A design procedure for the handling qualities optimization of the X-29A aircraft

NASA Technical Memorandum 4142

A Design Procedure for the

Handling Qualities Optimization

of the X-29A Aircraft

John T. Bosworth and Timothy H. Cox Ames Research Center Dryden Flight Research Facility Edwards, California National Aeronautics and Space Administration Office of Management Scientific and Technical Information Division A DESIGN PROCEDURE FOR THE HANDLING QUALITIES OPTIMIZATION OF THE X-29A AIRCRAFT John T. Bosworth* and Timothy H. Cox NASA Ames Research Center Dryden Flight Research Facility Edwards, Califomia Abstract compensated normal acceleration _'Z c pitch rate, deg/sec q A design technique for handling qualities improve- compensated pitch rate feedback qc ment was developed for the X-29A aircraft. As with 8 Laplace transform variable any new aircraft, the X-29A control law designers T sampling interval, sec were presented with a relatively high degree of uncer- samples per second sps tainty in their mathematical models. The presence of total feedback Yt uncertainties, and the high level of static instability of compensated total feedback Yt¢ the X-29A caused the control law designers to stress discrete transform variable z stability and robustness over handling qualities. Dur- ZOH zero order hold ing flight test, the mathematical models of the vehicle 6c canard surface deflection, deg were validated or corrected to match the vehicle dy- compensated canard position feedback namic behavior. The updated models were then used canard surface rate, deg/sec to fine tune the control system to provide fighter-like 5p longitudinal stick deflection, in.

handling characteristics. A design methodology was compensated pilot longitudinal stick input developed which works within the existing control sys- zero for the Neal-Smith compensator tem architecture to provide improved handling quali- pole for the Neal-Smith compensator 7-pz ties and acceptable stability with a minimum of cost in to frequency, rad/sec both implementation as well as software verification and validation.

Introduction Nomenclature A design process for improving the pitch axis han- dling qualities of a flight vehicle was developed for the e feedback error (6pc - Ytc) X-29A. The process is believed to be applicable to all square root of - 1 fighter-class airplanes that exhibit a linear response to FFr fast Fourier transformation small amplitude inputs. The method works with the Kl canard feedback gain existing flight control system architecture to fine tune Kz normal acceleration feedback gain the handling qualities of the vehicle. Since the proce- K3 pitch rate feedback gain dure is a fine tuning process, results from flight tests are K4 pilot command gain required to validate or update the mathematical models

K,, Neal-Smith compensator gain

used in the process.

*Member AIAA.

Control law development for new aircraft follows a Copyright ©1989 by the American Institute of Aeronautics and natural evolutionary process. The initial mathematical Astronautics, Inc. No copyright is asserted in the United States models have a relatively high degree of uncertainty, under Title 17, U.S. Code. The U.S. Government has a royalty-free which requires that the control law design stresses sta- license to exercise all rights under the copyright claimed herein bility and robustness to account for this uncertainty.

for Governmental purposes. All other rights are reserved by the copyright owner.

Consequently, other desired objectives such as perfor- mance andhandling qualities areoftensacrificed to a good level 1 fighter-type aircraft. The goal for the re- obtain the required robustness, which was true for the search phase of the flight-test program was to show that X-29A aircraft. With a highly unstable aircraft, it takes fighter-type agility characteristics could be designed into the X-29A.

very little control surface deflection to initiate a change in the pitch attitude of the aircraft. The majority of the This paper presents the design process that was de- control power is required to arrest the motion when the veloped to improve the handling qualities of the X-29A desired pitch attitude is achieved. With the modeling aircraft. It was a challenge to design the longitudinal uncertainties, the initial control designers reduced the control laws for the X-29A vehicle because of the con- allowed pitch acceleration to ensure that the resulting flicts between designing for stability robustness and motion could be controlled and arrested when desired.

good handling characteristics. The challenge was to After a vehicle is brought to flight test, the mathe- provide a suitable amount of stability without inhibit- matical models can be validated or updated to match ing the maneuverability of the vehicle. This issue and, the flight-test vehicle. Updating the models is not consequently, the longitudinal dynamics are the main a simple task, however, elimination of gross errors focus of the analysis presented here. Both predicted can be accomplished and a degree of validity can and flight-test results are presented for the new control be assessed.

law design.

