pilot station)........................................................ 14

Figure 3.2. Vectors of the j-th actuator............................................................................. 14

Figure 3.3. Variables (accelerations) flow........................................................................ 16

Figure 3.4. The modified version of the online implementation of the nonlinear washout 

filter (longitudinal channel) .............................................................................................. 17

Figure 3.5. Nonlinear Algorithm Implementation for Yaw Mode.................................... 19

Figure 3.6. Aircraft and Platform accelerations at the centroid of the motion platform... 20

Figure 3.7. The XY plane of the 

a

Fr

, when being placed at the centroid of the motion 

platform............................................................................................................................. 21

Figure 3.8. Tilt angular velocities for sway and surge channels....................................... 22

Figure 3.9. Aircraft and Simulator sensed Specific Forces and Angular Rates................ 22

Figure 4.1. Nonlinear Algorithm implementation for longitudinal mode. The dotted box 

in this figure encompasses the pitch channel. Adopted from Telban and Cardullo [1].... 26

Figure 4.2. Flowchart of the augmented nonlinear washout algorithm. NFILP and NFILQ 

are the Riccati equation solvers for the roll and pitch channels respectively ................... 28

Figure 4.3. NFILQ subroutine flowchart .......................................................................... 29

Figure 4.4. NFILP subroutine flowchart........................................................................... 30

Figure 4.5. STATE4 subroutine flowchart ....................................................................... 31

Figure 4.6. Sensed specific force and angular rates for the pitch channel, with the tuned 

version of the nonlinear washout filter ............................................................................. 32

Figure 4.7. Sensed specific force and angular rates for the pitch channel, with the tuned 

version of the nonlinear washout filter ............................................................................. 36

Figure B.1. 1. .................................................................................................................. 102

Figure B.1. 2. .................................................................................................................. 103

Figure B.1. 3. .................................................................................................................. 104

Figure B.1. 4. .................................................................................................................. 105

Figure B.1. 5. .................................................................................................................. 106

Figure B.1. 6. .................................................................................................................. 107

Figure B.1. 7. .................................................................................................................. 108
vii

Figure B.2. 1. .................................................................................................................. 109

Figure B.2. 2. .................................................................................................................. 110

Figure B.2. 3. .................................................................................................................. 111

Figure B.2. 4. .................................................................................................................. 111

Figure B.2. 5. .................................................................................................................. 112

Figure B.2. 6. .................................................................................................................. 113

Figure B.2. 7. .................................................................................................................. 114

Figure B.3. 1. .................................................................................................................. 115

Figure B.3. 2. .................................................................................................................. 116

Figure B.3. 3. .................................................................................................................. 117

Figure B.3. 4. .................................................................................................................. 118

Figure B.3. 5. .................................................................................................................. 119

Figure B.3. 6. .................................................................................................................. 120

Figure B.3. 7. .................................................................................................................. 121

Figure B.4. 1. .................................................................................................................. 122

Figure B.4. 2. .................................................................................................................. 123

Figure B.4. 3. .................................................................................................................. 124

Figure B.4. 4. .................................................................................................................. 124

Figure B.4. 5. .................................................................................................................. 125

Figure B.4. 6. .................................................................................................................. 126

Figure B.4. 7. .................................................................................................................. 127

Figure B.5. 1. .................................................................................................................. 128

Figure B.5. 2. .................................................................................................................. 129

Figure B.5. 3. .................................................................................................................. 130

Figure B.5. 4. .................................................................................................................. 130

Figure B.5. 5. .................................................................................................................. 131

Figure B.5. 6. .................................................................................................................. 132

Figure B.5. 7. .................................................................................................................. 133

Figure B.6. 1. .................................................................................................................. 134

Figure B.6. 2. .................................................................................................................. 135

Figure B.6. 3. .................................................................................................................. 136

Figure B.6. 4. .................................................................................................................. 137

Figure B.6. 5. .................................................................................................................. 138

Figure B.6. 6. .................................................................................................................. 139

Figure B.6. 7. .................................................................................................................. 140

Figure C.1. 1. .................................................................................................................. 141

Figure C.1. 2. .................................................................................................................. 142

Figure C.1. 3. .................................................................................................................. 143

Figure C.1. 4. .................................................................................................................. 144

Figure C.1. 5. .................................................................................................................. 145

Figure C.1. 6. .................................................................................................................. 146

Figure C.1. 7. .................................................................................................................. 147

Figure C.2. 1. .................................................................................................................. 148

Figure C.2. 2. .................................................................................................................. 149

Figure C.2. 3. .................................................................................................................. 150

Figure C.2. 4. .................................................................................................................. 151
viii

Figure C.2. 5. .................................................................................................................. 151

Figure C.2. 6. .................................................................................................................. 152

Figure C.2. 7. .................................................................................................................. 153

Figure C.3. 1. .................................................................................................................. 154

Figure C.3. 2. .................................................................................................................. 155

Figure C.3. 3. .................................................................................................................. 156

Figure C.3. 4. .................................................................................................................. 157

Figure C.3. 5. .................................................................................................................. 158

Figure C.3. 6. .................................................................................................................. 159

Figure C.3. 7. .................................................................................................................. 160

Figure C.4. 1. .................................................................................................................. 161

Figure C.4. 2. .................................................................................................................. 162

Figure C.4. 3. .................................................................................................................. 163

Figure C.4. 4. .................................................................................................................. 164

Figure C.4. 5. .................................................................................................................. 165

Figure C.4. 6. .................................................................................................................. 166

Figure C.4. 7. .................................................................................................................. 167

Figure C.5. 1. .................................................................................................................. 168

Figure C.5. 2. .................................................................................................................. 169

Figure C.5. 3. .................................................................................................................. 170

Figure C.5. 4. .................................................................................................................. 171

Figure C.5. 5. .................................................................................................................. 171

Figure C.5. 6. .................................................................................................................. 172

Figure C.5. 7. .................................................................................................................. 173

Figure C.6. 1. .................................................................................................................. 174

Figure C.6. 2. .................................................................................................................. 175

Figure C.6. 3. .................................................................................................................. 176

Figure C.6. 4. .................................................................................................................. 177

Figure C.6. 5. .................................................................................................................. 178

Figure C.6. 6. .................................................................................................................. 179

Figure C.6. 7. .................................................................................................................. 180

Figure D.1. 1. .................................................................................................................. 181

Figure D.1. 2. .................................................................................................................. 182

Figure D.1. 3. .................................................................................................................. 183

Figure D.1. 4. .................................................................................................................. 184

Figure D.1. 5. .................................................................................................................. 185

Figure D.1. 6. .................................................................................................................. 186

Figure D.1. 7. .................................................................................................................. 187

Figure D.2. 1. .................................................................................................................. 188

Figure D.2. 2. .................................................................................................................. 189

Figure D.2. 3. .................................................................................................................. 190

Figure D.2. 4. .................................................................................................................. 191

Figure D.2. 5. .................................................................................................................. 192

Figure D.2. 6. .................................................................................................................. 193

Figure D.2. 7. .................................................................................................................. 194
ix

Figure D.3. 1. .................................................................................................................. 195

Figure D.3. 2. .................................................................................................................. 196

Figure D.3. 3. .................................................................................................................. 197

Figure D.3. 4. .................................................................................................................. 198

Figure D.3. 5. .................................................................................................................. 199

Figure D.3. 6. .................................................................................................................. 200

Figure D.3. 7. .................................................................................................................. 201

Figure D.4. 1. .................................................................................................................. 202

Figure D.4. 2. .................................................................................................................. 203

Figure D.4. 3. .................................................................................................................. 204

Figure D.4. 4. .................................................................................................................. 205

Figure D.4. 5. .................................................................................................................. 206

Figure D.4. 6. .................................................................................................................. 207

Figure D.4. 7. .................................................................................................................. 208

Figure D.5. 1. .................................................................................................................. 209

Figure D.5. 2. .................................................................................................................. 210

Figure D.5. 3. .................................................................................................................. 211

Figure D.5. 4. .................................................................................................................. 212

Figure D.5. 5. .................................................................................................................. 213

Figure D.5. 6. .................................................................................................................. 214

Figure D.5. 7. .................................................................................................................. 215

Figure D.6. 1. .................................................................................................................. 216

Figure D.6. 2. .................................................................................................................. 217

Figure D.6. 3. .................................................................................................................. 218

Figure D.6. 4. .................................................................................................................. 219

Figure D.6. 5. .................................................................................................................. 220

Figure D.6. 6. .................................................................................................................. 221

Figure D.6. 7. .................................................................................................................. 222
x

III. Nomenclature

In order to be consistent with the original non-linear optimal algorithms developed 

report by Telban and Cardullo [1], similar nomenclature was adopted in the current 

report.

Symbols

a acceleration 

a a a x y z    

T

a

Aj coordinates of the upper bearing block of the j-th actuator 

Bj coordinates of the lower bearing block of the j-th actuator

A, B, C, D, H matrices of the state-space model of a control system 

A

system matrix of the standard form optimal control system

d e, , , ,   

NASA adaptive algorithm washout parameters 

E objective function or energy norm for neurocomputing approach

e pilot sensation error

Fr reference frame

f

specific force 

ˆ

f

sensed specific force

GO, GS gain sensitivities in the otolith and semicircular canals models

g acceleration due to gravity

J system cost function

K state feedback gain matrix

j

l

length of the j-th motion platform actuator

LSI transformation matrix from simulator into inertial frame
xi

P solution of the algebraic Riccati equation

Q, R, Rd weighting matrices in a cost function (tracking form)

Q2 weighting matrix for nonlinear algorithm control law

 R , R , R 1 2 12

weighting matrices in a cost function (standard form)

R radius vector

s Laplace variable

TS transformation matrix from angular velocity to Euler angle rates

T0, T1, T2, T3, T4 coefficients in the semicircular canal sensation model

u input to a control system

u

input to the standard form optimal control system

v error output of neurocomputing solver

w white noise

W(s) optimal algorithm transfer function matrix

x system state vector

y desired state space system output

z excitatory input signal for neurocomputing system

 prescribed degree of nonlinearity for nonlinear algorithm

β

Euler angles 

    

T

β

 pilot control input vector 

 filtered white noise break frequency

 learning parameter for neurocomputing solver



time constants in the semicircular and otolith sensation models

 density of the otoconial membrane
xii ω

angular velocity about the body frame 

  pqr

T ω 

ω

ˆ

sensed angular velocity

Subscripts

Subscripts indicate to what the main symbol is related.

( )A aircraft

( )CG center of gravity of aircraft

( )d simulator states included in the cost function

( )e sensation or perceptual error

( )I inertial reference frame

( )j j-th actuator of the motion platform

( )n white noise input states

( )OTO otolith model

( )PS pilot station

( )PA pilot in the aircraft

( )S simulator

( )SCC semicircular canals sensation model

( )ST simulator tilt coordination channel

( )VEST human vestibular system

( )VIS human visual system

( )x,y,z x, y, or z component

( ) relates to system with nonlinearity
xiii

Superscripts

Superscripts indicate which reference frame the main symbol is in

( )Ain aircraft reference frame FrA

( )Iin inertial reference frame FrI

( )Sin simulator reference frame FrS
1

1. Introduction

This report documents the modifications to the NASA Non-Linear Optimal Motion 

Cueing Algorithm. The report consists of two major parts. 

The first part describes modifications to the non-linear optimal algorithm, which are 

needed in order to perform filtering at the pilot station location as opposed to the original 

design of the algorithm where filtering was done at the centroid of the motion platform of 

the simulator. The essence of such a modification is in shifting the origin of the simulator 

attached reference frame from the centroid of the motion platform to wherever the 

location of the pilot station is. It could be the pilot’s head or pilot’s abdomen for instance. 

The new algorithm evaluation is also presented. 

The second part of the report describes the development of the non-linear optimal 

filters for the additional two rotational degrees of freedom such as pitch and roll. In the 

original design of the algorithm only scaling and limiting was implemented for these 

rotational degrees of freedom. Note, that for the yaw channel the nonlinear washout filter 

was successfully implemented by Telban and Cardullo [1]. This report also delivers the 

FORTRAN code necessary for successful implementation of these algorithms on the 

NASA Langley Visual Motion Simulator (VMS).

It is assumed that the reader is familiar with the original work on development of 

the non-linear optimal algorithm performed by Telban and Cardullo [1]. For that reason 

some of the sections of the report are relatively concise.

2. Background

Figure 2.1 illustrates the basic vehicle simulator structure. As one can see, the 

motion cueing algorithm plays an essential part in the entire simulator architecture. The 

prime objective of any motion cueing algorithm is to provide a human operator with an 

array of cues, which will evoke behavior consistent with that in the real aircraft. It is 

obvious that due to some physical limitations none of the existing ground simulators are 

capable of delivering that 100%. Hence, motion cueing algorithms are designed to “trick” 
2

a person into believing that he/she is experiencing cues similar to those in a real flight. 

The latest innovation in this area is the non-linear optimal algorithm designed by Robert 

Telban and Frank Cardullo [1]. This chapter is dedicated to describing basic concepts of 

the non-linear washout algorithm. However, for better understanding of the non-linear 

algorithm, the description of the linear optimal algorithm is given first. Some 

mathematical aspects of on-line implementation are addressed in this chapter along with 

the description of the human perceptual models utilized in the non-linear as well as lineal 

optimal algorithms. 

Figure 2.1. Vehicle simulator structure. Adopted from Telban and Cardullo [1]

2.1. Simulator geometry and reference frames

There are four reference frames involved in algorithm design: aircraft center of 

gravity reference frame (RF), FrCG, aircraft RF, FrA, simulator RF, FrS, and the inertial 

RF, FrI. Figure 2.2 illustrates these RFs as they are oriented in space and with respect to 

each other. It can be seen that FrCG has its origin in the center of gravity of the aircraft. 

FrS is attached to the centroid of the upper motion platform of the simulator. Zs is 

directed downward and perpendicular to the plane of the motion platform. Xs is looking 

Vehicle States

Desired 

Platform States

Actuator Extension

Commands

Simulator

Control Input

Vehicle Dynamics

Model

Motion Cueing 

Algorithm

Kinematic

Transformation

Platform

Dynamics

Platform

Motion
3

forward, whereas Ys is pointing toward the pilot’s right hand side. FrA is associated with 

the similar point in the aircraft cockpit as FrS on the simulator platform. All three RFs are 

parallel to each other. The inertial RF FrI is attached to the simulator motion system base. 

FrI is oriented in such a way that ZI is parallel to gravity vector and YI pointing to the 

right with respect to the simulator operator.

Figure 2.2. Reference frames used in the algorithm and their mutual orientation. 

Adopted from Telban and Cardullo [1]

The NASA Langley VMS motion system is a six degrees of freedom synergistic 

type device. The geometry of this motion system is shown in Figure 2.3.

XPA FrPA

FrA

FrPS

FrS

FrI

Aircraft

Simulator

ZPA

XA

ZA

ZPS

XS

ZS

XI

RA

RS

RI

XCG

ZCG

FrCG

RCG

ZI
4

Figure 2.3. VMS motion system geometry. Adapted from Telban and Cardullo [1]

3

l

2

l

5

l

1

l

4

l

6

l

OI

OS

4

3

5

6

2

1

A4

A5 A3

A6

A1

A2

5 4

3

6

1 2

Fixed

Platform

Motion

Platform
5

2.2. Human perceptual system models

Another characteristic of this motion cueing algorithm is that it incorporates a 

model of the human vestibular system, with the new semicircular canal and otoliths 

models. A new integrated visual-vestibular perception model is also involved in the 

design. Note that the models of semicircular canals, otoliths and visual-vestibular 

interaction constitute the perceptual model of a pilot. Figure 2.6 illustrates how such a 

model falls into the entire concept of washout filters.

2.2.1. Semicircular canals

The semicircular canals are responsible for sensing angular motion. For the 

implementation into the linear optimal as well as nonlinear optimal algorithms the 

following mathematical model of the semicircular canals was presented [1]:

 

   

 

 1 2  

1

,

1 1 1

c L a

SCC

a

s s s

K

s s s s

  

   

    

    

      

 (2.1)

where 

( ) c  s

is the deflection of the cupula (a leaf-like structure in the semicircular 

canals, which deflects if the head is accelerated or decelerated) and 

( )s

is the stimulus 

acceleration. This model takes into account both the semicircular canal dynamics and 

neural transduction dynamics. For implementation into the linear optimal and non-linear 

optimal cueing algorithms, angular velocity is employed as a stimulus, requiring the 

following transfer function:

 

   

 

  

ˆ 80 1 0.06

5.73 ,

1 80 1 5.73 1 0.005

s s s

s s s s









  

 (2.2)

where 

( )s

and 

( )s

are stimulus and sensed angular velocities respectively.

Note that for the online implementation of the algorithm, a reduced form of the 

transfer function was used, which is given in equation (2.3) 

 

    

ˆ 80 5.73 ,

1 80 1 5.73

s s

s s s







 

 (2.3)

 
6

2.2.2. Otoliths

The otolith organs are the elements of the vestibular system that provide linear 

motion sensation in humans and mammals. These organs are responsive to specific 

force, responding to both linear acceleration and tilting of the head with respect to the 

gravity vector. Telban and Cardullo [1] proposed the following otolith model, which 

provides the relationship between the sensed response and the specific force stimulus:

 

 1 2  

ˆ 1

,

1 1

L

OTO

f s

K

f s s



 





 

 (2.4)

where KOTO = 0.4, 1 = 5 sec, 2 = 0.016 sec, and L = 10 sec. For implementation 

into the motion cueing algorithms, Eq. 2.4 can be rewritten as

 

  

0

0 1

ˆ

, OTO

f s A

K

f s B s B







 

 (2.5)

where A0 = 1/L, B0 = 1/1, B1 = 1/2, and 

1 2 / . K K OTO OTO L



   

2.2.3. Human Vestibular model

The following section illustrates how the otolith and semicircular canals models 

are integrated together for further utilization in the nonlinear optimal washout algorithm. 

According to the formulation of the non-linear washout algorithm, which will be 

presented in the last section of this chapter, the human perceives the signal u, comprised 

of both the angular velocity and translational accelerations: 

1

2

.

x

u

u

a u

    

         

 (2.6)

The semicircular canal model (Eq. (2.2)) can be rewritten in a more formal way:
7

 

   

2

1

1

1 2

ˆ 1

,

1 1 1

SCC a L

a

G s s

u

s s s

  



  





  

 (2.7)

where values for semicircular canals time constants 1, 2, a, and L are given in Eq. 2.2, 

and GSCC is the angular velocity threshold that scales the response to threshold units. Eq. 

2.7, in turn, can be rewritten as

3 2

4 3

3 2 1

2 1 0

ˆ

,

T s T s

u

s T s T s T







  

 (2.8)

where:

1 2 1 2   1 2

0 1 2 3 2 4 2

1 2 1 2 1 2

1

, , , / , and / , a a

SCC SCC L

a a a

T T T T G T G          

        

   

    

and can be defined in state space notation as

ˆ

 ,

 

 

SCC SCC SCC SCC

SCC SCC SCC

x A x B u

C x D u

 (2.9)

which in observer canonical form is,

   

2 3 2 4

1 1 4 4

0 0 4

1 0 0

0 1 , 0 , 1 0 0 , and 0 .

0 0 0

T T T T

T TT T

T T T

     

   

         

         

A B C D SCC SCC SCC SCC

On the other hand, the otolith model (Eq. 2.4) can be redefined in a state space 

notion as: 

ˆ

,

x

f

 

 

OTO OTO OTO OTO

OTO OTO OTO

x A x B u

C x D u

 (2.10)

where 

xOTO

are the otoliths states, and

   

0 1 0 0 0 0

1 0 0 0

0 0 0 0 0 0 , ,

0 0 0 0 1 0

0 0 0 0

1 0 0 1 0 , 0 . OTO OTO Sz

c

b a d ac

e

f

b a h a f

G K R

   

   

  

 

      

   

OTO OTO

OTO ΟΤΟ

A B

C D
8

The representations in Eq. 2.9 and 2.10 can be combined to form a single 

representation for the human vestibular model:

ˆ ,

 

 

V V V V

V V V V

x A x B u

y C x D u

 (2.11)

where 

V x

and 

ˆ

V y

are, respectively, the combined states and sensed responses, and AV, 

BV, CV, and DV represent the vestibular models as one set of state equations:

, , , .

       

                   

SCC SCC SCC SCC

OTO OTO OTO OTO

V V V V

A 0 B C 0 D

A B C D

0 A B 0 C D

2.3. Linear Optimal Algorithm formulation

Before getting to the description of the non-linear optimal washout algorithm, 

some background information on the linear optimal algorithm is presented. Note that both 

algorithms are designed based on the same principles and concepts. The major 

differences are in real-time implementation of washout filters.

Figure 2.4 contains the block diagram of the linear optimal algorithm structure.

Vestibular

System

Platform

Dynamics

Vestibular

System W(s)

Aircraft

States uA

Simulator

States uS

Sensation

Error e

Aircraft Pilot

Simulator Pilot

Figure 2.4. Linear Optimal Algorithm Structure. Adopted from Telban and 

Cardullo [1]
9

Since the entire purpose of the washout filters is to minimize the sensation error, 

the transfer function matrix W(s), which relates the desired simulator motion input to the 

aircraft input, is to be determined. In other words the elements of W(s) are the 

coefficients of the washout filter. The linear optimal algorithm generates the desired 

transfer functions W(s) by solving the Riccati equation by an off-line program, which are 

then implemented on-line. Figure 2.5 illustrates how the linear optimal washout filters are 

implemented on-line.

Figure 2.5. Optimal Algorithm Implementation for Longitudinal Mode. Adopted 

from Telban and Cardullo [1]

2.4. Non-linear Optimal Algorithm

The non-linear optimal algorithm is formulated in a similar fashion to that of the 

linear optimal algorithm, except for the differences in computing the matrix W(s). The 

structure of the algorithm is shown in Figure 2.6.

As can be seen the solution to the Riccati equation, which was obtained offline in 

the linear optimal algorithm, is now implemented in real time, resulting in the necessary

matrix for computing the desired non-linear optimal filters.
10

Perceptual

System

Platform

Dynamics

Perceptual

System

Nonlinear

Cueing

Filters

Aircraft

States uA

Simulator

States uS

Perceptual

Error e

Control

Law

Riccati Eqn

Solver

Aircraft Pilot

Simulator Pilot





Figure 2.6. Non-linear Optimal Cueing Algorithm Structure. Adopted from Telban 

and Cardullo [1]

Figure 2.7 illustrates how the non-linear washout filter is formulated for the 

longitudinal mode.

Figure 2.7. Nonlinear optimal algorithm implementation. Longitudinal mode. 

Adopted from Telban and Cardullo [1]

LSI

Nonlinear

Scaling

TS

Nonlinear

Scaling

Tilt Rate

Limit

A

β

A

β

A

A

a

A ωA

I

A

a

S

β

+

βA +



βSR



βS



βST



I

S

I

S



State

Equations

1

s

1

s

1

s

Riccati 

Solver

I

S



Kα

State

Equations

Riccati 

Solver

Kα
11

There are two separate filtering channels for translational and rotational degrees 

of freedom with the cross-feed path providing tilt coordination cues.

The aircraft acceleration is first transformed from the simulator attached RF to the 

inertial RF. The signal is then passed through the non-linear scaling and limiting block. 

The resulting signal then becomes an input to the “State Equations” block, from which 

the simulator translational acceleration is produced. This acceleration is integrated twice 

to produce the simulator translational position command 

SI

. Signals 

SI

and 

I S

form a 

feedback loop and serve as inputs to the “Riccati Solver” block. The solution to the 

Riccati equation is the matrix K(α), which is fed back to “State Equations” block.

The aircraft angular velocity 

A A

is transformed to the Euler angular rate (

 A



). 

Next it is limited and scaled. A separate set of State equations is employed along with the 

Riccati solver. The resulting signal is



S - the simulator angular position command. For 

the previous on-line implementation, however, the case of a unity-gain pitch (and roll) 

filter was implemented. Hence, Figure 2.7 can be redrawn as it is shown in Figure 2.8.

Figure 2.8. Nonlinear Algorithm Implementation with Unity-Gain Pitch Filter. 

Adopted from Telban and Cardullo [1].
12

The simulator translational SI and angular



S position commands are then 

transformed from degrees-of-freedom space to simulator actuator space. Actuator 

commands are then generated to achieve the desired simulator platform motion.

As one might already be aware, solving the Riccati equation in real time is a 

computationally challenging task. Conventionally a Newton-Raphson technique is 

utilized for that purpose. The main drawback is that it involves a matrix inversion, which 

can result in singular solutions for ill-conditioned systems. The non-linear optimal 

algorithm uses the structured neural network to solve the Riccati equation in real time. 

The main advantage of the neural computing approach over the Newton-Raphson is 

speed due to the fact that neither matrix inversion nor computation of the Jacobian matrix 

as a Kronecker product is required. Moreover, the problem of having a singular solution 

eliminates itself, since no matrix inversion is involved.
13

3. Development of transformation equations for cues 

determined at pilot’s station

3.1. Modifications of the original nonlinear optimal algorithm

Before continuing with this section of the report a new terminology shall be 

introduced. Pilot’s Station (PS) is the point in the simulator cockpit where washout filters 

are applied. In the original design of the non-linear optimal algorithm filtering was 

applied at the origin of the simulator reference frame Frs. This report proposes 

modification to the original non-linear algorithm, which position the PS at the location of 

the pilot’s head. The rational here is such that filtering must be performed at the location 

of the pilot’s vestibular apparatus.

3.1.1. Filtering at Pilot’s Station.

According to the theory of washout filter development the location where the 

actual “filtering” is being performed is associated with the location of the origin of the 

simulator reference frame. As has been previously mentioned, in the original design of 

the algorithm the location of the origin of the simulator attached RF is at the centroid of 

the upper motion platform. Hence the essence of applying non-linear washout filters at 

the PS location as opposed to the centroid of the upper joint bearings of the motion 

platform is, in fact, the shift of the simulator related reference frame FrS from the motion 

platform to wherever the PS is located. The given shift vector 

RSS

(Figure 3.1) has the 

following coordinates in 

FrS

: [0.0254, -0.653, -2.1946] (unique to the NASA Langley 

Visual Motion Simulator, VMS). The vectors 

AiS

connect the origin of the PS to each 

platform attach point. 

BjS

vectors will change as well. These vectors are different from 

the original implementation and are computed by means of a simple coordinate 

transformation. Table 3.1 contains coordinates of 

AiS

vectors before and after the 

transformation.
14

Figure 3.1. Geometrical interpretation of the 

FrS

reference frame shift from 

OS

(centroid of the upper motion platform) to 

OPS

(pilot station)

Figure 3.2. Vectors of the j-th actuator

OI

OS

OPS

lj

Bj



Rss

Aj

Aj



Bj

RI

Rj

OI

OS

A4S

A3S

A2S

A1S

A5S

A6S

A6S



A5S



A3S



A4S



A2S

1S



A

RSS

S

X

A

Y

A

XI

YI ZI

OP

S
15

Figure 3.2 demonstrates the relative location of the upper and lower ball joint 

bearings of the j-th actuator of the simulator. It is quite obvious that when the location of 

the 

FrS

origin is shifted from 

OS

to 

OPS

, RIand 

Aj

(along with 

Bj

) are changed 

accordingly. 

Table 3.1. Upper and Lower ball joints coordinates

Original Modified

Vector coordinates Vector coordinates

A1

[2.1117179, 0.0762, 0.0]

A1



[2.0863179, 0.7112, 2.1946]

A2

[2.1117179, –0.0762, 0.0]

A2



[2.0863179, 0.5588, 2.1946]

A3

[-0.98986594, –1.8669, 0.0]

A3



[-1.01526594, –1.2319, 2.1946]

A4

[-1.12184942, –1.7907, 0.0]

A4



[-1.14724942, –1.1557, 2.1946]

A5

[-1.12184942, 1.7907, 0.0]

A5



[-1.14724942, 2.4257, 2.1946]

A6

[-0.98986594, 1.8669, 0.0]

A6



[-1.01526594, 2.5019, 2.1946]

B1

[1.5021, 1.9812, 2.5806]

B1



[1.4767, 2.6162, 4.77524]

B2

[1.5021, -1.9812, 2.5806]

B2



[1.4767, -1.3462, 4.77524]

B3

[0.9647, -2.2914, 2.5806]

B3



[0.9898, -1.6564, 4.77524]

B4

[-2.4668, -0.3102, 2.5806]

B4



[-2.4922,0.3247, 4.77524]

B5

[-2.4668, 0.3102, 2.5806]

B5



[-2.4922, 0.9452, 4.77524]

B6

[0.9647, 2.9214, 2.5806]

B6



[0.9393, 2.9264, 4.77524]

The reader should be aware that the data presented above are applicable solely to 

the VMS facility at NASA Langley.

3.1.2. Variable flow

According to the code available in the original NASA report by Telban and 

Cardullo [1] it is clear that the accelerations used as inputs to the non-linear washout 

filters are computed at the origin of the 

FrA

, i.e. at the centroid of the upper motion 

platform. The specific forces at the PS are then calculated utilizing the knowledge of the 

simulator cockpit geometry. Therefore, the variable flow (accelerations in particular) can 

be presented in a form of the following block diagram (Figure 3.3).
16

Figure 3.3. Variables (accelerations) flow

The following is a summary of changes to the original design of the algorithm that 

had been done in order to perform filtering at the PS. 

- An auxiliary block had been introduced into the block diagram of the online 

implementation of the original non-linear washout filter. This block 

calculates the a/c acceleration at the location of the pilot’s station in the 

aircraft reference frame (

FrA

). The modified version of the online 

implementation block diagram is given in Figure 3.4. The geometrical 

location of the PS in the VMS cockpit is known and defined by the vector 

[0.0254, 0.653, 2.1946] RSS  

in meters.

- Vectors, connecting the origin of the 

FrS

and the joints of the upper motion 

platform had been recalculated, taking into account the shift of 

FrS

from its 

former location at the centroid of the cockpit/upper motion platform to the 

new location at the pilot’s head (see section 3.1.1.).

Equations

Of

Motion

CG to Fra 

transformation

Non-linear 

Filters

Accelerations at the 

A/C center of gravity

Accelerations at the 

origin of Fra

NASA vehicle 

dynamics module
17

Figure 3.4. The modified version of the online implementation of the nonlinear 

washout filter (longitudinal channel)

3.1.3. Equations

The following are the equations for computing translational accelerations at the 

pilot station which are implemented in the “Translation to PS” block, in Figure 3.4.

