Reconfigurable Control Design for the Full 

X-33 Flight Envelope

M. Christopher Cotting and John J. Burken

NASA Dryden Flight Research Center 

Edwards, California

August 2001
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Reconfigurable Control Design for the Full 

X-33 Flight Envelope

M. Christopher Cotting and John J. Burken

NASA Dryden Flight Research Center 

Edwards, California

August 2001

National Aeronautics and

Space Administration

Dryden Flight Research Center

Edwards, California 93523-0273
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AIAA-2001-4379

RECONFIGURABLE CONTROL DESIGN FOR THE FULL 

X-33 FLIGHT ENVELOPE

M. Christopher Cotting* and John J. Burken†

NASA Dryden Flight Research Center

Edwards, California

Abstract

A reconfigurable control law for the full X-33 flight

envelope has been designed to accommodate a failed

control surface and redistribute the control effort among

the remaining working surfaces to retain satisfactory

stability and performance. An offline nonlinear

constrained optimization approach has been used for the

X-33 reconfigurable control design method. Using a

nonlinear, six-degree-of-freedom simulation, three

example failures are evaluated: ascent with a left body

flap jammed at maximum deflection; entry with a right

inboard elevon jammed at maximum deflection; and

landing with a left rudder jammed at maximum

deflection. Failure detection and identification are

accomplished in the actuator controller. Failure response

comparisons between the nominal control mixer and the

reconfigurable control subsystem (mixer) show the

benefits of reconfiguration. Single aerosurface jamming

failures are considered. The cases evaluated are

representative of the study conducted to prove the

adequate and safe performance of the reconfigurable

control mixer throughout the full flight envelope. The

X-33 flight control system incorporates reconfigurable

flight control in the existing baseline system.

Nomenclature

BFGS Broyden, Fletcher, Goldfarb and Shanno

EMA electromechanical actuator

G Hessian inverse (maps differences in 

position into differences in gradient)

H Hessian matrix

k iteration

ONCO offline nonlinear constrained optimization

dynamic pressure, lbf/ft2

Qalpha longitudinal aerodynamic loading 

parameter, ∗α

Qbeta directional aerodynamic loading parameter, 

∗β

RCS reaction control system

TAEM terminal area energy management

x tunable mixer gains

x vector

angle of attack, deg

angle of sideslip, deg

change in gradients

difference between two points on quadratic 

function

first partial derivative or gradient vector

Introduction 

Aircraft flight control systems are designed with

extensive redundancy to ensure sufficient failure

mitigation. Hydraulically powered actuators have been

used for the past 60 years and currently have a very low

probability of failure. The X-33 vehicle (fig. 1),

however, was designed to use one or more two-channel

electromechanical actuators (EMAs) to power all the

primary flight control surfaces. 

The X-33 fault tree analysis indicates that EMAs are

more likely to fail than hydraulic actuators; however, the

advantages of using EMAs for vehicles like the X-33

vehicle outweigh the disadvantages. For example, power

lines are easier to route than hydraulic lines, although

q

q

q
2

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the weight is approximately the same. Analysis also has

shown a few unlikely single-failure modes for the

EMAs, failures that most likely would result in jamming

of the associated aerosurface (the inability to move a

control surface from a position).

The baseline X-33 flight control system contains

control reconfiguration because the vehicle has low

control effector redundancy compared to other aircraft.

The primary motivation for pursuing reconfigurable

control for this vehicle has been to improve use of

functioning control effectors in the event of an effector

failure. Because the EMAs are relatively unproven

compared to modern hydromechanical actuators, the

reconfigurable control mixer was designed to allow the

vehicle to continue to operate in the event of an actuator

failure. Although arguments could be made that this

level of redundancy is not needed for an experimental

aircraft, the X-33 vehicle would have been a technology

demonstrator test bed to prove concepts for a

subsequent single-stage-to-orbit, heavy-lift vehicle. 