After the validation of the math models, the con- Aircraft Description straint on robustness can be relaxed and the control The X-29A is an experimental aircraft designed to laws can be adjusted to provide improved handling and demonstrate the integration of several modern tech- performance. However, at that point in the design pro- nologies into a highly maneuverable aircraft. It is a cess it is usually not feasible to make major changes relatively small, single-seat aircraft powered by a sin- to the control system. Working with the existing con- gle F404-GE-400 engine. The aircraft dimensions are trol law structure makes relatively minor changes to shown in Fig. 1, and the physical characteristics of the improve the handling and performance of the vehicle, airplane are presented in table 1.

which is more desirable than creating major architec- tural changes which are costly and often re-introduce The vehicle incorporates a forward-swept wing with a high level of uncertainty.

three surface pitch control and static instability to pro- vide a low-drag configuration. The aircraft wing struc- The envelope expansion flight-test phase of the ture includes aeroelastically tailored graphite-epoxy X-29A was completed in August 1987. During covers to help provide stiffness to overcome the tor- this period, dynamic stability and handling qualities sional divergence problems associated with forward- characteristics were investigated throughout the flight swept wings. The wing has a 5-percent thick supercrit- envelope) The envelope expansion process was ac- ical airfoil. Variable camber is provided by full span complished with only minor adjustments of the control trailing-edge flaps.

system gains required. A variety of tasks were flown to provide a qualitative look at the initial handling quali- The wing-canard planform results in a high level of ties of the vehicle. These tasks included normal accel- instability that has a time-to-double amplitude of ap- eration and pitch attitude captures, formation flying, proximately 150 msec at the worst case flight condi- and air-to-air and air-to-ground tracking. Even with tion. Longitudinal control of the aircraft is obtained the emphasis on robustness in the design process, the with active canard, symmetric flap, and strake surfaces handling qualities of the vehicle were rated as solid (Fig. 1). Lateral-directional motion is controlled by level 2. 2 Pilot comments on the original flying qual- conventional rudder and differential flap deflection.

ities indicated a stick harmony problem and sluggish- ness in the pitch axis. The longitudinal stick travel was Flight Control System Description then reduced by a factor of two, while maintaining the The X-29A airplane has a triplex digital flight- same stick force per 9- This reduction resulted in im- control system with an analog backup for each chan- proved vehicle handling characteristics. However, the nel. The system was designed to be operational after question remained as to whether a vehicle with a 35- a single sensor failure, and safe after the second fail- percent static margin could be driven to perform with ure. The digital control laws are executed at a rate of the initial accelerations and precise control required of 3. Definition of the cost function, and 40 samples/sec (sps). Roll, pitch, yaw, and thrust com- mands are generated by conventional lateral stick, lon- 4. Calculation of the cost function.

gitudinal stick, rudder pedal, and throttle inputs.

Precise control of the lateral-directional motion of These steps are discussed in more detail in the follow- the aircraft was obtained by feeding back roll rate, yaw ing sections.

rate, bank angle, and lateral acceleration. A simplified Selection of Design Goals block diagram of the lateral-directional control system is shown in Fig. 2. For low to moderate angles of The Neal-Smith analysis provides a good quantita- attack (less than 20 ° ) the lateral-directional dynamic tive method for assessing the handling qualities of a characteristics are relatively conventional and are not vehicle. 5 Unlike lower order equivalent systems anal- presented here.

ysis, the Neal-Smith technique applies to systems that do not exhibit classical second order behavior. In ad- The primary task of the longitudinal control sys- dition there is no ambiguity introduced by the "good- tem is to stabilize the aircraft. In addition to the sta- ness" of the fit of the higher order system to a low order bilization task, the control system automatically posi- match. The Neal-Smith technique takes the longitu- tions the canards, flaps, and strakes to minimize drag dinal stick position to pitch rate (or attitude) transfer in trimmed flight. A simplified diagram of the primary function, and closes the loop around it with a com- digital longitudinal control laws is shown in Fig. 3.