2 2

2 2

2 2

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

A A

x x A ss ss ss PS x y z

A A

y y A ss ss ss PS x y z

A A

z z A ss ss ss PS x y z

a a R q r R pq r R pr q

a a R pq r R p r R qr p

a a R pr q R qr p R p q

      

      

      

 (3.1)

where 

[ , , ] A A A A

PS x y z PS PS PS a a a a  , [ , , ] A A A AA x y z A A A

a a a a  , [ , , ] R R R R ss ss ss ss x y z

 , [ , , ] A A

 p r q , 

and 

[ , , ] A A pqr

respectively.

3.2. New algorithm evaluation

This section of the report presents the evaluation of the modified non-linear 

optimal washout algorithm. The evaluation is done in a form of a comparative analysis 

Translation 

to PS

Nonlinear 

scaling

State 

equations

Nonlinear 

scaling

State 

equations

Riccati 

solver

Riccati 

solver

Tilt rate 

limit

LSI

1

s

1

s

1

s

A aA

A aPS

I aA

K( ) 

SI SI SI

ST

 S  S

K( ) 

 A  SR

 A

A A TS
18

against the original non-linear optimal algorithm. Comparison is performed for 6 degrees 

of freedom (3 translational and 3 rotational) and is followed by a discussion.

Table 3.2 contains information on the degree of freedom and the corresponding 

type and characteristic of the input signal. In each case, the inputs are the accelerations 

m/s2for the translational and rad/s2for rotational degrees of freedom) measured at the 

aircraft centroid.

Table 3.2. Characteristics of the input signal for each degree of freedom

Appendix B contains a set of plots for each degree of freedom. Each set consists of 

the following graphs:

- Actuator extensions (6)

- Aircraft and Simulator Sensed Specific Force (3)

- Aircraft and Simulator Sensed Angular Rate (3)

- Platform Velocity in Inertial Coordinates (3)

- Desired and Actual Platform Displacement (3)

- Specific Force at Aircraft Pilot Head (3)

- Specific Force at Simulator Pilot Head (3)

- Aircraft Angular Rate (3)

- Platform Angular Rate (3)

- Aircraft Angular Position (3)

- Desired and Actual Platform Angular Position (3)

- Aircraft Acceleration at MB Centroid (3)

Degree of freedom Input Characteristics

Longitudinal (x-channel) Ramp to step Peak magnitude: 1 m/s2

Slope: 3 m/s2/s

Lateral (y-channel) Half sine Peak magnitude: 3 m/s2

Duration: 5 s

Vertical (z-channel) Pulse Peak magnitude: 1 m/s2

Duration: 10 s

Pitch Pulse doublet Magnitude: 0.1 rad/s2

Duration: 5 s

Roll Pulse doublet Magnitude: 0.1 rad/s2

Duration: 5 s

Yaw Pulse doublet Magnitude: 0.1 rad/s2

Duration: 5 s
19

- Platform Acceleration at MB Centroid (3)

3.3. Discussions

In this section the discussion of the peculiarities of the motion platform behavior 

associated with applying of the washout filter at the PS will be presented. For that 

purpose the yaw channel was chosen. Figure 3.5 illustrates how the nonlinear filter for 

the yaw channel was implemented online.

Figure 3.5. Nonlinear Algorithm Implementation for Yaw Mode

The characteristic feature of the yaw channel is that when excited there is no 

gravity alignment issue, which is associated with the longitudinal or lateral channel. In 

other words, there is no need to tilt the motion platform to produce the sustained 

acceleration cues.

The original nonlinear washout algorithm developed by Telban and Cardullo [1]

did a very good job in simulating cues, inherent to a pure yaw motion of the aircraft. 

However, when the filtering is performed at the PS a few differences (compared to the 

original algorithm) in the behavior of the platform can be observed. For example, Figure

3.6 contains graphs for the aircraft and platform accelerations at the motion platform 

centroid.
20

Figure 3.6. Aircraft and Platform accelerations at the centroid of the motion 

platform

It can easily be seen that accelerations in the X and Y channels are nonzero when 

filtering is done at the PS. If one looks at the physics of the yaw motion of the platform, it 

is possible to reason the presence of those accelerations. Figure 3.7 illustrates the 

geometry of the motion platform if observed from the top (Figure 3.1 if observed from 

the top). The Z axis of the 

FrA

is aimed away from the reader and is perpendicular to the 

drawing, given that the origin of the 

FrA

is placed at the centroid of the motion platform. 

Vector OA represents the XY component of the vector 

Rss

.

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-X (m/s/s)

A/C Accel. at MB Centroid

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Y (m/s/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Z (m/s/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Scc-X (m/s/s)

Platform Accel. at MB Centroid 

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Y (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Z (m/s/s)

original

modified

original

modified
21

Figure 3.7. The XY plane of the 

a

Fr

, when being placed at the centroid of the motion 

platform

Consider the clockwise rotation of the platform with the angular velocity 

z

. At 

point “A” this motion will result in the tangential acceleration 

a

. In 

FrA

vector 

t a

has 

components 

x a

and 

y a

. If filtering is performed at the PS, then accelerations 

x a

and 

y a

automatically form inputs to the translational and lateral channels of the washout 

algorithm. Which, in turn, results in the sway and surge motion of the platform (Figure

3.8). 

One should also note that accelerations and angular rates resulting from this minor 

surge and sway motion of the platform is either on or below the perceptual threshold. 

Moreover, the modified algorithm resulted in better (closer to the aircraft) reproduction 

of the specific force (Figure 3.9).

A

a x  a

y a

O

z

X

Y
22

Figure 3.8. Tilt angular velocities for sway and surge channels

Figure 3.9. Aircraft and Simulator sensed Specific Forces and Angular Rates

0 5 10 15 20 25 30

-3

-2

-1

0

1

2

3

x 10-3

t (sec)

angular velocity (rad/sec))

Sway

0 5 10 15 20 25 30

-0.01

-0.005

0

0.005

0.01

t (sec)

angular velocity (rad/sec)

Surge

original

modified

original

modified

0 5 10 15 20 25 30

-0.1

-0.05

0

0.05

0.1 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

0 5 10 15 20 25 30

-0.02

0

0.02

0.04 ASFY,SSFY (m/s

2

)

0 5 10 15 20 25 30

-5

0

5

t (sec) ASFZ,SSFZ (m/s

2

)

0 5 10 15 20 25 30

-0.2

-0.1

0

0.1

0.2

ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

0 5 10 15 20 25 30

-1

-0.5

0

0.5

ASW,SSW -q (deg/s)

0 5 10 15 20 25 30

-10

0

10

20

t (sec)

ASW,SSW -r (deg/s)

aircraft

original

modified

aircraft

original act.

modified act.
23

4. Design and Development of Nonlinear Optimal 

Filters for Two Rotational Degrees of Freedom

4.1. Problem description

According to the original design of the nonlinear algorithm, filtering in the 

channels of the rotational degrees of freedom, such as pitch and roll, was confined to 

limiting and scaling only. The major task of this part of the project is to develop 

nonlinear filters for two rotational degrees of freedom: pitch and roll.

4.2. Algorithm development

4.2.1. Pitch

The derivation process is similar to that performed by Telban [1] when designing 

the nonlinear filter for the yaw channel.

The semicircular canals model described in a form of a transfer function is given 

in Eq. (4.1), which is the reduced form of the semicircular model cited in Eq. (2.7). One 

can refer to the original report by Telban [1] for a detailed explanation on how such 

reduction was made. It is worth mentioning, however, that the simplified formula cuts 

down the computational burden substantially, which is essential for real time 

applications.

2

2

1 0

ˆ

,

G s SCC u

s T s T

 

 

 (4.1)

where 

ˆ



is the sensed angular velocity, 

GSCC

is the angular velocity threshold gain, 

which scales the response to the threshold units, and 

T1

and 

T0

relate to the semicircular 

canals time constants. 

In state space form this model constitutes the state equations:

SCC SCC SCC SCC

SCC SCC SCC

x A x B u

 C x D u

 

 

, (4.2)

where

1

0

1

,

0

SCC

T

A

T

  

    

1

0

0

,

0

SCC

SCC

SCC

G T

B

G T

  

     

CSCC 1 0 , D G SCC SCC  0 .
24

The additional state due to optokinetic influence must be added to these 

equations:

2

2

ˆ ˆ

OK e

T

s T

  



, where 

ˆ ˆ ˆ

   e A S 

, and 

T2

relates to the time constant 

OK  ,

The state equations become then:

SCC SCC SCC SCC

PE SCC SCC SCC

x A x B u

 C x D u

 

 

, (4.3)

where

1

0

2 2

1 0

0 0 ,

0

SCC

T

A T

T T

  

 

  

     

1

0

2

0

0 ,

0

SCC

SCC SCC

SCC

G T

B G T

G T

  

 

  

    

CSCC 1 0 1 , D G SCC SCC  0 .

The ultimate set of state equation should include the otolith model as well. In the 

case of pure pitch, however, the human otoliths are not engaged. Hence the final version 

of the state equation set will be as follows:

 

V V V V

PE V V V

x A x B u

y C x D u

 

 

, (4.4)

where 

V

x

, and 

PE y

are, respectively, the combined states and perceived responses, 

whereas matrices

, , , A A B B C C D D V SCC V SCC V SCC V SCC   

The next step is to add additional motion platform states 

d

x

and filtered white 

noise 

n

x .

d d d d s x A x B u  

, (4.5)

where 

d

x dt     

  

, and 

0 1

0 0

Ad

 

    

and 

0

1

Bd

 

    

In turn, the aircraft input can be expressed as a filtered white noise:
25 n n

A n

x x w

u x

    



, (4.6)

where 



is the break frequency for a given degree of freedom

The state equations given in Eq. 4.4, 4.5, and 4.6 can be combined to form the 

desired system equation

 

s

d s

x Ax Bu Hw

y e x Cx Du

  

  

, (4.7)

with

0 0

0

0 0 , , 0 , ,

0 0 0

0 0 0

v v v

v v v

SCC d d

A B B

C D D

A A B B H C D

I

 

      

          

                               

,

where y is the desired output, and 

 

T

e d n x x x x 

represents the combined states.

The standard optimal control form is then applied to form a cost function J, which 

is later enhanced by the additional term 

2 t

e



[2], where “α” is a scalar representing a 

minimum degree of stability in the closed loop system, α >0.

   

1

0

2

,

t

t

t

J E e dt 

      

T T x R x u R u 1 2

 (4.8)

where 

 R1

is positive definite and 

R2

is positive semi-definite.

The cost function constrains both the sensation error and the motion platform 

states.

The essence of the washout algorithm is to compute the simulator control input so 

that the given cost function is minimized. The solution is sought in the following form:

   , u K x S

 (4.9)

where K(α) is the feedback matrix, which depends upon the solution to the algebraic 

Riccati equation. For the sake of brevity however, the author will omit the derivation of 

the solution and will get down to the on-line implementation of the algorithm, the block 

diagram of which is given in Figure 4.1. It is worth mentioning that the variable α is set 

to depend upon the motion platform states: 

 

T

x Q x d 2 d

.
26

Figure 4.1. Nonlinear Algorithm implementation for longitudinal mode. The dotted 

box in this figure encompasses the pitch channel. Adopted from Telban and 

Cardullo [1]

4.2.2. Roll

For the roll channel, the filter development is analogous to the pitch channel. The 

sensed rotational motion 

ˆ



in Eq. 4.1 is replaced by 

ˆ



. The remaining development is 

identical in form to Eqs. 4.2 to 4.9, resulting in a matrix of fifth-order transfer functions 

W(s) for the lateral mode. The on-line implementation of this mode is identical to Figure

4.1.

Nonlinear 

scaling

State 

equations

Nonlinear 

scaling

State 

equations

Riccati 

solver

Riccati 

solver

Tilt rate 

limit

LSI

1

s

1

s

1

s

A

aA

I

aA

K( ) 

SI SI I S

ST

S

 S

K( ) 

 A

SR

 A

A A TS
27

4.2.3. Modifications to the on-line implementation code

This section contains block diagrams and flowcharts of the nonlinear washout 

algorithm augmented by the non-linear filters for pitch and roll channels. The format of 

presentation is similar to that used by Telban and Cardullo [1].

The flowchart for the augmented nonlinear algorithm subroutine NEWOPT4 is 

shown in Figure 4.2. The RESET/HOLD modes and transformation subroutines are 

identical to the optimal algorithm discussed in the preceding section

Two new subroutines, NFILP and NFILQ, accomplish the task of solving the 

Riccati equation in real time for the pitch and roll mode. The feedback matrices and 

updated motion states for each mode are then computed in the subroutine STATE4, 

which was also modified to accommodate new filters for pitch and roll. The subroutine 

INTEG4, which computes the desired simulator displacements and attitudes, taking into 

account the tilt coordination limits had to be modified as well. Appropriate flowcharts are 

given later in the text. Note that STATE4 has to be computed six times as opposed to four 

times in the original design. 
28

Figure 4.2. Flowchart of the augmented nonlinear washout algorithm. NFILP and 

NFILQ are the Riccati equation solvers for the roll and pitch channels respectively

Subroutine

NEWOPT4

RESET

HOLD

LIBA

GAINOPT4

NFILY

NFILZ

NFILR

OPERATE

INTEG4

RETURN

WTRIM3

RESETC2

Time Zero Initialization and 

Smooth Return of Motion Base 

to Neutral Position

Smooth Buildup of 

Motion Base Tilts to 

Trim Position

Nonlinear Scaling

Body to Inertial and Body to 

Euler Transformations

Longitudinal 

Neurocomputing Solver

Lateral 

Neurocomputing Solver

Vertical

Neurocomputing Solver

Yaw

Neurocomputing Solver

YES

YES

YES

NO

NO

NO

NFILX

Integration to Obtain 

Positions and Attitudes

STATE4

State Variable 

Computation

STATE4

(6 TIMES)

NFILP Roll

Neurocomputing Solver

NFILQ Pitch

Neurocomputing Solver
29

Figure 4.3. NFILQ subroutine flowchart









   

T

2

x Q x

A A I

Compute 

Matrices 

SP and PA

    α 1 

p = Pz

v = PSP - A P - PA - R z

Compute 

Matrices 

Avz, vzA, vPS

 1      

2

k k k k        T P P ΔP + ΔP

Training 

Iteration L=3?

Input Vector z

Matrices

  , , A S R α 1

NO

Simulator 

Position and 

Rate

THE APQO, BRBQ, R1PQ

APQ

PQ

ZQ

SPQ, PAPQ

UQ, PZQ

APUQ, UAPQ, UPBQ

  

T T T

α

T

ΔP = A vz + vz A - vp S

ΔP

SUMPQ, SUMPQT

PQ

PQ
30

Figure 4.4. NFILP subroutine flowchart









   

T

2

x Q x

A A I

Compute 

Matrices 

SP and PA

    α 1 

p = Pz

v = PSP - A P - PA - R z

Compute 

Matrices 

Avz, vzA, vPS

 1      

2

k k k k        T P P ΔP + ΔP

Training 

Iteration L=3?

Input Vector z

Matrices

  , , A S R α 1

NO

Simulator 

Position and 

Rate

PHI APPO, BRBP, R1PP

APP

PP

ZP

SPP, PAPP

UP, PZP

APUP, UAPP, UPBP

  

T T T

α

T

ΔP = A vz + vz A - vp S

ΔP

SUMPP, SUMPPT

PP

PP
31

Figure 4.5. STATE4 subroutine flowchart

Matrices

, , , ,

-1 R A B C D 2 V V V V

   

   

   

-1 T T T

1 2 V 11 d 21 V V

-1 T T

2 2 V 12 d 22

-1 T T T

3 2 V 13 d 23 V V

K = R B P + B P + D QC

K = R B P + B P

K = R B P + B P - D QD

   

 

dt t

dt t

     

     

e V V 1 e v 2 d v 3 A

d d 1 e d d 2 d d 3 A

x A - B K x - B K x - B I + K u

x -B K x - A - B K x - B K u

dt

dt









e e

d d

x x

x x

Riccati Solution 

P

K1X, K2X, K3X

XXI1, XXI2

XX

Compute 

Lateral, 

Vertical, Yaw, 

Roll and Pitch 

States

Prior Inputs and 

States

XY, XZ, XR, XP, XQ

2

nd

-Order Runge-Kutta 

Integration of States

A2NO, BADNO,

XXO, XYO, XZO, XRO, XPO, 

XQO

PX

Update the Prior Inputs and States

A2NO, BADNO,

XXO, XYO, 

XZO, XRO, XPO, XQO
32

4.4. Algorithm tuning

Figure 4.6 contains comparison graphs of augmented filtering algorithms versus 

original washout filters for the pitch channel. Sensed angular rate and specific forces at 

the PS are of particular interest here. 

0 5 10 15 20 25 30

-2

0

2

4 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

original

augmented

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1 ASFY,SSFY (m/s

2

)

0 5 10 15 20 25 30

-4

-3.5

-3

-2.5

t (sec) ASFZ,SSFZ (m/s

2

)

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1 ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

original

augmented

0 5 10 15 20 25 30

-10

0

10

20

ASW,SSW -q (deg/s)

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1

t (sec)

ASW,SSW -r (deg/s)

Figure 4.6. Sensed specific force and angular rates for the pitch channel, with the 

tuned version of the nonlinear washout filter

It can be seen that augmented filters respond in an “under-gained” manner. For 

example, sensed specific force at the PS appears to be less then with the original nonlinear washout filters. Such a tendency can be observed in the roll channel as well. In 

order to increase the performance of the augmented filters an auxiliary gain was 

introduced for the pitch and roll channels. Subroutine “integ4.f” (Telban and Cardullo 

[3]) was modified in the following manner to accommodate such a gain. Desired pitch 

and roll angles are “boosted” before being combined with the tilt signal (due to gravity 

align). The modified code is highlighted with yellow color. 
33

SUBROUTINE INTEG4

INCLUDE 'optint3.com'

INCLUDE 'comint2.com'

INCLUDE 'wcom2.com'

INCLUDE 'matrix1c.com'

INCLUDE 'nopt4.com'

C

C SURGE FILTER OUTPUT ASI(1) & BSDT(2)

C

ASI(1)=-K1X(2,1)*XX(1)-K1X(2,2)*XX(2)-K1X(2,3)*XX(3)

 x -K1X(2,4)*XX(4)-K1X(2,5)*XX(5)-K1X(2,6)*XX(6)

 x -K2X(2,1)*XX(7)-K2X(2,2)*XX(8)-K2X(2,3)*XX(9)

 x -K3X(2)*A2N(1)

BSDT(2)=-K1X(1,1)*XX(1)-K1X(1,2)*XX(2)-K1X(1,3)*XX(3)

 x -K1X(1,4)*XX(4)-K1X(1,5)*XX(5)-K1X(1,6)*XX(6)

 x -K2X(1,1)*XX(7)-K2X(1,2)*XX(8)-K2X(1,3)*XX(9)

 x -K3X(1)*A2N(1)

C

C SWAY FILTER OUTPUT ASI(2) & BSDT(1) 

C

ASI(2)=-K1Y(2,1)*XY(1)-K1Y(2,2)*XY(2)-K1Y(2,3)*XY(3)

 x -K1Y(2,4)*XY(4)-K1Y(2,5)*XY(5)-K1Y(2,6)*XY(6)

 x -K2Y(2,1)*XY(7)-K2Y(2,2)*XY(8)-K2Y(2,3)*XY(9)

 x -K3Y(2)*A2N(2)

BSDT(1)=-K1Y(1,1)*XY(1)-K1Y(1,2)*XY(2)-K1Y(1,3)*XY(3)

 x -K1Y(1,4)*XY(4)-K1Y(1,5)*XY(5)-K1Y(1,6)*XY(6)

 x -K2Y(1,1)*XY(7)-K2Y(1,2)*XY(8)-K2Y(1,3)*XY(9)

 x -K3Y(1)*A2N(2)

C

C HEAVE FILTER OUTPUT ASI(3) 

C 

 ASI(3)=(-K1Z(1)*XZ(1)-K1Z(2)*XZ(2)-K2Z(1)*XZ(3)

 x -K2Z(2)*XZ(4)-K2Z(3)*XZ(5)-K3Z*A2N(3))

C

C YAW FILTER OUTPUT BSDR(3)

C 

 BSDR(3)=-K1R(1)*XR(1)-K1R(2)*XR(2)-K1R(3)*XR(3)

 X -K2R*XR(4)-K3R*BADN(3)

C
34

C PITCH FILTER OUTPUT BSDR(2)

C 

 BSDR(2)=-K1P(1)*XP(1)-K1P(2)*XP(2)-K1P(3)*XP(3)

 X -K2P*XP(4)-K3P*BADN(2)

C

C ROLL FILTER OUTPUT BSDR(1)

C 

 BSDR(1)=-K1Q(1)*XQ(1)-K1Q(2)*XQ(2)-K1Q(3)*XQ(3)

 X -K2Q*XQ(4)-K3Q*BADN(1)

C

C LIMIT THE ANGULAR RATE IN THE CROSS-OVER TILT CHANNEL.

C THE REAL TILT POSITION WILL BE DETERMINED BY BOTH THE 

DESIRED 

C POSITION AND THE DIFFERENCE BETWEEN THE DESIRED AND REAL 

C TILT POSITION. 

C 

DO K=1,2

BETASR(K)=BETASRO(K)+DT*BSDRO(K) 

BETAST(K)=BETASTO(K)+DT*BSDTO(K)

DIF(K)=0.005*(BETAST(K)-BETASTLO(K))+(BETAST(K)-

BETASTO(K))

BETASTL(K)=BETASTLO(K)+MAX(-

BDLIM*DT,MIN(BDLIM*DT,DIF(K)))

C

C COMPUTE THE TILT ANGULAR VELOCITY

C

BSDTL(K)=(BETASTL(K)-BETASTLO(K))/DT

BSDRO(K) = BSDR(K)

BETASRO(K)=BETASR(K)

BETASTO(K)=BETAST(K)

BETASTLO(K)=BETASTL(K)

 BSDTO(K)=BSDT(K)

END DO

C

C COMBINE THE TILT AND ROTATIONAL CHANNELS TO OBTAIN

C THE DESIRED ANGULAR POSITION 

 G1=3

C

BETAS1(1)=BETASTL(1)+G1*BETASR(1)

BETAS1(2)=BETASTL(2)+G1*BETASR(2)

BETAS1(3)=XR(4) 

C
35

C USE DIFFERENCE BETWEEN DESIRED BETAST AND REAL BETAST

C TO GENERATE ADDITIONAL LINEAR RESPONSE AND ACHIEVE 

C COORDINATION BETWEEN THE LINEAR AND TILT CHANNELS 

C 

 SSI1(1)=XX(8)+RRS(3)*(BETAST(2)-BETASTL(2))

 SSI1(2)=XY(8)-RRS(3)*(BETAST(1)-BETASTL(1))

C

C FOR ON-GROUND MOTION, ADD RUNWAY ROUGHNESS EFFECT

C AMPLITUDE IS FAIRED UPON TOUCHDOWN OR TAKEOFF

C

 SSI1(3)=XZ(4)+XKA*SIN((WB+XKG*VGSPD)*T)

C

C Swap Variables To Match Modified Algorithm

C For Input to JACKDRVR

C

 

C

XDD = ASI(1)

YDD = ASI(2)

ZDD = ASI(3)

XD = XX(9)

YD = XY(9)

ZD = XZ(5)

X = SSI1(1)

Y = SSI1(2)

Z = SSI1(3)

PHI = BETAS1(1)

THE =BETAS1(2)

PSI = BETAS1(3)

PHID = BSDTL(1)+BSDR(1)

THED = BSDTL(2)+BSDR(2)

PSID = BSDR(3)

RETURN

END 

Trial and error method yields a value of G1 = 3, which provides best tuning of the 

algorithm. Figure 4.7 contains comparison graphs of the modified augmented filtering 

algorithms against the original washout filters. It can be seen that modified augmented 

filters result in better (at least the same order of magnitude) cueing at the PS.
36

0 5 10 15 20 25 30

-2

0

2

4 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

original

augmented

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1 ASFY,SSFY (m/s

2

)

0 5 10 15 20 25 30

-4

-3.5

-3

-2.5

t (sec) ASFZ,SSFZ (m/s

2

)

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1 ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

original

augmented

0 5 10 15 20 25 30

-10

0

10

20

ASW,SSW -q (deg/s)

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1

t (sec)

ASW,SSW -r (deg/s)

Figure 4.7. Sensed specific force and angular rates for the pitch channel, with the 

tuned version of the nonlinear washout filter

4.5. Discussion

A discussion of the benefits of applying the nonlinear filters to all degrees of 

freedom (augmented filtering), is presented using the pitch channel as an example. 

Appendix C contains a comprehensive set of graphs, which compares the augmented 

filtering with the original set of non-linear optimal filters. 

As can be seen, augmented filtering algorithms provide at least as much cueing as 

original filters. Figures C.1.5 and C.1.7 in Appendix C also clearly illustrate how 

nonlinear filters washout the simulator platform attitude, as opposed to the original filter 

design, which result in sustained cues. 
37

Recall that for the pitch channel, the reference signal was the pulse doublet. 

Figure C.1.1 clearly illustrates how nonlinear filters provide cue onset with the following 

washout. The same observation holds true for the roll channel as well (Appendix C).

It can also be seen that introduction of non-linear washout filters to the pitch and 

roll channels had no effect on other degrees of freedom.

It is useful to compare the augmented filtering algorithms against the original 

nonlinear filters applied at the PS. The latter were developed in Sections 3 of the current 

report. Such comparison makes sense since both filtering algorithms clearly have certain 

advantages over the original nonlinear filters. Appendix D contains a complete set of 

comparison graphs.

Using the pitch channel as an example it is possible to draw a few conclusions, 

which hold true for other degrees of freedom. It can be seen (Figure D.1.1) that original 

nonlinear filters applied at the PS as opposed to the augmented filters produce a 

noticeable accelerations at the MB centroid, which is undesirable. Moreover, as it has 

been noted previously, augmented filters provide cue washout (Figure D.1.2). Figure 

D.1.3 demonstrates, that if expressed in terms of the platform angular rate, both 

approaches yielded comparable results. Specific forces at the pilot’s head location (Figure 

D.1.4) are of almost the same magnitude. The augmented filters, however, produced the 

desired washout. Moreover, the augmented filters resulted in smaller displacements of the 

platform, which can be seen in Figure D.1.7.
38

Appendix A. Programming updates

1. Common variable listing

Followed is the common variables listing, which was enhanced due to introduction 

of the pitch and roll nonlinear filters. The listing contents had been preserved intact from 

the original work by Telban and Cardullo [3], save for some additions, which are marked 

in yellow. 