In designing the reconfigurable control system,

control surface jamming failures were assumed in each

of the eight aerosurfaces. Engine thrust vectoring and

reaction control system (RCS) thrusters, which are part

of the primary flight control system and enabled through

the nominal control system mixer, are not part of the

reconfigurable control system mixer and are not

discussed.

Reference 1 presents results of four reconfigurable

trade studies investigated on the X-33 entry flight phase

(from Mach 9 decreasing to Mach 3) and concludes that

an offline nonlinear constrained optimization (ONCO)

method should be used for the reconfiguration method.

Preliminary results of the offline method for portions of

the flight envelope also have been published.1

This report investigates the full X-33 flight envelope

and details the nonlinear simulation results discovered

in the final design of the reconfigurable flight control

mixer for the X-33 vehicle. Three specific cases are

evaluated in this report: a full-deflection body flap

jamming failure during the ascent phase of flight, a

full-deflection elevon jamming failure during the entry

phase, and a full-deflection rudder jamming failure

during the landing phase. 

Note that use of trade names or names of

manufacturers in this document does not constitute an

official endorsement of such products or manufacturers,

either expressed or implied, by the National Aeronautics

and Space Administration.

X-33 Vehicle Description

The X-33 vehicle is a subscale, suborbital

experimental vehicle designed to be a technology

demonstrator for a single-stage-to-orbit, heavy-lift

vehicle. The X-33 vehicle has four sets of aerosurfaces:

rudders, body flaps, and inboard and outboard elevons

(fig. 1). The X-33 vehicle was designed to use an

aerospike engine, which allows for pitch and roll thrust

vectoring as well as differential thrust yaw control. The

X-33 vehicle also was designed to use RCS thrusters for

added vehicle control during unpowered flight.

Nominal Control Description

Three major phases were to be encountered during the

flight of the X-33 vehicle. The ascent phase would have

begun at ignition of the main engines and continued

until “main engine cutoff.” This region of flight would

have contained augmented control by engine thrust

vectoring and would have been the only stable region of

the flight envelope. Command during this phase of flight

would have been accomplished using an Euler angle

controller. Longitudinal and directional aerodynamic

loading parameters were considered in control design to

ensure structural integrity during this phase of flight.

After main engine cutoff, the entry phase of flight

would have begun. This phase of flight would have

exhibited the worst region of instability for the vehicle,

especially in the low-angle-of-attack regions. The RCS

would have been used for augmented control in areas of

Figure 1. X-33 vehicle and aerosurfaces.
3

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low dynamic pressure in this region of flight. Control

during this phase would have been accomplished using

an aerodynamic angle control scheme. 

The terminal area energy management (TAEM)

phase, also considered the landing phase, would have

begun when the vehicle had slowed to Mach 3. This

region of flight also would have exhibited areas of

instability and been controlled by an acceleration

command controller. The X-33 vehicle was designed to

use EMAs to power all the primary flight control

surfaces. The X-33 vehicle also was designed to be

controlled through a triplex fly-by-wire flight control

system operating at 50 samples/sec.

 Figure 2 shows a simulated nominal X-33 trajectory.

The three flight phases are shown with ascent lasting

240 sec, entry lasting 260 sec, and TAEM lasting

265 sec. The vehicle reaches a maximum speed of

Mach 9 and an altitude of 210,000 ft. Dynamic pressure

changes from a maximum of 210 lbf/ft2 at 105 sec to

approximately 7 lbf/ft2 at 300 sec.

Figure 2. X-33 nominal trajectory.

Reconfigurable Control Design

The four reconfigurable control design methods

investigated for the X-33 vehicle were the redistributed

pseudo-inverse; general constrained optimization;

automated failure-dependent gain schedule; and the

offline, or predefined, nonlinear constrained

optimization methods.2 The ONCO approach was

chosen for implementation. The ONCO method and

preliminary results of this approach implemented in a

six-degree-of-freedom simulation are discussed next

and in reference 1. The ONCO method was chosen

because it could be easily tested and validated. The

X-33 vehicle has “smart actuators” that identify the

surface that failed and the last known position of the

failed surface. The failure could be a floating surface, a

jammed surface, or a surface “hardover.” Knowledge of

the actuator state simplifies reconfiguration because

fault detection and isolation is not needed as part of the

primary flight controller.