pensator. The compensator consists of a lead-lag filter Three feedback signals (pitch rate, normal acceIera- with a gain and a time delay (Fig. 4). The compen- tion, and canard position) are used to stabilize the air- sator provides a very simple model of the pilot func- craft, however, as can be seen from the block dia- tion. The compensator is not intended to model the dy- gram, they are summed at one point (Vt_ on Fig. 3).

namics of a pilot accurately, rather, it is used as an in- This means that the longitudinal axis can be treated dicator to measure the amount of compensation that is as a single-input, single-output system with one well- required to obtain certain desired closed-loop charac- defined open-loop transfer function. This allows for teristics (ideal tracking). The relative workload of the the use of gain and phase margins to assess the stabil- pilot is measured in terms of the amount of lead that is ity of the system.3 A more complete description of the required, and the peak magnitude of the compensated flight control system can be found in Ref. 4.

closed-loop frequency response. The peak magnitude Design Technique and pilot lead define a point on the Neal-Smith plane, which has experimentally defined level 1,2, and 3 han- It was a challenge to increase the responsiveness dling qualities boundaries.

of the X-29A vehicle while maintaining precise con- A validated linear model was used to calculate the trollability. A production aircraft would require good pitch rate due to longitudinal stick position frequency handling qualities throughout the flight envelope. The conditions.

X-29A handling qualities improvements were limited response (_)" at the two design flight to a specific part of the flight envelope because of These frequency responses were used to calculate the the fixed amount of test time available. Two de- two points shown on the Neal-Smith plane in Fig. 5.

sign points in the X-29A flight envelope were chosen For one of the design points, flight data from a fre- which demonstrated the improved handling. The de- quency sweep was available to validate the model.

sign points corresponded to break points in the longi- The Neal-Smith criterion indicates a relatively large tudinal gain tables. Therefore, changing the gains at amount of lead required of the pilot to obtain the de- the two selected break points affected an area of the sired tracking performance. This correlates well with flight envelope that was large enough to allow for nor- the pilot's desire for increased pitch responsiveness.

mal maneuvering without departing from the affected The design objective to obtain quicker pitch re- region of the change.

sponse without adversely affecting the controllability The process used to provide improved handling of is reached by reducing the amount of lead required by the X-29A vehicle involved four steps: the pilot and maintaining a low, closed-loop resonant peak. This design objective corresponds to moving the points on the Neal-Smith plane to the left into the cen- 1. Selection of the design goals, ter of the level 1 region. The design goal for the X-29A 2. Selection of the design variables, aircraft was to reduce the amount of lead required of the X-29A, in-flight measurements of the three feed-

thepilot,whilemaintaining acceptable stabilitymar-

backs as well as the feedback error (e on Fig. 3) were ginsandcontrol surface activity.

available for analysis. The contribution of each of the

Selection of Design Variables

feedbacks to the overall system behavior was directly

Choosing appropriate design variables is important

measurable. Thus, as long as the new gains did not in developing anefficient design algorithm. A suffi- drive the system to nonlinear behavior, the effect of

cientnumber ofvariables isrequired toprovide enough

each of the feedback gains was known to a high degree flexibilityto meet thedesign goals.However, if too of certainty.

manyvariables arechosen the number of possible

Definition ot" Cost Function

combinations increases significantly, whichresults in

The cost function is a numerical value that indicates

ahighcostfor computing the"optimal"solution and

how well a particular design meets the design goals.

theresulting design change maybemore complicated

The lower the cost function value, the closer the de-

thanrequired. An increased costin software verifica-

tionandvalidation istheresult.

sign comes to meeting the design requirements. For the X-29A, improvement of the vehicle handling qual-

It is desired to"fine tune"theflightcontrol system

ities was desired without losing too much stability or

toprovideimproved handling qualities withoutdras-

demanding too much surface activity.

ticchanges in controlsystem architecture. If thefine

tuningcanbe accomplished withgainchanges only, The desire for improved handling qualities corre-

thecostin terms of software verification andvalida-

sponds with moving the points on the Neal-Smith tiontimewill bereduced. If thefinetuningprocess plane to the left into the center of the level 1 region.