1.1. comint2.com 

Variable Description

X, Y, Z Desired Platform Displacements (m)

XD, YD, ZD Desired Platform Velocities (m/s)

XDD, YDD, ZDD Desired Platform Accelerations (m/s/s)

PHI, THE, PSI Desired Platform Attitudes (rad)

PHID, THED, PSID Desired Platform Angular Velocities (rad/s)

1.2. optint3.com

Variable Description

DT Time Step (Sec)

XX1(8), X1O(8) Filter State Variable 1 (Current and Prior Time)

X2(8), X2O(8) Filter State Variable 2 (Current and Prior Time)

X3(8), X3O(8) Filter State Variable 3 (Current and Prior Time)

X4(8), X4O(8) Filter State Variable 4 (Current and Prior Time)

X5(6), X5O(6) Filter State Variable 5 (Current and Prior Time)

X6(6), X6O(6) Filter State Variable 6 (Current and Prior Time)

ACA(3), ACAO(3) Aircraft Body Acceleration Vector (m/s/s)

BETAA(3) Aircraft Euler Angle Vector (rad) 

BETAAD(3) Aircraft Euler Rate Vector (rad/sec)

A2(3) Aircraft Inertial Acceleration Vector (m/s/s)

A2N(3), A2NO(3) Scaled Aircraft Inertial Acceleration Vector (m/s/s) 

BADN(3), BADNO(3) Scaled Aircraft Euler Rate Vector (rad/s)

ASI(3), ASIO(3) Desired Platform Acceleration Cue (m/s/s)

VSI(3), VSIO(3) Desired Platform Velocity (m/s)

SSIU(3), SSI1(3), SSIO(3) Desired Platform Displacement (m)

WAA(3) Aircraft Body Velocity Vector (rad/sec)

BSDT(2), BSDTO(2), BSDTL(2) Platform Tilt Cue (Current, Prior, and Limited) (rad/sec)

BETAS1(3) Desired Platform Angular Position (rad)

BDLIM Platform Tilt Cue Limit (rad/sec)

BSDR(3), BSDRO(3) Platform Rotational Cue (Current and Prior) (rad/sec)

BETASR(3), BETASRO(3) Platform Rotational Angle (Current and Prior) (rad/sec)
39

BETAST(2), BETASTO(2) Platform Tilt Angle (Current and Prior) (rad)

BETASTL(2), BETASTLO(2) Platform Tilt Angle with Limit (Current and Prior) (rad)

DIF(2) Difference between Current and Limited Tilt Angles

XH(2), XHO(2) Trim Filter State Variables

T1N1, T1DO, T2N1, T2DO Trim Filter Coefficients

XT, XTO, XT2, XT2O Augmented Turbulence Filter State Variables

ACZT Augmented Turbulence Acceleration

WGUST, WGUSTO Z-Axis Gust Velocity (m/sec)

G1D0, G1D1 Augumented Turbulence Filter Coefficients (Denominator)

G1N0, G1N1, G1N2 Augumented Turbulence Filter Coefficients (Numerator)

1.3. matrix1c.com

Variable Description

AAIS(3,6) Motion Base Actuator Coordinates (m)

BBII(3,6) Fixed Base Actuator Coordinates (m)

RRS(3) Vector from Motion Base Centroid to Pilot Head (m)

LENEUT Actuator Neutral Length (m)

LI(6) Desired Actuator Extensions (m)

RLI(6), RLIO(6) Actual Actuator Extensions (m)

LEGC(6) Actual Actuator Extensions (in)

SSI(3) Actual Simulator Displacements (m)

BETAS(3) Actual Simulator Attitudes (rad)

BRAKE(6) Actuator Braking Region Value

RATIO(6) Actuator Braking Ratio

LAVAIL Actuator Available Length (m)

RLID(6), RLIDO(6) Actuator Velocity (m/s)

RLIDD(6) Actuator Acceleration (m/s/s)

FLAG(6) Braking Region Flag (0 or 1)

FLAG2 Braking Region Flag (0 or 1)

IT2, NC2 Braking Recovery Indices 

SUMFLAG Sum of FLAG(6) Values

1.4. nopt4.com

Variable Description

Longitudinal Mode

ALPX, ALPXMAX Prescribed Nonlinearity 

APX(11,11), APXO(11) State Space System Matrix A

BRBX(11,11), R1PX(11,11), R2IX(2) System Weighting Matrix S, R1, R2

AVX(6,6), BVX(6,2), DQCX(6) Vestibular State Space Matrices AV, BV, DVQCV

K1X(2,6), K2X(2,3), K3X(2) Feedback Matrices K1, K2, K3

ZX(11,11) Neurocomputing Solver Bi-Polar Vectors Z

PX(11,11), PXVEC(66) Riccati Equation Solution P

XX(9), XXO(9) State Vector x

Lateral Mode

ALPY, ALPYMAX Prescribed Nonlinearity 

APY(11,11), APYO(11) State Space System Matrix A

BRBY(11,11), R1PX(11,11), R2IY(2) System Weighting Matrix S, R1, R2
40

AVY(6,6), BVY(6,2), DQCY(6) Vestibular State Space Matrices AV, BV, DVQCV

K1Y(2,6), K2Y(2,3), K3Y(2) Feedback Matrices K1, K2, K3

ZY(11,11) Neurocomputing Solver Bi-Polar Vectors Z

PY(11,11), PYVEC(66) Riccati Equation Solution P

XY(9), XYO(9) State Vector x

Yaw Mode

ALPR, ALPRMAX Prescribed Nonlinearity 

APR(5,5), APRO(5) State Space System Matrix A

BRBR(5,5), R1PR(5,5), R2IR System Weighting Matrix S, R1, R2

AVR(3,3), BVR(3), DQCR(3), DQDR Vestibular State Space Matrices AV, BV, DVQCV, DVQDV

K1R(3), K2R, K3R Feedback Matrices K1, K2, K3

ZR(5,5) Neurocomputing Solver Bi-Polar Vectors Z

PR(5,5), PRVEC(15) Riccati Equation Solution P

XR(4), XRO(4) State Vector x

Roll Mode

ALPP, ALPPMAX Prescribed Nonlinearity 

APP(5,5), APPO(5) State Space System Matrix A

BRBP(5,5), R1PP(5,5), R2IP System Weighting Matrix S, R1, R2

AVP(3,3), BVP(3), DQCP(3), DQDP Vestibular State Space Matrices AV, BV, DVQCV, DVQDV

K1P(3), K2P, K3P Feedback Matrices K1, K2, K3

ZP(5,5) Neurocomputing Solver Bi-Polar Vectors Z

PP(5,5), PPVEC(15) Riccati Equation Solution P

XP(4), XPO(4) State Vector x

Pitch Mode

ALPQ, ALPQMAX Prescribed Nonlinearity 

APQ(5,5), APQO(5) State Space System Matrix A

BRBQ(5,5), R1PQ(5,5), R2IQ System Weighting Matrix S, R1, R2

AVQ(3,3), BVQ(3), DQCQ(3), DQDQ Vestibular State Space Matrices AV, BV, DVQCV, DVQDV

K1Q(3), K2Q, K3Q Feedback Matrices K1, K2, K3

ZQ(5,5) Neurocomputing Solver Bi-Polar Vectors Z

PQ(5,5), PQVEC(15) Riccati Equation Solution P

XQ(4), XQO(4) State Vector x

Heave Mode

ALPZ, ALPZMAX Prescribed Nonlinearity 

APZ(6,6), APZO(6) State Space System Matrix A

BRBZ(6,6), R1PZ(6,6) System Weighting Matrix S, R1

AVZ(2,2), BVZ(2) Vestibular State Space Matrices AV, BV

K1Z(2), K2Z(2), K3Z Feedback Matrices K1, K2, K3

ZZ(6,6) Neurocomputing Solver Bi-Polar Vectors Z

PZ(6,6), PZVEC(21) Riccati Equation Solution P

XZ(5), XZO(5) State Vector x

Nonlinear Gains and Turbulence

GX4,GY4,GZ4,GP4,GQ4,GR4 In-Flight Polynomial Scaling Coefficients

AMX4,BMX4 In-Flight Translational and Rotational Limits

GZ40,GZ4S,AMX40,AMX4S On-Ground Scaling Coefficients and Limits

GT4 Augmented Turbulence Acceleration Gain

G2D0, G2D1 Augumented Turbulence Filter Coefficients (Denominator)
41

G2N0, G2N1, G2N2 Augumented Turbulence Filter Coefficients (Numerator)
42

2. Program Listing

Followed is the program listing of the on-line implementation of the augmented 

nonlinear washout algorithm.

2.1. gainopt4.f

C*************************************************************

C NONLINEAR ALGORITHM NONLINEAR GAIN SUBROUTINE.

C THE INPUT IS FIRST LIMITED AND THEN SCALED BY A POLYNOMIAL.

C*************************************************************

C 

 SUBROUTINE GAINOPT4

INCLUDE 'optint3.com'

INCLUDE 'nopt4.com'

 

 REAL AA4(3),BA4(3) 

C

C Take Absolute Value of Input

C

 AA4(1)=ABS(A2(1))

AA4(2)=ABS(A2(2))

AA4(3)=ABS(A2(3))

BA4(1)=ABS(BETAAD(1))

BA4(2)=ABS(BETAAD(2))

BA4(3)=ABS(BETAAD(3))

C

C Limit Translational and Rotational Inputs

C 

 AAM=MAX(AA4(1),AA4(2),AA4(3))

 BAM=MAX(BA4(1),BA4(2),BA4(3))

 IF(AAM.GT.AMX4) THEN

 RATIO=AMX4/AAM

 AA4(1)=AA4(1)*RATIO

 AA4(2)=AA4(2)*RATIO

 AA4(3)=AA4(3)*RATIO

 END IF 

 IF(BAM.GT.BMX4) THEN

 RATIO=BMX4/BAM

 BA4(1)=BA4(1)*RATIO

 BA4(2)=BA4(2)*RATIO

 BA4(3)=BA4(3)*RATIO

 END IF

C

C Perform Nonlinear Scaling of Inputs

C

 A2N(1)=(GX4(1)*AA4(1)+GX4(2)*AA4(1)**2.+GX4(3)*AA4(1)**3.)

 +*SIGN(1.,A2(1))

 A2N(2)=(GY4(1)*AA4(2)+GY4(2)*AA4(2)**2.+GY4(3)*AA4(2)**3.)

 +*SIGN(1.,A2(2))

 A2N(3)=(GZ4(1)*AA4(3)+GZ4(2)*AA4(3)**2.+GZ4(3)*AA4(3)**3.)

 +*SIGN(1.,A2(3))
43

 BADN(1)=(GP4(1)*BA4(1)+GP4(2)*BA4(1)**2.+GP4(3)*BA4(1)**3.)

 +*SIGN(1.,BETAAD(1))

 BADN(2)=(GQ4(1)*BA4(2)+GQ4(2)*BA4(2)**2.+GQ4(3)*BA4(2)**3.)

 +*SIGN(1.,BETAAD(2))

 BADN(3)=(GR4(1)*BA4(3)+GR4(2)*BA4(3)**2.+GR4(3)*BA4(3)**3.)

 +*SIGN(1.,BETAAD(3)) 

 

 RETURN

 END 

C
44

2.2. integ4.f

SUBROUTINE INTEG4

INCLUDE 'optint3.com'

INCLUDE 'comint2.com'

INCLUDE 'wcom2.com'

INCLUDE 'matrix1c.com'

INCLUDE 'nopt4.com'

C

C SURGE FILTER OUTPUT ASI(1) & BSDT(2)

C

ASI(1)=-K1X(2,1)*XX(1)-K1X(2,2)*XX(2)-K1X(2,3)*XX(3)

 x -K1X(2,4)*XX(4)-K1X(2,5)*XX(5)-K1X(2,6)*XX(6)

 x -K2X(2,1)*XX(7)-K2X(2,2)*XX(8)-K2X(2,3)*XX(9)

 x -K3X(2)*A2N(1)

BSDT(2)=-K1X(1,1)*XX(1)-K1X(1,2)*XX(2)-K1X(1,3)*XX(3)

 x -K1X(1,4)*XX(4)-K1X(1,5)*XX(5)-K1X(1,6)*XX(6)

 x -K2X(1,1)*XX(7)-K2X(1,2)*XX(8)-K2X(1,3)*XX(9)

 x -K3X(1)*A2N(1)

C

C SWAY FILTER OUTPUT ASI(2) & BSDT(1) 

C

ASI(2)=-K1Y(2,1)*XY(1)-K1Y(2,2)*XY(2)-K1Y(2,3)*XY(3)

 x -K1Y(2,4)*XY(4)-K1Y(2,5)*XY(5)-K1Y(2,6)*XY(6)

 x -K2Y(2,1)*XY(7)-K2Y(2,2)*XY(8)-K2Y(2,3)*XY(9)

 x -K3Y(2)*A2N(2)

BSDT(1)=-K1Y(1,1)*XY(1)-K1Y(1,2)*XY(2)-K1Y(1,3)*XY(3)

 x -K1Y(1,4)*XY(4)-K1Y(1,5)*XY(5)-K1Y(1,6)*XY(6)

 x -K2Y(1,1)*XY(7)-K2Y(1,2)*XY(8)-K2Y(1,3)*XY(9)

 x -K3Y(1)*A2N(2)

C

C HEAVE FILTER OUTPUT ASI(3) 

C 

 ASI(3)=(-K1Z(1)*XZ(1)-K1Z(2)*XZ(2)-K2Z(1)*XZ(3)

 x -K2Z(2)*XZ(4)-K2Z(3)*XZ(5)-K3Z*A2N(3))

C

C YAW FILTER OUTPUT BSDR(3)

C 

 BSDR(3)=-K1R(1)*XR(1)-K1R(2)*XR(2)-K1R(3)*XR(3)

 X -K2R*XR(4)-K3R*BADN(3)

C

C PITCH FILTER OUTPUT BSDR(2)

C 

 BSDR(2)=-K1P(1)*XP(1)-K1P(2)*XP(2)-K1P(3)*XP(3)

 X -K2P*XP(4)-K3P*BADN(2)

C

C ROLL FILTER OUTPUT BSDR(1)

C 

 BSDR(1)=-K1Q(1)*XQ(1)-K1Q(2)*XQ(2)-K1Q(3)*XQ(3)
45

 X -K2Q*XQ(4)-K3Q*BADN(1)

C

C LIMIT THE ANGULAR RATE IN THE CROSS-OVER TILT CHANNEL.

C THE REAL TILT POSITION WILL BE DETERMINED BY BOTH THE DESIRED 

C POSITION AND THE DIFFERENCE BETWEEN THE DESIRED AND REAL 

C TILT POSITION. 

C 

DO K=1,2

BETASR(K)=BETASRO(K)+DT*BSDRO(K) 

BETAST(K)=BETASTO(K)+DT*BSDTO(K)

DIF(K)=0.005*(BETAST(K)-BETASTLO(K))+(BETAST(K)-BETASTO(K))

BETASTL(K)=BETASTLO(K)+MAX(-BDLIM*DT,MIN(BDLIM*DT,DIF(K)))

C

C COMPUTE THE TILT ANGULAR VELOCITY

C

BSDTL(K)=(BETASTL(K)-BETASTLO(K))/DT

BSDRO(K) = BSDR(K)

BETASRO(K)=BETASR(K)

BETASTO(K)=BETAST(K)

BETASTLO(K)=BETASTL(K)

 BSDTO(K)=BSDT(K)

END DO

C

C COMBINE THE TILT AND ROTATIONAL CHANNELS TO OBTAIN

C THE DESIRED ANGULAR POSITION 

C

BETAS1(1)=BETASTL(1)+BETASR(1)

BETAS1(2)=BETASTL(2)+BETASR(2)

BETAS1(3)=XR(4) 

C

C USE DIFFERENCE BETWEEN DESIRED BETAST AND REAL BETAST

C TO GENERATE ADDITIONAL LINEAR RESPONSE AND ACHIEVE 

C COORDINATION BETWEEN THE LINEAR AND TILT CHANNELS 

C 

 SSI1(1)=XX(8)+RRS(3)*(BETAST(2)-BETASTL(2))

 SSI1(2)=XY(8)-RRS(3)*(BETAST(1)-BETASTL(1))

C

C FOR ON-GROUND MOTION, ADD RUNWAY ROUGHNESS EFFECT

C AMPLITUDE IS FAIRED UPON TOUCHDOWN OR TAKEOFF

C

 SSI1(3)=XZ(4)+XKA*SIN((WB+XKG*VGSPD)*T)

C

C Swap Variables To Match Modified Algorithm

C For Input to JACKDRVR

C

XDD = ASI(1)

YDD = ASI(2)

ZDD = ASI(3)

XD = XX(9)

YD = XY(9)

ZD = XZ(5)

X = SSI1(1)

Y = SSI1(2)

Z = SSI1(3)
46

PHI = BETAS1(1)

THE = BETAS1(2)

PSI = BETAS1(3)

PHID = BSDTL(1)+BSDR(1)

THED = BSDTL(2)+BSDR(2)

PSID = BSDR(3)

RETURN

END 
47

2.3. invplf.f

C THIS SUBROUTINE WILL UNDERTAKE AN INVERSE TRANSFORMATION DEVELOPED 

C BY THE NEWTON-RAPHSON TECHNIQUE. LEG EXTENSIONS WILL BE TRANSFORMED

C TO THE DEGREES OF FREEDOM. THIS INVERSE TRANSFORMATION IS PERFORMED 

C BY AN ITERATIVE METHOD DENOTED AS NEWTON-RAPHSON TECHNIQUE.

C ITERATIONS ARE TERMINATED WHEN THE DIFFERENCE BETWEEN TWO SUBSEQUENT

C ITERATIONS IS LESS THAN SOME ERROR CRITERION.

C RLI IS THE LEG EXTENSIONS. 

C SSI IS THE TRANSLATIONAL DISPLACEMENT OF THE PLATFORM.

C BETAS IS THE ANGULAR DISPLACEMENT OF THE PLATFORM.

C XS,YS,ZS: COORDINATES OF THE FIXED ENDS OF THE LEGS.

C XM,YM,ZM: COORDINATES OF THE MOVING ENDS OF THE LEGS.

C AAIS,BBII: GEOMETRY OF THE MOTION SYSTEM. 

C SSIIN: INITIAL TRANSLATIONAL DISPLACEMENT.

C RRS: VECTOR NOT USED BY THIS SUBROUTINE.

C LENEUT: LENGTH OF LEGS IN NEUTRAL POSITION.

C

SUBROUTINE INVPLF

 REAL RAML(6),XS(6),YS(6),ZS(6),XM(6),YM(6),ZM(6)

 REAL F(6),PFX(6),PFY(6),PFZ(6),PFS(6),PFT(6),PFP(6),

 + A(3,3),ZEBRA(36),P

 

INCLUDE 'matrix1c.com'

 

 DATA IFLAG/0/ 

C**********************************************

C INITIALIZE SIMULATOR POSITION.

 DATA X/0./,Y/0./,Z/0./,P/0./,T/0./,S/0./

C********************************************** 

C

 SAVE

 IF(IFLAG.EQ.0) THEN

 DO JACK=1,6

 XM(JACK)=AAIS(1,JACK)

 YM(JACK)=AAIS(2,JACK)

 ZM(JACK)=AAIS(3,JACK)

 XS(JACK)=BBII(1,JACK)

 YS(JACK)=BBII(2,JACK)

 ZS(JACK)=BBII(3,JACK)

 END DO 

 IFLAG=1

 END IF 

C*********************** 

C X=SSI(1)+SSIIN(1)

C Y=SSI(2)+SSIIN(2)

C Z=SSI(3)+SSIIN(3)

C P=BETAS(1)

C T=BETAS(2)

C S=BETAS(3) 

C***********************

 DO JACK=1,6

 RAML(JACK)=RLI(JACK)+LENEUT

 END DO
48

 IT=0

9 CONTINUE

 A(1,1)=COS(S)*COS(T)

 A(1,2)=SIN(S)*COS(T)

 A(1,3)=-SIN(T)

 A(2,1)=COS(S)*SIN(T)*SIN(P)-SIN(S)*COS(P)

 A(2,2)=SIN(S)*SIN(T)*SIN(P)+COS(S)*COS(P)

 A(2,3)=COS(T)*SIN(P)

 A(3,1)=COS(S)*SIN(T)*COS(P)+SIN(S)*SIN(P)

 A(3,2)=SIN(S)*SIN(T)*COS(P)-COS(S)*SIN(P)

 A(3,3)=COS(T)*COS(P) 

 DO 17 I=1,6

 F(I)=XM(I)**2.+YM(I)**2.+ZM(I)**2.+XS(I)**2.+YS(I)**2.+

 + ZS(I)**2.+X**2.+Y**2.+Z**2.-RAML(I)**2.

 + +2.*(X-XS(I))*(XM(I)*A(1,1)+YM(I)*A(2,1)+ZM(I)*A(3,1))

 + +2.*(Y-YS(I))*(XM(I)*A(1,2)+YM(I)*A(2,2)+ZM(I)*A(3,2)) 

 + +2.*(Z-ZS(I))*(XM(I)*A(1,3)+YM(I)*A(2,3)+ZM(I)*A(3,3)) 

 + -2.*(X*XS(I)+Y*YS(I)+Z*ZS(I))

 PFX(I)=2.*(X+XM(I)*A(1,1)+YM(I)*A(2,1)+ZM(I)*A(3,1)-XS(I))

 PFY(I)=2.*(Y+XM(I)*A(1,2)+YM(I)*A(2,2)+ZM(I)*A(3,2)-YS(I))

 PFZ(I)=2.*(Z+XM(I)*A(1,3)+YM(I)*A(2,3)+ZM(I)*A(3,3)-ZS(I))

 PFS(I)=-2.*(X-XS(I))*(XM(I)*A(1,2)+YM(I)*A(2,2)+ZM(I)*A(3,2)) 

 + +2.*(Y-YS(I))*(XM(I)*A(1,1)+YM(I)*A(2,1)+ZM(I)*A(3,1)) 

 PFT(I)= 2.*(X-XS(I))*(-XM(I)*SIN(T)*COS(S)+YM(I)*SIN(P)*COS(T)* 

 + COS(S)+ZM(I)*COS(P)*COS(T)*COS(S))+2.*(Y-YS(I))*(-XM(I)*

 + SIN(T)*SIN(S)+YM(I)*SIN(P)*COS(T)*SIN(S)+ZM(I)*COS(P)*COS(T)

 + *SIN(S))-2.*(Z-ZS(I))*(XM(I)*COS(T)+YM(I)*SIN(P)*SIN(T)

 + +ZM(I)*COS(P)* SIN(T)) 

 PFP(I)=2.*(X-XS(I))*(YM(I)*A(3,1)-ZM(I)*A(2,1))

 + +2.*(Y-YS(I))*(YM(I)*A(3,2)-ZM(I)*A(2,2))

 + +2.*(Z-ZS(I))*(YM(I)*A(3,3)-ZM(I)*A(2,3)) 

17 CONTINUE

 DO 1 N=1,6

 ZEBRA(N) =PFX(N)

 ZEBRA(N+6) =PFY(N)

 ZEBRA(N+12)=PFZ(N)

 ZEBRA(N+18)=PFS(N)

 ZEBRA(N+24)=PFT(N)

 ZEBRA(N+30)=PFP(N) 

1 CONTINUE 

 N=6

 CALL SIMQ(ZEBRA,F,N,KS)

 IF(KS.EQ.1) THEN

 WRITE(*,*) ' 1 MATRIX IS SINGULAR'

 GOTO 22

 END IF

 IT=IT+1

 IF(IT.EQ.51) GO TO 22

 X=X-F(1)

 Y=Y-F(2)

 Z=Z-F(3)

 S=S-F(4)

 T=T-F(5)

 P=P-F(6)

 ZLIM1=0.01

 ZLIM2=0.1/57.296

 IF(MAX(ABS(F(1)),ABS(F(2)),ABS(F(3))).GT.ZLIM1) GO TO 9
49

 IF(MAX(ABS(F(4)),ABS(F(5)),ABS(F(6))).GT.ZLIM2) GO TO 9

22 SSI(1)=X

 SSI(2)=Y

 SSI(3)=Z

 BETAS(1)=P

 BETAS(2)=T

 BETAS(3)=S

 RETURN

 END

C
50

2.4. jackdrvr.f

C COMPUTE THE ACTUATOR EXTENSION COMMANDS BASED ON POSITION

C IN INERTIAL FRAME.

C

 SUBROUTINE JACKDRVR

 INCLUDE 'matrix1c.com'

INCLUDE 'comint2.com'

INCLUDE 'optint3.com'

REAL DUMMY31A(3,1),LLIS(3,3),L1(6),L2(6),L3(6),LENGTHTOT(6)

 REAL LLIMH,LLIML

C

C********** Langley VMS motion system geometry **********

 DATA LENEUT/3.2649/

 DATA RRS/0.0254,-0.635,-2.1946/

 DATA AAIS/2.1117179, 0.0762, 0.0,

 x 2.1117179, -0.0762, 0.0,

 x -0.98986594, -1.8669, 0.0,

 x -1.12184942, -1.7907, 0.0,

 x -1.12184942, 1.7907, 0.0,

 x -0.98986594, 1.8669, 0.0/

 DATA BBII/ 1.5021179, 1.9812, 2.58064,

 x 1.5021179, -1.9812, 2.58064,

 x 0.96471232, -2.29147116, 2.58064,

 x -2.46682768, -0.31027116, 2.58064,

 x -2.46682768, 0.31027116, 2.58064,

 x 0.96471232, 2.29147116, 2.58064/

DATA RLI/6*0./, SSI/3*0.0/, BETAS/3*0.0/

C******************************************************** 

C

C McFadden Actuator Stroke Limit

C (When Used Replace LLIMH/LLIML with LLIM)

C DATA LLIM/0.92075/

C

C Langley VMS Actuator Stroke Limits

 DATA LLIMH/0.7864/,LLIML/0.6487/

C

DATA ACMAX/0.7/

 DATA FLAG/6*0/,FLAG2/0/,IT2/400/,NC2/400/,SUMFLAG/0/ 

 DATA RLID/6*0./,RLIDD/6*0./,RLIO/6*0./,RLIDO/6*0./

 

C

C EXACT ANGLE COMPUTATIONS

C

 SINPHI = SIN(PHI)

 SINTH = SIN(THE)

 SINPSI = SIN(PSI)

 COSPHI = COS(PHI)

 COSTH = COS(THE)

 COSPSI = COS(PSI)
51

C

C FORM LLIS TRANSFORMATION MATRIX

C 

 LLIS(1,1) = COSPSI*COSTH

 LLIS(2,1) = SINPSI*COSTH

 LLIS(3,1) = -SINTH

 LLIS(1,2) = COSPSI*SINTH*SINPHI - SINPSI*COSPHI

 LLIS(2,2) = SINPSI*SINTH*SINPHI + COSPSI*COSPHI

 LLIS(3,2) = COSTH*SINPHI

 LLIS(1,3) = COSPSI*SINTH*COSPHI + SINPSI*SINPHI

 LLIS(2,3) = SINPSI*SINTH*COSPHI - COSPSI*SINPHI

 LLIS(3,3) = COSTH*COSPHI 

C

C Compute Leg Extensions

C 

 DO JACK = 1,6

 CALL VMULT(LLIS,AAIS(1,JACK),DUMMY31A,3,3,1) 

 L1(JACK) = DUMMY31A(1,1) + X - BBII(1,JACK)

L2(JACK) = DUMMY31A(2,1) + Y - BBII(2,JACK)

L3(JACK) = DUMMY31A(3,1) + Z - BBII(3,JACK)

 LENGTHTOT(JACK) = SQRT(L1(JACK)**2+L2(JACK)**2+L3(JACK)**2)

 LI(JACK)=LENGTHTOT(JACK) - LENEUT

 END DO

C

C****************** JACK EXTENSION LIMITING ***********************

 DO JACK=1,6

 IF(FLAG(JACK).EQ.1) GOTO 5

C

C Avail. Length for Same +/- Extension Limits

C LAVAIL=LLIM-RLI(JACK)*SIGN(1.,RLID(JACK))

C

C Avail. Length for Different +/- Extension Limits

C

 IF (RLI(JACK).GT.0.) THEN

 LAVAIL=LLIMH-RLI(JACK)*SIGN(1.,RLID(JACK))

 ELSE

 LAVAIL=LLIML-RLI(JACK)*SIGN(1.,RLID(JACK))

 END IF

C

 BRAKE(JACK)=ABS(RLID(JACK))**2-1.98*ACMAX*LAVAIL

 IF(BRAKE(JACK).LT.0.) GOTO 5

 FLAG(JACK)=1

 VLEAD=RLID(JACK)

 FLAG2=1

 DO JK=1,6

 IF(FLAG(JK).EQ.0) THEN

 RATIO(JK)=ABS(RLID(JK)/VLEAD)

 ELSE

 RATIO(JK)=1.

 END IF

 END DO

5 END DO

 SUMFLAG=FLAG(1)+FLAG(2)+FLAG(3)+FLAG(4)+FLAG(5)+FLAG(6)

C

C
52

C When brake is set, determine if brake should be released

C

DXX=ABS(X)-ABS(SSI(1))

DYY=ABS(Y)-ABS(SSI(2))

DZZ=ABS(Z)-ABS(SSI(3))

DPHI=ABS(PHI)-ABS(BETAS(1))

DTHE=ABS(THE)-ABS(BETAS(2))

DPSI=ABS(PSI)-ABS(BETAS(3))

DMAX=MAX(DXX,DYY,DZZ,DPHI,DTHE,DPSI)

DMIN=MIN(DXX,DYY,DZZ,DPHI,DTHE,DPSI)

IF((DMAX.LE.1.E-5).AND.(DMIN.LE.-0.01)) THEN

ID=0

ELSE

ID=1

END IF

 DO JACK=1,6

 IF(FLAG(JACK).EQ.0) GOTO 20

 RLIDD(JACK)=-ACMAX*SIGN(1.,RLID(JACK))

 RLID(JACK) = RLID(JACK)+RLIDD(JACK)*H

 GOTO 30

20 IF(SUMFLAG.EQ.0) GOTO 50

 IF(ABS(RLID(JACK)).GT.0.001) THEN

 RLIDD(JACK)=-ACMAX*SIGN(1.,RLID(JACK))*RATIO(JACK)

 RLID(JACK) = RLID(JACK)+RLIDD(JACK)*H

 END IF

30 IF(ABS(RLID(JACK)).GT.(ACMAX*H)) THEN

 RLI(JACK)=RLI(JACK)+RLID(JACK)*H

 ELSE

 RLID(JACK)=0.

 FLAG(JACK)=0

 END IF

 GOTO 70

50 IF(FLAG2.EQ.0) GOTO 60

 IF(ID.NE.0) GOTO 70

 FLAG2=0

 IT2=0

60 RLI(JACK) =RLI(JACK) +

 + (1.-COS(3.1416/2.*IT2/NC2))*(LI(JACK)-RLI(JACK))

 IF((JACK.EQ.6).AND.(IT2.LT.NC2)) IT2=IT2+1

C

70 END DO

C

 DO JACK=1,6

C

C Same +/- Extension limits

C RLI(JACK)=MIN(0.999*LLIM,MAX(-0.999*LLIM,RLI(JACK)))

C

C Different +/- Extension Limits

 RLI(JACK)=MIN(0.999*LLIMH,MAX(-0.999*LLIML,RLI(JACK)))

C

RLID(JACK)=(RLI(JACK)-RLIO(JACK))/H

RLIDD(JACK)=(RLID(JACK)-RLIDO(JACK))/H

C

 RLIO(JACK)=RLI(JACK)

 RLIDO(JACK)=RLID(JACK)

 END DO
53

RETURN

END

 

 
54

2.5. liba.f

C

C

C COMPUTE THE TRANSFORMATION MATRICES LIA AND TS

C 

 SUBROUTINE LIBA

INCLUDE 'optint3.com'

 REAL LIA(3,3), TA(3,3)

DATA TA/1.,3*0.0,1.,3*0.0,1./ 

C

C EXACT ANGLE COMPUTATIONS

C

 SINPHI = SIN(BETAA(1))

 SINTH = SIN(BETAA(2))

 SINPSI = SIN(BETAA(3))

 COSPHI = COS(BETAA(1))

 COSTH = COS(BETAA(2))

 COSPSI = COS(BETAA(3))

TANTH = SINTH/COSTH

C

C FORM LIA TRANSFORMATION MATRIX

C 

 LIA(1,1) = COSPSI*COSTH

 LIA(2,1) = SINPSI*COSTH

 LIA(3,1) = -SINTH

 LIA(1,2) = COSPSI*SINTH*SINPHI - SINPSI*COSPHI

 LIA(2,2) = SINPSI*SINTH*SINPHI + COSPSI*COSPHI

 LIA(3,2) = COSTH*SINPHI

 LIA(1,3) = COSPSI*SINTH*COSPHI + SINPSI*SINPHI

 LIA(2,3) = SINPSI*SINTH*COSPHI - COSPSI*SINPHI

 LIA(3,3) = COSTH*COSPHI

C

C FORM TA TRANSFORMATION MATRIX

C

 TA(1,2)=SINPHI*TANTH

 TA(1,3)=COSPHI*TANTH

 TA(2,2)=COSPHI

 TA(2,3)=-SINPHI

 TA(3,2)=SINPHI/COSTH

 TA(3,3)=COSPHI/COSTH 

C

C Compute Inertial Accleration A2

C 

CALL VMULT(LIA,ACA,A2,3,3,1) 

C

C Compute euler Rates BETAAD

C

 CALL VMULT(TA,WAA,BETAAD,3,3,1)

 RETURN

 END
55

2.6. newopt4.f

C***** SUBROUTINE NEWOPT4.F ******

C

C NONLINEAR WASHOUT ALGORITHM: ANG. VELOCITY DEVELOPMENT. 

C GIVEN A/C ACCELS ACA AND EULER RATES BETAAD, 

C COMPUTE SIMULATOR INERTIAL DISPLACEMENT AND EULER ANGLES.

