NASA Technical Memorandum 4752

Biomechanically Induced and

Controller Coupled Oscillations

Experienced on the F-16XL

Aircraft During Rolling

Maneuvers

John W. Smith and Terry Montgomery

Dryden Flight Research Center

Edwards, California

National Aeronautics and

Space Administration

Office of Management

Scientific and Technical

Information Program

1996

ABSTRACT

During rapid rolling maneuvers, the F-16 XL aircraft

exhibits a 2.5 Hz lightly damped roll oscillation, perceived and described as "roll ratcheting." This phenomenon is common with fly-by-wire control systems,

particularly when primary control is derived through a

pedestal-mounted sidearm controller. Analytical studies have been conducted to model the nature of the

integrated control characteristics. The analytical results

complement the flight observations. A three-degree-offreedom linearized set of aerodynamic matrices was

assembled tO simulate the aircraft plant. The lateraldirectional control system was modeled as a linear system. A combination of two second-order transfer functions was derived to couple the lateral acceleration

feedthrough effect of the operator's ann and controller

to the roll stick force input. From the combined systems, open-loop frequency responses and a time history

were derived, describing and predicting an analogous

in-flight situation. This report describes the primary

control, aircraft angular rate, and position time

responses of the F-16 XL-2 aircraft during subsonic

and high-dynamic-pressure rolling maneuvers. The

analytical description of the pilot's arm and controller

can be applied to other aircraft or simulations to assess

roll ratcheting susceptibility.

INTRODUCTION

During rolling maneuvers and tracking tasks, many

modern fighter aircraft tend to experience roll instabilities or damped oscillations. These oscillations are

noticeable at initiation and recovery following large

primary roll control commands. Large roll rate commands require high gradient gains and high roll acceleration to achieve and to recover from the roll in a

desired manner. The periodic motions that often follow

are sustained by the pilot/vehicle coupled interactions.

Pilots and investigators generally refer to these interactions as either pilot-induced oscillations (PIOs) or "roll

ratcheting." The brief discussion that follows attempts

to distinguish between the two.

Usually, PIOs predominate during tracking tasks or

following large, rapid control inputs. For example, during a tracking task, the pilot is actively minimizing the

error or command signal. If the product of the pilot's

gain and the system gain increases sufficiently, then the

pilot/vehicle closed-loop system tends toward neutral

stability. Neutral stability PIOs most often develop at a

crossover frequency within the range of 0.5 to 1.0 Hz.

Roll ratcheting predominates during roll recovery

and is generally associated with or caused by an interaction of the dynamic characteristics of the

neuromuscular limb system, the aircraft, and the

mechanical controller. The biomechanical nature of the

phenomenon is similar to a "bobweight" in its

feedthrough effect and produces oscillations within a

frequency range of 2 to 3 Hz. The magnitude and

damping are governed by the arm weight, the controller

weight, the wrist interface, and the control system gain

(primarily the commanded roll gradient gain).

During the F-16 XL-2 functional test flight phase, a

minimal number of rapid rolling maneuvers and recovery tests were conducted. At the end of the final functional test flight, the copilot, maneuvering and

maintaining control from the aft seat, initiated and

completed three rapid 360 ° rolling maneuvers at Mach

0.9 and an altitude of 11,600 ft. During the roll recovery portion, as the copilot attempted to capture a

desired roll angle, the aircraft exhibited a considerable

amount of lightly damped roll oscillations. These oscillations continued through more than 10 cycles at a frequency of 2.5 Hz. Particularly important, the roll

controller force transducer (measured at the controller)

recorded the same characteristic oscillations as other

aircraft control and response parameters. Based on the

flight experience and confirmed feedthrough effects

existing at the controller, the observed phenomenon

was believed to offer a good example of roll ratcheting

for analysis and reporting.

Similar phenomena were encountered during other

flight test programs.l-5 The Air Force conducted F-16

XL rolling maneuver evaluations. At Mach 0.9 at an

altitude of 5200 ft, their pilots experienced roll ratcheting. Tracking studies using a variable-stability aircraft

showed that roll ratcheting tendencies increase as augmented roll damping is increased and that pilot rating

increases correspondingly. 4'5 Using simulation and

analytical studies where tracking tasks were generated

by comparing position or target feedbacks to a forcing

function, the problem has been defined and investigated extensively. 6-10

In addition to presenting the actual flight data, this

report also analyzes the biomechanical nature of the

"bobweight" feedthrough effect and associated phenomenon. Linear models of the aircraft dynamics, control system, and the arm, wrist, and controller were

combined to model the phenomenon.

A mathematical model and description for the pilot's

arm and controller were developed. Extensive use was

made of existing data to define the wrist and arm
dynamic characteristics.l°These characteristics

includewrist damping,springconstants,pilot's arm

equivalentweight,frequency,anddamping.Previous

testshad beenconductedwith the pilot partially

restrainedon a vibratingplatformwhile performing

single-axistrackingtasks,l0 Variouscontrollerswere

firmly mountedto thevibratingplatform.Fromthese

tests,thebiodynamiconstantsandcoefficientsforthe

armandwristinterfacecomplianceweredetermined.

Thecombinationof limb dynamics,controllerdynamics,andtheirequivalentweighteffectsarereferredto

as the manipulationdynamics.The mathematical

descriptionofthemanipulationdynamicswasconcatenatedwithandintegratedintotheaircraftaerodynamicsandaugmentationsystems.

A linear mathematicalmodel for the integrated

aircraftaerodynamicsandaugmentationsystemswas

derived.Theaircraftderivativesusedtodefinetheplant

were available from previously reported flight

results.3.11-14Wind-tunneldatafor individuallymeasuredcontrol derivativeswerealsoavailable.14The

completesetof dimensionalderivatives,asdefinedin

appendixesA andB, wasassembledasmatricesin a

state-spaceformat.Usinga FORTRANcontrolprogram,15open-loopfrequencyresponsesanda typical

timehistorywerecalculated.

This reportdescribestheF-16XL-2 roll ratcheting

in-flight experience.Mathematicaland theoretical

analysesare presentedto describeand predictthe

characteristicsof the roll ratchetingphenomenon

causedbya"bobweight" feedthrough effect. The flight

test results and analytical predictions reported here

were conducted at the NASA Dryden Flight Research

Center, Edwards, California.

VEHICLE DESCRIPTION

The following sections provide a general description

of the basic F-16 XL aircraft and aircraft control

systems. Instrumentation and recording systems used

to obtain the flight data were developed by NASA

Dryden.

Aircraft

Two F-16 XL aircraft were designed and built by

General Dynamics (Fort Worth, Texas) for a U.S. Air

Force contract. The aircraft were initially considered

prototypes, emphasizing the muitirole fighter capability. At the start of the flight test phase, these aircraft

were formally referred to as demonstrators. Both aircraft are modifications of the F-16 A/B aircraft. The

forward and midfuselage have been extended by 56 in.

The design planform incorporated a cranked arrow

wing. The number 2 aircraft, of concern in this report,

is a two-seat fighter using an F-ll0 GE-129 engine

(General Electric, Lynn, Massachusetts) at the time of

flight 12. Figure l shows the relative size and location

Figure 1. The F-16 XL-2 aircraft surfaces and pertinent control units.
of theprimaryandsecondarycontrolsurfacesandrelevantcontrolsystemunits.Table1showsthepertinent

physicalcharacteristicsandgeometryof theaircraft.

Flight Control Systems

The F-16 XL aircraft derives total vehicle control

from aerodynamic surfaces. The surface positions

depend on the primary control input and the feedback

response as measured by the aircraft rate sensors.

Aerodynamic Surfaces

Flightpath control, in both pitch and roll, is achieved

by a blend of the aileron and elevon surfaces. The surfaces are faired along the trailing-edge segments of the

Table 1. The F-16 XL-2 physical and geometric characteristics (ref. 3).

Wing

Area, ft 2 663.259

Span (theo.), in. 388.84

Aspect ratio 1.583

Taper ratio 0.128

Leading-edge sweep

Inboard 70°

Outboard 50°

Incidence --0.65 ° at BL 41.50, --4.104 ° at 136.1 and tip

Dihedral 0°

Mean aerodynamic chord, (?) ft 24.7

Elevon area, ft 2 44.055

Aileron area, ft 2 29.445

Leading edge flap Area, ft 2 18.197

Vertical tail

Area, ft 54.75

Span, in. 101.00

Aspect ratio 1.294

Taper ratio 0.437

Leading-edge sweep 44.5 °

Bicon airfoil, percent

Root 5.3

Tip 3.0

Rudder area, ft 2 11.65

Speed brake area, ft 2 14.26

Control-surface authority (normal to HL)

Elevons 30 ° up, and down

Ailerons 20 ° up, 30 ° down

Leading-edge flaps 6.4 ° up, 36.5 ° down

Rudder 30 ° left and right

Speed brakes 60 ° up and down

Control-surface rates, deg/sec at zero load

Elevons 60

Ailerons 60

Leading-edge flaps 31

Rudder 90

Speed brakes, per panel 30

Pertinent physical locations cg - 45% FS 324

Lateral acceleration sensor FS l 18

Aft cockpit controller FS 162
wing.Directionalcontrolisaccomplishedbyaconventionalruddermountedonthetrailingedgeof asingle

verticalstabilizer.