This can be expressed mathematically by finding the

requires additional dynamic elements (such asa lead-

lagorwashout falter) thepoles or zeros ofthefiltercan combination of design variables that define a point on the Neal-Smith plane which has a minimum distance

beused asdesign variables. Adding dynamic elements

oftensignificantly increases thecostof implementing from the desired point in the center of the level 1 re-

thechange. gion. The point defined as the desired Neal-Smith cri-

teflon was nominally 0.0 dB and 10.0 ° (see Fig. 5).

Thedesign variables should bechosen sothattheir

This point was easily changed to allow the designer to

effecton thesystem canbeaccurately predicted. For

assess the trade-offs between the design goal and the

example, on the X-29Atherearethreecontrolsur-

design constraints.

faces andthreefeedback variables whichareused to

The stability margin constraint was met by selecting

controlthelongitudinal motion.A designer could al-

lowthegains oneach of thecontrolsurfaces to vary, a minimum level of gain and phase margin which, if whichwouldchange thewaytheforward-loop com- not met, added a large value to the cost function. The mand is proportioned tothethree surfaces. Thischoice values of the minimum acceptable stability levels were of design variables wouldrequire precise knowledge nominally 6.0 dB and 40.0 °. This constraint could be

of theindividual controlsurface effectiveness deriva-

changed by the designer to allow quick assessment of tives.Because of themultipleactivecontrol surfaces design trade-offs.

thatmove in phase witheach other, thecontribution of

The requirement for reasonable surface activity can

each individual surface to theresulting motion of the

be achieved by calculating the stick-to-surface deflec-

aircraft could notbedirectly measured. Thischoice of

tion (or rate) and putting limits on the gain peak or re- design variables wouldinvolvesome risk.

quiting a certain amount of gain roll off. This con- Thedesign variables used for theX-29Awerethe straint is similar to imposing restrictions on the band- gains on eachof the threefeedbacks aswell asthe width of the system. This requirement will also tend to gain onthepilotcommand. Thegain onthepilotcom- eliminate the control system designs that would cause mand wasallowed tovaryonlyto maintain thesame aeroservoelastic instabilities. For the X-29A design, a stickforceper g since the design goal was to improve limit was placed on the maximum amplitude of the ca- the dynamic response of the vehicle, not to change the nard rate due to longitudinal stick position frequency steady-state response. The four design variables pro- response l _)" Although this constraint does not guar- vided enough flexibility to provide improved handling antee there will be no rate limiting during untrimmed with adequate stability, and the implementation of the or higher g flight, it will tend to eliminate designs with change required only a small software change. For severe rate limiting problems.

from algebraic manipulation of subsystem frequency

Thecostfunction, a realvalued scalar, wasdefined

responses and the design variables as follows: asfollows:

costfunction = resonant peak error

K-4 _'p, q + pilot corn nsation error sca_ee factor (1) + constraint penalty where: ( 8cc 6¢ nzc qcq_ Yt, _ Yt_ Kl _c e + K2-- + K3--- e Vt e q e (2) the distance between the resonant peak error = achieved resonant peak _p 1.0+ _ KI 6_ e + K2 + -_ q e] e and the desired resonant O) peak (0.0 dB) the distance between the pilot compensation error = Figure 7 shows a block diagram that defines the sub- achieved pilot compen- system transfer functions. The subsystem frequency sation and the desired responses were calculated and stored as vectors of amount of pilot compen- complex numbers which were a function of frequency sation (10.0 °) (w). These were obtained from the s and z plane de- 10000.0 if the sta- constraint penalty = scriptions of the subsystem transfer functions by the following substitutions: bility margin constraint was violated, 10000.0 if 8=j_d the surface activity con- z = cos(wT) + j sin(wT) straint was violated, 0.0 otherwise The sample and hold devices were modeled with the scale factor = 7.0, which is commonly approximation of a zero order hold: used to compensate for 1 - e -sT the difference in magni- ZOH - sT tude of the units of dB The aircraft aerodynamic frequency responses were and deg (this value is usually used in lower or- obtained from standard linear equations of motion of the airframe at each of the two flight conditions.