C

 SUBROUTINE NEWOPT4(MODE) 

INCLUDE 'comint2.com'

INCLUDE 'wcom2.com'

INCLUDE 'optint3.com'

INCLUDE 'nopt4.com'

INCLUDE 'matrix1c.com'

C DATA IRESET/0/,IHOLD/0/

C

C Compute Fairing Parameters

C

SQWASH=SQWASHP*EA+SQWASHI*(1.0-EA)

DELSQ=MAX(MIN(SQWASH-SQWASHP,1.0),-1.0)

SQWASHP=SQWASH+DELSQ

A=1.0-SQWASHP

AA=1.0-SQWASHI

C

C Fairing of Heave Nonlinear Gain and Limit

C

GZ4(1)=AA*GZ40(1)+SQWASHI*GZ4S(1)

GZ4(2)=AA*GZ40(2)+SQWASHI*GZ4S(2)

GZ4(3)=AA*GZ40(3)+SQWASHI*GZ4S(3)

AMX4=AA*AMX40+SQWASHI*AMX4S

C

C Fairing of Runway Roughness Amplitude

C

XKA=A*XKA0+SQWASHP*XKAS

 

IF(MODE.EQ.1) THEN 

H = DT

C

C Set "old" variables for future use in HOLD and OPERATE modes

C

DO I=1,3

A2NO(I)=0.

BADNO(I)=0.

END DO

DO I=1,9

XXO(I)=0.

XYO(I)=0.
56

END DO

DO J=1,11

DO I=1,11

IF (I.GE.J) THEN

PX(I,J)=PXVEC((J-1)*11-J*(J-1)/2+I)

PX(J,I)=PX(I,J)

PY(I,J)=PYVEC((J-1)*11-J*(J-1)/2+I)

PY(J,I)=PY(I,J)

END IF

END DO

END DO

DO I=1,4

XRO(I)=0.

 XPO(I)=0.

 XQO(I)=0.

END DO

DO J=1,5

DO I=1,5

IF (I.GE.J) THEN

PR(I,J)=PRVEC((J-1)*5-J*(J-1)/2+I)

PR(J,I)=PR(I,J)

 PP(I,J)=PPVEC((J-1)*5-J*(J-1)/2+I)

PP(J,I)=PP(I,J)

 PQ(I,J)=PQVEC((J-1)*5-J*(J-1)/2+I)

PQ(J,I)=PQ(I,J)

END IF

END DO

END DO

DO I=1,5

XZO(I)=0.

END DO

DO J=1,6

DO I=1,6

IF (I.GE.J) THEN

PZ(I,J)=PZVEC((J-1)*6-J*(J-1)/2+I)

PZ(J,I)=PZ(I,J)

END IF

END DO

END DO

CALL RESETC2

C

C Set "old" variables for future use in HOLD and OPERATE modes

C

BETASRO(1)=PHI

BETASRO(2)=THE

BSDRO(1)=PHID

 BSDRO(2)=THED

DO I=1,2

XHO(I)=0.
57

ACAO(I)=0.

BSDTO(I)=0.

BETASTO(I)=0.

BETASTLO(I)=0.

XTO=0.

XT2O=0.

WGUSTO=0.

ACZT=0.

END DO

 GO TO 1

END IF

IF(MODE.EQ.2) THEN

CALL WTRIM3

END IF

C

C Compute Augmented Acceleration from W-Gust 

C

IF(MODE.EQ.3) THEN

WGAV=0.5*(WGUST+WGUSTO)

XT=XTO+DT*(-G2D1*XTO+XT2O+(G2N1-G2D1*G2N2)*WGAV)

XTAV=0.5*(XT+XTO)

XT2=XT2O+DT*(-G2D0*XTAV+(G2N0-G2D0*G2N2)*WGAV)

ACZT=XT+G2N2*WGUST

XTO=XT

XT2O=XT2

WGUSTO=WGUST

C

C (first-order turbulence model no longer used)

C

C XT=XTO+DT*(-G1D0*XTO+(G1N0-G1D0*G1N1)*WGUSTO)

C XTO=XT

C WGUSTO=WGUST

C ACZT=XT+G1N1*WGUST

END IF

CALL LIBA

CALL GAINOPT4

A2N(3)=A2N(3)+GT4*ACZT

IF(MODE.EQ.3) THEN 

CALL NFILX

CALL NFILY

CALL NFILZ

CALL NFILR

 CALL NFILP

 CALL NFILQ

CALL STATE4

ELSE IF(MODE.EQ.2) THEN

CALL STATE4

CALL STATE4

CALL STATE4

CALL STATE4

 CALL STATE4

 CALL STATE4

END IF
58

 

IF(MODE.EQ.3) CALL INTEG4 

 1 RETURN 

 END 

C
59

2.7. nfilr.f

C

C Yaw Filter Neurocomputing Solver for the Riccati Equation

C

SUBROUTINE NFILR

INCLUDE 'comint2.com'

INCLUDE 'nopt4.com'

REAL SPR(5,5),SUMER,SUMPR,SUMPRT

REAL PAPR(5,5),UPBR(5,5),UAPR(5,5),APUR(5,5)

REAL EUR(5,5),UR(5),PZR(5)

C

C Compute Prescribed Nonlinearity Alpha

C 

ALPR=PSI*Q2R*PSI

IF(ALPR.GE.ALPRMAX) ALPR=ALPRMAX

DO I=1,5

APR(I,I)=APRO(I)+ALPR

END DO

C

C Start Training Iterations & Initialize Variables

C

DO L=1,3

DO I=1,5

DO J=1,5

SPR(I,J)=0.

UPBR(I,J)=0.

PAPR(I,J)=0.

UAPR(I,J)=0.

APUR(I,J)=0.

END DO

END DO

C

C Compute Matrix Products SP and PA

C

DO I=1,5

DO J=1,5

DO K=1,5

SPR(I,J)=SPR(I,J)+BRBR(I,K)*PR(K,J)

END DO

END DO

DO K=1,5

PAPR(I,1)=PAPR(I,1)+PR(I,K)*APR(K,1)

PAPR(I,3)=PAPR(I,3)+PR(I,K)*APR(K,3)

PAPR(I,5)=PAPR(I,5)+PR(I,K)*APR(K,5)

END DO

PAPR(I,2)=PR(I,1)*APR(1,2)+PR(I,2)*APR(2,2)

PAPR(I,4)=PR(I,4)*APR(4,4)

END DO

C

C Compute Error Signal v, Vector p and Matrix Product pz

C Note: Matrix Product A'P is transpose of PA by symmetry of P
60

C

DO I=1,5

UR(I)=0.

PZR(I)=0.

DO J=1,5

IF(I.LE.J) THEN

SUMER=0.

DO K=1,5

SUMER=SUMER+PR(I,K)*SPR(K,J)

END DO

EUR(I,J)=SUMER-PAPR(I,J)-PAPR(J,I)-R1PR(I,J)

EUR(J,I)=EUR(I,J)

END IF

UR(I)=UR(I)+EUR(I,J)*ZR(L,J)

PZR(I)=PZR(I)+PR(I,J)*ZR(L,J)

END DO

END DO

C

C Compute Matrix Product Avz

C

DO I=1,2

DO J=1,5

DO K=1,3

APUR(I,J)=APUR(I,J)+APR(I,K)*UR(K)*ZR(L,J)

END DO

APUR(I,J)=APUR(I,J)+APR(I,5)*UR(5)*ZR(L,J)

END DO

END DO

DO I=3,4

DO J=1,5

APUR(I,J)=APUR(I,J)+APR(I,1)*UR(1)*ZR(L,J)

DO K=3,5

APUR(I,J)=APUR(I,J)+APR(I,K)*UR(K)*ZR(L,J)

END DO

END DO

END DO

DO J=1,5

APUR(5,J)=APR(5,5)*UR(5)*ZR(L,J)

END DO

C

C Compute Matrix Product vzA

C

DO I=1,5

DO K=1,5

UAPR(I,1)=UAPR(I,1)+UR(I)*ZR(L,K)*APR(K,1)

UAPR(I,3)=UAPR(I,3)+UR(I)*ZR(L,K)*APR(K,3)

UAPR(I,5)=UAPR(I,5)+UR(I)*ZR(L,K)*APR(K,5)

END DO

UAPR(I,2)=UR(I)*ZR(L,1)*APR(1,2)

 x +UR(I)*ZR(L,2)*APR(2,2)

UAPR(I,4)=UR(I)*ZR(L,4)*APR(4,4)

END DO

C

C Compute Matrix Product vp'S

C

DO I=1,5

DO J=1,4
61

DO K=1,4

UPBR(I,J)=UPBR(I,J)+UR(I)*PZR(K)*BRBR(K,J)

END DO

END DO

END DO

C

C Sum Avz + vzA + vp'S and integrate to update Riccati Solution P

C

DO I=1,5

DO J=1,5

IF(I.LE.J) THEN

SUMPR=APUR(I,J)+UAPR(I,J)-UPBR(I,J)

IF(I.NE.J) THEN

SUMPRT=APUR(J,I)+UAPR(J,I)-UPBR(J,I)

ELSE 

SUMPRT=SUMPR

END IF

PR(I,J)=PR(I,J)+MUR*(SUMPR+SUMPRT)

PR(J,I)=PR(I,J)

END IF

END DO

END DO

END DO

RETURN

END
62

2.8. nfilp.f

C

C Roll Filter Neurocomputing Solver for the Riccati Equation

C

SUBROUTINE NFILP

INCLUDE 'comint2.com'

INCLUDE 'nopt4.com'

REAL SPP(5,5),SUMEP,SUMPP,SUMPPT

REAL PAPP(5,5),UPBP(5,5),UAPP(5,5),APUP(5,5)

REAL EUP(5,5),UP(5),PZP(5)

C

C Compute Prescribed Nonlinearity Alpha

C 

ALPP=PHI*Q2P*PHI

IF(ALPP.GE.ALPPMAX) ALPP=ALPPMAX

DO I=1,5

APP(I,I)=APPO(I)+ALPP

END DO

C

C Start Training Iterations & Initialize Variables

C

DO L=1,3

DO I=1,5

DO J=1,5

SPP(I,J)=0.

UPBP(I,J)=0.

PAPP(I,J)=0.

UAPP(I,J)=0.

APUP(I,J)=0.

END DO

END DO

C

C Compute Matrix Products SP and PA

C

DO I=1,5

DO J=1,5

DO K=1,5

SPP(I,J)=SPP(I,J)+BRBP(I,K)*PP(K,J)

END DO

END DO

DO K=1,5

PAPP(I,1)=PAPP(I,1)+PP(I,K)*APP(K,1)

PAPP(I,3)=PAPP(I,3)+PP(I,K)*APP(K,3)

PAPP(I,5)=PAPP(I,5)+PP(I,K)*APP(K,5)

END DO

PAPP(I,2)=PP(I,1)*APP(1,2)+PP(I,2)*APP(2,2)

PAPP(I,4)=PP(I,4)*APP(4,4)

END DO

C

C Compute Error Signal v, Vector p and Matrix Product pz

C Note: Matrix Product A'P is transpose of PA by symmetry of P
63

C

DO I=1,5

UP(I)=0.

PZP(I)=0.

DO J=1,5

IF(I.LE.J) THEN

SUMEP=0.

DO K=1,5

SUMEP=SUMEP+PP(I,K)*SPP(K,J)

END DO

EUP(I,J)=SUMEP-PAPP(I,J)-PAPP(J,I)-R1PP(I,J)

EUP(J,I)=EUP(I,J)

END IF

UP(I)=UP(I)+EUP(I,J)*ZP(L,J)

PZP(I)=PZP(I)+PP(I,J)*ZP(L,J)

END DO

END DO

C

C Compute Matrix Product Avz

C

DO I=1,2

DO J=1,5

DO K=1,3

APUP(I,J)=APUP(I,J)+APP(I,K)*UP(K)*ZP(L,J)

END DO

APUP(I,J)=APUP(I,J)+APP(I,5)*UP(5)*ZP(L,J)

END DO

END DO

DO I=3,4

DO J=1,5

APUP(I,J)=APUP(I,J)+APP(I,1)*UP(1)*ZP(L,J)

DO K=3,5

APUP(I,J)=APUP(I,J)+APP(I,K)*UP(K)*ZP(L,J)

END DO

END DO

END DO

DO J=1,5

APUP(5,J)=APP(5,5)*UP(5)*ZP(L,J)

END DO

C

C Compute Matrix Product vzA

C

DO I=1,5

DO K=1,5

UAPP(I,1)=UAPP(I,1)+UP(I)*ZP(L,K)*APP(K,1)

UAPP(I,3)=UAPP(I,3)+UP(I)*ZP(L,K)*APP(K,3)

UAPP(I,5)=UAPP(I,5)+UP(I)*ZP(L,K)*APP(K,5)

END DO

UAPP(I,2)=UP(I)*ZP(L,1)*APP(1,2)

 x +UP(I)*ZP(L,2)*APP(2,2)

UAPP(I,4)=UP(I)*ZP(L,4)*APP(4,4)

END DO

C

C Compute Matrix Product vp'S

C

DO I=1,5

DO J=1,4
64

DO K=1,4

UPBP(I,J)=UPBP(I,J)+UP(I)*PZP(K)*BRBP(K,J)

END DO

END DO

END DO

C

C Sum Avz + vzA + vp'S and integrate to update Riccati Solution P

C

DO I=1,5

DO J=1,5

IF(I.LE.J) THEN

SUMPP=APUP(I,J)+UAPP(I,J)-UPBP(I,J)

IF(I.NE.J) THEN

SUMPPT=APUP(J,I)+UAPP(J,I)-UPBP(J,I)

ELSE 

SUMPPT=SUMPP

END IF

PP(I,J)=PP(I,J)+MUP*(SUMPP+SUMPPT)

PP(J,I)=PP(I,J)

END IF

END DO

END DO

END DO

RETURN

END
65

2.9. nfilq.f

C

C Pitch Filter Neurocomputing Solver for the Riccati Equation

C

SUBROUTINE NFILQ

INCLUDE 'comint2.com'

INCLUDE 'nopt4.com'

REAL SPQ(5,5),SUMEQ,SUMPQ,SUMPQT

REAL PAPQ(5,5),UPBQ(5,5),UAPQ(5,5),APUQ(5,5)

REAL EUQ(5,5),UQ(5),PZQ(5)

C

C Compute Prescribed Nonlinearity Alpha

C 

ALPQ=THE*Q2Q*THE

IF(ALPQ.GE.ALPQMAX) ALPQ=ALPQMAX

DO I=1,5

APQ(I,I)=APQO(I)+ALPQ

END DO

C

C Start Training Iterations & Initialize Variables

C

DO L=1,3

DO I=1,5

DO J=1,5

SPQ(I,J)=0.

UPBQ(I,J)=0.

PAPQ(I,J)=0.

UAPQ(I,J)=0.

APUQ(I,J)=0.

END DO

END DO

C

C Compute Matrix Products SP and PA

C

DO I=1,5

DO J=1,5

DO K=1,5

SPQ(I,J)=SPQ(I,J)+BRBQ(I,K)*PQ(K,J)

END DO

END DO

DO K=1,5

PAPQ(I,1)=PAPQ(I,1)+PQ(I,K)*APQ(K,1)

PAPQ(I,3)=PAPQ(I,3)+PQ(I,K)*APQ(K,3)

PAPQ(I,5)=PAPQ(I,5)+PQ(I,K)*APQ(K,5)

END DO

PAPQ(I,2)=PQ(I,1)*APQ(1,2)+PQ(I,2)*APQ(2,2)

PAPQ(I,4)=PQ(I,4)*APQ(4,4)

END DO

C

C Compute Error Signal v, Vector p and Matrix Product pz
66

C Note: Matrix Product A'P is transpose of PA by symmetry of P

C

DO I=1,5

UQ(I)=0.

PZQ(I)=0.

DO J=1,5

IF(I.LE.J) THEN

SUMEQ=0.

DO K=1,5

SUMEQ=SUMEQ+PQ(I,K)*SPQ(K,J)

END DO

EUQ(I,J)=SUMEQ-PAPQ(I,J)-PAPQ(J,I)-R1PQ(I,J)

EUQ(J,I)=EUQ(I,J)

END IF

UQ(I)=UQ(I)+EUQ(I,J)*ZQ(L,J)

PZQ(I)=PZQ(I)+PQ(I,J)*ZQ(L,J)

END DO

END DO

C

C Compute Matrix Product Avz

C

DO I=1,2

DO J=1,5

DO K=1,3

APUQ(I,J)=APUQ(I,J)+APQ(I,K)*UQ(K)*ZQ(L,J)

END DO

APUQ(I,J)=APUQ(I,J)+APQ(I,5)*UQ(5)*ZQ(L,J)

END DO

END DO

DO I=3,4

DO J=1,5

APUQ(I,J)=APUQ(I,J)+APQ(I,1)*UQ(1)*ZQ(L,J)

DO K=3,5

APUQ(I,J)=APUQ(I,J)+APQ(I,K)*UQ(K)*ZQ(L,J)

END DO

END DO

END DO

DO J=1,5

APUQ(5,J)=APQ(5,5)*UQ(5)*ZQ(L,J)

END DO

C

C Compute Matrix Product vzA

C

DO I=1,5

DO K=1,5

UAPQ(I,1)=UAPQ(I,1)+UQ(I)*ZQ(L,K)*APQ(K,1)

UAPQ(I,3)=UAPQ(I,3)+UQ(I)*ZQ(L,K)*APQ(K,3)

UAPQ(I,5)=UAPQ(I,5)+UQ(I)*ZQ(L,K)*APQ(K,5)

END DO

UAPQ(I,2)=UQ(I)*ZQ(L,1)*APQ(1,2)

 x +UQ(I)*ZQ(L,2)*APQ(2,2)

UAPQ(I,4)=UQ(I)*ZQ(L,4)*APQ(4,4)

END DO

C

C Compute Matrix Product vp'S

C

DO I=1,5
67

DO J=1,4

DO K=1,4

UPBQ(I,J)=UPBQ(I,J)+UQ(I)*PZQ(K)*BRBQ(K,J)

END DO

END DO

END DO

C

C Sum Avz + vzA + vp'S and integrate to update Riccati Solution P

C

DO I=1,5

DO J=1,5

IF(I.LE.J) THEN

SUMPQ=APUQ(I,J)+UAPQ(I,J)-UPBQ(I,J)

IF(I.NE.J) THEN

SUMPQT=APUQ(J,I)+UAPQ(J,I)-UPBQ(J,I)

ELSE 

SUMPQT=SUMPQ

END IF

PQ(I,J)=PQ(I,J)+MUQ*(SUMPQ+SUMPQT)

PQ(J,I)=PQ(I,J)

END IF

END DO

END DO

END DO

RETURN

END
68

2.10. nfilx.f

C

C Surge Filter Neurocomputing Solver for the Riccati Equation

C

SUBROUTINE NFILX

INCLUDE 'comint2.com'

INCLUDE 'nopt4.com'

REAL SPX(11,11),SUMEX,SUMPX,SUMPXT

REAL PAPX(11,11),UPBX(11,11),UAPX(11,11),APUX(11,11)

REAL EUX(11,11),UX(11),PZX(11)

C

C Compute Prescribed Nonlinearity Alpha

C

ALPX=X*Q2X(1)*X+XD*Q2X(2)*XD

IF(ALPX.GT.ALPXMAX) ALPX=ALPXMAX

DO I=1,11

APX(I,I)=APXO(I)+ALPX

END DO

C

C Start Training Iterations & Initialize Variables

C

DO L=1,3

DO I=1,11

DO J=1,11

SPX(I,J)=0.0

PAPX(I,J)=0.0

UPBX(I,J)=0.0

UAPX(I,J)=0.0

APUX(I,J)=0.0

END DO

END DO

C

C Compute Matrix Product SP

C

DO I=1,6

DO J=1,11

DO K=1,6

SPX(I,J)=SPX(I,J)+BRBX(I,K)*PX(K,J)

END DO

SPX(I,J)=SPX(I,J)+BRBX(I,9)*PX(9,J)

END DO

END DO

DO J=1,11

DO K=1,6

SPX(9,J)=SPX(9,J)+BRBX(9,K)*PX(K,J)

END DO

SPX(9,J)=SPX(9,J)+BRBX(9,9)*PX(9,J)

END DO

C

C Compute Matrix Product PA
69

C

DO I=1,11

DO J=1,6

DO K=1,6

PAPX(I,J)=PAPX(I,J)+PX(I,K)*APX(K,J)

END DO

END DO

PAPX(I,7)=PX(I,7)*APX(7,7)

PAPX(I,8)=PX(I,7)*APX(7,8)+PX(I,8)*APX(8,8)

PAPX(I,9)=PX(I,8)*APX(8,9)+PX(I,9)*APX(9,9)

DO K=1,6

PAPX(I,10)=PAPX(I,10)+PX(I,K)*APX(K,10)

END DO

PAPX(I,10)=PAPX(I,10)+PX(I,10)*APX(10,10)

DO K=1,6

PAPX(I,11)=PAPX(I,11)+PX(I,K)*APX(K,11)

END DO

PAPX(I,11)=PAPX(I,11)+PX(I,11)*APX(11,11)

END DO

C

C Compute Error Signal v, Vector p and Matrix Product vz

C Note: Matrix Product A'P is transpose of PA by symmetry of P 

C

DO I=1,11

UX(I)=0.

PZX(I)=0.

DO J=1,11

IF(I.LE.J) THEN

SUMEX=0.

DO K=1,11

SUMEX=SUMEX+PX(I,K)*SPX(K,J)

END DO

EUX(I,J)=SUMEX-PAPX(J,I)-PAPX(I,J)-R1PX(I,J)

EUX(J,I)=EUX(I,J)

END IF

UX(I)=UX(I)+EUX(I,J)*ZX(L,J)

PZX(I)=PZX(I)+PX(I,J)*ZX(L,J)

END DO

END DO

C

C Compute Matrix Product Avz

C

DO I=1,6

DO J=1,11

DO K=1,6

APUX(I,J)=APUX(I,J)+APX(I,K)*UX(K)*ZX(L,J)

END DO

APUX(I,J)=APUX(I,J)+APX(I,10)*UX(10)*ZX(L,J)

 x +APX(I,11)*UX(11)*ZX(L,J)

END DO

END DO

DO J=1,11

APUX(7,J)=APX(7,7)*UX(7)*ZX(L,J)

 x +APX(7,8)*UX(8)*ZX(L,J)

APUX(8,J)=APX(8,8)*UX(8)*ZX(L,J)

 x +APX(8,9)*UX(9)*ZX(L,J)

APUX(9,J)=APX(9,9)*UX(9)*ZX(L,J)
70

APUX(10,J)=APX(10,10)*UX(10)*ZX(L,J)

APUX(11,J)=APX(11,11)*UX(11)*ZX(L,J)

END DO

C

C Compute Matrix Product vzA

C

DO I=1,11

DO J=1,6

DO K=1,6

UAPX(I,J)=UAPX(I,J)+UX(I)*ZX(L,K)*APX(K,J)

END DO

END DO

UAPX(I,7)=UX(I)*ZX(L,7)*APX(7,7)

UAPX(I,8)=UX(I)*ZX(L,7)*APX(7,8)

 x +UX(I)*ZX(L,8)*APX(8,8)

UAPX(I,9)=UX(I)*ZX(L,8)*APX(8,9)

 x +UX(I)*ZX(L,9)*APX(9,9)

DO K=1,6

 UAPX(I,10)=UAPX(I,10)+UX(I)*ZX(L,K)*APX(K,10)

END DO

 UAPX(I,10)=UAPX(I,10)+UX(I)*ZX(L,10)*APX(10,10)

DO K=1,6

 UAPX(I,11)=UAPX(I,11)+UX(I)*ZX(L,K)*APX(K,11)

END DO

 UAPX(I,11)=UAPX(I,11)+UX(I)*ZX(L,11)*APX(11,11)

END DO

C

C Compute Matrix Product vp'S

C

DO I=1,11

DO J=1,6

DO K=1,6

 UPBX(I,J)=UPBX(I,J)+UX(I)*PZX(K)*BRBX(K,J)

END DO

 UPBX(I,J)=UPBX(I,J)+UX(I)*PZX(9)*BRBX(9,J)

END DO

DO K=1,6

 UPBX(I,9)=UPBX(I,9)+UX(I)*PZX(K)*BRBX(K,9)

END DO

 UPBX(I,9)=UPBX(I,9)+UX(I)*PZX(9)*BRBX(9,9)

END DO

C

C Sum Avz + vzA + vp'S and integrate to update Riccati Solution P

C

DO I=1,11

DO J=1,11

 IF(I.LE.J) THEN

 SUMPX=APUX(I,J)+UAPX(I,J)-UPBX(I,J)

 IF(I.NE.J) THEN

SUMPXT=APUX(J,I)+UAPX(J,I)-UPBX(J,I)

 ELSE

SUMPXT=SUMPX

 END IF

PX(I,J)=PX(I,J)+MUX*(SUMPX+SUMPXT)

PX(J,I)=PX(I,J)

 END IF

END DO
71

END DO

END DO 

RETURN

END
72

2.11. nfily.f

C

C Sway Filter Neurocomputing Solver for the Riccati Equation

C

SUBROUTINE NFILY

INCLUDE 'comint2.com'

INCLUDE 'nopt4.com'

REAL SPY(11,11),SUMEY,SUMPY,SUMPYT

REAL PAPY(11,11),UPBY(11,11),UAPY(11,11),APUY(11,11)

REAL EUY(11,11),UY(11),PZY(11) 

C

C Compute Prescribed Nonlinearity Alpha

C

ALPY=Y*Q2Y(1)*Y+YD*Q2Y(2)*YD

IF(ALPY.GT.ALPYMAX) ALPY=ALPYMAX

DO I=1,11

APY(I,I)=APYO(I)+ALPY

END DO

C

C Start Training Iterations & Initialize Variables

C

DO L=1,3

DO I=1,11

DO J=1,11

SPY(I,J)=0.0

PAPY(I,J)=0.0

UPBY(I,J)=0.0

UAPY(I,J)=0.0

APUY(I,J)=0.0

END DO

END DO

C

C Compute Matrix Product SP

C

DO I=1,6

DO J=1,11

DO K=1,6

SPY(I,J)=SPY(I,J)+BRBY(I,K)*PY(K,J)

END DO

SPY(I,J)=SPY(I,J)+BRBY(I,9)*PY(9,J)

END DO

END DO

DO J=1,11

DO K=1,6

SPY(9,J)=SPY(9,J)+BRBY(9,K)*PY(K,J)

END DO

SPY(9,J)=SPY(9,J)+BRBY(9,9)*PY(9,J)

END DO

C

C Compute Matrix Product PA
73

C

DO I=1,11

DO J=1,6

DO K=1,6

PAPY(I,J)=PAPY(I,J)+PY(I,K)*APY(K,J)

END DO

END DO

PAPY(I,7)=PY(I,7)*APY(7,7)

PAPY(I,8)=PY(I,7)*APY(7,8)+PY(I,8)*APY(8,8)

PAPY(I,9)=PY(I,8)*APY(8,9)+PY(I,9)*APY(9,9)

DO K=1,6

PAPY(I,10)=PAPY(I,10)+PY(I,K)*APY(K,10)

END DO

PAPY(I,10)=PAPY(I,10)+PY(I,10)*APY(10,10)

DO K=1,6

PAPY(I,11)=PAPY(I,11)+PY(I,K)*APY(K,11)

END DO

PAPY(I,11)=PAPY(I,11)+PY(I,11)*APY(11,11)

END DO

C

C Compute Error Signal v, Vector p and Matrix Product vz

C Note: Matrix Product A'P is transpose of PA by symmetry of P 

C

DO I=1,11

UY(I)=0.

PZY(I)=0.

DO J=1,11

IF(I.LE.J) THEN

SUMEY=0.

DO K=1,11

SUMEY=SUMEY+PY(I,K)*SPY(K,J)

END DO

EUY(I,J)=SUMEY-PAPY(J,I)-PAPY(I,J)-R1PY(I,J)

EUY(J,I)=EUY(I,J)

END IF

UY(I)=UY(I)+EUY(I,J)*ZY(L,J)

PZY(I)=PZY(I)+PY(I,J)*ZY(L,J)

END DO

END DO

C

C Compute Matrix Product Avz

C

DO I=1,6

DO J=1,11

DO K=1,6

APUY(I,J)=APUY(I,J)+APY(I,K)*UY(K)*ZY(L,J)

END DO

APUY(I,J)=APUY(I,J)+APY(I,10)*UY(10)*ZY(L,J)

 x +APY(I,11)*UY(11)*ZY(L,J)

END DO

END DO

DO J=1,11

APUY(7,J)=APY(7,7)*UY(7)*ZY(L,J)

 x +APY(7,8)*UY(8)*ZY(L,J)

APUY(8,J)=APY(8,8)*UY(8)*ZY(L,J)

 x +APY(8,9)*UY(9)*ZY(L,J)
74

APUY(9,J)=APY(9,9)*UY(9)*ZY(L,J)

APUY(10,J)=APUY(10,J)+APY(10,10)*UY(10)*ZY(L,J)

APUY(11,J)=APUY(11,J)+APY(11,11)*UY(11)*ZY(L,J)

END DO

C

C Compute Matrix Product vzA

C

DO I=1,11

DO J=1,6

DO K=1,6

UAPY(I,J)=UAPY(I,J)+UY(I)*ZY(L,K)*APY(K,J)

END DO

END DO

UAPY(I,7)=UY(I)*ZY(L,7)*APY(7,7)

UAPY(I,8)=UY(I)*ZY(L,7)*APY(7,8)

x +UY(I)*ZY(L,8)*APY(8,8)

UAPY(I,9)=UY(I)*ZY(L,8)*APY(8,9)

 x +UY(I)*ZY(L,9)*APY(9,9)

DO K=1,6

UAPY(I,10)=UAPY(I,10)+UY(I)*ZY(L,K)*APY(K,10)

END DO

UAPY(I,10)=UAPY(I,10)+UY(I)*ZY(L,10)*APY(10,10)

DO K=1,6

UAPY(I,11)=UAPY(I,11)+UY(I)*ZY(L,K)*APY(K,11)

END DO

UAPY(I,11)=UAPY(I,11)+UY(I)*ZY(L,11)*APY(11,11)

END DO

C

C Compute Matrix Product vp'S

C

DO I=1,11

DO J=1,6

DO K=1,6

UPBY(I,J)=UPBY(I,J)+UY(I)*PZY(K)*BRBY(K,J)

END DO

UPBY(I,J)=UPBY(I,J)+UY(I)*PZY(9)*BRBY(9,J)

END DO

DO K=1,6

UPBY(I,9)=UPBY(I,9)+UY(I)*PZY(K)*BRBY(K,9)

END DO

UPBY(I,9)=UPBY(I,9)+UY(I)*PZY(9)*BRBY(9,9)

END DO

C

C Sum Avz + vzA + vp'S and integrate to update Riccati Solution P

C

DO I=1,11

DO J=1,11

IF(I.LE.J) THEN

SUMPY=APUY(I,J)+UAPY(I,J)-UPBY(I,J)

IF(I.NE.J) THEN

SUMPYT=APUY(J,I)+UAPY(J,I)-UPBY(J,I)

ELSE 

SUMPYT=SUMPY

END IF

PY(I,J)=PY(I,J)+MUY*(SUMPY+SUMPYT)

PY(J,I)=PY(I,J)

END IF
75

END DO

END DO

END DO

RETURN

END
76

2.12. nfilz.f

C

C Heave Filter Neurocomputing Solver for the Riccati Equation

C 

SUBROUTINE NFILZ

INCLUDE 'comint2.com'

INCLUDE 'nopt4.com'

REAL SPZ(6,6),SUMEZ,SUMPZ,SUMPZT

REAL PAPZ(6,6),UPBZ(6,6),UAPZ(6,6),APUZ(6,6)

REAL EUZ(6,6),UZ(6),PZZ(6)

 

C

C Compute Prescribed Nonlinearity Alpha

C

ALPZ=Z*Q2Z(1)*Z+ZD*Q2Z(2)*ZD

IF(ALPZ.GT.ALPZMAX) ALPZ=ALPZMAX

DO I=1,6

APZ(I,I)=APZO(I)+ALPZ

END DO

C

C Start Training Iterations & Initialize Variables

C

DO L=1,3

DO I=1,6

DO J=1,6

SPZ(I,J)=0.