Fly-By-Wire and Primary Control

A full fly-by-wire analog system is used in all three

axes. The system is fully quadruple-redundant. Electrical signals from the analog flight control computers go

directly to the integrated servoactuators. These actuators provide the force and position for the primary control surfaces. The electromechanical actuators are

single-fail-operate components.

Secondary Systems

Leading-edge flaps (LEFs) are located outboard on

the cranked portion of the wing. The LEFs are scheduled to operate symmetrically as a function of angle of

attack and Mach number. Limited LEF differential trim

input is available in conjunction with the normal aileron roll trim:

ALEF (maximum) = 3.0 °

for qc > 2176 lb/ft 2

(1)

The LEFs also provide partial spin recovery by operating differentially (ALEF -- 40 °) for angles of attack

greater than 35 ° .

Speed brakes are located on the aft portion of the

fuselage inboard of the elevons and in the horizontal

plane. The brakes operate by rotating into the vertical

directions to provide deceleration and additional spin

recovery capability.

Sidearm Controller and Augmentation

The F-16 XL airplane has the same two-axes

minimum displacement sidearm controller used on production F-16 aircraft. Figure 2(a) shows the relative

%%

F__, A FYc'AYc

- Yc - Yc

(a) Location of the pedestal-mounted controller within the cockpit.

Figure 2. Pitch and roll minimum displacement sidearm controller.

950161
cockpit location and the size and shape of the controller. Figure 2(b) shows the wrist and elbow rests provided on F-16 aircraft. Use of the rests is optional; the

rests can be stowed. Most pilots use only the elbow rest

during rolling maneuvers.

By applying force to the controller, the pilot initiates

pitch and roll inputs to a rate command augmentation

system rather than to controlling surface positions

directly. Longitudinal force input commands a blend of

pitch rate and normal acceleration. The pitch feedback

loops attempt to provide response characteristics

invariant with flight conditions. Lateral force inputs

command roll rate according to a roll command gradient schedule (fig. 3). The gradient consists of linear

(b) Wrist and elbow rest locations.

Figure 2. Concluded.

_C '

deglaec

300 --

250

200

150

100

50

I

2O

Galn

_(_c 0 deglsec

_-_-c = Ib

_)c _ deg/sec

_FYc Ib

z1(_c= 15deglaec

AFYc Ib

A_c deg/aec

_--- 30

AFVc Ib

Range

0 5 10 15

FYc, Ib

950163

Figure 3. Roll command gradient and gain over the linear range.

0 <-FYc<_ 1 Ib

1 S FYc< 5 Ib

5 <_FYc<- 9 Ib

9 < FYc< 17 Ib
constant rate gains/lb over the ranges shown with a

maximum commanded roll rate of 300 deg/sec. A force

input of 9 lb and larger produces a maximum gain of

30 (deg/sec)/lb. The force is actually determined by a

transducer measuring displacement, Fy c = FYc(X c).

While force and displacement are well-correlated statically, the phase lag between applied force and resulting

displacement is important in any transient analysis. A

breakout force of +1 lb is required for any transducer

output, after which the transducer output is essentially

linear up to a maximum displacement of 0.25 in. at

20 lb (a spring constant of 80 lb/in or 960 lb/ft). Total

surface position command is proportional to the error

signal, e, as shown by the functional roll control system

diagram (fig. 4). Favorable roll-yaw coordination is

provided through a scheduled and function-generated

aileron-rudder interconnect.

A typical rate damper stability augmentation system

is implemented in the yaw axis to accomplish both

dynamic and static stability. Aircraft dynamic stability

is augmented by a washout yaw rate feedback. Static

directional stability is augmented by lateral acceleration feedback.

A more complete and detailed description of the

flight control, its design and final configuration philosophy, and the surface rates and authorities has previously been given. 13' 16

Instrumentation

The F-16 XL-2 instrumentation was designed,

installed, and maintained by the NASA Dryden Flight

Research Center. Most of the data originate from flight

control sensors and are obtained from the avionics data

bus. The data presented in this report were recorded

from pulse-code-modulation telemetry. The aircraft

rates, surface positions, and aircraft system functions

were recorded at 50 samples/sec. Tables 1 and 2 show

flight control accelerometer locations.

FLIGHT TEST EXPERIENCE

Many modem fighter aircraft experience roll

oscillations. The occurrences follow rapid rolling

maneuvers, particularly those performed at highdynamic pressures.

Roll Ratcheting

During F-16 XL-2 flight 12, which in part was a

functional check flight, the copilot performed three

fairly rapid 360 ° rolling maneuvers from the aft cockpit. The copilot reported severe roll ratcheting particularly at high commanded roll rates and in the recovery.

See fig. 9 _ fig. 2

................ A%

i Manipulation : Time AFy"_ (FYc) Roll--l_- elevon

, dynamics : delay ratio

I I "

_ ! , I , ,

I'yp-;'_lArm,wrist, N ' Xc _grad-lentl-l/;_ll-;-_._)m--I Kp = 0.12 _ F10 = 0.5 _eR- 8eL

I and II Xc I:-- _k:.............._ _ _ .... " ,._ ], 2

: Icontro"erlL--:-Ii 1.2÷45.÷4521 I[---q........ ,-',I ."

', I I ! I- ._ -_.,_- _ ; _ARI =-1.01 : I "g

, i- ; _1 is+qor I : I Iill _ '_

: .._.T_w , -]_L-.- ' ARI ,, i_I 135 _aR-_aL c>.

,

I ' ,,_T "'c I ,I 1_21 ,--" --" I _l_n_• rl fr I 'I II s + 135 _

..... f .......... I_""_r-liEa----'-II/ term I(L_'-IARI - 03 T

/a,, -o ,I5_'.al, !_'1 I, ,c

i "'t _ '..-':-."_'-" '- ............ a ,

=2.0 x 10 -3 _.i 3s(s + 7.5) I_1,,.( I 52 + 12"25+ 612 11_,_-_.SrSr 5r

,t(s + 15)(S + 1)1 , _ (S + 61) 2

=5 X 10-45 I

any._r--T_-I I

_ Sensor location; ays= ay+ r J-x

P

r

ISA =

27.142

s 2 + 2 x 0.975 x 27.14a + 27.14 2

950164

Figure 4. Basic F-16 XL function roll control system for the flight conditions listed in table 2.
Table2 showstheflight conditionstypicalof all three

maneuvers.

Table 2. Flight conditions,mass properties,and

dimensions.

Machnumber 0.9

Altitude,ft 11,600

Dynamicpressure,lb/ft2 790

Trueairspeed,ft/sec 964

Angleof attack,deg 1.77< a < 4.0 °

Angle of attack and pitch attitude,

deg 3

Center of gravity, % ? 45

Weight, lb 28,318

Impact pressure, lb/ft 2 957.3

Impact pressure/static pressure 0.7

Vehicle moments of inertia, slug ft 2

I x 22,352

ly 104,027

Iz 123,293

Ix z -559

Longitudinal distance, ft

(A/C accelerometer location,

relative to cg and body axis) 17.0

Vertical distance, ft

(A/C accelerometer location,

relative to cg and body axis) 0.0

Controller location

Longitudinal distance, ft 13.5

Vertical distance, ft 1.0

Figures 5 and 6 show time histories of the aircraft

response and control parameters. Figure 5 shows the

time response of the lateral controller force, bank

angle, rolling angular rate, and lateral acceleration at

the sensor for the three rolling maneuvers and recovery.

The direction of the roll is indicated. Initially, the copilot banked right to approximately 60 ° and rapidly completed a full 360 ° roll to the left. The copilot continued

the roll to the left at a slow rate and stabilized in a leftbank attitude for approximately 5 sec. From a wingslevel attitude, the copilot completed another 360 ° left

roll and stabilized the aircraft near 0 ° for approximately l0 sec before initiating a full 360 ° roll to the

right.

At the recovery portion of all three rolling maneuvers, where Fy (x_) > 9 lb, the aircraft exhibited a

I c Cl considerable amount of roll ratcheting. The data show

the oscillations are generally superimposed on a

commanded and derived roll response. Consequently,

for one-half cycle of each oscillation, the motion

appears to the pilot as a periodic hesitation in the roll

response. Thus, the terminology "roll ratcheting" is

very descriptive of the phenomenon displayed.

Pilot Remarks and Comments

The copilot who performed the rolling maneuvers

has a considerable amount of time and experience in

flying F-16 aircraft. From a discussion with the copilot

following the flight and a review of the flight data, the

subsequent impressions were obtained, and the

copilot's remarks and comments are summarized as

follows.