der equivalent systems matching) In the initial setup of the problem, the frequency re- sponses of the subsystem transfer functions are calcu- lated and stored in memory. For a given set of de- Calculation of Cost Function sign variables, the closed-loop, open-loop, and stick- to-canard rate frequency responses, and consequently For this particular design process, the design goals the cost function can be quickly computed. For each must all be calculated as a function of the frequency design iteration the cost function is obtained very response of the system. With the cost function de- fined in terms of frequency domain transfer functions, quickly by algebraic manipulation of the subsystem frequency responses and the design variables. Cal- block diagram algebraic manipulations can be used to culating the cost function quickly is important for provide a quick and efficient means of calculating the an iterative search for an optimal set of design vari- various required frequency responses. 6 The cost func- tion is determined from three different transfer func- ables, since many combinations of design variables need to be evaluated. The subsystem transfer functions tions; the closed-loop stick-to-pitch rate transfer func- should be chosen to leave a minimum amount of cal- tion (6_) (for determining the Neal-Smith criterion), culation required to evaluate each combination of the the open-loop transfer function (_t__) (for calculating x e / design variables.

stability margins (see Fig. 6)), and the stick-to-canard rate There are many computer algorithms available that transfer function (_) (for limiting surface activ- will minimize a cost function by varying design ity). These three frequency responses were obtained

parameters. 7 A gradient search algorithm wasused for

change. The aerodynamic model was composed of a theX-29Adesign problem. Thestability andcontrol fourth-order rigid body model that did not include the

surface activitydesign constraints introduced a step

higher frequency structural modes. The other states

discontinuity in thecost function. Since theminimiza-

were made up of sensors, notch filters, prefllters, actu-

tionalgorithm uses numerical derivatives to calculate

ators, and control system dynamics.

thegradients, a smooth, continuous function wasnot

A time history comparison of the linear model and

required forconvergence to a solution. However, the

vehicle responses to pilot inputs is shown in Fig. 8.

problem is highlynonlinear andmanylocalminima

From the time history data it can be seen that the model

exist.A unique globalminimum is notguaranteed to

is fairy close to the actual vehicle performance. A

exist.It wasfoundthatreasonable solutions could be

more critical look at the data shows small differences

obtained with theproper selection of starting condi-

that may or may not be important. It was found, how-

tionsof the algorithm. An interactive program was

ever, that with pilot-generated frequency sweeps and developed which allowed the user to control the start- fast Fourier transformation (FFT) techniques, a direct ing gains, the range of variation of each gain, and the measurement of the subsystem frequency responses cost function constraints. Thus by varying the start- could be obtained (Figs. 9-11). The transfer functions ing conditions and design goals and using quick local from e to the three feedback gains which were used by searches, the user could iterate to a reasonable solution the linear model, were incorporated into the design al- fairly quickly.

gorithm. The frequency responses derived from flight The flight-measured frequency responses could in data provided a direct validation of the transfer func- theory be used in the design process. In practice, tions which were used in the design process. Because the minimization of the cost function is adversely af- the linear model is used for fine tuning the control sys- fected by scatter in the data. A smooth, noise-free fre- tem, a high degree of accuracy is required. If signifi- quency response, such as one calculated from a lin- cant differences between the model and flight data are ear model that has been validated by flight test, pro- present, the transfer functions should be adjusted to ac- count for the differences.

vided better convergence of the numerical gradient search algorithm.