PAPZ(I,J)=0.

UPBZ(I,J)=0.

UAPZ(I,J)=0.

APUZ(I,J)=0.

END DO

END DO

C

C Compute Matrix Product SP

C

DO I=1,2

DO J=1,6

SPZ(I,J)=BRBZ(I,1)*PZ(1,J)

 x +BRBZ(I,2)*PZ(2,J)+BRBZ(I,5)*PZ(5,J)

END DO

END DO

DO J=1,6

SPZ(5,J)=BRBZ(5,1)*PZ(1,J)

 x +BRBZ(5,2)*PZ(2,J)+BRBZ(5,5)*PZ(5,J)

END DO

C

C Compute Matrix Product PA

C

DO I=1,6

PAPZ(I,1)=PZ(I,1)*APZ(1,1)+PZ(I,2)*APZ(2,1)
77

PAPZ(I,2)=PZ(I,1)*APZ(1,2)+PZ(I,2)*APZ(2,2)

PAPZ(I,3)=PZ(I,3)*APZ(3,3)

PAPZ(I,4)=PZ(I,3)*APZ(3,4)+PZ(I,4)*APZ(4,4)

PAPZ(I,5)=PZ(I,4)*APZ(4,5)+PZ(I,5)*APZ(5,5)

PAPZ(I,6)=PZ(I,1)*APZ(1,6)+PZ(I,2)*APZ(2,6)

 x +PZ(I,6)*APZ(6,6)

END DO

C

C Compute Error Signal v, Vector p and Matrix Product vz

C Note: Matrix Product A'P is transpose of PA by symmetry of P 

C

DO I=1,6

UZ(I)=0.

PZZ(I)=0.

DO J=1,6

IF(I.LE.J) THEN

SUMEZ=0.

DO K=1,6

SUMEZ=SUMEZ+PZ(I,K)*SPZ(K,J)

END DO

EUZ(I,J)=SUMEZ-PAPZ(J,I)-PAPZ(I,J)-R1PZ(I,J)

EUZ(J,I)=EUZ(I,J)

END IF

UZ(I)=UZ(I)+EUZ(I,J)*ZZ(L,J)

PZZ(I)=PZZ(I)+PZ(I,J)*ZZ(L,J)

END DO

END DO

C

C Compute Matrix Product Avz

C

DO I=1,2

DO J=1,6

APUZ(I,J)=APZ(I,1)*UZ(1)*ZZ(L,J)

 x +APZ(I,2)*UZ(2)*ZZ(L,J)+APZ(I,6)*UZ(6)*ZZ(L,J)

END DO

END DO

DO J=1,6

APUZ(3,J)=APZ(3,3)*UZ(3)*ZZ(L,J)

 x +APZ(3,4)*UZ(4)*ZZ(L,J)

APUZ(4,J)=APZ(4,4)*UZ(4)*ZZ(L,J)

 x +APZ(4,5)*UZ(5)*ZZ(L,J)

APUZ(5,J)=APZ(5,5)*UZ(5)*ZZ(L,J)

APUZ(6,J)=APZ(6,6)*UZ(6)*ZZ(L,J)

END DO

C

C Compute Matrix Product vzA

C

DO I=1,6

UAPZ(I,1)=UZ(I)*ZZ(L,1)*APZ(1,1)+UZ(I)*ZZ(L,2)*APZ(2,1)

UAPZ(I,2)=UZ(I)*ZZ(L,1)*APZ(1,2)+UZ(I)*ZZ(L,2)*APZ(2,2)

UAPZ(I,3)=UZ(I)*ZZ(L,3)*APZ(3,3)

UAPZ(I,4)=UZ(I)*ZZ(L,3)*APZ(3,4)+UZ(I)*ZZ(L,4)*APZ(4,4)

 UAPZ(I,5)=UZ(I)*ZZ(L,4)*APZ(4,5)+UZ(I)*ZZ(L,5)*APZ(5,5)

UAPZ(I,6)=UZ(I)*ZZ(L,1)*APZ(1,6)

 x +UZ(I)*ZZ(L,2)*APZ(2,6)+UZ(I)*ZZ(L,6)*APZ(6,6)
78

END DO

C

C Compute Matrix Product vp'S

C

DO I=1,6

DO J=1,2

UPBZ(I,J)=UZ(I)*PZZ(1)*BRBZ(1,J)

 x +UZ(I)*PZZ(2)*BRBZ(2,J)+UZ(I)*PZZ(5)*BRBZ(5,J)

END DO

UPBZ(I,5)=UZ(I)*PZZ(1)*BRBZ(1,5)

 x +UZ(I)*PZZ(2)*BRBZ(2,5)+UZ(I)*PZZ(5)*BRBZ(5,5)

END DO

C

C Sum Avz + vzA + vp'S and integrate to update Riccati Solution P

C

DO I=1,6

DO J=1,6

IF(I.LE.J) THEN

SUMPZ=APUZ(I,J)+UAPZ(I,J)-UPBZ(I,J)

IF(I.NE.J) THEN

SUMPZT=APUZ(J,I)+UAPZ(J,I)-UPBZ(J,I)

ELSE 

SUMPZT=SUMPZ

END IF

PZ(I,J)=PZ(I,J)+MUZ*(SUMPZ+SUMPZT)

PZ(J,I)=PZ(I,J)

END IF

END DO

END DO

END DO

 

RETURN

END

 
79

2.13. resetc2.f

 SUBROUTINE RESETC2

C

C THIS ROUTINE:

C

C (1) DOES T=0 INITIALIZATION OF MOTION VARIABLES

C

C (2) USES A SECOND ORDER SCHEME TO DRIVE TO THE NEUTRAL

C POSITION. (OVERDAMPED OSCILLATOR; ZETA = 1.5, OMEGAN = 1.0 )

C

 INCLUDE 'comint2.com'

INCLUDE 'wcom2.com'

INCLUDE 'matrix1c.com'

 

C**********************************************************************

C

C GAINS, ACCELERATION AND VELOCITY LIMITS FOR SECOND ORDER.

C

C VALUES FOR ACCELERATION AND VELOCITY ARE METERS/SEC**2

C AND METERS/SEC. ROTATIONS AND ROTATIONAL VELOCITIES

C ARE IN RADIANS AND RADIANS/SECOND.

C

C**********************************************************************

C

C .03492 RADIANS/SEC**2 == 2.0 DEG/SEC**2

C .294 METERS/SEC**2 == .03 G

C

 PARAMETER (A_ACCLIM = .03491)

 PARAMETER (T_ACCLIM = .294 )

C

C THESE PARAMETERS ARE SET TO THE PERFORMANCE LIMIT OF THE BASE

C

C .2617 RAD/SEC == 15 DEG/SEC

C .610 METERS/SEC

C

 PARAMETER (A_VELLIM = .2617 )

 PARAMETER (T_VELLIM = .610 )

C

C VALUES FOR X FILTER

C

 DATA XDDLIM / T_ACCLIM /

 DATA XDLIM / T_VELLIM /

C

C VALUES FOR Y FILTER

C

 DATA YDDLIM / T_ACCLIM /

 DATA YDLIM / T_VELLIM /

C

C VALUES FOR Z FILTER

C

 DATA ZDDLIM / T_ACCLIM /

 DATA ZDLIM / T_VELLIM /
80

C

C VALUES FOR PSI FILTER

C

 DATA PSIDDLIM / A_ACCLIM /

 DATA PSIDLIM / A_VELLIM /

C

C VALUES FOR THETA FILTER

C

 DATA THEDDLIM / A_ACCLIM /

 DATA THEDLIM / A_VELLIM /

C

C VALUES FOR PHI FILTER

C

 DATA PHIDDLIM / A_ACCLIM /

 DATA PHIDLIM / A_VELLIM /

 DATA TWOZOMGN/ 3.0 /

C

C local functions

 CLIMIT(X,XMIN,XMAX) = MIN( MAX( X, XMIN ), XMAX )

C

C If last operate run ended braked, reset braking algorithm

C to unbraked state

C

IF (FLAG2.EQ.1) THEN

X = SSI(1)

Y = SSI(2)

Z = SSI(3)

PHI = BETAS(1)

THE = BETAS(2)

PSI = BETAS(3)

DO IJ=1,6

RLID(IJ)=0.

RLIDO(IJ)=0.

END DO

 IT2=0

 FLAG2=0

END IF

C

C T = 0 INITIALIZATION;

C

 T = 0.

 INT = 0

 DXDLX = 0.

 DXDLXD = 0.

 DXDDX = 0.

 DXDDXD = 0.

 DTHDDX = 0.

 LAMX = LAMX0

 DELX = DELX0

 DYDLY = 0.

 DYDLYD = 0.

 DYDDY = 0.

 DYDDYD = 0.

 DPHDDY = 0.

 LAMY = LAMY0

 DELY = DELY0
81

 DZDEZ = 0.

 DZDEZD = 0.

 ETAZ = ETAZ0

 DPSDE = 0.

 ETAPS = ETAPS0

 

C

C FADE TO THE NEUTRAL POSITION USING SECOND ORDER FILTER TO ROVIDE

C VELOCITY AND ACCELERATION CONTROL.

C

C

C DRIVE X TO NEUTRAL POSITION (X = 0)

C

 XDDF = -X - TWOZOMGN*XD

 XDD = CLIMIT(XDDF,-XDDLIM,XDDLIM)

 XDF = XD + XDD*H

 XD = CLIMIT(XDF,-XDLIM,XDLIM)

 X = X + XD*H

C

C DRIVE Y TO NEUTRAL POSITION (Y = 0)

C

 YDDF = -Y - TWOZOMGN*YD

 YDD = CLIMIT(YDDF,-YDDLIM,YDDLIM)

 YDF = YD + YDD*H

 YD = CLIMIT(YDF,-YDLIM,YDLIM)

 Y = Y + YD*H

C

C DRIVE Z TO NEUTRAL POSITION (Z = 0)

C

 ZDDF = -Z - TWOZOMGN*ZD

 ZDD = CLIMIT(ZDDF,-ZDDLIM,ZDDLIM)

 ZDF = ZD + ZDD*H

 ZD = CLIMIT(ZDF,-ZDLIM,ZDLIM)

 Z = Z + ZD*H

C

C DRIVE PSI TO NEUTRAL POSITION (PSI = 0)

C

 PSIDDF = -PSI - TWOZOMGN*PSID

 PSIDDFL = CLIMIT(PSIDDF,-PSIDDLIM,PSIDDLIM)

 PSIDF = PSID + PSIDDFL*H

 PSID = CLIMIT(PSIDF,-PSIDLIM,PSIDLIM)

 PSI = PSI + PSID*H

C

C DRIVE THETA TO NEUTRAL POSITION (THETA = 0)

C

 THEDDF = -THE - TWOZOMGN*THED

 THEDDFL = CLIMIT(THEDDF,-THEDDLIM,THEDDLIM)

 THEDF = THED + THEDDFL*H

 THED = CLIMIT(THEDF,-THEDLIM,THEDLIM)

 THE = THE + THED*H

C

C DRIVE PHI TO NEUTRAL POSITION (PHI = 0)

C

 PHIDDF = -PHI - TWOZOMGN*PHID

 PHIDDFL = CLIMIT(PHIDDF,-PHIDDLIM,PHIDDLIM)

 PHIDF = PHID + PHIDDFL*H

 PHID = CLIMIT(PHIDF,-PHIDLIM,PHIDLIM)
82

 PHI = PHI + PHID*H

C

C DUMMY INTEGRATIONS

C

 XD1 = XD

 DXDLXD1 = DXDLXD

 DXDDXD1 = DXDDXD

 YD1 = YD

 DYDLYD1 = DYDLYD

 DYDDYD1 = DYDDYD

 ZD1 = ZD

 DZDEZD1 = DZDEZD

 RETURN

 END
83

2.14. simq.f

 SUBROUTINE SIMQ(A,B,N,KS)

 DIMENSION A(36),B(6)

 TOL=0.

 KS=0

 JJ=-N

 DO 65 J=1,N

 JY=J+1

 JJ=JJ+N+1

 BIGA=0.

 IT=JJ-J

 DO 30 I=J,N

 IJ=IT+I

 IF(ABS(BIGA)-ABS(A(IJ))) 20,30,30

20 BIGA=A(IJ)

 IMAX=I

30 CONTINUE

 IF(ABS(BIGA)-TOL) 35,35,40

35 KS=1

 RETURN

40 I1=J+N*(J-2)

 IT=IMAX-J

 DO 50 K=J,N

 I1=I1+N

 I2=I1+IT 

 SAVE1=A(I1)

 A(I1)=A(I2)

 A(I2)=SAVE1 

50 A(I1)=A(I1)/BIGA 

 SAVE1=B(IMAX) 

 B(IMAX)=B(J)

 B(J)=SAVE1/BIGA

 IF(J-N) 55,70,55

55 IQS=N*(J-1)

 DO 65 IX=JY,N

 IXJ=IQS+IX

 IT=J-IX

 DO 60 JX=JY,N

 IXJX=N*(JX-1)+IX

 JJX=IXJX+IT

60 A(IXJX)=A(IXJX)-(A(IXJ)*A(JJX))

65 B(IX)=B(IX)-(B(J)*A(IXJ))

70 NY=N-1

 IT=N*N

 DO 80 J=1,NY

 IA=IT-J

 IB=N-J

 IC=N

 DO 80 K=1,J

 B(IB)=B(IB)-A(IA)*B(IC)

 IA=IA-N

80 IC=IC-1

 RETURN 

 END

C
84

2.15. state4.f

C

C NONLINEAR STATE SPACE FILTERS (ALL IN INERTIAL FRAME):

C

SUBROUTINE STATE4

INCLUDE 'optint3.com'

INCLUDE 'nopt4.com'

REAL ABK1X(6,6),BK2X(6,3),BK3X(6),XXI1(9),XXI2(9)

REAL ABK1Y(6,6),BK2Y(6,3),BK3Y(6),XYI1(9),XYI2(9) 

REAL XZI1(5),XZI2(5),XRI1(4),XRI2(4)

REAL XPI1(4),XPI2(4),XQI1(4),XQI2(4)

C

C ROLL AND PITCH UNITY GAIN FILTERS

C

C BSDR(1)=BADNO(1)

C BSDR(2)=BADNO(2)

C

C 9TH ORDER SURGE/PITCH STATE SPACE FILTER 

C

DO I=1,6

DO J=1,6

K1X(1,J)=R2IX(1)*

 x (BVX(1,1)*PX(1,J)+BVX(2,1)*PX(2,J)+BVX(3,1)*PX(3,J)

 x +BVX(4,1)*PX(4,J)+BVX(5,1)*PX(5,J)+BVX(6,1)*PX(6,J)

 x +DQCX(J))

K1X(2,J)=R2IX(2)*

 x (BVX(1,2)*PX(1,J)+BVX(2,2)*PX(2,J)+BVX(3,2)*PX(3,J)

 x +BVX(4,2)*PX(4,J)+BVX(5,2)*PX(5,J)+BVX(6,2)*PX(6,J)

 x +PX(9,J))

ABK1X(I,J)=

 x AVX(I,J)-BVX(I,1)*K1X(1,J)-BVX(I,2)*K1X(2,J)

 END DO 

END DO

DO I=1,6

DO J=1,3

K2X(1,J)=R2IX(1)*

 x (BVX(1,1)*PX(1,J+6)+BVX(2,1)*PX(2,J+6)+BVX(3,1)*PX(3,J+6)

 x +BVX(4,1)*PX(4,J+6)+BVX(5,1)*PX(5,J+6)+BVX(6,1)*PX(6,J+6))

K2X(2,J)=R2IX(2)*

 x (BVX(1,2)*PX(1,J+6)+BVX(2,2)*PX(2,J+6)+BVX(3,2)*PX(3,J+6)

 x +BVX(4,2)*PX(4,J+6)+BVX(5,2)*PX(5,J+6)+BVX(6,2)*PX(6,J+6)

 x +PX(9,J+6))

 

 BK2X(I,J)=BVX(I,1)*K2X(1,J)+BVX(I,2)*K2X(2,J)

END DO 

END DO

K3X(1)=R2IX(1)*
85

 x (BVX(1,1)*PX(1,11)+BVX(2,1)*PX(2,11)+BVX(3,1)*PX(3,11)

 x +BVX(4,1)*PX(4,11)+BVX(5,1)*PX(5,11)+BVX(6,1)*PX(6,11))

 

 K3X(2)=R2IX(2)*

 x (BVX(1,2)*PX(1,11)+BVX(2,2)*PX(2,11)+BVX(3,2)*PX(3,11)

 x +BVX(4,2)*PX(4,11)+BVX(5,2)*PX(5,11)+BVX(6,2)*PX(6,11)

 x +PX(9,11)) 

DO I=1,6

BK3X(I)=BVX(I,1)*K3X(1)+BVX(I,2)*(1.0+K3X(2))

END DO

DO I=1,6

XXI1(I)=DT*

 x (ABK1X(I,1)*XXO(1)+ABK1X(I,2)*XXO(2)+ABK1X(I,3)*XXO(3)

 x +ABK1X(I,4)*XXO(4)+ABK1X(I,5)*XXO(5)+ABK1X(I,6)*XXO(6)

 x -BK2X(I,1)*XXO(7)-BK2X(I,2)*XXO(8)-BK2X(I,3)*XXO(9) 

 x -BK3X(I)*A2NO(1))

 END DO

XXI1(7)=DT*XXO(8)

XXI1(8)=DT*XXO(9)

XXI1(9)=DT*

 x (-K1X(2,1)*XXO(1)-K1X(2,2)*XXO(2)-K1X(2,3)*XXO(3)

 x -K1X(2,4)*XXO(4)-K1X(2,5)*XXO(5)-K1X(2,6)*XXO(6)

 x -K2X(2,1)*XXO(7)-K2X(2,2)*XXO(8)-K2X(2,3)*XXO(9)

 x -K3X(2)*A2NO(1)) 

DO I=1,6

XXI2(I)=DT*

 x (ABK1X(I,1)*(XXO(1)+XXI1(1))+ABK1X(I,2)*(XXO(2)+XXI1(2))

 x +ABK1X(I,3)*(XXO(3)+XXI1(3))+ABK1X(I,4)*(XXO(4)+XXI1(4))

 x +ABK1X(I,5)*(XXO(5)+XXI1(5))+ABK1X(I,6)*(XXO(6)+XXI1(6))

 x -BK2X(I,1)*(XXO(7)+XXI1(7))-BK2X(I,2)*(XXO(8)+XXI1(8))

 x -BK2X(I,3)*(XXO(9)+XXI1(9))-BK3X(I)*A2N(1)) 

 END DO

XXI2(7)=DT*(XXO(8)+XXI1(8))

XXI2(8)=DT*(XXO(9)+XXI1(9))

XXI2(9)=DT*(-K1X(2,1)*(XXO(1)+XXI1(1))

 x -K1X(2,2)*(XXO(2)+XXI1(2))-K1X(2,3)*(XXO(3)+XXI1(3))

 x -K1X(2,4)*(XXO(4)+XXI1(4))-K1X(2,5)*(XXO(5)+XXI1(5))

 x -K1X(2,6)*(XXO(6)+XXI1(6))-K2X(2,1)*(XXO(7)+XXI1(7))

 x -K2X(2,2)*(XXO(8)+XXI1(8))-K2X(2,3)*(XXO(9)+XXI1(9))

 x -K3X(2)*A2N(1))

DO I=1,9

XX(I)=XXO(I)+0.5*(XXI1(I)+XXI2(I))

END DO

C

C 9TH ORDER SWAY/ROLL STATE SPACE FILTER 

C

DO I=1,6

DO J=1,6

K1Y(1,J)=R2IY(1)*

 x (BVY(1,1)*PY(1,J)+BVY(2,1)*PY(2,J)+BVY(3,1)*PY(3,J)

 x +BVY(4,1)*PY(4,J)+BVY(5,1)*PY(5,J)+BVY(6,1)*PY(6,J)

 x +DQCY(J))
86

K1Y(2,J)=R2IY(2)*

 x (BVY(1,2)*PY(1,J)+BVY(2,2)*PY(2,J)+BVY(3,2)*PY(3,J)

 x +BVY(4,2)*PY(4,J)+BVY(5,2)*PY(5,J)+BVY(6,2)*PY(6,J)

 x +PY(9,J))

ABK1Y(I,J)=

 x AVY(I,J)-BVY(I,1)*K1Y(1,J)-BVY(I,2)*K1Y(2,J)

 END DO 

END DO

DO I=1,6

DO J=1,3

K2Y(1,J)=R2IY(1)*

 x (BVY(1,1)*PY(1,J+6)+BVY(2,1)*PY(2,J+6)+BVY(3,1)*PY(3,J+6)

 x +BVY(4,1)*PY(4,J+6)+BVY(5,1)*PY(5,J+6)+BVY(6,1)*PY(6,J+6))

K2Y(2,J)=R2IY(2)*

 x (BVY(1,2)*PY(1,J+6)+BVY(2,2)*PY(2,J+6)+BVY(3,2)*PY(3,J+6)

 x +BVY(4,2)*PY(4,J+6)+BVY(5,2)*PY(5,J+6)+BVY(6,2)*PY(6,J+6)

 x +PY(9,J+6))

 

 BK2Y(I,J)=BVY(I,1)*K2Y(1,J)+BVY(I,2)*K2Y(2,J)

END DO 

END DO

K3Y(1)=R2IY(1)*

 x (BVY(1,1)*PY(1,11)+BVY(2,1)*PY(2,11)+BVY(3,1)*PY(3,11)

 x +BVY(4,1)*PY(4,11)+BVY(5,1)*PY(5,11)+BVY(6,1)*PY(6,11))

 

 K3Y(2)=R2IY(2)*

 x (BVY(1,2)*PY(1,11)+BVY(2,2)*PY(2,11)+BVY(3,2)*PY(3,11)

 x +BVY(4,2)*PY(4,11)+BVY(5,2)*PY(5,11)+BVY(6,2)*PY(6,11)

 x +PY(9,11)) 

DO I=1,6

BK3Y(I)=BVY(I,1)*K3Y(1)+BVY(I,2)*(1.0+K3Y(2))

END DO

DO I=1,6

XYI1(I)=DT*

 x (ABK1Y(I,1)*XYO(1)+ABK1Y(I,2)*XYO(2)+ABK1Y(I,3)*XYO(3)

 x +ABK1Y(I,4)*XYO(4)+ABK1Y(I,5)*XYO(5)+ABK1Y(I,6)*XYO(6)

 x -BK2Y(I,1)*XYO(7)-BK2Y(I,2)*XYO(8)-BK2Y(I,3)*XYO(9) 

 x -BK3Y(I)*A2NO(2))

 END DO

XYI1(7)=DT*XYO(8)

XYI1(8)=DT*XYO(9)

XYI1(9)=DT*

 x (-K1Y(2,1)*XYO(1)-K1Y(2,2)*XYO(2)-K1Y(2,3)*XYO(3)

 x -K1Y(2,4)*XYO(4)-K1Y(2,5)*XYO(5)-K1Y(2,6)*XYO(6)

 x -K2Y(2,1)*XYO(7)-K2Y(2,2)*XYO(8)-K2Y(2,3)*XYO(9)

 x -K3Y(2)*A2NO(2)) 

DO I=1,6

XYI2(I)=DT*

 x (ABK1Y(I,1)*(XYO(1)+XYI1(1))+ABK1Y(I,2)*(XYO(2)+XYI1(2))

 x +ABK1Y(I,3)*(XYO(3)+XYI1(3))+ABK1Y(I,4)*(XYO(4)+XYI1(4))
87

 x +ABK1Y(I,5)*(XYO(5)+XYI1(5))+ABK1Y(I,6)*(XYO(6)+XYI1(6))

 x -BK2Y(I,1)*(XYO(7)+XYI1(7))-BK2Y(I,2)*(XYO(8)+XYI1(8))

 x -BK2Y(I,3)*(XYO(9)+XYI1(9))-BK3Y(I)*A2N(2)) 

 END DO

XYI2(7)=DT*(XYO(8)+XYI1(8))

XYI2(8)=DT*(XYO(9)+XYI1(9))

XYI2(9)=DT*(-K1Y(2,1)*(XYO(1)+XYI1(1))

 x -K1Y(2,2)*(XYO(2)+XYI1(2))-K1Y(2,3)*(XYO(3)+XYI1(3))

 x -K1Y(2,4)*(XYO(4)+XYI1(4))-K1Y(2,5)*(XYO(5)+XYI1(5))

 x -K1Y(2,6)*(XYO(6)+XYI1(6))-K2Y(2,1)*(XYO(7)+XYI1(7))

 x -K2Y(2,2)*(XYO(8)+XYI1(8))-K2Y(2,3)*(XYO(9)+XYI1(9))

 x -K3Y(2)*A2N(2))

DO I=1,9

XY(I)=XYO(I)+0.5*(XYI1(I)+XYI2(I))

END DO 

C

C 5TH ORDER HEAVE STATE SPACE FILTER 

C

K1Z(1)=BVZ(1)*PZ(1,1)+BVZ(2)*PZ(2,1)+PZ(5,1) 

K1Z(2)=BVZ(1)*PZ(1,2)+BVZ(2)*PZ(2,2)+PZ(5,2)

K2Z(1)=BVZ(1)*PZ(1,3)+BVZ(2)*PZ(2,3)+PZ(5,3)

K2Z(2)=BVZ(1)*PZ(1,4)+BVZ(2)*PZ(2,4)+PZ(5,4)

K2Z(3)=BVZ(1)*PZ(1,5)+BVZ(2)*PZ(2,5)+PZ(5,5)

 K3Z=BVZ(1)*PZ(1,6)+BVZ(2)*PZ(2,6)+PZ(5,6) 

DO I=1,2

XZI1(I)=DT*

 x ((AVZ(I,1)-BVZ(I)*K1Z(1))*XZO(1)

 x +(AVZ(I,2)-BVZ(I)*K1Z(2))*XZO(2) 

 x -BVZ(I)*(K2Z(1)*XZO(3)+K2Z(2)*XZO(4)+K2Z(3)*XZO(5))

 x -BVZ(I)*(1+K3Z)*A2NO(3))

 END DO

XZI1(3)=DT*XZO(4)

XZI1(4)=DT*XZO(5)

XZI1(5)=DT*(-K1Z(1)*XZO(1)-K1Z(2)*XZO(2)-K2Z(1)*XZO(3)

 x -K2Z(2)*XZO(4)-K2Z(3)*XZO(5)-K3Z*A2NO(3))

DO I=1,2

XZI2(I)=DT*

 x ((AVZ(I,1)-BVZ(I)*K1Z(1))*(XZO(1)+XZI1(1))

 x +(AVZ(I,2)-BVZ(I)*K1Z(2))*(XZO(2)+XZI1(2)) 

 x -BVZ(I)*(K2Z(1)*(XZO(3)+XZI1(3))+K2Z(2)*(XZO(4)+XZI1(4))

 x +K2Z(3)*(XZO(5)+XZI1(5)))

 x -BVZ(I)*(1+K3Z)*A2N(3))

 END DO

XZI2(3)=DT*(XZO(4)+XZI1(4))

XZI2(4)=DT*(XZO(5)+XZI1(5))

XZI2(5)=DT*(-K1Z(1)*(XZO(1)+XZI1(1))

 x -K1Z(2)*(XZO(2)+XZI1(2))

 x -K2Z(1)*(XZO(3)+XZI1(3))

 x -K2Z(2)*(XZO(4)+XZI1(4))

 x -K2Z(3)*(XZO(5)+XZI1(5))-K3Z*A2N(3))

DO I=1,5

XZ(I)=XZO(I)+0.5*(XZI1(I)+XZI2(I))

END DO
88

C

C 4TH ORDER YAW STATE SPACE FILTER 

C

DO I=1,3

K1R(I)=R2IR*

 x (BVR(1)*PR(1,I)+BVR(2)*PR(2,I)+BVR(3)*PR(3,I)+PR(4,I)+DQCR(I)) 

 

END DO

K2R=R2IR*

 x (BVR(1)*PR(1,4)+BVR(2)*PR(2,4)+BVR(3)*PR(3,4)+PR(4,4))

K3R=R2IR*

 x (BVR(1)*PR(1,5)+BVR(2)*PR(2,5)+BVR(3)*PR(3,5)+PR(4,5)-DQDR)

 