Offline Nonlinear Constrained Optimization 

With prior knowledge of the failure assumed, a table

lookup of the failure to determine the controller changes

meets the requirements of reconfiguration and is an

approach that could be easily implemented. A table

lookup of the gains has the added advantage of being

easily tested in the validation and verification process

required before the first vehicle flight. Therefore, an

offline method of reconfiguration was decided to have

the best chance of success for the X-33 flight program,

and the ONCO method was chosen. 

Figure 3 shows the control block diagram for the

entry phase of X-33 flight. For this ONCO type of

reconfiguration, the mixer is modified. Figures 4 and 5

show the nominal entry and reconfigurable mixers,

respectively. The reconfigurable control mixer has more

interconnect gains than the nominal control mixer. The

roll command is sent to all the remaining actuators

through a set of gains; whereas with the nominal mixer,

the roll command is sent only to the elevons. The

procedure of increasing interconnects was duplicated

for the pitch and yaw commands. When a failure occurs,

the nominal mixer is disabled and the reconfigurable

mixer is brought online within 280 msec of the failure.

This procedure of using or changing the mixer to

accommodate the failure is repeated for the ascent and

TAEM control phases.

Figure 3. X-33 entry flight control.
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Figure 4. Nominal entry control mixer.

Figure 5. Reconfigurable control entry control mixer.
5

American Institute of Aeronautics and Astronautics

The mixer gains were determined beforehand (offline)

using a sequential quadratic programming method. This

quasiNewton method is solved for each iteration of the

quadratic programming problem and updates an

estimate of the Hessian of the Lagrangian using a

formula known as the BFGS formula because it was

suggested by Broyden, Fletcher, Goldfarb and Shanno.3

Equation (1) shows the constrained nonlinear

optimization:

(1)

If is twice differentiable, then a matrix of second

partial derivatives or Hessian matrix exists; where is

the tunable mixer gains, and

where is a positive semidefinite matrix and .

The is approximated by a symmetric

positive definite matrix . The expression shown in

equation (2) is sometimes called the quasiNewton

condition.3, 4

(2)

An important relationship suggested by Broyden,

Fletcher, Goldfarb and Shanno is known as the BFGS

formula: 4

(3)

The ONCO method optimizes a time-domain

response. Using equation (3) to constrain the timedomain errors and allowing the gains shown in figure 5

to be the tunable parameters (gains in the mixer), a

series of closed-loop offline simulations are run. After a

simulation run (usually a step-command response), the

errors between the commanded and the actual response

are summed and a new simulation trial is run with the

modified gain set. The modified gain set is the result of

using equation (3) to find a constrained optimal

reduction in the summed error. 

The simulation commands were a combination of roll

and pitch steps in which the size of the roll command

was 20° and the size of the pitch command was 2°. The

sizes of the roll and pitch commands were found to be

large enough to stress the algorithm optimization. A

stressed algorithm occurs when a control surface

rate-limits or surface position saturates. At this

condition, the control surface enters into a nonlinear

region. Simultaneously executing a pitch and roll

command was necessary to couple the dynamics.

Optimization based on the BFGS formula was found

to work satisfactorily for the X-33 reconfigurable

control law design. The limitations of the sequential

quadratic programming method are that the function to

be minimized and the constraints must be continuous,

and the method might give only local solutions. The

controls tool package used for the reconfiguration

development is a well-known control tool set.5 The

interested reader is recommended to see the

proportional, integral, differential demonstration

included in nonlinear control design blockset for use

with the Matlab® Simulink® (MathWorks Inc., Natick,

Massachusetts) package.5

Results and Conclusions Using a Nonlinear 

Simulation

The initial mixer gains were implemented in a sixdegree-of-freedom simulation. During initial testing of

the reconfigured mixer gains, some rate limiting and

position saturation of the actuators were observed. The

gains were determined to be too large because of

differences between the linear models and the nonlinear

simulation. Using empirical methods, the gains were

reduced, which resulted in very good six-degree-offreedom results. 