The copilot was definitely aware of the ratcheting

response. The copilot's primary attention was focused

on the nose of the aircraft, so impressions were formed

from the cyclic behavior and roll rate hesitation. The

cockpit motion was of little concern during the occurrence. The copilot also thought that the body, torso, and

shoulders were restrained sufficiently to be minimally

responsive. The elbow rest was in use while the rolls

were executed. The copilot felt the forces were low or

unchanging at the arm during the ratcheting acceleration experienced. This observation and comment is

understandable because the controller force transducer

was responding to inertia forces of the arm and

controller. The calculation of the controller displacement resulting from the observed variation in controller

force supports this explanation. The minimum displacement controller has a stiffness defined by

Fy¢(Xc) = 20 lb; x c = 0.25 in. (2)

The measured controller force variations (from figure 5(a)) are

AFYc = 2.5 lb peak-to-peak (3)

Then Ax c = (2.5/20) • 0.25 = 0.031 in. peak-to-peak as

indicated in the Aircraft and Controller Cycle

Response section. This small controller displacement

seems to explain the lack of pilot observation.
20 m

FYc(Xc)' 0

Ib

-10

10

- 2O

0

Left

roll_

First 20 sec----_ I

I

10 20

Right

Ratche r°ll_'_Z'_t[__

roll -'

l i I I

30 40 50 60

Time, eec

(a) Stick force (from the stick position transducer).

I

70

950165

deg

200

100

-100

_- Right roll

#

_- Left roll

I I

_- Left roll

-200 i First 20 sec_ I [ ]

0 10 20 30 40 50 60

Time, sec

70

950166

(b) Bank angle.

Figure 5. The F-16 XL-2 time histories during rolling maneuvers at the flight conditions listed in table 2.
Pp

deglsec

2OO

IO0

0

- 100

- 2OO

0

F

__.__

.... __._

First 20 sec----_,.- I

I I I I I

30 40 50

Time, sec

10 20

i I

6O 7O

950167

(c) Roll rate.

.25 --

aY s,

g

.2O

.15

.I0

.05

- .05

- .10

- .15

m

F'r==O'e°---'l I I I I I

0 10 20 30 40 50 60 70

Time, sec 950166

(d) Lateral acceleration (from the accelerometer in the front cockpit).

Figure 5. Concluded.
Aircraft and Controller Cyclic Response

By comparing the data from the three rolls (fig. 5), it

is evident that the most extensive ratcheting occurred

during recovery of the first rolling maneuver

(10<t<2Osec). The discussion and analyses that

follow consider the first rolling maneuver and recovery

as distinctive representations of the displayed

phenomenon.

Figure 6 shows time histories of the first 20 sec of the

data shown in figure 5. These data present a complete

360 ° left rolling maneuver and recovery. All the aircraft

response data relevant to the lateral control and the

appropriate control surface positions are shown. The

most interesting time span of the time histories exhibiting the roll ratcheting is from 13 to 17 sec. These data

show the existence of 10 cycles of oscillatory motion

lightly damped and at a frequency of 16 rad/sec or

10

5

0

FYc(Xc)' -5

Ib

-10

-15

-20

Ratcheting response/

'_/I ///11111 -

//////i /

Roll command _ /

-- gradient

- 30Olsec/Ib

I I I I 1

0 4 8 12 16 20

Time, eec 95ol69

(a) Stick force (from the stick position transducer).

(_)9

deg

2OO

IO0

-tO0

m

i 1 t

4 8 12

Time, sec

(b) Bank angle.

_- Left roll

-2oo I I

0 16 20

950170

Figure 6. The F-16 XL-2 expanded time histories during rolling maneuvers at flight conditions listed in table 2.

I0
approximately 2.5 Hz. This frequency falls within the

range of frequencies considered typical of roll ratcheting as reported in various references. 1-3

Note that the lateral controller force, which is a function of controller transducer output calibrated in lb, is

very active during the roll ratcheting recovery

(fig. 6(a)). This trace portrays a very lightly damped

system oscillation and suggests that the controller is

actually being excited through a "bobweight" effect

that is sustained by lateral acceleration. At the initiation

of the recovery, the force level IFYcl was greater than

9 lb. Figure 3 shows that the controller gradient doubles at a force level of 9 lb. The phenomenon observed

is easily excited and sustained at high force levels.

Fully saturated roll inputs (IFYcl> 17 would not

provide a gradient gain for the feedthrough process.

However, during a typical recovery from a saturated

40--

0

P' - 40

deglsec

- 8O

- 120

I I I I i

0 4 8

Time, eec

(c) Roll rate.

12 16 20

950171

.15 --

aY s,

g

.10

.O5

-.05

m

- .10 --

- .15 1

0 4 8 12 16 20

Time, eec 950172

(d) Lateral acceleration (from the accelerometer in the front cockpit).

Figure 6. Continued.

11
condition, the roll ratcheting oscillations are likely to

occur.

The time history data indicate a reduction in the

oscillatory amplitudes as the controller force level

decreases (fig. 6). The estimated peak-to-peak variations of the distinctive aircraft responses during the roll

ratcheting segment are as follows:

Frequency range = 2.24 Hz < f< 2.83 Hz

= 14 < o_< 18 rad/sec

o_ = 16rad/sec (average)

Aa Ys-- 0.09 g

Ap = 21 deg/sec

AFyc(Xc) = 2.5 lb

Ax c = 0.031 in.

Ap = Apo)= 336 deg/sec 2

Aar(p) ---0.18g (at the controller)

The peak-to-peak roll response, Ap = 21 deg/sec,

resulting from a controller force variation of

AFyc (Xc) = 2.5 lb shows an amplitude of 8.4 (deg/sec)/

lb for a frequency of 2.5 Hz. This change is approximately 28 percent of the commanded steady-state gain

response (30 (deg/sec)/lb) for a controller force level of

9 lb and greater. The acceleration variation measured at

the sensor indicates a maximum of Aa yo = 0.09 g. This

variation gradually decreases after the f_rst four cycles.

Little, if any, response is evident in the yaw rate, r, time

histories. All primary control surfaces exhibit the ratcheting oscillation. The rudder is particularly active and

indicates a peak-to-peak displacement of more than 4°

as a result of ay feedback.

Although the accelerations are vector quantities, a

rough estimate of the pilot's arm weight can be

obtained by adding the peak-to-peak magnitudes of the

two components. This approach assumes that the arm

can be modeled as a point mass at the controller

(termed an equivalent weight).

l

Aarc= Aays + Ap_;l z = lft

= 0.09 + 0.18

= 0.27 g

(4)

8 --

rl

deg/sec 0

-4

-8

0

_f ....

I I I I

4 8 12 16

Time, sec

(e) Yaw rate.

Figure 6. Continued.

2O

950173

12
3 --

deg

2 --

1

0

1

-2

-3 --

-4

0

\

I I I I i

4 8 12 16 20

Time, sec 9so174

(f) Side slip.

10

_aL' 0

deg

-10

10

_aR' 0

deg

-10

_e L,

deg

(_eR,

deg

I I I

__I I I I I I

0 4 8 12 16 20

Time, sec 950175

(g) Aileron and elevon positions.

Figure 6. Continued.

13
LEF

-- 0°, streamlined -. _ "

_._--6.4_< LEF < 0.0 ° / \

Up - 6.4 0 _

I I I .... 1

0 4 8 12 16

Time, sec

i

2O

950176

(h) Leading-edge flap position.

6 --

_r,

deg

-4'----

-6 I I I

0 4 8 12

Time, sec

(i) Rudder position.

Figure 6. Concluded.

! I

16 2O

950177

because

then

AFyc= 2.5 lb (5)

AFy c - 9.3 lb

Wr(e)- Aay_

(6)

In modeling the pilot's arm, wrist, and hand and the

sidearm controller, rotational as well as translational

elements exist. The model converts the rotational elements into translational elements by defining

equivalent weights that include moment of inertia

terms. The equivalent weight of the arm, W@(e), is

equal to the total equivalent weight of the arm and controller, WT(e ) , minus the weight of the controller, W c .

The controller weighs 1.25 lb.

W@(e) = WT(e)- W c = 9.30- 1.25

W@(e) = 8.05 lb

(7)

14
ANALYSIS AND DISCUSSION

Previous roll ratcheting investigations and analyses

considered the pilot not only as a connective link but as

an active element of the closed-loop process. The following discussion considers the pilot's role as the

active controlling element. However, the major investigation and analysis focuses on the force feedthrough

effect resulting from lateral acceleration and the partially restrained controller and arm masses.

Roll Ratcheting Investigation, Scope, and

Definitions

Studies of roll ratcheting oscillations encountered by

high performance aircraft have considered the pilot's

role in a closed-loop process. 4' 5 The biomechanical

feedthrough effect caused by the product of the lateral

acceleration and the sum of the arm and controller

masses have also been studied.l°

Figure 7 shows two simplified illustrations depicting

the control process in deriving a roll rate, capturing a

roll attitude, or maintaining a bank angle. Figure 7(a)

shows a simulated forcing function, q_le pilot, while

continuously observing the desired error signal,

actively tries to minimize the signal. How well the task

is accomplished becomes a qualitative assessment and

may be quantized as indicated for a comparison with

another test configuration. The variables in most cases

are the pilot or operator, the controller, and the controlled element. Analytically, the operator is modeled

by a transfer function composed of a gain constant, a

time delay, and some form of equalization. The controller is represented by its dynamic response characteristics. The controlled element is defined by the

aircraft transfer functions.