DO I=1,3

XRI1(I)=DT*

 x ((AVR(I,1)-BVR(I)*K1R(1))*XRO(1)

 x +(AVR(I,2)-BVR(I)*K1R(2))*XRO(2)

 x +(AVR(I,3)-BVR(I)*K1R(3))*XRO(3)

 x -BVR(I)*K2R*XRO(4)

 x -BVR(I)*(1+K3R)*BADNO(3))

 END DO

XRI1(4)=DT*(-K1R(1)*XRO(1)-K1R(2)*XRO(2)

 x -K1R(3)*XRO(3)-K2R*XRO(4)-K3R*BADNO(3)) 

DO I=1,3

XRI2(I)=DT*

 x ((AVR(I,1)-BVR(I)*K1R(1))*(XRO(1)+XRI1(1))

 x +(AVR(I,2)-BVR(I)*K1R(2))*(XRO(2)+XRI1(2))

 x +(AVR(I,3)-BVR(I)*K1R(3))*(XRO(3)+XRI1(3))

 x -BVR(I)*K2R*(XRO(4)+XRI1(4))

 x -BVR(I)*(1+K3R)*BADN(3))

 END DO

XRI2(4)=DT*(-K1R(1)*(XRO(1)+XRI1(1))

 x -K1R(2)*(XRO(2)+XRI1(2))

 x -K1R(3)*(XRO(3)+XRI1(3))

 x -K2R*(XRO(4)+XRI1(4))-K3R*BADN(3))

DO I=1,4

XR(I)=XRO(I)+0.5*(XRI1(I)+XRI2(I))

END DO 

C

C 4TH ORDER PITCH STATE SPACE FILTER 

C

DO I=1,3

K1P(I)=R2IP*

 x (BVP(1)*PP(1,I)+BVP(2)*PP(2,I)+BVP(3)*PP(3,I)+PP(4,I)+DQCP(I)) 

 

END DO

K2P=R2IP*

 x (BVP(1)*PP(1,4)+BVP(2)*PP(2,4)+BVP(3)*PP(3,4)+PP(4,4))

K3P=R2IP*

 x (BVP(1)*PP(1,5)+BVP(2)*PP(2,5)+BVP(3)*PP(3,5)+PP(4,5)-DQDP)

 

DO I=1,3

XPI1(I)=DT*

 x ((AVP(I,1)-BVP(I)*K1P(1))*XPO(1)
89

 x +(AVP(I,2)-BVP(I)*K1P(2))*XPO(2)

 x +(AVP(I,3)-BVP(I)*K1P(3))*XPO(3)

 x -BVP(I)*K2P*XPO(4)

 x -BVP(I)*(1+K3P)*BADNO(2))

 END DO

XPI1(4)=DT*(-K1P(1)*XPO(1)-K1P(2)*XPO(2)

 x -K1P(3)*XPO(3)-K2P*XPO(4)-K3P*BADNO(2)) 

DO I=1,3

XPI2(I)=DT*

 x ((AVP(I,1)-BVP(I)*K1P(1))*(XPO(1)+XPI1(1))

 x +(AVP(I,2)-BVP(I)*K1P(2))*(XPO(2)+XPI1(2))

 x +(AVP(I,3)-BVP(I)*K1P(3))*(XPO(3)+XPI1(3))

 x -BVP(I)*K2P*(XPO(4)+XPI1(4))

 x -BVP(I)*(1+K3P)*BADN(2))

 END DO

XPI2(4)=DT*(-K1P(1)*(XPO(1)+XPI1(1))

 x -K1P(2)*(XPO(2)+XPI1(2))

 x -K1P(3)*(XPO(3)+XPI1(3))

 x -K2P*(XPO(4)+XPI1(4))-K3P*BADN(2))

DO I=1,4

XP(I)=XPO(I)+0.5*(XPI1(I)+XPI2(I))

END DO

C

C 4TH ORDER ROLL STATE SPACE FILTER 

C

DO I=1,3

K1Q(I)=R2IQ*

 x (BVQ(1)*PQ(1,I)+BVQ(2)*PQ(2,I)+BVQ(3)*PQ(3,I)+PQ(4,I)+DQCQ(I)) 

 

END DO

K2Q=R2IQ*

 x (BVQ(1)*PQ(1,4)+BVQ(2)*PQ(2,4)+BVQ(3)*PQ(3,4)+PQ(4,4))

K3Q=R2IQ*

 x (BVQ(1)*PQ(1,5)+BVQ(2)*PQ(2,5)+BVQ(3)*PQ(3,5)+PQ(4,5)-DQDQ)

 

DO I=1,3

XQI1(I)=DT*

 x ((AVQ(I,1)-BVQ(I)*K1Q(1))*XQO(1)

 x +(AVQ(I,2)-BVQ(I)*K1Q(2))*XQO(2)

 x +(AVQ(I,3)-BVQ(I)*K1Q(3))*XQO(3)

 x -BVQ(I)*K2Q*XQO(4)

 x -BVQ(I)*(1+K3Q)*BADNO(1))

 END DO

XQI1(4)=DT*(-K1Q(1)*XQO(1)-K1Q(2)*XQO(2)

 x -K1Q(3)*XQO(3)-K2Q*XQO(4)-K3Q*BADNO(1)) 

DO I=1,3

XQI2(I)=DT*

 x ((AVQ(I,1)-BVQ(I)*K1Q(1))*(XQO(1)+XQI1(1))

 x +(AVQ(I,2)-BVQ(I)*K1Q(2))*(XQO(2)+XQI1(2))

 x +(AVQ(I,3)-BVQ(I)*K1Q(3))*(XQO(3)+XQI1(3))

 x -BVQ(I)*K2Q*(XQO(4)+XQI1(4))

 x -BVQ(I)*(1+K3Q)*BADN(1))

 END DO

XQI2(4)=DT*(-K1Q(1)*(XQO(1)+XQI1(1))
90

 x -K1Q(2)*(XQO(2)+XQI1(2))

 x -K1Q(3)*(XQO(3)+XQI1(3))

 x -K2Q*(XQO(4)+XQI1(4))-K3Q*BADN(1))

DO I=1,4

XQ(I)=XQO(I)+0.5*(XQI1(I)+XQI2(I))

END DO

C

C************* UPDATE ALL THE DUMMY VARIABLES: ********************

C 

DO I=1,9

 XXO(I)=XX(I)

XYO(I)=XY(I)

 END DO

C

DO I=1,5

XZO(I)=XZ(I)

END DO

DO I=1,4

 XRO(I)=XR(I)

 XPO(I)=XP(I)

 XQO(I)=XQ(I)

 END DO

A2NO(1) = A2N(1)

A2NO(2) = A2N(2)

A2NO(3) = A2N(3)

BADNO(1) = BADN(1)

BADNO(2) = BADN(2)

BADNO(3) = BADN(3)

 

RETURN

END
91

2.16. vmult.f

C

C**********************************************************************

C Subroutine VMULT : MATRIX MULTIPLICATION.

C**********************************************************************

C

 SUBROUTINE VMULT(A,B,C,K,L,M)

 DIMENSION A(K,L),B(K,L),C(K,M)

 DO 20 KK = 1,K

 DO 20 MM = 1,M

 C(KK,MM) = 0.0

 DO 20 LL = 1,L

 C(KK,MM) = C(KK,MM) + A(KK,LL)*B(LL,MM)

 20 CONTINUE

 RETURN

 END

2.17. winit4.f

 SUBROUTINE WINIT4

C

C THIS ROUTINE LOADS THE INITIAL VALUES INTO THE WASHOUT

C PARAMETER ARRAYS. 

C

INCLUDE 'nopt4.com'

REAL BRBXVEC(66),R1PXVEC(66),ZXVEC(66)

REAL BRBYVEC(66),R1PYVEC(66),ZYVEC(66)

REAL BRBRVEC(15),R1PRVEC(15),ZRVEC(15)

REAL BRBPVEC(15),R1PPVEC(15),ZPVEC(15)

REAL BRBQVEC(15),R1PQVEC(15),ZQVEC(15)

REAL BRBZVEC(21),R1PZVEC(21),ZZVEC(21)

C

C Initialization of Nonlinear Algorithm Inputs

C

DATA XXO/9*0./XYO/9*0./,XRO/4*0./,XPO/4*0./,XQO/4*0./,XZO/5*0./

C 

C Parameters for nonlinear roll/sway channel filters. 

C

DATA ALPY /0.0/, ALPYMAX /1.0/, Q2Y /0.0,0.8/, MUY /4.0E-6 /

DATA APY /

 + -0.48601433, 1.50095561, 0.43295640, -2.00166583, 2.30852675,

 + 0.93783312, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,

 + -0.22785440, 1.23627334, 0.43548518, -2.00719798, 2.32816934,

 + 0.92719057, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,

 + 0.00000000, 0.00000000, 0.00000000, -0.50000000, 0.50000000,

 + -0.00000000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,

 + 0.17852148, -0.42864297, 0.00091112, -0.01882892, 0.19024153,

 + 0.74839400, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,

 + 0.84518815, 0.23802370, 0.00091112, 0.18117108, -0.00975847,

 + 0.08172733, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,

 + 0.47047268, -2.17119788, -0.42654860, 1.84882203, -2.39757925,
92

 + -1.63405743, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,

 + 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000,

 + 0.00000000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,

 + 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000,

 + 0.00000000, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000,

 + 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000,

 + 0.00000000, 0.0000, 1.0000, 0.0000, 0.0000, 0.0000,

 + -0.00007038, 0.00070080, 0.00016391, -0.00074143, 0.00089035,

 + 0.00036336, 0.0000, 0.0000, 0.0000, -1.000000, 0.0000,

 + -1.33333333, -1.33333333, 0.00000000, -0.20000000, 0.20000000,

 + 1.33333333, 0.0000, 0.0000, 0.0000, 0.0000, -3.14159265/

 DATA BRBYVEC /

 + 1.77789635, 1.77659704, -0.00027616, 0.26791584, -0.26816675,

 + -1.77838998, 0.0000, 0.0000, 1.33333333, 0.0000, 0.0000,

 + 1.78953524, 0.00274996, 0.25422767, -0.25172914,

 + -1.77168162, 0.0000, 0.0000, 1.33333333, 0.0000, 0.0000,

 + 0.00064319, -0.00290936, 0.00349374,

 + 0.00142583, 0.0000, 0.0000, -0.00000000, 0.0000, 0.0000,

 + 0.05316003, -0.05580338,

 + -0.27311620, 0.0000, 0.0000, 0.20000000, 0.0000, 0.0000,

 + 0.05897769,

 + 0.27441166, 0.0000, 0.0000, -0.20000000, 0.0000, 0.0000,

 + 1.78093859, 0.0000, 0.0000, -1.33333333, 0.0000, 0.0000,

 + 0.0000, 0.0000, 0.00000000, 0.0000, 0.0000,

 + 0.0000, 0.00000000, 0.0000, 0.0000,

 + 1.00000000, 0.0000, 0.0000,

 + 0.0000, 0.0000,

 + 0.0000/

 DATA R1PYVEC /

 + 8.63477261, 7.08082902, 0.00000000, -0.55988506, -0.55988506,

 +-12.57237449, 0.0000, 0.0000, 0.0000, -0.11033547, 0.0000,

 + 5.80695939, 0.00000000, -0.45897456, -0.45897456,

 +-10.30873990, 0.0000, 0.0000, 0.0000, -0.11097991, 0.0000,

 + 0.00000000, -0.00000000, -0.00000000,

 + -0.00000000, 0.0000, 0.0000, 0.0000, 0.00000000, 0.0000,

 + 0.03635800, 0.03635800,

 + 0.81558635, 0.0000, 0.0000, 0.0000, -0.00023219, 0.0000,

 + 0.03635800,

 + 0.81558635, 0.0000, 0.0000, 0.0000, -0.00023219, 0.0000,

 + 18.30829171, 0.0000, 0.0000, 0.0000, 0.10870250, 0.0000,

 + 8.00000000, 0.0000, 0.0000, 0.0000, 0.0000,

 + 4.00000000, 0.0000, 0.0000, 0.0000,

 + 1.00000000, 0.0000, 0.0000,

 + 1.0000, 0.00000000,

 + 0.0000/

 DATA R2IY /4.17714546E-005, 1.00000000/

 DATA AVY /

 + -0.3001182, -0.3501544, -0.0, -0.0432552, -0.0432552, -

0.0219541,

 + -0.0408725, -0.6256486, -0.0, -0.0373488, -0.0373488, -

0.0382025,

 + 0.0000000, 0.0000000, 0.0, -0.5000000, 0.5000000, -

0.0000000,

 + 0.1789127, -0.4325385, 0.0, -0.0147076, 0.1852924, 

0.7463742,

 + 0.8455793, 0.2341282, -0.0, 0.1852924, -0.0147076, 

0.0797075,
93

 + 0.2873278, -0.3474845, 0.0, -0.0806039, -0.0806039, -

0.6884752/

 DATA BVY /

 + 1.684826,-16.777107, -3.924000, 17.749601,-21.314831, -

8.698809,

 + 1.333333, 1.333333, -0.000000, 0.200000, -0.200000, -

1.333333/

 DATA DQCY /

 + 2641.408443, 2656.836237, -0.000000,

 + 5.558626, 5.558626, -2602.315320/

 DATA ZYVEC /

 + 1.0, -1.0, -1.0, -1.0, -1.0,

 + -1.0, -1.0, -1.0, -1.0, -1.0, -

1.0,

 + 1.0, -1.0, -1.0, -1.0,

 + -1.0, -1.0, -1.0, -1.0, -1.0, -

1.0,

 + 1.0, -1.0, -1.0,

 + -1.0, -1.0, -1.0, -1.0, -1.0, -

1.0,

 + 1.0, -1.0,

 + -1.0, -1.0, -1.0, -1.0, -1.0, -

1.0,

 + 1.0,

 + -1.0, -1.0, -1.0, -1.0, -1.0, -

1.0,

 + 1.0, -1.0, -1.0, -1.0, -1.0, -

1.0,

 + 1.0, -1.0, -1.0, -1.0, -1.0,

 + 1.0, -1.0, -1.0, -1.0,

 + 1.0, -1.0, -1.0,

 + 1.0, -1.0,

 + 1.0/

 DATA PYVEC /

 + 8.78919914,

 + 8.64675152, 2.04454782, -5.18310331, 3.53876667, -7.88399752,

 + -8.38739821,-21.02141997,-25.10394095, 0.01775090, -6.40258907,

 + 9.07316301, 2.21477279, -4.18934594, 4.64570745, -7.69883299,

 + -8.39486263,-21.05959150,-25.21567898, 0.01774509, -6.43447599,

 + 0.71635788, -1.20003026, 0.98991751, -1.32889642,

 + -1.74100084, -4.45442250, -5.59861393, 0.02613645, -1.44219625,

 + 5.44431336, 0.18951117, 3.77151434,

 + 4.13378917, 10.88195613, 13.90068610, -0.02161095, 3.56872382,

 + 4.49770413, -3.84403097,

 + -4.01767838,-10.33185268,-12.56415459, 0.02169120, -3.19600160,

 + 8.54553179,

 + 8.27250466, 20.46798345, 23.69772741, -0.01783242, 6.00808010,

 + 23.81195147, 33.64457162, 29.33323432, -0.00748064, 6.63816656,

 + 71.85128707, 71.56090170, -0.03103290, 16.77905545,

 + 82.30634518, -0.06573714, 19.98961531,

 + 0.49999450, -0.01797396,

 + 5.06794969/

 

DO J=1,11

APYO(J)=APY(J,J)

DO I=1,11

IF(I.GE.J) THEN
94

BRBY(I,J)=BRBYVEC((J-1)*11-J*(J-1)/2+I)

BRBY(J,I)=BRBY(I,J)

R1PY(I,J)=R1PYVEC((J-1)*11-J*(J-1)/2+I)

R1PY(J,I)=R1PY(I,J)

PY(I,J)=PYVEC((J-1)*11-J*(J-1)/2+I)

PY(J,I)=PY(I,J)

ZY(I,J)=ZYVEC((J-1)*11-J*(J-1)/2+I)

ZY(J,I)=ZY(I,J)

END IF

END DO

END DO 

c

c Parameters for nonlinear pitch/surge channel filters. 

c

DATA ALPX /0.0/, ALPXMAX /1.0/, Q2X /0.0,0.6/, MUX /4.0E-6/

DATA APX /

 + 0.35214308, -1.72273247, 0.43037039, -2.38099014, 1.90345806,

 + -1.44348410, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,

 + 0.60755620, -1.99016155, 0.42784160, -2.36134755, 1.89792591,

 + -1.45137984, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,

 + 0.00000000, 0.00000000, 0.00000000, -0.50000000, 0.50000000,

 + -0.00000000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,

 + 0.17753181, -0.42963264, -0.00091112, -0.00975847, 0.18117108,

 + 0.74938368, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,

 + 0.84419847, 0.23703402, -0.00091112, 0.19024153, -0.01882892,

 + 0.08271701, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,

 + -0.37464499, 1.04552994, -0.43677819, 2.29193764, -2.05630186,

 + 0.75422005, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,

 + 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000,

 + 0.00000000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,

 + 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000,

 + 0.00000000, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000,

 + 0.00000000, 0.00000000, 0.00000000, 0.00000000, 0.00000000,

 + 0.00000000, 0.0000, 1.0000, 0.0000, 0.0000, 0.0000,

 + -0.00024842, 0.00052276, -0.00016391, 0.00089035, -0.00074143,

 + 0.00054140, 0.0000, 0.0000, 0.0000, -1.000000, 0.0000,

 + -1.33333333, -1.33333333, 0.00000000, -0.20000000, 0.20000000,

 + 1.33333333, 0.0000, 0.0000, 0.0000, 0.0000, -3.14159265/

 DATA BRBXVEC /

 + 1.77925517, 1.77466884, 0.00097480, 0.26137162, -0.26225730,

 + -1.78099759, 0.0000, 0.0000, 1.33333333, 0.0000, 0.0000,

 + 1.78432002, -0.00205131, 0.27780923, -0.27594547,

 + -1.77100221, 0.0000, 0.0000, 1.33333333, 0.0000, 0.0000,

 + 0.00064319, -0.00349374, 0.00290936,

 + -0.00212447, 0.0000, 0.0000, -0.00000000, 0.0000, 0.0000,

 + 0.05897769, -0.05580338,

 + -0.25512671, 0.0000, 0.0000, 0.20000000, 0.0000, 0.0000,

 + 0.05316003,

 + 0.25705694, 0.0000, 0.0000, -0.20000000, 0.0000, 0.0000,

 + 1.78479499, 0.0000, 0.0000, -1.33333333, 0.0000, 0.0000,

 + 0.0000, 0.0000, 0.00000000, 0.0000, 0.0000,

 + 0.0000, 0.00000000, 0.0000, 0.0000,

 + 1.00000000, 0.0000, 0.0000,

 + 0.0000, 0.0000,

 + 0.0000/

 DATA R1PXVEC /
95

 + 12.10587580, 13.94623075, -0.00000000, 0.66307892, 0.66307892,

 + -7.44252436, 0.0000, 0.0000, 0.0000, 0.10967645, 0.0000,

 + 16.06665966, -0.00000000, 0.76398942, 0.76398942,

 + -8.57318831, 0.0000, 0.0000, 0.0000, 0.10903201, 0.0000,

 + 0.00000000, -0.00000000, -0.00000000,

 + 0.00000000, 0.0000, 0.0000, 0.0000, 0.00000000, 0.0000,

 + 0.03635800, 0.03635800,

 + -0.40737763, 0.0000, 0.0000, 0.0000, -0.00023219, 0.0000,

 + 0.03635800,

 + -0.40737763, 0.0000, 0.0000, 0.0000, -0.00023219, 0.0000,

 + 4.57748825, 0.0000, 0.0000, 0.0000, -0.11130943, 0.0000,

 + 8.00000000, 0.0000, 0.0000, 0.0000, 0.0000,

 + 4.00000000, 0.0000, 0.0000, 0.0000,

 + 1.00000000, 0.0000, 0.0000,

 + 1.0000, 0.00000000,

 + 0.0000/

 DATA R2IX /4.17714546E-005, 1.00000000/

 DATA AVX /

 + -0.3001182, -0.3501544, -0.0, -0.0432552, -0.0432552, -

0.0219541,

 + -0.0408725, -0.6256486, -0.0, -0.0373488, -0.0373488, -

0.0382025,

 + 0.0000000, 0.0000000, 0.0, -0.5000000, 0.5000000, -

0.0000000,

 + 0.1789127, -0.4325385, 0.0, -0.0147076, 0.1852924, 

0.7463742,

 + 0.8455793, 0.2341282, -0.0, 0.1852924, -0.0147076, 

0.0797075,

 + 0.2873278, -0.3474845, 0.0, -0.0806039, -0.0806039, -

0.6884752/

 DATA BVX /

 + 5.947141,-12.514793, 3.924000,-21.314831, 17.749601,-

12.961123,

 + 1.333333, 1.333333, -0.000000, 0.200000, -0.200000, -

1.333333/

 DATA DQCX /

 + -2625.631557, -2610.203763, -0.000000,

 + 5.558626, 5.558626, 2664.724680/

DATA ZXVEC /

 + 1.0, -1.0, -1.0, -1.0, -1.0,

 + -1.0, -1.0, -1.0, -1.0, -1.0, -

1.0,

 + 1.0, -1.0, -1.0, -1.0,

 + -1.0, -1.0, -1.0, -1.0, -1.0, -

1.0,

 + 1.0, -1.0, -1.0,

 + -1.0, -1.0, -1.0, -1.0, -1.0, -

1.0,

 + 1.0, -1.0,

 + -1.0, -1.0, -1.0, -1.0, -1.0, -

1.0,

 + 1.0,

 + -1.0, -1.0, -1.0, -1.0, -1.0, -

1.0,

 + 1.0, -1.0, -1.0, -1.0, -1.0, -

1.0,

 + 1.0, -1.0, -1.0, -1.0, -1.0,
96

 + 1.0, -1.0, -1.0, -1.0,

 + 1.0, -1.0, -1.0,

 + 1.0, -1.0,

 + 1.0/

 DATA PXVEC /

 + 8.30351624,

 + 8.09520238, 1.68093020, -4.48023672, 3.57953908, -8.19270520,

 + -8.31577879,-20.67790997,-24.24095727, -0.01780137, -6.16084104,

 + 8.45574766, 1.51070523, -3.37329594, 4.57329645, -7.94167444,

 + -8.30831437,-20.63973845,-24.12921925, -0.01780718, -6.12895412,

 + 0.71635788, -0.98991751, 1.20003026, -2.39658160,

 + -1.74100084, -4.45442250, -5.59861393, -0.02613645, -1.44219625,

 + 4.49770413, 0.18951117, 4.17497242,

 + 4.01767838, 10.33185268, 12.56415459, 0.02169120, 3.19600160,

 + 5.44431336, -4.99112805,

 + -4.13378917,-10.88195613,-13.90068610, -0.02161095, -3.56872382,

 + 9.64863006,

 + 8.43067234, 21.23134650, 25.64717081, 0.01771985, 6.55535001,

 + 23.81195147, 33.64457162, 29.33323432, 0.00748064, 6.63816656,

 + 71.85128707, 71.56090170, 0.03103290, 16.77905545,

 + 82.30634518, 0.06573714, 19.98961531,

 + 0.49999450, 0.01797396,

 + 5.06794969/

 

 DO J=1,11

APXO(J)=APX(J,J)

DO I=1,11

IF(I.GE.J) THEN

BRBX(I,J)=BRBXVEC((J-1)*11-J*(J-1)/2+I)

BRBX(J,I)=BRBX(I,J)

R1PX(I,J)=R1PXVEC((J-1)*11-J*(J-1)/2+I)

R1PX(J,I)=R1PX(I,J)

PX(I,J)=PXVEC((J-1)*11-J*(J-1)/2+I)

PX(J,I)=PX(I,J)

ZX(I,J)=ZXVEC((J-1)*11-J*(J-1)/2+I)

ZX(J,I)=ZX(I,J)

END IF

END DO

END DO 

c 

c Parameters for nonlinear yaw channel filters. 

c

DATA ALPR /0.0/, ALPRMAX /1.0/, Q2R /120.0/, MUR /2.0E-6 / 

 DATA APR /

 +-1.45728460E-004,-1.69985373E-006,-4.89593935E-004,

 +-2.79035083E-002, 0.0,

 + 1.0, 0.0, 0.0, 0.0, 0.0,

 +1.86874341E-001,2.17980102E-003,-4.89593935E-004,

 +-2.79035083E-002,0.00000000E+000,

 + 0.0, 0.0, 0.0, 0.0, 0.0,

 +5.21851607E-003,6.08715277E-005,1.75322913E-002,

 +9.99220787E-001, -1.0/

 DATA BRBRVEC /

 +3.49492524E-002,4.07666539E-004,1.17416612E-001,-5.21851607E-003,

 + 0.0,

 +4.75523782E-006,1.36960937E-003,-6.08715277E-005, 0.0,
97

 +3.94476555E-001,-1.75322913E-002, 0.0,

 +7.79212948E-004, 0.0,

 + 0.0/

 DATA R1PRVEC /

 +7.79212948E-004, 0.0,7.79212948E-004, 0.0,-2.79035083E-002,

 +0.00000000E+000, 0.0,0.00000000E+000, 0.0,

 +7.79212948E-004, 0.0,-2.79035083E-002,

 +2.00000000E+002, 0.0,

 +9.99220787E-001/

 DATA R2IR /7.79212948E-004/

 DATA AVR /

 +-1.87020070E-001,-2.18150087E-003,-6.28318531E-001,

 +1.00000000E+000,0.00000000E+000,0.00000000E+000,

 +0.00000000E+000,0.00000000E+000,-6.28318531E-001/

 DATA BVR /-6.69716293E+000,-7.81192456E-002,-2.25000000E+001/

 DATA DQCR / 35.80986220, 0.00000000, 35.80986220/

 DATA DQDR /1.28234623E+003/

 DATA ZRVEC /

 + 1.0, -1.0, -1.0, -1.0, -1.0,

 + 1.0, -1.0, -1.0, -1.0,

 + 1.0, -1.0, -1.0,

 + 1.0, -1.0,

 + 1.0/

 DATA PRVEC /

 + 0.52254103, 0.13331932, 0.53598671, -7.30258353, -6.33348013,

 + 5.01432503, 1.07135777, 6.89175648, 5.57001008,

 + 0.73962239, -5.97893648, -5.25519323,

 + 323.73106725, 186.47187109,

 + 139.87165376/

DO J=1,5

APRO(J)=APR(J,J)

DO I=1,5

IF(I.GE.J) THEN

BRBR(I,J)=BRBRVEC((J-1)*5-J*(J-1)/2+I)

BRBR(J,I)=BRBR(I,J)

R1PR(I,J)=R1PRVEC((J-1)*5-J*(J-1)/2+I)

R1PR(J,I)=R1PR(I,J)

PR(I,J)=PRVEC((J-1)*5-J*(J-1)/2+I)

PR(J,I)=PR(I,J)

ZR(I,J)=ZRVEC((J-1)*5-J*(J-1)/2+I)

ZR(J,I)=ZR(I,J)

END IF

END DO

END DO 

c 

c Parameters for nonlinear pitch channel filters. 