Later in the program, improved linear models were

developed that very closely matched the nonlinear sixdegree-of-freedom simulation, so the gain reductions

were not needed. Special attention to the linear models

is extremely important in the design of the controller,

especially in gain development. Examples are presented

to show that control reconfiguration addresses three

different failures in three different flight phases.

Ascent Phase

The ascent controller is a Euler command tracking

system.6 During the ascent phase, attitude control is

provided by rocket engine thrust-vector control and the

aerosurfaces. When a control surface is jammed, all the

remaining operational control surfaces are used for

control in conjunction with the thrust-vector control.

Figure 6(a) shows the response for the nominal and

reconfigurable control systems of the vehicle with a

worst-case hardover left body flap jamming at 25°

Minimum xf (x) subject to G(x) 0

f (x)

x

G(x)

2

= f (x)

G H G

–1

G

(k)

–1

H

(k)

H

(k + 1) (k) (k)

=

H BFGS

(k + 1) H 1

T

H

T

+ -------------

δδ

T

T

--------

δγ

T

H Hγδ

T

+

T

= + – ---------------------------------
6

American Institute of Aeronautics and Astronautics

20 sec after lift-off. The time history shows the nominal

controller with the failed surface held the pitch angle

error to within 5° in the longitudinal axis. With the

reconfigurable controller, pitch angle error was reduced

to 2°. Figure 6(b) shows the lateral axis response to the

left body flap failure. Bank angle was controlled to

within 8° with the nominal controller and to within 3°

with the reconfigurable control system. 

(a) Pitch attitude.

(b) Roll attitude.

During the ascent phase of flight, the aerodynamic

loads on the aircraft must be kept to a minimum so that

the structural integrity is not jeopardized. Two of the

design parameters used for structural load minimization

are the longitudinal and directional aerodynamic

loading parameters, Qalpha and Qbeta. For the

directional axis, if the angle of sideslip, , is close to

0°, then the side loads (Qbeta) will not be a structural

problem. Figure 6(c) shows times histories of Qalpha

and Qbeta for the failed ascent case with both nominal

and reconfigurable control mixers. The results show that

a reduction in aerodynamic loads will occur if

reconfigurable controls are used.

(c) Aero load indicator.

Figure 6. Ascent time responses.

Figure 6(d) shows plots of the control effectors

(surface positions) from the nominal and reconfigurable

mixer simulation flights. When the left body flap was

jammed at 25° (down), the nominal controller did fully

compensate for this reaction using thrust vectoring

available from the engine. The reconfigurable mixer,

however, did result in lower Qalpha and Qbeta.

The body flaps are the most effective aerodynamic

surfaces on the X-33 vehicle but are the most difficult to

reconfigure in the event of a failure. Overall ascent

results show that the nominal controller can handle any

aerosurface failure; however, the reconfigurable

controller holds the vehicle closer to the desired flight

trajectory.

Entry Phase

The entry controller is an angle-of-attack command

tracking system for the longitudinal axis and a bank

command system for the lateral axis. The entry control

system has aerosurfaces and eight RCS jets (the thrust

from each RCS jet is 500 lbf) for control effectors.

Approximately 10 sec into the entry phase, the right

inboard elevon was failed to 25° (fig. 7(a)). A minor
7

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transient appeared for this case because of the low value

of dynamic pressure that was present at the time of

failure. The nominal mixer maintained control of the

vehicle for approximately 70 sec before the vehicle

departed in the lateral-directional axis (fig. 7(b)). A few

seconds later, the vehicle also departed longitudinally.

For the same failure, the reconfigured mixer was able to

follow the commands for the entire entry flight phase.

(a) Angle of attack.

(b) Lateral-directional.

Figure 7. Entry time responses.

Figure 7(c) shows plots of the control effectors

(surface positions) from the two simulated flights. When

the right inboard elevon was jammed at 25° (down), the

left inboard nominal controller did not fully compensate

for this reaction; and as a result, the vehicle departed.