Figure 7(a) depicts a task system of an in-flight

investigation using a T-33 variable stability aircraft 4' 5

exemplifying the study of the pilot's role. During tracking tasks, the investigators varied such parameters as

time delays, prefilter lag-lead models, and augmented

roll mode damping. One reported finding was that roll

ratcheting tendencies increase with augmented roll

damping and the subsequent oscillations resulted in

poor pilot ratings. This finding is logically consistent

with the conclusions of this report. Increasing the augmented roll damping, decreases steady-state roll rate

response to a pilot input. Large pilot inputs or a high

gain on the pilot input are, therefore, required to minimize the error signal, which is a function of roll rate

Task

reference

_-- Typical pilot-operator task 1

maintaining a small E(t); rms2E(t) =_ ,I Tl_(t)ldt

C---'_ontrolier Controlled element

_¢1

aY1;

Bobweight, feedthrough loop

(a) System with a forcing function or task reference; operator controlling to minimize an error signal.

c(p, _)

950178

Fyp °ontro,,.rt__1

and operator aircraft and

arm dynamics systems

I ay17

Bobweight, feedthrough loop

C(p, ¢)

950179

(b) System to achieve desired roll rate and roll attitude.

Figure 7. Basic human operator system concepts for acquiring a prescribed task.

15
andbankangle.Thelargeinputsresultin largeinitial

roll andlateralaccelerationresponses, whichleadtoan

increasein roll ratchetingoscillations.Largeinputs

alsoresultin increasedstickgain(vianonlinearstick

gearing).Suchgainsalsoleadto an increasein roll

ratchetingsusceptibility.

Thepresentinvestigationsimplyconsidersthepilot

performingin-flightrollingmaneuverswithnominimizationtaskrequired.Figure7(b) showsthis control

process.First,thepilot appliesa roll controlforceto

the controller,Fyp, to achieve the desired roll rate.

Then, the force is decreased or reversed near the

desired roll attitude. Rolling the aircraft generates tangential acceleration components at the controller composed of, lxi', lzp and aircraft lateral acceleration, ay.

The product of the equivalent weight and sum of the

accelerations causes an additional force input, AF, that

is superimposed on the reference force input,

(Fr, e + AF). This reaction results in a closed-loop

feedthrough effect that produces an overall reduction in

gain margin. This closed-loop process is generally

referred to as a "bobweight" effect.

Assuming the arm is modeled as a cylinder with uniform mass distribution rotated about an endpoint, then

the equivalent weight of the arm at the controller is

equal to one-half the weight of the arm, W@, plus the

moment of inertia effect. The moment of inertia effect

is W@/3.

%

W@(e)= --_-- + 0.33 W@ (8)

Using the equivalent weight of the arm as estimated

in equation 7 from the flight data, then

have previously been given. 17 The arm component

weights for a 165-1b adult male cadaver, expressed as a

percentage of total body weight, are as follows:

Entire arm 6.59 percent

Upper arm 3.44 percent

Forearm and hand 3.15 percent

Forearm 2.26 percent

Hand 0.89 percent

Based on the F-16 XL pilot's weight, 160 Ib, the

comparable arm components weights are estimated to

be

Entire arm 10.54 lb

Upper arm 5.50 lb

Forearm and hand 5.04 lb

Forearm 3.62 lb

Hand 1.42 lb

Assuming that the elbow rest was ineffective during

the oscillations, then the equivalent weight at the controller would be determined from the weight of the

entire arm ( W@= 10.54) as follows:

W@

W@(e) = T + 0.33W@

10.54

- _ + 0.33.(10.54) 2

W@(e) = 8.75 Ib

(10)

Subsequent analytical calculations vary the equivalent

weight of the entire arm arbitrarily between the two

extremes (3.93 < W@(e) < 10.75).

8.05= 0.83%

w@=9.71b

(9)

If the elbow rest completely immobilized the upper

arm, then the equivalent weight would be determined

from the forearm and hand. The flight-determined arm

weight of 9.7 lb appears to be approximately twice the

expected weight for forearm and hand (approximately

5 lb). Apparently, the elbow rest was only partially

effective in restricting the motions of the upper arm.

The total body weights of four cadavers and the

weights of body components including arm segments

Integrated Modeling Description

Figure 4 shows a functional block diagram of the

F-16 XL roll control system. Pilot input, Fyp, is indicated as the reference input to the controller. A force

input initiates the roll command through the force and

roll gradient and is summed with the augmentation roll

rate feedback. The result generates a roll response

through the plant aerodynamics that is proportional to

the error signal. Figure 4 shows the aileron-to-rudder

interconnect and the angle of attack and roll rate (otp

16
term) configurationson the F-16 XL airplane.The

input/outputrelationshipsfor theplant aerodynamics

aredescribedin appendixB. Lateral-tangentialccelerationsatthecontrolleraregeneratedbecauseof the

roll responseandtheadditionallateraldegreesof freedom.Theseaccelerationsarecomputedin g. Along

with the respective equivalent weights of the controller

and pilot's arm, these accelerations provide a forcefeedthrough process back into and through the controller. The dynamic response of the controller was determined from release tests with various weights added.

The results are presented in appendix C. The natural

frequency of the controller is well-separated from the

ratcheting frequency. Consequently, the controller

dynamics have a small effect on the ratcheting

response. The response of the controller at the ratcheting frequency can be determined by the second-order

response curves found in any dynamics text.

For co/o3 n < 0.3 and _ = 0.05, the gain is approximately 1.0.

The manipulation dynamics are shown in the biomechanical feedthrough model (fig. 8). This particular

illustration was adapted from a description previously

given. 10 An extensive amount of experimental and

analytical research regarding the biomechanical forces

derived from accelerations was conducted, l° This

report relies heavily on those efforts and measurements. The complete formulation of the second-order

systems and equation characteristics are derived in

appendix D.

Figure 9 shows a mathematical model of the

biomechanical nature of an operator's arm and wrist

and the controller. The spring constant, damping coefficient, and time constants assigned to the respective

second-order system equations were derived from the

vibration platform and experimental tests previously

performed. 1° By letting s _ 0, the steady-state gains

become

g.

1

K@ + K i

K@

K@ + K i

- 0.72

- 0.28

(11)

or the total steady-state force to the roll command

gradient is

slf.moFYc = 0.721Fyt ,- W@(e)ayx)- Wcayx (12)

1

Vertical

plane

Horizontal

plane

f #

/ #

F ./

/ #

/

/ /

I /

//

i /

" / FYc _ ... I

//i ,,iI

//I w

/ I-stera, I_ ay h,l

_.cceleration _' _ r.-----_ D(_) M

"/I v I

"/I r/ / / /A "-F

" / _"_1//Shoulder//4 6

Airframe

Kc Transducer

Hand/control

Controller grip interface

characteristics characteristics

Xc

Arm/muscle

characteristics

Stick or

controller

Grip

Limb

Body

semirestrained

to the airframe

950180

Figure 8. Feedthrough mechanical controller model with lateral force and acceleration input.l°

17
F ++ I

I Ir,,,. ,2 +

I I "'+ (K_+ Ki) (1_+ Ki)

Arm and wrist

IW(_)(s) + Wc I Interface dynamic'

tK_ Ki) X (B_ K_

..2 +(D_+Di),,,+1

m® (K_+ Ki) (K_+ Ki)

Di_ 1 , Ki K_

--Ki - --11.6 ("_-'_T) : 0.72, (K(_)÷ Ki) : 0.28

Entire Equivalent weight

arm

weight _(e) + W c = WT(S)

4.72 3.93 1.25

7.20 6.00 1.25

* 10.50 8.75 1.25

12.95 10.75 1.25

* Considered typical

** n_ : w_,te;/g --_j. .

Controller

dyn,,mic,,

(Wc = 1.25 Ib)

Mass Moment of

effect inertia effect

w®(e): w_ +

o)® _® m(®+ i) C.(®+i)

5.18 8.80 0.28 16.82 0.66

7.25 7.13 0.23 13.45 0.54

10.00 5.90 0.19 11.14 0.45

12.00 5.30 0.17 10.05 0.40

r I Aircraft roll rate

command system

"Y+ L acceleration

the+'n+'nt"' controller

at L

From ref. 10

KI = 24.26

Di = 2.09

946 0.61

950181

Figure 9. Biomechanical model and mathematical description of the operator's arm and controller dynamics

(appendix D). The controller spring gradient, K c .... cancels out.

If the operator's hand is removed from the controller,

then Fye, K i, and D i = 0. Expectantly, this leaves the

controller weight, W c, as the only force feedthrough

loop into the aircraft roll command system. However

because Fyp = 0, the roll command gradient gain is

very small (fig. 3). Consequently, little, if any,

feedthrough effect would excite the forward loop.

The equivalent weights (fig. 9) are considered

representative and within the normal range of a typical

arm and controller. The equivalent controller weight,

Wc , is considered equal to the actual weight of the controller at the disconnect location. The equivalent

weights are used instead of mass and inertia because

the calculated or measured tangential acceleration at

the controller are conveniently expressed in g units.