DATA ALPQ /0.0/, ALPQMAX /1.0/, Q2Q /200.0/, MUQ /2.0E-6 / 

 DATA APQ/

 +0.0,0.0,0.0,

 +0.0, 0.0,
98

 + 1.0, 0.0, 0.0, 0.0, 0.0,

 +5.86874341E-001,7.17980102E-003,-2.89593935E-004,

 +-2.79035083E-002,0.00000000E+000,

 + 0.0, 0.0, 0.0, 0.0, 0.0,

 +5.21851607E-003,6.08715277E-005,1.75322913E-002,

 +9.99220787E-001, -1.0/

 DATA BRBQVEC /

 +3.49492524E-002,4.07666539E-004,1.17416612E-001,-5.21851607E-003,

 + 0.0,

 +4.75523782E-006,1.36960937E-003,-6.08715277E-005, 0.0,

 +3.94476555E-001,-1.75322913E-002, 0.0,

 +7.79212948E-004, 0.0,

 + 0.0/

 DATA R1PQVEC /

 +7.79212948E-004, 0.0,7.79212948E-004, 0.0,-2.79035083E-002,

 +0.00000000E+000, 0.0,0.00000000E+000, 0.0,

 +7.79212948E-004, 0.0,-2.79035083E-002,

 +2.00000000E+002, 0.0,

 +9.99220787E-001/

 DATA R2IQ /7.79212948E-004/

 DATA AVQ /

 +-1.87020070E-001,-2.18150087E-003,-6.28318531E-001,

 +1.00000000E+000,0.00000000E+000,0.00000000E+000,

 +0.00000000E+000,0.00000000E+000,-6.28318531E-001/

 DATA BVQ /-6.69716293E+000,-7.81192456E-002,-2.25000000E+001/

 DATA DQCQ / 35.80986220, 0.00000000, 35.80986220/

 DATA DQDQ /1.28234623E+003/

 DATA ZQVEC /

 + 1.0, -1.0, -1.0, -1.0, -1.0,

 + 1.0, -1.0, -1.0, -1.0,

 + 1.0, -1.0, -1.0,

 + 1.0, -1.0,

 + 1.0/

 DATA PQVEC /

 + 0.52254103, 0.13331932, 0.53598671, -7.30258353, -6.33348013,

 + 5.01432503, 1.07135777, 6.89175648, 5.57001008,

 + 0.73962239, -5.97893648, -5.25519323,

 + 323.73106725, 186.47187109,

 + 139.87165376/

DO J=1,5

APQO(J)=APQ(J,J)

DO I=1,5

IF(I.GE.J) THEN

BRBQ(I,J)=BRBQVEC((J-1)*5-J*(J-1)/2+I)

BRBQ(J,I)=BRBQ(I,J)

R1PQ(I,J)=R1PQVEC((J-1)*5-J*(J-1)/2+I)

R1PQ(J,I)=R1PQ(I,J)

PQ(I,J)=PQVEC((J-1)*5-J*(J-1)/2+I)

PQ(J,I)=PQ(I,J)

ZQ(I,J)=ZQVEC((J-1)*5-J*(J-1)/2+I)

ZQ(J,I)=ZQ(I,J)

END IF

END DO

END DO 

c 

c Parameters for nonlinear roll channel filters. 
99

c

DATA ALPP /0.0/, ALPPMAX /1.0/, Q2P /120.0/, MUP /2.0E-6 / 

 DATA APP /

 +-1.45728460E-004,-1.69985373E-006,-4.89593935E-004,

 +-2.79035083E-002, 0.0,

 + 1.0, 0.0, 0.0, 0.0, 0.0,

 +1.86874341E-001,2.17980102E-003,-4.89593935E-004,

 +-2.79035083E-002,0.00000000E+000,

 + 0.0, 0.0, 0.0, 0.0, 0.0,

 +5.21851607E-003,6.08715277E-005,1.75322913E-002,

 +9.99220787E-001, -1.0/

 DATA BRBPVEC /

 +3.49492524E-002,4.07666539E-004,1.17416612E-001,-5.21851607E-003,

 + 0.0,

 +4.75523782E-006,1.36960937E-003,-6.08715277E-005, 0.0,

 +3.94476555E-001,-1.75322913E-002, 0.0,

 +7.79212948E-004, 0.0,

 + 0.0/

 DATA R1PPVEC /

 +7.79212948E-004, 0.0,7.79212948E-004, 0.0,-2.79035083E-002,

 +0.00000000E+000, 0.0,0.00000000E+000, 0.0,

 +7.79212948E-004, 0.0,-2.79035083E-002,

 +2.00000000E+002, 0.0,

 +9.99220787E-001/

 DATA R2IP /7.79212948E-004/

 DATA AVP /

 +-1.87020070E-001,-2.18150087E-003,-6.28318531E-001,

 +1.00000000E+000,0.00000000E+000,0.00000000E+000,

 +0.00000000E+000,0.00000000E+000,-6.28318531E-001/

 DATA BVP /-6.69716293E+000,-7.81192456E-002,-2.25000000E+001/

 DATA DQCP / 35.80986220, 0.00000000, 35.80986220/

 DATA DQDP /1.28234623E+003/

 DATA ZPVEC /

 + 1.0, -1.0, -1.0, -1.0, -1.0,

 + 1.0, -1.0, -1.0, -1.0,

 + 1.0, -1.0, -1.0,

 + 1.0, -1.0,

 + 1.0/

 DATA PPVEC /

 + 0.52254103, 0.13331932, 0.53598671, -7.30258353, -6.33348013,

 + 5.01432503, 1.07135777, 6.89175648, 5.57001008,

 + 0.73962239, -5.97893648, -5.25519323,

 + 323.73106725, 186.47187109,

 + 139.87165376/

DO J=1,5

APPO(J)=APP(J,J)

DO I=1,5

IF(I.GE.J) THEN

BRBP(I,J)=BRBPVEC((J-1)*5-J*(J-1)/2+I)

BRBP(J,I)=BRBP(I,J)

R1PP(I,J)=R1PPVEC((J-1)*5-J*(J-1)/2+I)

R1PP(J,I)=R1PP(I,J)

PP(I,J)=PPVEC((J-1)*5-J*(J-1)/2+I)

PP(J,I)=PP(I,J)

ZP(I,J)=ZPVEC((J-1)*5-J*(J-1)/2+I)
100

ZP(J,I)=ZP(I,J)

END IF

END DO

END DO

c 

c Parameters for nonlinear heave channel filters. 

c

DATA ALPZ /0.0/, ALPZMAX /0.2/, Q2Z /1.0,2.0/, MUZ /1.0E-7 /

 

DATA APZ /

 + -0.060606, 0.139394, 0.0000, 0.0000, 0.0000, 

0.000000,

 + -0.567713, -0.767713, 0.0000, 0.0000, 0.0000, 

0.000000,

 + 0.000000, 0.000000, 0.0000, 0.0000, 0.0000, 

0.000000,

 + 0.000000, 0.000000, 1.0000, 0.0000, 0.0000, 

0.000000,

 + 0.000000, 0.000000, 0.0000, 1.0000, 0.0000, 

0.000000,

 + -1.717157, -2.282843, 0.0000, 0.0000, 0.0000, -

62.831853/

 DATA BRBZVEC /

 + 2.948629, 3.920000, 0.0000, 0.0000, 1.717157, 

0.0000,

 + 5.211371, 0.0000, 0.0000, 2.282843, 0.0000,

 + 0.000000, 0.0000, 0.0000, 0.0000,

 + 0.000000, 0.0000, 0.0000,

 + 1.000000, 0.0000,

 + 0.000000/

 DATA R1PZVEC /

 + 200.0000, 200.0000, 0.0000, 0.0000, 0.0000, 

0.0000,

 + 200.0000, 0.0000, 0.0000, 0.0000, 0.0000,

 + 40.0000, 0.0000, 0.0000, 0.0000,

 + 400.0000, 0.0000, 0.0000,

 + 40.0000, 0.0000,

 + 0.0000/

 DATA AVZ / -0.060606, 0.139394, -0.567713, -0.767713/

 DATA BVZ / 1.717157, 2.282843/

 DATA ZZVEC /

 + 1.0, -1.0, -1.0, -1.0, -1.0, -1.0,

 + 1.0, -1.0, -1.0, -1.0, -1.0,

 + 1.0, -1.0, -1.0, -1.0,

 + 1.0, -1.0, -1.0,

 + 1.0, -1.0,

 + 1.0/

 DATA PZVEC /

 + 910.190970, -315.435226, -1.160668, -79.558688, -844.169063,

 + -13.404542, 327.670260, -60.259856, -315.797740, -198.948877,

 + -3.146942, 193.813146, 269.544193, 145.881379, 2.202307,

 + 1160.148818, 888.175899, 13.591950, 1946.358732, 30.388540,

 + 0.480397/
101

DO J=1,6

APZO(J)=APZ(J,J)

DO I=1,6

IF(I.GE.J) THEN

BRBZ(I,J)=BRBZVEC((J-1)*6-J*(J-1)/2+I)

BRBZ(J,I)=BRBZ(I,J)

R1PZ(I,J)=R1PZVEC((J-1)*6-J*(J-1)/2+I)

R1PZ(J,I)=R1PZ(I,J)

PZ(I,J)=PZVEC((J-1)*6-J*(J-1)/2+I)

PZ(J,I)=PZ(I,J)

ZZ(I,J)=ZZVEC((J-1)*6-J*(J-1)/2+I)

ZZ(J,I)=ZZ(I,J)

END IF

END DO

END DO

c

c Nonlinear Scaling Coefficients

c

DATA GX4/0.5,-0.05,0.002/

 DATA GY4/0.4,-0.035,0.001/ 

 DATA GZ40/0.6,-0.082,0.0038/

DATA GZ4S/2.0,-0.05, 0.0/ 

 DATA GP4/0.3,-0.3,0.1/ 

DATA GQ4/0.3,-0.3,0.1/

 DATA GR4/1.1,-1.46,0.64/

c

c Translational and Rotational Limits

c

 DATA AMX40/10./,BMX4/1./,AMX4S/20./

c

c Augmented Turbulence Parameters

c

DATA G2D0,G2D1,G2N0,G2N1,G2N2

 + /25.0,12.5,2.5,12.0,14.4/

DATA GT4/1.2/

 RETURN

 END
102

Appendix B. Non-linear optimal algorithm: filtering at 

platform centroid (original) vs. filtering at PS (modified)

Nonlinear optimal algorithm when filtered at the centroid of the motion platform 

(original) versus filtering at the pilot station (modified). 

General note: if only one or two curves are visible on the plot, assume that the 

remaining curves are underneath the visible ones.

1. Pitch

0 5 10 15 20 25 30

-2

0

2

4 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

original

modified

0 5 10 15 20 25 30

-2

0

2

x 10-6 ASFY,SSFY (m/s

2

)

0 5 10 15 20 25 30

-4

-3.5

-3

-2.5

t (sec) ASFZ,SSFZ (m/s

2

)

0 5 10 15 20 25 30

-1

0

1 ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

original act.

modified act.

0 5 10 15 20 25 30

-10

0

10

20

ASW,SSW -q (deg/s)

0 5 10 15 20 25 30

-1

0

1

t (sec)

ASW,SSW -r (deg/s)

Figure B.1. 1. 
103

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec) Svi-X (m/s)

Platorm Vel in Inertial Coord.

original

modified

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Y (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Z (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-X & SD-X (m)

Desired & Actual Platform Displ

original des.

modified des.

original act.

modified act.

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Y & SD-Y (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Z & SD-Z (m)

Figure B.1. 2. 
104

0 10 20 30

-5

0

5

10

t (sec) AF-X (m/s

2

)

Specific Force at A/C Pilot Head

original

modified

0 10 20 30

-1

0

1

t (sec) AF-Y (m/s

2

)

0 10 20 30

-10

-9

-8

-7

t (sec) AF-Z (m/s

2

)

0 10 20 30

-1

0

1

2

t (sec) SF-X (m/s

2

)

Specific Force at Simu. Pilot Head

original

modified

0 10 20 30

-4

-2

0

2

x 10-6

t (sec) SF-Y (m/s

2

)

0 10 20 30

-10

-9.8

-9.6

t (sec) SF-Z (m/s

2

)

Figure B.1. 3. 
105

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-p (deg/s)

Aircraft Angular Rate

original

modified

0 5 10 15 20 25 30

-10

0

10

t (sec)

AW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-r (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-p (deg/s)

Platform Angular Rate

original

modified

0 5 10 15 20 25 30

-10

0

10

t (sec)

SW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-r (deg/s)

Figure B.1. 4. 
106

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Aircraft Angular Position

original

modified

0 5 10 15 20 25 30

-20

0

20

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Des. and Actual Platform Ang Pos

original des.

modified des.

original act.

modified act.

0 5 10 15 20 25 30

-20

0

20

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

Figure B.1. 5. 
107

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-X (m/s/s)

A/C Accel. at MB Centroid

original

modified

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Y (m/s/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Z (m/s/s)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec) Scc-X (m/s/s)

Platform Accel. at MB Centroid 

original

modified

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Y (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Z (m/s/s)

Figure B.1. 6. 
108

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Leg 1 (m)

Actuator Extension

original

modified

0 5 10 15 20 25 30

-0.5

0

0.5

Actuator Extension

t (sec)

Leg 2 (m)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Leg 3 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 4 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 5 (m)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Leg 6 (m)

Figure B.1. 7. 
109

2. Roll

0 5 10 15 20 25 30

-2

-1

0

1

2 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

original

modified

0 5 10 15 20 25 30

-4

-2

0

2 ASFY,SSFY (m/s

2

)

0 5 10 15 20 25 30

-4

-3.5

-3

-2.5

t (sec) ASFZ,SSFZ (m/s

2

)

0 5 10 15 20 25 30

-10

0

10

20 ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

original act.

modified act.

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1 ASW,SSW -q (deg/s)

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1

t (sec) ASW,SSW -r (deg/s)

Figure B.2. 1.
110

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-X (m/s)

Platorm Vel in Inertial Coord.

original

modified

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Y (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Z (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-X & SD-X (m)

Desired & Actual Platform Displ

original des.

modified des.

original act.

modified act.

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Y & SD-Y (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Z & SD-Z (m)

Figure B.2. 2.

0 5 10 15 20 25 30

-1

0

1

t (sec) AF-X (m/s

2

)

Specific Force at A/C Pilot Head

original

modified

0 5 10 15 20 25 30

-10

-5

0

5

t (sec) AF-Y (m/s

2

)

0 5 10 15 20 25 30

-10

-9

-8

-7

t (sec) AF-Z (m/s

2

)

0 5 10 15 20 25 30

-1

0

1

t (sec) SF-X (m/s

2

)

Specific Force at Simu. Pilot Head

original

modified

0 5 10 15 20 25 30

-2

-1

0

1

t (sec) SF-Y (m/s

2

)

0 5 10 15 20 25 30

-10

-9.8

-9.6

t (sec) SF-Z (m/s

2

)
111

Figure B.2. 3.

0 5 10 15 20 25 30

-10

0

10

t (sec)

AW-p (deg/s)

Aircraft Angular Rate

original

modified

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-r (deg/s)

0 5 10 15 20 25 30

-10

0

10

t (sec)

SW-p (deg/s)

Platform Angular Rate

original

modified

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-r (deg/s)

Figure B.2. 4.
112

0 5 10 15 20 25 30

-20

0

20

t (sec)

Phi (deg)

Aircraft Angular Position

original

modified

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

0 5 10 15 20 25 30

-20

0

20

t (sec)

Phi (deg)

Des. and Actual Platform Ang Pos

original des.

modified des.

original act.

modified act.

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

Figure B.2. 5.
113

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-X (m/s/s)

A/C Accel. at MB Centroid

original

modified

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Y (m/s/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Z (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-X (m/s/s)

Platform Accel. at MB Centroid 

original

modified

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec) Scc-Y (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Z (m/s/s)

Figure B.2. 6.
114

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 1 (m)

Actuator Extension

original

modified

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

Actuator Extension

t (sec)

Leg 2 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 3 (m)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Leg 4 (m)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Leg 5 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 6 (m)

Figure B.2. 7.
115

3. Yaw

0 5 10 15 20 25 30

-0.1

-0.05

0

0.05

0.1 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

original

modified

0 5 10 15 20 25 30

-0.02

0

0.02

0.04 ASFY,SSFY (m/s

2

)

0 5 10 15 20 25 30

-4

-3.5

-3

-2.5

t (sec) ASFZ,SSFZ (m/s

2

)

0 5 10 15 20 25 30

-0.2

-0.1

0

0.1

0.2

ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

original act.

modified act.

0 5 10 15 20 25 30

-1

-0.5

0

0.5

ASW,SSW -q (deg/s)

0 5 10 15 20 25 30

-10

0

10

20

t (sec)

ASW,SSW -r (deg/s)

Figure B.3. 1.
116

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-X (m/s)

Platorm Vel in Inertial Coord.

original

modified

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Y (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Z (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-X & SD-X (m)

Desired & Actual Platform Displ

original des.

modified des.

original act.

modified act.

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Y & SD-Y (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Z & SD-Z (m)

Figure B.3. 2.
117

0 10 20 30

-0.1

0

0.1

t (sec) AF-X (m/s

2

)

Specific Force at A/C Pilot Head

original

modified

0 10 20 30

-0.05

0

0.05

t (sec) AF-Y (m/s

2

)

0 10 20 30

-11

-10

-9

-8

t (sec) AF-Z (m/s

2

)

0 10 20 30

-0.1

0

0.1

t (sec) SF-X (m/s

2

)

Specific Force at Simu. Pilot Head

original

modified

0 10 20 30

-0.05

0

0.05

t (sec) SF-Y (m/s

2

)

0 10 20 30

-9.82

-9.81

-9.8

t (sec) SF-Z (m/s

2

)

Figure B.3. 3.
118

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-p (deg/s)

Aircraft Angular Rate

original

modified

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

AW-q (deg/s)

0 5 10 15 20 25 30

-10

0

10

t (sec)

AW-r (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-p (deg/s)

Platform Angular Rate

original

modified

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

SW-q (deg/s)

0 5 10 15 20 25 30

-10

0

10

t (sec)

SW-r (deg/s)

Figure B.3. 4.
119

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Aircraft Angular Position

original

modified

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-20

0

20

t (sec)

Psi (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Des. and Actual Platform Ang Pos

original des.

modified des.

original act.

modified act.

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-20

0

20

t (sec)

Psi (deg)

Figure B.3. 5.
120

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-X (m/s/s)

A/C Accel. at MB Centroid

original

modified

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Y (m/s/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Z (m/s/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Scc-X (m/s/s)

Platform Accel. at MB Centroid 

original

modified

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Y (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Z (m/s/s)

Figure B.3. 6.
121

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 1 (m)

Actuator Extension

original

modified

0 5 10 15 20 25 30

-0.2

0

0.2

Actuator Extension

t (sec)

Leg 2 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 3 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 4 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 5 (m)

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec)

Leg 6 (m)

Figure B.3. 7.
122

4. Surge

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

original

modified

0 5 10 15 20 25 30

-1

0

1

2

3 ASFY,SSFY (m/s

2

)

0 5 10 15 20 25 30

-4.5

-4

-3.5

t (sec) ASFZ,SSFZ (m/s

2

)

0 5 10 15 20 25 30

-5

0

5 ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

original act.

modified act.

0 5 10 15 20 25 30

-1

0

1

2

x 10-4 ASW,SSW -q (deg/s)

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1

t (sec) ASW,SSW -r (deg/s)

Figure B.4. 1.
123

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-X (m/s)

Platorm Vel in Inertial Coord.

original

modified

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec) Svi-Y (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Z (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-X & SD-X (m)

Desired & Actual Platform Displ

original des.

modified des.

original act.

modified act.

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec) SDdes-Y & SD-Y (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Z & SD-Z (m)

Figure B.4. 2.

0 5 10 15 20 25 30

-1

0

1

t (sec) AF-X (m/s

2

)

Specific Force at A/C Pilot Head

original

modified

0 5 10 15 20 25 30

0

1

2

3

t (sec) AF-Y (m/s

2

)

0 5 10 15 20 25 30

-11

-10

-9

-8

t (sec) AF-Z (m/s

2

)

0 5 10 15 20 25 30

-1

0

1

t (sec) SF-X (m/s

2

)

Specific Force at Simu. Pilot Head

original

modified

0 5 10 15 20 25 30

-0.5

0

0.5

1

t (sec) SF-Y (m/s

2

)

0 5 10 15 20 25 30

-10.5

-10

-9.5

t (sec) SF-Z (m/s

2

)
124

Figure B.4. 3.

0 5 10 15 20 25 30

-5

0

5

t (sec)

AW-p (deg/s)

Aircraft Angular Rate

original

modified

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-r (deg/s)

0 5 10 15 20 25 30

-5

0

5

t (sec)

SW-p (deg/s)

Platform Angular Rate

original

modified

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-r (deg/s)

Figure B.4. 4.
125

0 5 10 15 20 25 30

-2

0

2

t (sec)

Phi (deg)

Aircraft Angular Position

original

modified

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

0 5 10 15 20 25 30

-2

0

2

t (sec)

Phi (deg)

Des. and Actual Platform Ang Pos

original des.

modified des.

original act.

modified act.

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

Figure B.4. 5.
126

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-X (m/s/s)

A/C Accel. at MB Centroid

original

modified

0 5 10 15 20 25 30

-2

0

2

t (sec) Acc-Y (m/s/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Z (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-X (m/s/s)

Platform Accel. at MB Centroid 

original

modified

0 5 10 15 20 25 30

-1

0

1

t (sec) Scc-Y (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Z (m/s/s)

Figure B.4. 6.
127

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 1 (m)

Actuator Extension

original

modified

0 5 10 15 20 25 30

-0.2

0

0.2

Actuator Extension

t (sec)

Leg 2 (m)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec)

Leg 3 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 4 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 5 (m)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec)

Leg 6 (m)

Figure B.4. 7.
128

5. Sway

0 5 10 15 20 25 30

-1

0

1 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

original

modified

0 5 10 15 20 25 30

-2

0

2

4 ASFY,SSFY (m/s

2

)

0 5 10 15 20 25 30

-4.5

-4

-3.5

t (sec) ASFZ,SSFZ (m/s

2

)

0 5 10 15 20 25 30

-5

0

5 ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

original

modified

0 5 10 15 20 25 30

-1

0

1

2

x 10-4 ASW,SSW -q (deg/s)

0 5 10 15 20 25 30

-1

0

1

t (sec) ASW,SSW -r (deg/s)

Figure B.5. 1.
129

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-X (m/s)

Platorm Vel in Inertial Coord.

original

modified

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec) Svi-Y (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Z (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-X & SD-X (m)

Desired & Actual Platform Displ

original des.

modified des.

original act.

modified act.

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec) SDdes-Y & SD-Y (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Z & SD-Z (m)

Figure B.5. 2.

0 5 10 15 20 25 30

-1

0

1

t (sec) AF-X (m/s

2

)

Specific Force at A/C Pilot Head

original

modified

0 5 10 15 20 25 30

0

1

2

3

t (sec) AF-Y (m/s

2

)

0 5 10 15 20 25 30

-11

-10

-9

-8

t (sec) AF-Z (m/s

2

)

0 5 10 15 20 25 30

-1

0

1

t (sec) SF-X (m/s

2

)

Specific Force at Simu. Pilot Head

original

modified

0 5 10 15 20 25 30

-0.5

0

0.5

1

t (sec) SF-Y (m/s

2

)

0 5 10 15 20 25 30

-10.5

-10

-9.5

t (sec) SF-Z (m/s

2

)
130

Figure B.5. 3.

0 5 10 15 20 25 30

-5

0

5

t (sec)

AW-p (deg/s)

Aircraft Angular Rate

original

modified

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-r (deg/s)

0 5 10 15 20 25 30

-5

0

5

t (sec)

SW-p (deg/s)

Platform Angular Rate

original

modified

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-r (deg/s)

Figure B.5. 4.
131

0 5 10 15 20 25 30

-2

0

2

t (sec)

Phi (deg)

Aircraft Angular Position

original

modified

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

0 5 10 15 20 25 30

-2

0

2

t (sec)

Phi (deg)

Des. and Actual Platform Ang Pos

original des.

modified des.

original act.

modified act.

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

Figure B.5. 5.
132

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-X (m/s/s)

A/C Accel. at MB Centroid

original

modified

0 5 10 15 20 25 30

-2

0

2

t (sec) Acc-Y (m/s/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Z (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-X (m/s/s)

Platform Accel. at MB Centroid 

original

modified

0 5 10 15 20 25 30

-1

0

1

t (sec) Scc-Y (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Z (m/s/s)

Figure B.5. 6.
133

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 1 (m)

Actuator Extension

original

modified

0 5 10 15 20 25 30

-0.2

0

0.2

Actuator Extension

t (sec)

Leg 2 (m)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec)

Leg 3 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 4 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 5 (m)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec)

Leg 6 (m)

Figure B.5. 7.
134

6. Heave

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

original

modified

0 5 10 15 20 25 30

-2

-1

0

1

2

x 10-6 ASFY,SSFY (m/s

2

)

0 5 10 15 20 25 30

-4.5

-4

-3.5

t (sec) ASFZ,SSFZ (m/s

2

)

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1 ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

original act.

modified act.

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1 ASW,SSW -q (deg/s)

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1

t (sec)

ASW,SSW -r (deg/s)

Figure B.6. 1.
135

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-X (m/s)

Platorm Vel in Inertial Coord.

original

modified

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Y (m/s)

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec) Svi-Z (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-X & SD-X (m)

Desired & Actual Platform Displ

original des.

modified des.

original act.

modified act.

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Y & SD-Y (m)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec) SDdes-Z & SD-Z (m)

Figure B.6. 2.
136

0 5 10 15 20 25 30

-1

0

1

t (sec) AF-X (m/s

2

)

Specific Force at A/C Pilot Head

original

modified

0 5 10 15 20 25 30

-1

0

1

t (sec) AF-Y (m/s

2

)

0 5 10 15 20 25 30

-10

-9.5

-9

-8.5

t (sec) AF-Z (m/s

2

)

0 5 10 15 20 25 30

-1

0

1

t (sec) SF-X (m/s

2

)

Specific Force at Simu. Pilot Head

original

modified

0 5 10 15 20 25 30

-4

-2

0

2

x 10-6

t (sec) SF-Y (m/s

2

)

0 5 10 15 20 25 30

-10.5

-10

-9.5

-9

t (sec) SF-Z (m/s

2

)

Figure B.6. 3.
137

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-p (deg/s)

Aircraft Angular Rate

original

modified

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-r (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-p (deg/s)

Platform Angular Rate

original

modified

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-r (deg/s)

Figure B.6. 4.
138

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Aircraft Angular Position

original

modified

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Des. and Actual Platform Ang Pos

original des.

modified des.

original act.

modified act.

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

Figure B.6. 5.
139

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-X (m/s/s)

A/C Accel. at MB Centroid

original

modified

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Y (m/s/s)

0 5 10 15 20 25 30

-1

0

1

t (sec) Acc-Z (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-X (m/s/s)

Platform Accel. at MB Centroid 

original

modified

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Y (m/s/s)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec) Scc-Z (m/s/s)

Figure B.6. 6.
140

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec)

Leg 1 (m)

Actuator Extension

original

modified

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

Actuator Extension

t (sec)

Leg 2 (m)

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec)

Leg 3 (m)

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec)

Leg 4 (m)

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec)

Leg 5 (m)

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec)

Leg 6 (m)

Figure B.6. 7.
141

Appendix C. Non-linear optimal algorithm: original vs.

augmented

General note: if only one or two curves are visible on the plot, assume that the 

remaining curves are underneath the visible ones.

1. Pitch

0 5 10 15 20 25 30

-2

0

2

4 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

original

augmented

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1 ASFY,SSFY (m/s

2

)

0 5 10 15 20 25 30

-4

-3.5

-3

-2.5

t (sec) ASFZ,SSFZ (m/s

2

)

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1 ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

original

augmented

0 5 10 15 20 25 30

-10

0

10

20

ASW,SSW -q (deg/s)

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1

t (sec)

ASW,SSW -r (deg/s)

Figure C.1. 1.
142

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-X (m/s)

Platorm Vel in Inertial Coord.

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Y (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Z (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-X & SD-X (m)

Desired & Actual Platform Displ

original des.

augmented des.

original act.

augmented act.

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Y & SD-Y (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Z & SD-Z (m)

Figure C.1. 2.
143

0 10 20 30

-5

0

5

10

t (sec) AF-X (m/s

2

)

Specific Force at A/C Pilot Head

original

augmented

0 10 20 30

-1

0

1

t (sec) AF-Y (m/s

2

)

0 10 20 30

-10

-9

-8

-7

t (sec) AF-Z (m/s

2

)

0 10 20 30

-1

0

1

2

t (sec) SF-X (m/s

2

)

Specific Force at Simu. Pilot Head

original

augmented

0 10 20 30

-1

0

1

t (sec) SF-Y (m/s

2

)

0 10 20 30

-10

-9.8

-9.6

t (sec) SF-Z (m/s

2

)

Figure C.1. 3.
144

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-p (deg/s)

Aircraft Angular Rate

original

augmented

0 5 10 15 20 25 30

-10

0

10

t (sec)

AW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-r (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-p (deg/s)

Platform Angular Rate

original

augmented

0 5 10 15 20 25 30

-10

0

10

t (sec)

SW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-r (deg/s)

Figure C.1. 4.
145

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Aircraft Angular Position

original

augmented

0 5 10 15 20 25 30

-20

0

20

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Des. and Actual Platform Ang Pos

original des.

augmented des.

original act.

augmented act.

0 5 10 15 20 25 30

-20

0

20

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

Figure C.1. 5.
146

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-X (m/s/s)

A/C Accel. at MB Centroid

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Y (m/s/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Z (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-X (m/s/s)

Platform Accel. at MB Centroid 

original

augmented

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Y (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Z (m/s/s)

Figure C.1. 6.
147

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 1 (m)

Actuator Extension

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

Actuator Extension

t (sec)

Leg 2 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 3 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 4 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 5 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 6 (m)

Figure C.1. 7.
148

2. Roll

0 5 10 15 20 25 30

-2

0

2

4 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

original

augmented

0 5 10 15 20 25 30

-1

-0.5

0

0.5 ASFY,SSFY (m/s

2

)

0 5 10 15 20 25 30

-4

-3.5

-3

-2.5

t (sec) ASFZ,SSFZ (m/s

2

)

0 5 10 15 20 25 30

-5

0

5 ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

original

augmented

0 5 10 15 20 25 30

-10

0

10

20

ASW,SSW -q (deg/s)

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1

t (sec)

ASW,SSW -r (deg/s)

Figure C.2. 1.
149

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-X (m/s)

Platorm Vel in Inertial Coord.

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Y (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Z (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-X & SD-X (m)

Desired & Actual Platform Displ

original des.

augmented des.

original act.

augmented act.

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Y & SD-Y (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Z & SD-Z (m)

Figure C.2. 2.
150

0 5 10 15 20 25 30

-1

0

1

t (sec) AF-X (m/s

2

)

Specific Force at A/C Pilot Head

original

augmented

0 5 10 15 20 25 30

-10

-5

0

5

t (sec) AF-Y (m/s

2

)

0 5 10 15 20 25 30

-10

-9

-8

-7

t (sec) AF-Z (m/s

2

)

0 5 10 15 20 25 30

-1

0

1

t (sec) SF-X (m/s

2

)

Specific Force at Simu. Pilot Head

original

augmented

0 5 10 15 20 25 30

-2

-1

0

1

t (sec) SF-Y (m/s

2

)

0 5 10 15 20 25 30

-10

-9.8

-9.6

t (sec) SF-Z (m/s

2

)

Figure C.2. 3.

0 5 10 15 20 25 30

-10

0

10

t (sec)

AW-p (deg/s)

Aircraft Angular Rate

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-r (deg/s)

0 5 10 15 20 25 30

-10

0

10

t (sec)

SW-p (deg/s)

Platform Angular Rate

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-r (deg/s)
151

Figure C.2. 4.

0 5 10 15 20 25 30

-20

0

20

t (sec)

Phi (deg)

Aircraft Angular Position

original

augmented

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

0 5 10 15 20 25 30

-20

0

20

t (sec)

Phi (deg)

Des. and Actual Platform Ang Pos

original des.

augmented des.

original act.

augmented act.

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

Figure C.2. 5.
152

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-X (m/s/s)

A/C Accel. at MB Centroid

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Y (m/s/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Z (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-X (m/s/s)

Platform Accel. at MB Centroid 

original

augmented

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Y (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Z (m/s/s)

Figure C.2. 6.
153

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec)

Leg 1 (m)

Actuator Extension

original

augmented

0 5 10 15 20 25 30

-0.1

0

0.1

Actuator Extension

t (sec)

Leg 2 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 3 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 4 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 5 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 6 (m)

Figure C.2. 7.
154

3. Yaw

0 5 10 15 20 25 30

-0.1

-0.05

0

0.05

0.1 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

original

augmented

0 5 10 15 20 25 30

-0.01

0

0.01

0.02

0.03 ASFY,SSFY (m/s

2

)

0 5 10 15 20 25 30

-4

-3.5

-3

-2.5

t (sec) ASFZ,SSFZ (m/s

2

)

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1 ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

original act.

augmented act.

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1 ASW,SSW -q (deg/s)

0 5 10 15 20 25 30

-10

0

10

20

t (sec)

ASW,SSW -r (deg/s)

Figure C.3. 1.
155

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-X (m/s)

Platorm Vel in Inertial Coord.

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Y (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Z (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-X & SD-X (m)

Desired & Actual Platform Displ

original des.

augmented des.

original act.

augmented act.