The departure was not immediate because of nominal

controller compensation with RCS control effectors.

(d) Control surface.

Figure 6. Concluded.
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However, figure 6(c) also shows the reconfigurable

controller compensated for the right inboard elevon

jamming by commanding the left inboard elevon to 23°.

The reconfigurable controller uses elevons, flaps, and

rudders to control the vehicle and achieve the desired

tracking commands from guidance. As figure 7 shows,

reconfigurable controls allow the vehicle to continue on

the desired trajectory to a safe entry conclusion

(Mach 3).

Terminal Area Energy Management Phase

The TAEM phase controller has a normal acceleration

command system for the longitudinal axis and a bank

command system for the lateral axis. The TAEM control

system uses aerosurfaces and RCS jets until the vehicle

reaches a speed of Mach 2.

Approximately 20 sec into the TAEM flight phase, the

left rudder was jammed at −30° (trailing-edge right). A

rudder failure was chosen for this case because of the

“heading alignment cone” maneuver that was performed

during this phase and the corresponding turn

coordination difficulties encountered with a 270-deg

turn. 

Figure 8(a) shows the nominal TAEM controller

normal acceleration and angle-of-attack time histories

depart before 40 sec have elapsed. The corresponding

lateral axis results present a departure in at 50 sec for

the nominal controller (fig. 8(b)). Figure 8(c) shows the

longitudinal and lateral ground track. The nominal

controller cannot execute the turn. The reconfigurable

controller, however, continues down to a survivable

landing. 

The reconfigurable controller executed a successful

landing with a sink rate of 7 ft/sec (fig. 7(c)). Desired

sink rate landing criterion for this vehicle is 5 ft/sec,

with an acceptable sink rate not to exceed 10 ft/sec.

Although landing performance was not desired, it did

fall within acceptable parameters; and unlike the

nominal controller, it did allow the aircraft to land safely

with an aerodynamic surface failure.

Figure 8(d) shows plots of the control effectors

(surface positions) from the nominal and reconfigurable

mixer simulation flights. When the left rudder was

jammed at −30° (right), the nominal controller did not

fully compensate for this reaction. The reconfigurable

controller did allow for a landing of the vehicle within

acceptable parameters. 

(c) Control surface.

Figure 7. Concluded.
9

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(a) Normal acceleration and angle of attack. (b) Lateral-directional.

(c) Landing criteria.

Figure 8. TAEM time responses.
10

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Full Flight Envelope Results

During the ascent phase, the nominal and

reconfigurable controller worked well. The

reconfigurable controller had lower aerodynamic loads

than the nominal controller during ascent. Table 1 shows

the X-33 failure accommodation. The ascent

reconfigurable phase was successful for all surface

failures at speeds from Mach 0 to Mach 9. The entry

phase, however, had a different outcome. The

reconfigurable controller could handle all elevon failures

for all Mach numbers. The body flap was the limiting

factor in the entry phase of flight. The reconfigurable

controller could handle only body flap jams between –3°

and 5° and a limited range from Mach 3 to Mach 5.2.

The rudders were fully reconfigurable for the entire

entry envelope. The TAEM phase also was limited in

scope. The elevons and rudders could fail at any position

during TAEM and land safely. The body flap, however,

was limited from –3° to 5°.

(d) Control surface.

Figure 8. Concluded.

Table 1. X-33 surface failure accommodation.