Mathematical Computations

The flight control system (fig. 4) was linearized about

the same flight test conditions (table 2) as the

aerodynamics for the plant. A unique nonlinear closedloop system, called a dual lag, is implemented on the

F-16 XL airplane. This system provides a different

command response depending on initial input, control

bias, and frequency. Consequently, the control bias

must be considered when determining the input/output

relationship. Appendix E shows the development of an

averaged linear transfer function for a sinusoidal input

at the flight-experienced roll rate condition.

C____oo = 10(s + 40) (13)

R! (s + 6)(s + 67)

The open- and closed-loop total system characteristics were determined by using a FORTRAN control

program. 15 Figure 10 shows an open-loop frequency

response of the tangential acceleration/command force,

ay/Fyc. For the observed in-flight ratcheting frequency, 16 rad/sec, the computed system shows a gain

margin of 27 dB and a phase margin of 70 °. At the

crossover frequency, COco= 26 rad/sec, the gain margin

is 35 dB. Note that a gain increase of 10 dB exists near

the ratcheting frequency. This gain increase undoubtedly increases the tendency of the system toward instability when coupled with the manipulation dynamics.

18
FYc

dB

Phase,

- 90

deg

- 180

Ratcheting

frequency

COco

1 10 100

03,radlsec

950182

Figure 10. Open-loop tangential acceleration frequency response (conditions: Oc/Fyc

manipulation dynamics or time delay at the flight conditions shown in table 2).

= 30 (deg/sec)/lb. No

19
Figure 11 shows a comparisonof the vector

components of the tangential accelerations at the controller using the same open-loop computation (except

09 = 15.6). The tangential accelerations are caused by

roll acceleration, p, and the lateral-translational

acceleration, ay + lxf. Aa y resulting from p lags the

translational acceleration b_, approximately 180 °, and

the amplitude of the p vector is 2.17 times greater than

the translational vector, f(ay, i'). The resultant vector

is also shown and has a phase angle of -107 ° with a

magnitude of 0.047 g.

Biodynamic Response

Figure 8 shows the ann, wrist interface, and controller feedthrough model. Manipulation dynamic characteristics are derived and developed in appendix D.

Figure 9 shows the numerical values. The total system

is thus described by inserting the manipulation transfer

functions into the aircraft and functional control system

diagram (fig. 4). Using this completely integrated

model and applying the mathematical control program

connective procedures, 15 the dynamic characteristics

and time responses of the total system were obtained.

Figure 12 shows the open-loop frequency responses

for four equivalent total weight conditions: WT(e) =

5.18, 7.25, 10.00, and 12.00 lb. For WT(e) = 5.18 lb,

the open-loop system indicates a sufficient gain margin

of 15 dB at coco = 20 rad/sec. Progressively increasing

the equivalent total weight decreases the crossover frequency and decreases the gain margin. At an equivalent

total weight of 12 lb, the system becomes very lightly

damped at a frequency of approximately 10 rad/sec. A

nominal and perhaps typical value for an equivalent

total weight is believed to be approximately 10.0 lb,

which means that the equivalent arm weight about the

shoulder is as follows:

W_(e) = WT(e)- W c = 8.75 lb (14)

The equivalent weight includes a moment of inertia

effect;

W@(e) = W@ (entire arm)/2

+ 0.33 W@ (moment of interia) = 0.8 lb

(15)

j(o

.O6

.04

.02

-.02

-.04

-.06

//_/Aayz= f(ay))

= I.oasl

.It z 32 °

/....-

./_ 32 °

Aay. : f(I)) ,_1

= 1.0781 //1

/s/$1

-.04 -.02 0

_107 °

_-- Resultant

ay: = 1.o4681

L -107 °

-.o8 I I I

-.06 .02 .04 .06

950183

Figure 11. Open-loop vector components of the resultant tangential acceleration at the controller (_c/Fyc = 30

(deg/sec)/Ib; co = 15.6 rad/sec. No manipulation dynamics or time delay at the flight conditions shown in table 2).

20
I WT(e) , Fyp

dB

Phase,

deg

20

- 20

- 40

- 60

-8O

90--

30--

- 30 --

- 90 --

- 150 --

- 210 --

- 270

.1

V

•- .............. ._ ---__ :_ _- .,

5.18 \

__ - ...... 7.25 \

..... 10.0 \

.... 12.0

I I IIIIIit I I I llilll I I IIIIII1

I I III1111

1 10 100

co, radlsec

950184

Figure 12. Open-loop frequency response as a function of total equivalent weight (fig. 9) (conditions: manipulation

dynamics with no time delay at the flight conditions shown in table 2).

or the actual weight of the entire arm is

W@ = 10.5 lb (16)

An arm weight of 10.5 lb is believed to approximate

the pilot's arm weight and yet be conservative enough

to provide sufficient damping.

Figure 13 shows a computed time history for a l-lb

step input at Fyp. Eigenvalues show the mode to have

a natural frequency of 14.3 rad/sec and a damping ratio

of 0.15. This frequency is within the range observed

from the flight data. To determine the effects of time

delays, 50 msec of delay was added in the forward loop

of the system (fig. 4). This delay changed the natural

frequency and damping ratio to o3n = 13.2 rad/sec and

=0.10.

21
AFyp,

Ib

1,0 a

I I I I

AWT(e ) x aye,

Ib 0

_y1:(lly + ,tx_), _.04

g

-.o8 I I 1 I I

AFy c,

Ib

1

o.... ...... i

.O6

.04

.02

0

- .02

--.04

0

-- From the eigenvalues:

__ O)n = 14.3 rad/sec

-- _/V_ =0"15 Ap,

deg/s ec

I I t I I

1 2 3 4 5

Time, eec

20 f

t I I

0 1 2 3 4 5

Time, $ec

950185

Figure 13. Analytically obtained time history in response to a unit step input (conditions: WT(e ) = 10 Ib,

_c/Fyc = 30 (deg/sec)/lb, no time delay, at the flight conditions of table 2).

CONCLUSIONS

The F-16 XL-2 airplane is a modified version of the

production F-16 aircraft. Modifications include extending the forward and midfuselage by 56 in. and changing the wing to an advanced cranked arrow type. In

place of horizontal tails, the F-16 XL-2 airplane derives

total pitch and roll control by elevons and ailerons

mounted along the trailing edge and throughout the

span of the wing. The aircraft has a fly-by-wire analog

flight control system approximately identical to the

early F-16 aircraft. A minimum-displacement, twoaxes, sidearm controller is used to command the pitch

and roll rates.

During a functional check flight, the copilot, flying in

the aft seat, completed three rapid rolling maneuvers.

Upon recovery from each maneuver, the copilot

reported roll ratcheting oscillations that lasted through

10 cycles at a frequency of 2.5 Hz. The roll command

gradient gain was at its maximum of 30 (deg/sec)/lb

initially and remained near the maximum throughout

the oscillations.

The following conclusions were reached from flight

test results and the analytical studies regarding the

phenomenon:

1. During the roll oscillations, the controller transducer showed oscillations of the same extent,

phase, and continuation as other aircraft roll

response parameters. The data support the hypothesis that the oscillations were commanded through

the controller.

2. Based on the controller force data, the maximum

peak-to-peak controller displacement during the

roll ratcheting oscillations was very small, Ax c <

0.032 in. This displacement indicates small arm

motions. The copilot observed no arm forces or

motions and believed that there were none.

3. All primary control surfaces followed the roll

ratcheting oscillations induced by tangential accelerations at the controller.

22
4. Theopen-loop,computedtangentialresponseof

thebasicaircraft,ay/Fy c, shows about 10 dB of

gain increase near the roll ratcheting frequency.

Coupling with the manipulation dynamics causes

the closed-loop system to be prone to ratcheting

instability.

5. The tangential component of the acceleration at

the controller caused by rolling acceleration, lzp,

is approximately 2.2 times larger than the component caused by aircraft lateral acceleration, a y+ lxi'. This observation indicates that roll

ratcheting depends largely on p and on the distance of the controller above the roll axis.

6. The dynamic characteristics of the controller have

only a slight effect on roll ratcheting. The ratcheting frequency is well-separated from the natural

frequency of the controller determined in

appendix C.

7. Both crossover frequency and gain margin

decrease when equivalent arm weight, W@(e),

increases.

8. Based on estimates from one in-flight rolling

maneuver, the wrist and elbow rests appear to be

.

10.

11.

ineffective in restraining the arm from the small

motions associated with roll ratcheting. The estimate of equivalent arm weight based on flight data

more nearly matches the weight of the whole arm

than just the forearm and hand.

Following a step input of Fyp = 1 lb with a roll

command gradient gain of 30 (deg/sec)/lb and an

entire arm weight of 10.5 lb, the integrated system

exhibits a slightly damped oscillation: _ = 0.15 at

a natural frequency of 14.3 rad/sec.

Adding a time delay of 0.05 sec in the forward

loop decreased the damping and frequency to _ =

0.10 and con = 13.2 rad/sec.

A technique for predicting roll ratcheting has been

developed. The method requires an augmented aircraft model, the derived aircraft accelerations at

the controller, and the pilot arm weight. The

method and equations can be applied to other

aircraft and included in simulation studies.

Dryden Flight Research Center

National Aeronautics and Space Administration

Edwards, California, October 28, 1994

23
APPENDIX A

NOMENCLATURE

Abbreviations

ARI

FS

GE

ISA

LEF

PIO

TF

XL

aileron-to-rudder interconnect

fuselage station, in.