Nonlinear Simulation Validation of Validation of the X-29A Mathematical Model New Design For the handling qualities re-design, accurate mod- The design process works with a linear representa- els of the vehicle are required. In general, param- tion of a nonlinear system. It then becomes impor- eter estimation techniques are used in flight test for tant to execute the new control laws on a nonlinear model verification. Aerodynamic stability and control simulation to ensure that the new gains do not drive derivatives are extracted from time history data. These the system to nonlinear behavior. When implemented derivatives are then compared with the wind-tunnel on a nonlinear simulation, the new gains verified the predictions which were used to develop the simulation quicker pitch acceleration, but the new system showed models. In the case of the X-29A longitudinal axis, a greater tendency to rate limit the surfaces during the presence of multiple active control surfaces and large amplitude maneuvering. An extensive amount of the high degree of static instability made it difficult to testing was done to ensure that the airplane would not obtain the individual control effectiveness derivatives.

depart into a tumble mode because of control surface In addition, the high-gain full-authority flight-control rate limiting during aggressive maneuvers.

system itself provides a significant amount of com- Another important consideration of the design pro- plexity that must be modeled correctly. The handling cess is that the design algorithm provides a point by qualities re-design procedure discussed herein requires point optimized design at each specific flight condi- a verified frequency response which accurately repre- tion. When the new gains are incorporated into a gain sents the dynamics of the entire system, including both schedule, the system behavior must be assessed be- the aerodynamics and the flight-control system.

tween the design points to ensure that the resulting It was found that a fiftieth-order model was adequate interpolated gains also provide desired system behav- for predicting the dynamic behavior of the X-29A in ior. A practical design can be obtained by constraining the flight regime that would be affected by the design the amount of gain variation allowed between break points. After nonlinear simulation, constraints were test. In-flight measured frequency responses indicated points on the Neal-Smith plane with approximately added to the design algorithm to reduce the range of gain values to reasonable numbers. 0.0 dB of resonant peak and 20.0 ° of lead required by the pilot. In general, the pilot comments indicated a The nonlinear simulation also showed the perfor- marked improvement in the performance of the new mance of the design during rapid transition between flight-control system.

the design points. If the gains are too sensitive to flight condition, problems can occur when the gain up- "The aircraft pitch response was instinctively dates lag behind the changes in aerodynamic condi- correct. [The pilot] was able to control the tions. The simulation also provides an assessment of pitch axis in fine tracking without consciously the failure tolerance of the new design. None of these providing compensation. The initial acceler- concerns can be addressed with linear simulation.

ations were comparable to [other fighter class Pilot-qualitative comments and evaluation of the airplanes]. [The pilots] no longer had to re- nonlinear simulation were not significant factors in duce the aggressiveness of the tasks due to evaluating the improved control system. The simu- lags in the response."

lation was fixed base with a very limited visual sys- Figure 15 shows the response of the aircraft to a step tem and thus not suitable for fine-tuning handling characteristics. input and how it compares to the linear model. The step response verifies that the initial pitch accelera- Results tions which were predicted by the linear model were obtained in flight. Despite the pitch rate overshoot, the Predicted Characteristics closed-loop pilot plus aircraft response was very pre- Figure 12 shows the Neal-Smith criterion predicted dictable and controllable as was predicted by the Neal- by the linear model with the optimized flight-control Smith analysis. The pilot comments indicated that system gains. The design goal of 10.0 ° of lead and 0.0 dB resonant peak was not achieved because of the "having the initial pitch acceleration gave design constraints, however, the amount of pilot lead [them] something to work with so that [they] was reduced by approximately 50 percent. The closed- could cause quick, precise changes in tight loop resonant peak achieved by the modified gains was tracking tasks. Whereas, with the old gains below 1.0 dB for each of the design points. This re- the sluggish response caused [them] to con- suited in Neal-Smith criteria which were well within sciously back off on the task to compensate the level 1 region of the Neal-Smith plane.

for lags in the aircraft."