Phase

Surface Ascent Entry TAEM

Elevons All Mach numbers (Mach 0–9);

all surface positions

All Mach numbers (Mach 9–3);

all surface positions

All Mach numbers (Mach 3–0);

all surface positions

Body flap All Mach numbers (Mach 0–9);

all surface positions

Limited surface positions;

Mach 3.0–5.2

flap deflection −3°–5°

Limited surface positions;

Mach 0–2.5

flap deflection −3°–5°

Rudders All Mach numbers (Mach 0–9);

all surface positions

All Mach numbers (Mach 9–3);

all surface positions

All Mach numbers (Mach 3–0);

all surface positions
11

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Concluding Remarks

A reconfigurable control system was designed and

implemented in a nonlinear, six-degree-of-freedom

simulation for the X-33 vehicle. After significant

testing, this system was determined to be a viable option

to improve reliability concerns about a new actuator

subsystem for the vehicle. Because of these concerns

with the actuator subsystem, the reconfiguration design

scope was limited to only control surface failures. The

offline nonlinear constrained optimization approach was

shown to be an adequate design methodology after

testing this algorithm with many failure scenarios. The

three failure examples presented (a left body flap during

ascent, an inboard elevon during entry, and a rudder

during landing) are examples from a much larger test

matrix conducted to prove system viability. The overall

design effort showed that certain control failures were

much easier to accommodate than others. 

Based on the results of the fully nonlinear simulator

work, the project determined that the control

reconfiguration system should be included onboard the

X-33 vehicle. The X-33 vehicle would have been the

first non–controls-research vehicle to incorporate

reconfigurable flight control in the baseline control

system. 

References

1Wagner, Elaine A., John J. Burken, Curtis E. Hanson,

and Jerry M. Wohletz, “Deterministic Reconfigurable

Control Design For the X-33 Vehicle,” AIAA-98-4413,

Aug. 1999.

2Virnig, John C. and David S. Bodden, “Multivariable

Control Allocation and Control Law Conditioning When

Control Effectors Limit,” AIAA-94-3609, Aug. 1994.

3Fletcher, R. and M. J. D. Powell, “A Rapidly

Convergent Descent Method for Minimization,” The

Complete Journal, vol. 6, no. 2, July 1963, pp. 163–168.

4Fletcher, R., Practical Methods of Optimization:

Volume 1, Unconstrained Optimization, John Wiley &

Sons, Chichester, 1980.

5Nonlinear Control Design Blockset, The MathWorks

Inc., Natick, Mass., 1997.

6Hall, Charles E., Michael W. Gallaher, Neal E.

Hendrix, “X-33 Attitude Control System Design for

Ascent, Transition, and Entry Flight Regimes,”

AIAA-98-4411, Aug. 1998.
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298-102

Reconfigurable Control Design for the Full X-33 Flight Envelope

WU 715-33-02-E8-23-00-T19

M. Christopher Cotting and John J. Burken

NASA Dryden Flight Research Center

P.O. Box 273

Edwards, California 93523-0273

H-2458

National Aeronautics and Space Administration

Washington, DC 20546-0001 NASA/TM-2001-210396

A reconfigurable control law for the full X-33 flight envelope has been designed to accommodate a failed control surface

and redistribute the control effort among the remaining working surfaces to retain satisfactory stability and performance.

An offline nonlinear constrained optimization approach has been used for the X-33 reconfigurable control design method.

Using a nonlinear, six-degree-of-freedom simulation, three example failures are evaluated: ascent with a left body flap

jammed at maximum deflection; entry with a right inboard elevon jammed at maximum deflection; and landing with a left

rudder jammed at maximum deflection. Failure detection and identification are accomplished in the actuator controller.

Failure response comparisons between the nominal control mixer and the reconfigurable control subsystem (mixer) show

the benefits of reconfiguration. Single aerosurface jamming failures are considered. The cases evaluated are representative

of the study conducted to prove the adequate and safe performance of the reconfigurable control mixer throughout the full

flight envelope. The X-33 flight control system incorporates reconfigurable flight control in the existing baseline system.

Control System Reconfiguration, Emergency Backup System, Reusable Launch

Vehicles, X-33 Flight Control A03

11

Unclassified Unclassified Unclassified Unlimited

August 2001 Technical Memorandum

Presented at AIAA Guidance, Navigation & Control Conference, Montreal, Quebec, Canada, August 6–10,

2001, AIAA-2001-4379.

Unclassified—Unlimited

Subject Category 08

This report is available at http://www.dfrc.nasa.gov/DTRS/