General Electric

integrated servo actuator

leading-edge flap

pilot-induced oscillation

transfer function

extra-long

Symbols

A

ay

d Yc

a Ys

a y_

B

b

C

Ct

Clp

C1r

Cl_

Cl_a

Cl_ e

Cl_

Cn

matrix coefficient, (A" = C-1A )

lateral acceleration at the center of

gravity, g

lateral acceleration at the controller, g

lateral acceleration at the sensor, g

tangential acceleration at the controller, g

matrix coefficient, (B'= C-1B)

reference span, ft

matrix coefficient

rolling-moment coefficient, rolling

moment/qsb

roll-damping derivative,

Cl/3(pb / ( 2 V) ), rad -1

rolling moment due to yaw rate,

_Cl/3(rb/2V), rad -1

effective dihedral derivative,

_Cl/_, deg -1

differential aileron roll effectiveness

derivative, 3Cl/O5 a, deg -1

differential elevon roll effectiveness

derivative, _CI/O_ e, deg -1

rolling moment due to rudder deflection,

_Cl/_r, deg -1

yawing-moment coefficient, yawing

moment/qsb

Cnp

Cn r

Cn_

Cn s

a

Cns e

Cnsr

CO

Cy

Cyp

Cy_

Cy_

C Yr_

CY8

CYSr

cg

D

D@

D c

D i

(e)

F

Fy

FY c

FY e

FlO

f()

IX, I y, I Z

Ixz

yawing moment due to roll rate,

OCn/O(pb/2V), rad -l

yawing damping derivative,

OCn/O(rb/2V), rad -1

directional stability derivative,

_Cn/_, deg -1

yawing moment due to aileron deflection,

3Cn/O_a, deg -1

yawing moment due to elevon deflection,

_Cn/_)e, deg -1

rudder effectiveness derivative,

OCn/O_ r, deg -1

generalized control system output

side force coefficient, side force/qs

side force due to roll rate,

OCy/Op, deg -1

side force due to yaw rate,

OCy/Or, deg -1

side force due to sideslip,

OCy/O_, deg -1

side force due to aileron deflection,

3Cy/O_a, deg -1

side force due to elevon deflection,

3Cy/O_e, deg -1

side force due to rudder deflection,

_Cy/OSr, deg -1

mean aerodynamic chord, ft

center of gravity, % ? and FS

damping, lb sec/ft

damping of the arm, lb sec/ft

damping of the controller, lb sec/ft

damping of the wrist and hand interface,

lb sec/ft

equivalent

force, lb

lateral controller force, lb

lateral controller force, lb

lateral controller force pilot input, lb

roll-to-rudder gain schedule,tiM)

function of parameter inside parentheses

vehicle moments of inertia, slug ft 2

product of inertia, slug ft 2

24
j(o

K

K@

K c

K i

Kp

Ix

lz

m

m@

m e

P

p

Ps

q

qc

RI

r

S

S

t

V

W

W@

W@(e)

W c

W T

Wr(e)

X

x@

X c

(t

5

e

A

imaginary part of Laplace transform

variable, rad/sec

gain constant

arm spring constant, lb/ft

controller string constant, lb/ft

wrist spring constant, lb/ft

roll rate gain

longitudinal distance, ft

vertical distance, ft

aircraft mass, (lb-sec2)/ft

mass of arm, (lb-sec2)/ft

mass of controller, (lb-sec2)/ft

rolling angular rate, deg/sec

roll acceleration, deg/sec/sec

static atmospheric pressure, lb/ft 2

dynamic pressure, lb/ft 2

impact pressure, lb/ft 2

generalized reference input

yawing angular rate, deg/sec

reference planform area, ft 2

Laplace transform variable, (a + j03 ),

rad/sec

time, sec

true airspeed, ft/sec

weight, lb

weight of the arm, lb

equivalent weight of the arm, lb

weight of the controller, lb

total weight of the controller plus added

weight, lb

total equivalent weight of the arm and

controller, lb

output quantity

arm displacement, ft

transducer displacement, in. and ft

angle of attack, deg

angle of sideslip, deg

control surface deflection, deg

error signal

damping ratio

small change

A@

Ac

_)e

_r

0

(Y

i#c/ Fy

Ai_c/AFyc

CO

(D co

(od

COn

(Or

II

IIdB

arm transfer function denominator

controller transfer function denominator

differential aileron deflection,

(_iaR - _aL )/2, deg

differential elevon deflection,

(_ el ¢ -- _)eL)/2, deg

rudder deflection, deg

pitch altitude, deg

real part of Laplace transform, rad/sec

bank angle, deg

roll rate command gradient, (deg/sec)/lb

roll rate gradient gain, (deg/sec)/lb

frequency, rad/sec

crossover frequency, rad/sec

damped frequency, rad/sec

natural frequency, rad/sec

ratcheting frequency, rad/sec

absolute value

amplitude ratio, dB

Sign Conventions

Trailing edge down is positive for _aL, _aR, _eL,

_ieR. Trailing edge left is positive for 5 r. Accelerations

are positive forward, right, and down. Angles and

rates are positive right wing down, nose up, and nose

right. Angle of attack is positive with the nose (longitudinal axis) above the velocity vector. Angle of sideslip is positive with the nose left of the velocity vector.

Subscripts

@

C

D

i

L

n

o

P

R

arln

controller

damped

wrist interface

left

natural

trim condition

pilot

right

25
T total

X, Y, Z vehicle body axis

x tangential

Dot over quantity denotes first derivative with respect

to time.

Dimensional Coefficients

The dimensional coefficients are defined as follows:

L_ = _x Cll_

N B = clSb C

I z nl_

YB = _-QCy_

_tSb 2

Np = 2---_zCnp

Yp 77Sb C

= 2mV2 Yp

LS_, 8_, 8_ =

Y8_, 8,, 8_ =

+ sin a - sin

qla-_bxC l8 a 6e, 5 r

_z Cnsa . Se, 8 r

"_CY5 a, 8¢ _r

71Sb2

Lr = 2-'-Q_Xg-.'Ir

?lSb 2

N r = 2--_zCnr

?lSb C

Yr = _ Yr-- COS_ = --COS_

26
APPENDIX B

DERIVATIVES AND AIRCRAFT PLANT

FORMULATION

In general, the aircraft lateral-directional aerodynamic derivatives were obtained from either an average

or the mean value of available flight data for a Mach

number near 0.9. 3, 9, 10, 11 Wind-tunnel data were used

in obtaining the control effectiveness of the elevon and

aileron control derivatives. 12

The coefficients listed in equation (B-l) were

obtained with reference to the wind or stability axis.

These coefficients provide the basic aerodynamics for

generating the plant output and the integrated augmented aircraft response.

Clf_ = -0.0016

Cn_ = 0.002

Cy_ = -0.012

Clp = -0.24

Cnp = -0.02

Cyp (Yp = sintx)

Ct_ = 0.10

Cnr = -0.2

CYr = (Yr=-COSO0

Cla,_ = -0.0013

C% = -0.0005

Cys,, = 0.002

Clf e = -0.0011

Cnf e = -0.0007

Cyf = 0.002

Cl_ _ = 0.0003

(B-l)

Cn__ = -0.0006

Cy_ = 0.001

First, it was necessary to translate the coefficients

from the stability to the body axis and then convert to

the dimensional coefficients (eq. (B-2)) using the flight

data and the physical characteristics (table 2).

7?SbC

L_ = -_x tO

N_ = ?TSbc

lz nf_

z_s

Y_ = -_--_Cyg

?lSb 2

Lp = 2--'_xL'lp

ZlSb2

Np = 2---_zCnp

Yp = sin ct

?lSb C

L S a, _ e' 8 r ---- "_X Ira' re' fr

Nsa' Be' 8r --_ _Z bcnSa' re' fir

z_s

YS_, 8_, 8_ = -_--QCy_, Be'_r

?lSb2r ,

L r = 2--_X,.-.lr

?lSb 2

N r = 2--_-zCnr

Yr = -cosCt

(B-2)

Using the state-space notation, the lateral-directional

equations can be arranged initially in a matrix format

as

27
CSc = Ax + Bu

1 0 0 0 YI3 sinct -cosa gcos0 o

0 1 -lxz 0 V°

Ix = Lf_ Lp L r O.

0 - lxz 1 0 Np N r O.

I Z

0 0 0 l 1.0 tan0 0 0.

YSa Y6r Y_e

+ L5 a L8 r L8 e

N8 a NS r N6 e

O. O. O.

y = Hx+G._

1 0 0

= 0 1 0

0 0 1

V V

r -_esin% _ecos%-cos0_

(B-3)

liooo

I_P+ 0 0

-?7

°° Jl J

The plant output quantities (y) as a function of the

input functions (u) can be reduced simply to

.fc = A'x + B'u

y = Hx+Gx

Where the prime indicates premultiplication by C -1,

Sc = A'x + B_u

= Y0.ino Lf_ Lp L r l /LsoLsr L_ e _a

Np N r 0 ! Jl_Jr LNoS.aN_rNo6.eJ 1.0 tan0 o 0 0.

y = nx + Gx (B-4)

The complete computational procedure, including

the axis rotation, is accomplished by using a FORTRAN program developed at the NASA Dryden Flight

Research Center. Numerical values for the matrix coefficients A', B', H, and G at the example flight conditions are presented as equation (B-5).