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Y & SD-Y (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Z & SD-Z (m)

Figure C.3. 2.
156

0 10 20 30

-0.1

0

0.1

t (sec) AF-X (m/s

2

)

Specific Force at A/C Pilot Head

original

augmented

0 10 20 30

-0.05

0

0.05

t (sec) AF-Y (m/s

2

)

0 10 20 30

-11

-10

-9

-8

t (sec) AF-Z (m/s

2

)

0 10 20 30

-0.05

0

0.05

t (sec) SF-X (m/s

2

)

Specific Force at Simu. Pilot Head

original

augmented

0 10 20 30

-2

0

2

4

x 10-3

t (sec) SF-Y (m/s

2

)

0 10 20 30

-9.8062

-9.8062

-9.8062

t (sec) SF-Z (m/s

2

)

Figure C.3. 3.
157

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-p (deg/s)

Aircraft Angular Rate

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-q (deg/s)

0 5 10 15 20 25 30

-10

0

10

t (sec)

AW-r (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-p (deg/s)

Platform Angular Rate

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-q (deg/s)

0 5 10 15 20 25 30

-10

0

10

t (sec)

SW-r (deg/s)

Figure C.3. 4.
158

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Aircraft Angular Position

original

augmented

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-20

0

20

t (sec)

Psi (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Des. and Actual Platform Ang Pos

original des.

augmented des.

original act.

augmented act.

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-20

0

20

t (sec)

Psi (deg)

Figure C.3. 5.
159

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-X (m/s/s)

A/C Accel. at MB Centroid

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Y (m/s/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Z (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-X (m/s/s)

Platform Accel. at MB Centroid 

original

augmented

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Y (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Z (m/s/s)

Figure C.3. 6.
160

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 1 (m)

Actuator Extension

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

Actuator Extension

t (sec)

Leg 2 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 3 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 4 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 5 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 6 (m)

Figure C.3. 7.
161

4. Surge

0 5 10 15 20 25 30

0

0.2

0.4

0.6

0.8 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

original

augmented

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1 ASFY,SSFY (m/s

2

)

0 5 10 15 20 25 30

-3.94

-3.92

-3.9

t (sec) ASFZ,SSFZ (m/s

2

)

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1 ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

original

augmented

0 5 10 15 20 25 30

-2

0

2

4 ASW,SSW -q (deg/s)

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1

t (sec)

ASW,SSW -r (deg/s)

Figure C.4. 1.
162

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec) Svi-X (m/s)

Platorm Vel in Inertial Coord.

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Y (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Z (m/s)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec) SDdes-X & SD-X (m)

Desired & Actual Platform Displ

original des.

augmented des.

original act.

augmented act.

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Y & SD-Y (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Z & SD-Z (m)

Figure C.4. 2.
163

0 10 20 30

0

0.5

1

t (sec) AF-X (m/s

2

)

Specific Force at A/C Pilot Head

original

augmented

0 10 20 30

-1

0

1

t (sec) AF-Y (m/s

2

)

0 10 20 30

-11

-10

-9

-8

t (sec) AF-Z (m/s

2

)

0 10 20 30

0

0.5

1

t (sec) SF-X (m/s

2

)

Specific Force at Simu. Pilot Head

original

augmented

0 10 20 30

-1

0

1

t (sec) SF-Y (m/s

2

)

0 10 20 30

-9.81

-9.8

-9.79

t (sec) SF-Z (m/s

2

)

Figure C.4. 3.
164

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-p (deg/s)

Aircraft Angular Rate

original

augmented

0 5 10 15 20 25 30

-2

0

2

t (sec)

AW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-r (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-p (deg/s)

Platform Angular Rate

original

augmented

0 5 10 15 20 25 30

-2

0

2

t (sec)

SW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-r (deg/s)

Figure C.4. 4.
165

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Aircraft Angular Position

original

augmented

0 5 10 15 20 25 30

-4

-2

0

2

4

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Des. and Actual Platform Ang Pos

original des.

augmented des.

original act.

augmented act.

0 5 10 15 20 25 30

-4

-2

0

2

4

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

Figure C.4. 5.
166

0 5 10 15 20 25 30

-1

0

1

t (sec) Acc-X (m/s/s)

A/C Accel. at MB Centroid

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Y (m/s/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Z (m/s/s)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec) Scc-X (m/s/s)

Platform Accel. at MB Centroid 

original

augmented

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Y (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Z (m/s/s)

Figure C.4. 6.
167

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 1 (m)

Actuator Extension

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

Actuator Extension

t (sec)

Leg 2 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 3 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 4 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 5 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 6 (m)

Figure C.4. 7.
168

5. Sway

0 10 20 30

-1

0

1 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

original

augmented

0 10 20 30

-5

0

5 ASFY,SSFY (m/s

2

)

0 10 20 30

-4.2

-4

-3.8

-3.6

t (sec)

ASFZ,SSFZ (m/s

2

)

0 10 20 30

-5

0

5 ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

original

augmented

0 10 20 30

-2

0

2

x 10-4 ASW,SSW -q (deg/s)

0 10 20 30

-1

0

1

t (sec)

ASW,SSW -r (deg/s)

Figure C.5. 1.
169

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-X (m/s)

Platorm Vel in Inertial Coord.

original

augmented

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec) Svi-Y (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Z (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-X & SD-X (m)

Desired & Actual Platform Displ

original des.

augmented des.

original act.

augmented act.

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec) SDdes-Y & SD-Y (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Z & SD-Z (m)

Figure C.5. 2.
170

0 10 20 30

-1

0

1

t (sec)

AF-X (m/s

2

)

Specific Force at A/C Pilot Head

original

augmented

0 10 20 30

0

2

4

t (sec)

AF-Y (m/s

2

)

0 10 20 30

-12

-10

-8

t (sec)

AF-Z (m/s

2

)

0 10 20 30

-1

0

1

t (sec)

SF-X (m/s

2

)

Specific Force at Simu. Pilot Head

original

augmented

0 10 20 30

-1

0

1

t (sec)

SF-Y (m/s

2

)

0 10 20 30

-10.5

-10

-9.5

t (sec)

SF-Z (m/s

2

)

Figure C.5. 3.

0 5 10 15 20 25 30

-5

0

5

t (sec)

AW-p (deg/s)

Aircraft Angular Rate

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-r (deg/s)

0 5 10 15 20 25 30

-5

0

5

t (sec)

SW-p (deg/s)

Platform Angular Rate

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-r (deg/s)
171

Figure C.5. 4.

0 5 10 15 20 25 30

-2

0

2

t (sec)

Phi (deg)

Aircraft Angular Position

original

augmented

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

0 5 10 15 20 25 30

-2

0

2

t (sec)

Phi (deg)

Des. and Actual Platform Ang Pos

original des.

augmented des.

original act.

augmented act.

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

Figure C.5. 5.
172

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-X (m/s/s)

A/C Accel. at MB Centroid

original

augmented

0 5 10 15 20 25 30

-2

0

2

t (sec) Acc-Y (m/s/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Z (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-X (m/s/s)

Platform Accel. at MB Centroid 

original

augmented

0 5 10 15 20 25 30

-1

0

1

t (sec) Scc-Y (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Z (m/s/s)

Figure C.5. 6.
173

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 1 (m)

Actuator Extension

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

Actuator Extension

t (sec)

Leg 2 (m)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec)

Leg 3 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 4 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 5 (m)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec)

Leg 6 (m)

Figure C.5. 7.
174

6. Heave

0 5 10 15 20 25 30

-0.1

-0.05

0

0.05

0.1 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

original

augmented

0 5 10 15 20 25 30

-0.01

0

0.01

0.02

0.03 ASFY,SSFY (m/s

2

)

0 5 10 15 20 25 30

-4

-3.5

-3

-2.5

t (sec) ASFZ,SSFZ (m/s

2

)

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1 ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

original

augmented

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1 ASW,SSW -q (deg/s)

0 5 10 15 20 25 30

-10

0

10

20

t (sec)

ASW,SSW -r (deg/s)

Figure C.6. 1.
175

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-X (m/s)

Platorm Vel in Inertial Coord.

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Y (m/s)

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec) Svi-Z (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-X & SD-X (m)

Desired & Actual Platform Displ

original des.

augmented des.

original act.

augmented act.

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Y & SD-Y (m)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec) SDdes-Z & SD-Z (m)

Figure C.6. 2.
176

0 5 10 15 20 25 30

-1

0

1

t (sec) AF-X (m/s

2

)

Specific Force at A/C Pilot Head

original

augmented

0 5 10 15 20 25 30

-1

0

1

t (sec) AF-Y (m/s

2

)

0 5 10 15 20 25 30

-10

-9.5

-9

-8.5

t (sec) AF-Z (m/s

2

)

0 5 10 15 20 25 30

-1

0

1

t (sec) SF-X (m/s

2

)

Specific Force at Simu. Pilot Head

original

augmented

0 5 10 15 20 25 30

-1

0

1

t (sec) SF-Y (m/s

2

)

0 5 10 15 20 25 30

-10.5

-10

-9.5

-9

t (sec) SF-Z (m/s

2

)

Figure C.6. 3.
177

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-p (deg/s)

Aircraft Angular Rate

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-r (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-p (deg/s)

Platform Angular Rate

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-r (deg/s)

Figure C.6. 4.
178

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Aircraft Angular Position

original

augmented

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Des. and Actual Platform Ang Pos

original des.

augmented des.

original act.

augmented act.

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

Figure C.6. 5.
179

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-X (m/s/s)

A/C Accel. at MB Centroid

original

augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Y (m/s/s)

0 5 10 15 20 25 30

-1

0

1

t (sec) Acc-Z (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-X (m/s/s)

Platform Accel. at MB Centroid 

original

augmented

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Y (m/s/s)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec) Scc-Z (m/s/s)

Figure C.6. 6.
180

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec)

Leg 1 (m)

Actuator Extension

original

augmented

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

Actuator Extension

t (sec)

Leg 2 (m)

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec)

Leg 3 (m)

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec)

Leg 4 (m)

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec)

Leg 5 (m)

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec)

Leg 6 (m)

Figure C.6. 7.
181

Appendix D. Non-linear optimal algorithm: original 

applied at PS (filt. @ PS Original) vs. augmented 

(Augmented)

General note: if only one or two curves are visible on the plot, assume that the 

remaining curves are underneath the visible ones.

1. Pitch

0 5 10 15 20 25 30

-0.2

-0.1

0

0.1

0.2

t (sec) Acc-X (m/s/s)

A/C Accel. at MB Centroid

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.2

-0.1

0

0.1

0.2

t (sec) Acc-Y (m/s/s)

0 5 10 15 20 25 30

-0.2

-0.1

0

0.1

0.2

t (sec) Acc-Z (m/s/s)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec) Scc-X (m/s/s)

Platform Accel. at MB Centroid 

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.1

-0.05

0

0.05

0.1

t (sec) Scc-Y (m/s/s)

0 5 10 15 20 25 30

-0.1

-0.05

0

0.05

0.1

t (sec) Scc-Z (m/s/s)

Figure D.1. 1.
182

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Aircraft Angular Position

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-20

0

20

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Des. and Actual Platform Ang Pos

filt. @ PS Original des.

Augmented des.

filt. @ PS Original act.

Augmented act.

0 5 10 15 20 25 30

-20

0

20

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

Figure D.1. 2.
183

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-p (deg/s)

Aircraft Angular Rate

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-10

0

10

t (sec)

AW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-r (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-p (deg/s)

Platform Angular Rate

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-10

0

10

t (sec)

SW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-r (deg/s)

Figure D.1. 3.
184

0 10 20 30

-5

0

5

10

t (sec) AF-X (m/s

2

)

Specific Force at A/C Pilot Head

filt. @ PS Original

Augmented

0 10 20 30

-1

0

1

t (sec) AF-Y (m/s

2

)

0 10 20 30

-10

-9

-8

-7

t (sec) AF-Z (m/s

2

)

0 10 20 30

-1

0

1

2

t (sec) SF-X (m/s

2

)

Specific Force at Simu. Pilot Head

filt. @ PS Original

Augmented

0 10 20 30

-4

-2

0

2

x 10-6

t (sec) SF-Y (m/s

2

)

0 10 20 30

-10

-9.8

-9.6

t (sec) SF-Z (m/s

2

)

Figure D.1. 4.
185

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-X (m/s)

Platorm Vel in Inertial Coord.

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Y (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Z (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-X & SD-X (m)

Desired & Actual Platform Displ

filt. @ PS Original des.

Augmented des.

filt. @ PS Original act.

Augmented act.

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Y & SD-Y (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Z & SD-Z (m)

Figure D.1. 5.
186

0 5 10 15 20 25 30

-2

0

2

4 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-2

0

2

x 10-6 ASFY,SSFY (m/s

2

)

0 5 10 15 20 25 30

-5

0

5

t (sec) ASFZ,SSFZ (m/s

2

)

0 5 10 15 20 25 30

-1

0

1 ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-10

0

10

20

ASW,SSW -q (deg/s)

0 5 10 15 20 25 30

-1

0

1

t (sec)

ASW,SSW -r (deg/s)

Figure D.1. 6.
187

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Leg 1 (m)

Actuator Extension

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.5

0

0.5

Actuator Extension

t (sec)

Leg 2 (m)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Leg 3 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 4 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 5 (m)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Leg 6 (m)

Figure D.1. 7.
188

2. Roll

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-X (m/s/s)

A/C Accel. at MB Centroid

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Y (m/s/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Z (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-X (m/s/s)

Platform Accel. at MB Centroid 

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec) Scc-Y (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Z (m/s/s)

Figure D.2. 1.
189

0 5 10 15 20 25 30

-20

0

20

t (sec)

Phi (deg)

Aircraft Angular Position

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

0 5 10 15 20 25 30

-20

0

20

t (sec)

Phi (deg)

Des. and Actual Platform Ang Pos

filt. @ PS Original des.

Augmented des.

filt. @ PS Original act.

Augmented act.

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

Figure D.2. 2.
190

0 5 10 15 20 25 30

-10

0

10

t (sec)

AW-p (deg/s)

Aircraft Angular Rate

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-r (deg/s)

0 5 10 15 20 25 30

-10

0

10

t (sec)

SW-p (deg/s)

Platform Angular Rate

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-r (deg/s)

Figure D.2. 3.
191

0 10 20 30

-1

0

1

t (sec)

AF-X (m/s

2

)

Specific Force at A/C Pilot Head

filt. @ PS Original

Augmented

0 10 20 30

-10

-5

0

5

t (sec)

AF-Y (m/s

2

)

0 10 20 30

-10

-9

-8

-7

t (sec)

AF-Z (m/s

2

)

0 10 20 30

-1

0

1

t (sec)

SF-X (m/s

2

)

Specific Force at Simu. Pilot Head

filt. @ PS Original

Augmented

0 10 20 30

-2

-1

0

1

t (sec)

SF-Y (m/s

2

)

0 10 20 30

-10

-9.8

-9.6

t (sec)

SF-Z (m/s

2

)

Figure D.2. 4.
192

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-X (m/s)

Platorm Vel in Inertial Coord.

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Y (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Z (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-X & SD-X (m)

Desired & Actual Platform Displ

filt. @ PS Original des.

Augmented des.

filt. @ PS Original act.

Augmented act.

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Y & SD-Y (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Z & SD-Z (m)

Figure D.2. 5.
193

0 10 20 30

-1

0

1 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

filt. @ PS Original

Augmented

0 10 20 30

-4

-2

0

2 ASFY,SSFY (m/s

2

)

0 10 20 30

-5

0

5

t (sec)

ASFZ,SSFZ (m/s

2

)

0 10 20 30

-10

0

10

20

ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

filt. @ PS Original

Augmented

0 10 20 30

-1

0

1 ASW,SSW -q (deg/s)

0 10 20 30

-1

0

1

t (sec)

ASW,SSW -r (deg/s)

Figure D.2. 6.
194

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 1 (m)

Actuator Extension

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

Actuator Extension

t (sec)

Leg 2 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 3 (m)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Leg 4 (m)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Leg 5 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 6 (m)

Figure D.2. 7.
195

3. Yaw

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-p (deg/s)

Aircraft Angular Rate

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

AW-q (deg/s)

0 5 10 15 20 25 30

-10

0

10

t (sec)

AW-r (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-p (deg/s)

Platform Angular Rate

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

SW-q (deg/s)

0 5 10 15 20 25 30

-10

0

10

t (sec)

SW-r (deg/s)

Figure D.3. 1.
196

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-X (m/s/s)

A/C Accel. at MB Centroid

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Y (m/s/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Z (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-X (m/s/s)

Platform Accel. at MB Centroid 

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Y (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Z (m/s/s)

Figure D.3. 2.
197

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Aircraft Angular Position

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-20

0

20

t (sec)

Psi (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Des. and Actual Platform Ang Pos

filt. @ PS Original des.

Augmented des.

filt. @ PS Original act.

Augmented act.

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-20

0

20

t (sec)

Psi (deg)

Figure D.3. 3.
198

0 10 20 30

-0.1

0

0.1

t (sec) AF-X (m/s

2

)

Specific Force at A/C Pilot Head

filt. @ PS Original

Augmented

0 10 20 30

-0.05

0

0.05

t (sec) AF-Y (m/s

2

)

0 10 20 30

-11

-10

-9

-8

t (sec) AF-Z (m/s

2

)

0 10 20 30

-0.1

0

0.1

t (sec) SF-X (m/s

2

)

Specific Force at Simu. Pilot Head

filt. @ PS Original

Augmented

0 10 20 30

-0.05

0

0.05

t (sec) SF-Y (m/s

2

)

0 10 20 30

-9.82

-9.81

-9.8

t (sec) SF-Z (m/s

2

)

Figure D.3. 4.
199

0 5 10 15 20 25 30

-0.2

-0.1

0

0.1

0.2

t (sec) Svi-X (m/s)

Platorm Vel in Inertial Coord.

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.2

-0.1

0

0.1

0.2

t (sec) Svi-Y (m/s)

0 5 10 15 20 25 30

-0.2

-0.1

0

0.1

0.2

t (sec) Svi-Z (m/s)

0 5 10 15 20 25 30

-0.2

-0.1

0

0.1

0.2

t (sec) SDdes-X & SD-X (m)

Desired & Actual Platform Displ

filt. @ PS Original des.

Augmented des.

filt. @ PS Original act.

Augmented act.

0 5 10 15 20 25 30

-0.2

-0.1

0

0.1

0.2

t (sec) SDdes-Y & SD-Y (m)

0 5 10 15 20 25 30

-0.2

-0.1

0

0.1

0.2

t (sec) SDdes-Z & SD-Z (m)

Figure D.3. 5.
200

0 5 10 15 20 25 30

-0.1

-0.05

0

0.05

0.1 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.02

0

0.02

0.04 ASFY,SSFY (m/s

2

)

0 5 10 15 20 25 30

-5

0

5

t (sec) ASFZ,SSFZ (m/s

2

)

0 5 10 15 20 25 30

-0.2

-0.1

0

0.1

0.2

ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-1

-0.5

0

0.5

ASW,SSW -q (deg/s)

0 5 10 15 20 25 30

-10

0

10

20

t (sec)

ASW,SSW -r (deg/s)

Figure D.3. 6.
201

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 1 (m)

Actuator Extension

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.2

0

0.2

Actuator Extension

t (sec)

Leg 2 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 3 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 4 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 5 (m)

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec)

Leg 6 (m)

Figure D.3. 7.
202

4. Surge

0 5 10 15 20 25 30

-1

0

1

t (sec) Acc-X (m/s/s)

A/C Accel. at MB Centroid

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Y (m/s/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Z (m/s/s)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec) Scc-X (m/s/s)

Platform Accel. at MB Centroid 

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Y (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Z (m/s/s)

Figure D.4. 1.
203

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Aircraft Angular Position

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-4

-2

0

2

4

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Des. and Actual Platform Ang Pos

filt. @ PS Original des.

Augmented des.

filt. @ PS Original act.

Augmented act.

0 5 10 15 20 25 30

-4

-2

0

2

4

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

Figure D.4. 2.
204

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-p (deg/s)

Aircraft Angular Rate

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-2

0

2

t (sec)

AW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-r (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-p (deg/s)

Platform Angular Rate

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-2

0

2

t (sec)

SW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-r (deg/s)

Figure D.4. 3.
205

0 5 10 15 20 25 30

0

0.5

1

t (sec) AF-X (m/s

2

)

Specific Force at A/C Pilot Head

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-1

-0.5

0

0.5

1

t (sec) AF-Y (m/s

2

)

0 5 10 15 20 25 30

-11

-10

-9

-8

t (sec) AF-Z (m/s

2

)

0 5 10 15 20 25 30

0

0.2

0.4

0.6

0.8

t (sec) SF-X (m/s

2

)

Specific Force at Simu. Pilot Head

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-4

-2

0

2

x 10-6

t (sec) SF-Y (m/s

2

)

0 5 10 15 20 25 30

-9.81

-9.805

-9.8

-9.795

-9.79

t (sec) SF-Z (m/s

2

)

Figure D.4. 4.
206

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec) Svi-X (m/s)

Platorm Vel in Inertial Coord.

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Y (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Z (m/s)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec) SDdes-X & SD-X (m)

Desired & Actual Platform Displ

filt. @ PS Original des.

Augmented des.

filt. @ PS Original act.

Augmented act.

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Y & SD-Y (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Z & SD-Z (m)

Figure D.4. 5.
207

0 5 10 15 20 25 30

0

0.5

1 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-2

0

2

x 10-6 ASFY,SSFY (m/s

2

)

0 5 10 15 20 25 30

-5

0

5

t (sec) ASFZ,SSFZ (m/s

2

)

0 5 10 15 20 25 30

-1

0

1 ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-2

0

2

4 ASW,SSW -q (deg/s)

0 5 10 15 20 25 30

-1

0

1

t (sec)

ASW,SSW -r (deg/s)

Figure D.4. 6.
208

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 1 (m)

Actuator Extension

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.2

0

0.2

Actuator Extension

t (sec)

Leg 2 (m)

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec)

Leg 3 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 4 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 5 (m)

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec)

Leg 6 (m)

Figure D.4. 7.
209

5. Sway

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-X (m/s/s)

A/C Accel. at MB Centroid

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-2

0

2

t (sec) Acc-Y (m/s/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Z (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-X (m/s/s)

Platform Accel. at MB Centroid 

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-1

0

1

t (sec) Scc-Y (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Z (m/s/s)

Figure D.5. 1.
210

0 5 10 15 20 25 30

-2

0

2

t (sec)

Phi (deg)

Aircraft Angular Position

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

0 5 10 15 20 25 30

-2

0

2

t (sec)

Phi (deg)

Des. and Actual Platform Ang Pos

filt. @ PS Original des.

Augmented des.

filt. @ PS Original act.

Augmented act.

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

Figure D.5. 2.
211

0 5 10 15 20 25 30

-5

0

5

t (sec)

AW-p (deg/s)

Aircraft Angular Rate

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-r (deg/s)

0 5 10 15 20 25 30

-5

0

5

t (sec)

SW-p (deg/s)

Platform Angular Rate

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-r (deg/s)

Figure D.5. 3.
212

0 10 20 30

-1

0

1

t (sec) AF-X (m/s

2

)

Specific Force at A/C Pilot Head

filt. @ PS Original

Augmented

0 10 20 30

0

1

2

3

t (sec) AF-Y (m/s

2

)

0 10 20 30

-11

-10

-9

-8

t (sec) AF-Z (m/s

2

)

0 10 20 30

-1

0

1

t (sec) SF-X (m/s

2

)

Specific Force at Simu. Pilot Head

filt. @ PS Original

Augmented

0 10 20 30

-0.5

0

0.5

1

t (sec) SF-Y (m/s

2

)

0 10 20 30

-10.5

-10

-9.5

t (sec) SF-Z (m/s

2

)

Figure D.5. 4.
213

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-X (m/s)

Platorm Vel in Inertial Coord.

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec) Svi-Y (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Z (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-X & SD-X (m)

Desired & Actual Platform Displ

filt. @ PS Original des.

Augmented des.

filt. @ PS Original act.

Augmented act.

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec) SDdes-Y & SD-Y (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Z & SD-Z (m)

Figure D.5. 5.
214

0 10 20 30

-1

0

1 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

filt. @ PS Original

Augmented

0 10 20 30

-2

0

2

4 ASFY,SSFY (m/s

2

)

0 10 20 30

-5

0

5

t (sec) ASFZ,SSFZ (m/s

2

)

0 10 20 30

-5

0

5 ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

filt. @ PS Original

Augmented

0 10 20 30

-1

0

1

2

x 10-4 ASW,SSW -q (deg/s)

0 10 20 30

-1

0

1

t (sec)

ASW,SSW -r (deg/s)

Figure D.5. 6.
215

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 1 (m)

Actuator Extension

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.2

0

0.2

Actuator Extension

t (sec)

Leg 2 (m)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec)

Leg 3 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 4 (m)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

Leg 5 (m)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec)

Leg 6 (m)

Figure D.5. 7.
216

6. Heave

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-X (m/s/s)

A/C Accel. at MB Centroid

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Acc-Y (m/s/s)

0 5 10 15 20 25 30

-1

0

1

t (sec) Acc-Z (m/s/s)

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-X (m/s/s)

Platform Accel. at MB Centroid 

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.1

0

0.1

t (sec) Scc-Y (m/s/s)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec) Scc-Z (m/s/s)

Figure D.6. 1.
217

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Aircraft Angular Position

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Phi (deg)

Des. and Actual Platform Ang Pos

filt. @ PS Original des.

Augmented des.

filt. @ PS Original act.

Augmented act.

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Theta (deg)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec)

Psi (deg)

Figure D.6. 2.
218

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-p (deg/s)

Aircraft Angular Rate

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

AW-r (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-p (deg/s)

Platform Angular Rate

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-q (deg/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec)

SW-r (deg/s)

Figure D.6. 3.
219

0 5 10 15 20 25 30

-1

0

1

t (sec) AF-X (m/s

2

)

Specific Force at A/C Pilot Head

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-1

0

1

t (sec) AF-Y (m/s

2

)

0 5 10 15 20 25 30

-10

-9.5

-9

-8.5

t (sec) AF-Z (m/s

2

)

0 5 10 15 20 25 30

-1

0

1

t (sec) SF-X (m/s

2

)

Specific Force at Simu. Pilot Head

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-4

-2

0

2

x 10-6

t (sec) SF-Y (m/s

2

)

0 5 10 15 20 25 30

-10.5

-10

-9.5

-9

t (sec) SF-Z (m/s

2

)

Figure D.6. 4.
220

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-X (m/s)

Platorm Vel in Inertial Coord.

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) Svi-Y (m/s)

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec) Svi-Z (m/s)

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-X & SD-X (m)

Desired & Actual Platform Displ

filt. @ PS Original des.

Augmented des.

filt. @ PS Original act.

Augmented act.

0 5 10 15 20 25 30

-0.2

0

0.2

t (sec) SDdes-Y & SD-Y (m)

0 5 10 15 20 25 30

-0.5

0

0.5

t (sec) SDdes-Z & SD-Z (m)

Figure D.6. 5.
221

0 5 10 15 20 25 30

-1

0

1 ASFX,SSFX (m/s

2

)

A/C(..) & Simu.(-) Sensed Specific Force

aircraft

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-2

0

2

x 10-6 ASFY,SSFY (m/s

2

)

0 5 10 15 20 25 30

-5

0

5

t (sec) ASFZ,SSFZ (m/s

2

)

0 5 10 15 20 25 30

-1

0

1 ASW,SSW -p (deg/s)

A/C(..) & Simu.(-) Sensed Angular Rate

aircraft

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-1

0

1 ASW,SSW -q (deg/s)

0 5 10 15 20 25 30

-1

0

1

t (sec)

ASW,SSW -r (deg/s)

Figure D.6. 6.
222

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec)

Leg 1 (m)

Actuator Extension

filt. @ PS Original

Augmented

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

Actuator Extension

t (sec)

Leg 2 (m)

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec)

Leg 3 (m)

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec)

Leg 4 (m)

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec)

Leg 5 (m)

0 5 10 15 20 25 30

-0.4

-0.2

0

0.2

0.4

t (sec)

Leg 6 (m)

Figure D.6. 7.
223

References

[1] Telban, R. J., Cardullo, F. M.: “Motion Cueing Algorithm Development: HumanCentered Linear and Nonlinear Approaches”, NASA Langley Research Center, 

NASA/CR-2005-213747, 2005.

[2] Anderson, B. D., Moore, J. B.: Linear Optimal Control. Englewood Cliffs, NJ: 

Prentice-Hall, 1971

[3] Telban, R. J., Cardullo, F. M.: “Motion Cueing Algorithm Development: HumanCentered Linear and Nonlinear Approaches”, NASA Langley Research Center, 

NASA/CR-2005-2137476 2005.
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

2. REPORT TYPE 

Contractor Report

 4. TITLE AND SUBTITLE

Nonlinear Motion Cueing Algorithm: Filtering at Pilot Station and 

Development of the Nonlinear Optimal Filters for Pitch and Roll

5a. CONTRACT NUMBER

NNL06AA74T

 6. AUTHOR(S)

Zaychik, Kirill B.; Cardullo, Frank, M.

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

 NASA Langley Research Center 

Hampton, Virginia 23681-2199 

 

 

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National Aeronautics and Space Administration

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14. ABSTRACT

Telban and Cardullo have developed and successfully implemented the non-linear optimal motion cueing algorithm at the Visual Motion 

Simulator (VMS) at the NASA Langley Research Center in 2005. The latest version of the non-linear algorithm performed filtering of 

motion cues in all degrees-of-freedom except for pitch and roll. This manuscript describes the development and implementation of the 

non-linear optimal motion cueing algorithm for the pitch and roll degrees of freedom. Presented results indicate improved cues in the 

specified channels as compared to the original design. To further advance motion cueing in general, this manuscript describes modifications 

to the existing algorithm, which allow for filtering at the location of the pilot’s head as opposed to the centroid of the motion platform. The 

rational for such modification to the cueing algorithms is that the location of the pilot’s vestibular system must be taken into account as 

opposed to the off-set of the centroid of the cockpit relative to the center of rotation alone. Results provided in this report suggest improved 

performance of the motion cueing algorithm. 

15. SUBJECT TERMS

Cueing Algorithms; Flight Simulator; Motion Systems

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01- 05 - 2012