I

I --.4172 .0523 --.9986 .033i

_ [ "_73° 172 B3.0602 1.2365 0,

L,575 . -0369-4511 1.0 .0524 00.

t

0.071 .0348 .0695-

-54.285 14.267-45.26

-4.152 --4.588 -5.659

0. 0. 0.

(B-5)

n

-1. O. O. O.

O. 1. O. O.

O. O. 1. O.

O. O. O. 1.

0. -1.567 29.92-.99_

a

0. 0. 0. 01

0. 0. 0. 0.

0. 0. 0. 0.

0. 0. 0. 0.

29.93 0. .53 0.

The final linearized numerical matrix coefficients

(eq. (B-5)) are a suitable aerodynamic state-space

representation for integration into the FORTRAN control program. 13 Output-dependent variables of the

aerodynamic plant provide the rates and accelerations

necessary for augmenting the aircraft.

28
APPENDIX C

MINIMUM DISPLACEMENT

CONTROLLER DYNAMICS

The F-16 XL-2 aircraft was constructed with a dual

cockpit during the modification and assembly. Both

crew members are provided with identical two-axes,

pedestal-mounted, minimum displacement controllers

that are located on the right side of the cockpit. The

controller is positioned slightly forward of the center of

gravity of the pilot's body to permit a semi-relaxed arm

position.

In both axes, the controller senses displacement measured through the transducer displaced by force up to a

maximum displacement of _+0.25 in. The transducer is

calibrated in lb. A breakout force of 1 lb is required

before any displacement results. The spring constant up

to the maximum deflection is approximately 960 lb/ft

(fig. C-I).

20

16

F 12

YC'

Ib 8

4

-- /--Breakout

/ force : 1 Ib_ AFy,, -/

M.x,mum 

I 1 I I I I T

.03 .06 .09 .12 .16 .19 .22 .25

Xc, in.

96OO84

Figure C-1. Spring gradient of the minimum displacement controller.

To get some idea of the dynamic response of the controller as a function of mass, extra weights were added

by wrapping lead strips around the controller grip. The

controller, W c, weighs 1.25 lb.

The controller was pulled to maximum deflection

and released. Figure C-2 shows a typical response for a

total weight, W T, of 5.18 lb (W added = 3.93 lb). For

this particular weight and test, the controller exhibited

a damped frequency, cod , of 76.6 rad/sec at a damping

ratio, 4, of 0.09 following the release.

20 m

FYc,

Ib

10--

0--

I I

.2 .4

-10

-2o I I I

0 .6 .8 1.0

Time, sec

960085

Figure C-2. Typical controller response following a

Fyc = 20 lb release: W T = 5.18 lb, period = 0.082 sec,

cod = 76.6 rad/sec, _ = 0.09 and K c = 960 lb/ft.

Figure C-3 shows a summary of this test and two

additional test weight conditions. For the controller

alone (W c = 1.25 lb), the release results in no overshoot. A dashed line is drawn through the damping

ratio data points. A constant value of damping force

(D c = 2.24 (lb-sec)/ft was used to estimate the damping ratio from 5.18 to 9 lb. The solid line on the frequency figure indicates the natural frequency by using

con = JKcg/W T. The two data points were the

damped frequency obtained from the response for the

indicated added total weight.

29
1.0 I Q 0 Musured

--- Estimated

.8

%

.6

%

.4 ', Dcg

,2 %. •

. 1 I I'PI i I t

160

140

120

O)n 100

and 80

rsd/sec 60

40--

20--

Kc = 960 Ib/ft

s W c = 1.25 Ib I i I I I 1 I I

1 2 3 4 5 6 7 8 9

W T ~ Ib 960086

Figure C-3. Controller frequency and damping as a function of total weight, W c + W(added).

30
APPENDIX D

BIOMECHANICAL MODELING AND

MANIPULATION DYNAMICS

The following description, derivations, and modeling

aspects of the "bobweight" effects rely heavily on the

experimental and analytical studies. 10A large vibration

platform was used on which a control operator was

restrained at the seat to the platform. The platform was

subjected to lateral accelerations ranging in frequencies

from 0 to 10 Hz. The operator performed isolated-axisdisplayed control tasks. Two types of center-stick controllers were mounted on the platform: a spring stick

and a stiff stick. These controllers were investigated

throughout the lateral control tests. From these experiments, the most significant modal responses were

derived from the biomechanical nature of the arm/

muscle coupled through the hand/grip interface to the

controller.

Figure D-1 shows a biomechanical model, showing

the lateral forces and accelerations, and a mathematical

description of the dynamic elements. 10 The directions

of the forces, accelerations, and displacements are

defined as positive to the right. Consider a minimum

displacement controller, K c = 960 lb/ft, with aircraft

accelerations measured in g and the mass properties

defined in terms of equivalent or effective weights

(fig. D-1). The forces and elements can be summed and

resolved as two equations with two unknowns, x c and

X@.

[m cS2 + (D i + D c)s + K i+ K c]X c

- (Dis + Ki)x @ = Wc(-ay)

(D-l)

or

- (Dis + Ki)x c

+ [m@s 2 + (D i + D@)s + K i + K@]x@

= W@(e)(-ay) + Fye

(D-2)

[A c + (Dis + Ki)]x c - (Dis + Ki)x @

= Wc(-av)

(D-3)

- (Dis + Ki)x c + [A@ + (Dis + Ki)]x @

= W@(e)(-ay) + Fyp

(D-4)

where

Airframe

""

KC y Transducer L_

__ Xc Vertlcal controller or Stick

plane r/ /-- Hand/control

Controller I I / grip interface

characteristics U KI / characteristics

r., __Oi/_. x(_:) _Grip

r _ Xc Fyp

r ./ Fy c /

f #

! r / K_ Arm/muscle _ Limb

Horizontal / Lateral _ ay _ W(_) i characteristics

'_acceleration_' _ _ D(_) I

plane NI ,'/I I¢" I Lj /

Semi'restrained1 -_ Body

/I Illl | shoulder "1

,, uuI..nd;or;o.

960087

Figure D-1. Feedthrough mechanical controller model with lateral force and acceleration input.l°

31
Ac = mcS2 + DcS + K c

A@ = m@s 2 + D@s + K@

m c = Wc/g

m@ = W@(e)/g

Solving equations (D-3) and (D-4) for x@ and combining gives the following equation for the biodynamics:

xc - (D-5)

-a Yx

Fyp (Dis + Ki)/-ayx + (Dis + Ki)(W@(e ) + Wc) + A@ W c

(Dis + Ki)(A@ + Ac) + A@A c

However, A c is much larger than A@; therefore,

A@ + Ac - Ac . For the lower frequency range of interest, o_< 30 rad/sec, A c can be approximated by the

controller spring constant, K c . Equation (D-6) then

becomes (for a positive a y) as follows:

X c

m

a y,

Fyr(Dis + Ki)/ay_

Kc[(Dis + Ki) + A@]

(Dis + Ki)(W@(e) + W c)

Kc[(Dis + Ki) + A@]

A@ W c

B

Kc[(Dis + Ki) + A@]

(D-6)

Equation (D-6) can be represented as a feedthrough

system with tangential acceleration a y_ at the controller as the input and Fyc as the output (fig. D-2).

For simplification, the initial and end blocks can be

AFyc

thought of as unity where K c = Ax---_"(fig. (C-1)).

The feedback block, Dis + Ki/(Dis + K i) + A@,

can be further moved to the forward loop and simplified to a block diagram with Fye and art as the inputs

and Fro as the output or input to the roll command

gradient (fig. (D-3)).

Fy. 

Iw .,.wol

[

(DIS + KI) + A(_

96OO83

Figure D-3. Equivalent representation of figure (D-2)

with pilot input.

Measured values for the coefficients and gains were

determined from vibration tests as (ref. 10)

K@ = 9.46 lb/fl

K i = 24.26 Ib/ft

D@ = 0.61 (lb-sec)/ft

D i = 2.09 (lb-sec)/ft

K i

- 0.72

K@ + K i

K@ - 0.28

K@ + K i

(D-7)

+ + _t__ + ___FYc

II

i ( aY z

960082

Figure D-2. Representation of equation (D-6).

The equivalent weight for the controller is

The dynamic

W c = 1.25 lb (D-8)

response of the controller was

approximated by the spring constant, K¢ = 960 lb/ft.

The measured dynamic characteristics are presented in

appendix C.

32
APPENDIX E

DUAL LAG EQUIVALENT TRANSFER

FUNCTION

All F-16 aircraft have a unique feedback system

device in the forward command path referred to as a

dual lag. This device provides for a softer roll-in and a

sharper rollout command, thereby minimizing the tendency to overshoot. Figure E-1 shows the analog system as excerpted from the functional block diagram 14

describing the roll system of the F- 16 XL airplane.

A bias of _+_20deg/sec exists on the feedback C.

Hence, any output within that range would be derived

simply by computing CO = lORI/(s + 10). For outputs greater than +20 deg/sec, the output would be

modified by the feedback functions to the extent of the

output exceeding the bias.

® ®

® ®

_-- 20 deg/sec

CO

4.

÷

20 deg/sec

96OO88

Figure E-1. The nonlinear dual-lag system.

The commanded roll rate and bias become important

considerations as noted with reference to the roll ratcheting experienced, described, and analyzed in this

report (fig. 5 and 6). The oscillation is initially biased at

an offset near --60 deg/sec. In addition, the oscillation

varies +10 deg/sec about the offset at the ratcheting

frequency near 16.4 rad/sec. For one-half cycle, where

(CO + ACO) < -60 deg/sec, the output/input would be

as follows:

CO] 1 10(s + 20)

-_-_1 _ cycle = (s + 3)(s + 67) (E-I)

Because the diode ® is downstream of the washout,

for the rest of the cycle and for (CO + ACO) > -60

deg/sec, the response would be as follows:

[co]_ lO

-_-]_ cycle - (s + 10) (E-2)

Consequently, for sinusoidal inputs, a piecewise

description of the output would be required. However,

to avoid employing the complexity of using describing

functions, which would result in a derivation as a function of frequency and amplitude, a linear compromise

was considered sufficient for determining the amplitude and phase. Figure E-2 shows this compromise

with just the asymptotes depicting the transfer

functions.

The two dashed lines, as indicated, represent the two

transfer functions 10/(s + 10) and 10(s + 20)/(s + 3)

(s+67). The solid line represents the linear

compromise:

CO _ 10(s + 40) (E-3)

RI (s + 6)(s + 67)

At the ratcheting frequency, 16.4 rad/sec, this function will give a linear amplitude ratio of 0.358 and a

phase angle of -61.33 ° . The actual amplitude ratio is

pointed out by the asterisk. The amplitude ratios of the

two other functions are indicated by the small circles at

the ratcheting frequency.

33
I IdB

10

-10

- 20

-3O

- 4O

(_) ActuaITFamplitude

ratio at (o r

10 (s + 2 "_/" "- "(_-. ,, /-- 10

(s+3)(,+67)-- -. /",_'./ (s+lO)

Equivalent TF / • ,. _ _ " ,,

Io(,+4o) __/ ". _ "-.

(s + 6) (s + 67) (Or

10 100

(o, - rad/sec

960O89

Figure E-2. Asymptotic approximations of the dual-lag transfer functions.

34
REFERENCES

1Bailey, R. E. And Knotts, L. H., Interaction of Feel

System and Flight Control Dynamics on Lateral Flying

Qualities, NASA CR-179445, 1990.

2Hall, G. Warren and Smith, Rogers E., Flight Investigation of Fighter Side-Stick Force-Deflection Characteristics, AFFDL-TR-75-39, May 1975.

3Scofield, Jan W., Scott, Sheryl R., and Thomas,

Edwin A., F16XL Phase I Flying Qualities Evaluation,

AFFTC-TR-83-26, Sep. 1983.

4Monagan, Stephen J., Smith, Rogers E., and Bailey,

Randall E., Lateral Flying Qualities of Highly

Augmented Fighter Aircraft, AFWAL-TR-81-3171,

vol. I, Mar. 1982.

5Chalk, C. R., "Excessive Roll Damping Can Cause

Roll Ratchet," Journal of Guidance, Control and

Dynamics, vol. 6, May-June 1983, pp. 218-219.

6McRuer, D. T. and Magdaleno, R. E., Human Pilot

Dynamics With Various Manipulators, AFFDL-TR-66-

138, Dec. 1966.

7Johnston, Donald E. and Aponso, Bimal L., Design

Considerations of Manipulator and Feel System Characteristics in Roll Tracking, NASA CR-4111, 1988.

8Magdaleno, R. E. and McRuer, D. T., Experimental

Validation and Analytical Elaboration for Models of

the Pilot's Neuromuscular Subsystem in Tracking

Tasks, NASA CR-1757, 1971.

9Johnston, D. E. and McRuer D. T., Investigation of

Interactions Between Limb-Manipulator Dynamics

and Effective Vehicle Roll Control Characteristics,

NASA CR-3983, 1986.

10Allen, R. Wade, Jex, Henry R., and Magdaleno,

Raymond E., Manual Control Performance and

Dynamic Response During Sinusoidal Vibration, STI

TR-1013-2, Oct. 1973.

11Tiemey, Shery! S. and Thomas, Edwin A., F-16XL

Follow-On Development Flying Qualities Evaluation,

AFFTC-TR-85-31, Nov. 1985.

12Humphries, John A. and Caughlin, Donald J.,

F-16XL Flying Qualities With the Large Normal Shock

Inlet, AFFTC-TR-85-34, Feb. 1986.

13Loman, R. B., Wilson, J. W., and Johnson, S. D.,

F-16XL Stability and Control Flight Test Report,

400PR106, Addendum I, Dec. 1985.

14von Bose, D. R., Tierney, P. K., and Wilson, J. W.,

F-16XL Stability and Control Data Substantiation

Report, 400PR050, May 1982.

15Edwards, John W., A FORTRAN Program for the

Analysis of Linear Continuous and Sampled-Data Systems, NASA TM-X-56038, 1976.

16Forgey, D. H., Wilde, W. C., and Weis, N. N.,

F-16XL Flight Control System Description Report,

400PR042, Dec. 1985.

17Krogman, Wilton Marion and Johnston, Francis E.,

Human Mechanics: Four Monographs Abridged,

AMRL-TDR-63-123, Dec. 1963.

35
REPORT DOCUMENTATION PAGE FormApproved

OMB NO. 0704-0188

Public reporting burden for this collect=on o/;_,;uf,,,at_on is estimated to e_raga 1 hour per response, including the time for revmwing instructK)ns, searching existing data sources,

gathering and maintaining the data needed, and completing and reviewing the collection o! information. Send comments regarding this burden estimate or any other aspect of this collectK)n of information, including suggestions for reducing this burden, to Washington Heedcluarters Servmes, Directorate for Information Operations and Reports. 1215 Jefferson Davis

Highway, Suite 1204. Arlington. VA 222024302. and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, De 20503

1. AGENCY USE ONLY (Lc,_vi b;,,.k) 2. REPORT DATE 3. REPOFrr TYPtE AND DATES COVERED

July 1996 Technical Memorandum

4.TITLE AND StJDI,o-E 5. FUNDING NUMBERS

Biomechanically Induced and Controller Coupled Oscillations Experienced

on the F-16XL Aircraft During Rolling Maneuvers

s. _aJ'rHoR(s)

John W. Smith and Terry Montgomery

7, #F-_FORMING ORGANIZATION NAME(S) AND ADDRESStES)

NASA Dryden Flight Research Center

P.O. Box 273

Edwards, California 93523-0273

IL SPONSORING/MONOTORING AGENCY NAME(S) AND ADDRESStES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

11. SUPPLEM_._I'ARY Nut,S

WU 505-68

8. PERFORMING ORGANIZATION

REPORT NUMBER

H-2031

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM-4752

1211. DiSTHiBUTION/AVAILABILITY STATEMENT

Unclassified--Unlimited

Subject Category 08

12b. DISTRIBUTION CODE

13. ASS I HACT (Maximum 200 _s)

During rapid rolling maneuvers, the F-16 XL aircraft exhibits a 2.5 Hz lightly damped roll oscillation, perceived and described as "roll ratcheting." This phenomenon is common with fly-by-wire control systems, particularly when primary control is derived through a pedestal-mounted sidearm controller. Analytical studies

have been conducted to model the nature of the integrated control characteristics. The analytical results complement the flight observations. A three-degree-of-freedom linearized set of aerodynamic matrices was assembled

to simulate the aircraft plant. The lateral-directional control system was modeled as a linear system. A combination of two second-order transfer functions was derived to couple the lateral acceleration feedthrough effect

of the operator's arm and controller to the roll stick force input. From the combined systems, open-loop frequency responses and a time history were derived, describing and predicting an analogous in-flight situation.

This report describes the primary control, aircraft angular rate, and position time responses of the F-16 XL-2

aircraft during subsonic and high-dynamic-pressure rolling maneuvers. The analytical description of the pilot's

arm and controller can be applied to other aircraft or simulations to assess roll ratcheting susceptibility.

14. SUBJECTTERMS

Biomechanics; F-16XL airplane; Flying qualities; Handling qualities; Human factors;

Pilot induced oscillations; Roll control; Roll ratcheting

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION lg. SECURITY CLASSIFICATION

OF REPORT OF THIS PAGE OF ABSTRACT

Unclassified Unclassified Unclassified

NSN 7540-01-280.5500 Available from the NASA Center for AeroSpace Information, 800 Elkridge Landing Road,

Linthicum Heights, MD 21090; (301)621-0390

! 15. NUMBER OF PAGES

38

16. PRICE CODE

AO3

20. LIMITATION OF ABSTRACT

Unlimited

Standard Form 298 (Rev. 2-89)

PfelK:rlbedby ANSI Std Z39-18

298-102