The design process showed a definite trade-off be- Despite the validation of the linear and nonlin- tween the design constraints and the achievable Neal- ear models and the extensive analysis performed, the Smith criterion. The modified design gains demon- phase margin with the new gains measured from flight strated a slightly reduced level of stability margin data was significantly less than what was predicted (Fig. 13) and increased surface activity. Figure 14 from the linear model (see Fig. 16). The difference shows a comparison of the step response of the linear is suspected to be a result of the strake flap actuator model with the old and new gains. It can be seen that rate limiting. Although the strake rate limiting had the new gains provide increased initial pitch acceler- very little effect on the three forward-loop frequency ations in part by allowing the pitch rate to overshoot responses (Figs. 17-19), the seemingly insignificant the final value. The low value obtained for the closed- differences were enough to cause a large change in loop resonant peak, however, indicates that even with the phase margin. It is suspected that the differences the open-loop overshoot the response in a closed-loop seen on the open-loop frequency response measvre- tracking task is controllable and predictable. Figure 14 ments are the result of the difference between sum- also shows the increased level of surface activity re- ming in-phase or out-of-phase feedbacks. The non- quired to obtain the crisper pitch response.

linear simulation was not accurate enough to predict Flight Test of New Design this occurrence.

Figure 12 shows that the Neal-Smith criteria pre- The Neal-Smith criteria obtained from the flight- dicted by the linear model were verified by flight testing of the new design shows that the desired ob-

comparable to thoseof existingstate-of-the-art air-

jcctivewasachieved because thepointsontheNeal-

craft,however, it should benotedthatthemaximum

Smithplaneweremovedtowardthe centerof the

lcvell region (Fig.12).(Theeffects of thestrake rate 9 capability (6.4 9), and the minimum accepted sta- limitingwereoutside thefrequency range of pilotin- bility margin levels of the X-29A were significantly terest.) Thecrisper pitchresponse wasobtained with less than those required by an operational production higher levels of surface activity.Thenewsystem ap- fighter aircraft.

proached butdidnotexceed themaximum capability

This design methodology could be used to opti- of thesystem.

mize the longitudinal handling qualities of any exist- ing fighter-class airplane that exhibits a linear response

ConcludingRemarks

to small amplitude inputs. The cost of the resulting

Thedesign methodology outlined in thispaper pro-

re-design can be reduced by limiting the extent of the

ridesa practical means for improving the handling

change to the minimum required to obtain the desired

qualities of a flightvehicle withoutexcessive system

results. This is a practical approach that has been

re-design. Themethod provided a100 percent increase

shown to work on a real problem.

inthepitchacceleration oftheX-29Avehicle withpre-

References

cisecontrol.Themethod allows thedesigner to work

with theexisting controlsystem architecture to fine-

l Gera, J., and Bosworth, J.T., Dynamic Stability and

tune thehandling qualities oftheaircraft. Theiterative

Handling Qualities Tests on a Highly Augmented, Stat-

procedure allowsthedesigner toquicklyassess trade-

ically Unstable Airplane, NASA TM-88297, 1987.

offsbetween design goals andconstraints.

2,,Military Specification -- Flying Qualities of Pi- Themethod isalinearanalysis technique, however, loted Airplanes," MIL-F-8785C, Nov. 1980.

andtheeffects of nonlinear elements should bestud-

3 Bosworth, J.T., and West, J.C., "Real-Time Open-

icd on a nonlinear simulation.Themethod requires

Loop Frequency Response Analysis of Flight Test accurate transfer function descriptions of thevehicle.

Data," AIAA-86-9738, Apr. 1986.

Thcse canbeobtained byusing flightdata tovalidate or

update linear models of the vehicle. Fast Fourier trans-

4Whitaker, A., and Chin, J., "X-29 Digital Flighl

formation (FFT)techniques canbeusedto measure

Control System Design," AGARD-CP-384, presentcd

subsystem frequency responses which arerequired for

at the AGARD Symposium on Active Control Sys-

thedesign method. Thisprovides a means forincor-

tems, Toronto, Canada, Oct. 1984.

porating flight-test results intothedesign process.

5 Neal, T.P., and Smith, R.E., An In-Flight Inves-

Thefinaldesign for theX-29Aresulted in a lower

tigation to Develop Control System Design Crite-

phase margin thanwaspredicted. Thiswascaused by

ria for Fighter Airplanes, Vol. I, AFFDL-TR-70-74,

a sensitivity of thesystem to ratelimitingwhichhad

Dec. 1970.

been observed atotherflightconditions withtheorigi-

6 Friedland, B., Control System Design: An Intro-

nalcontrol system gains, buthadnotbeen completely

duction to State-Space Methods, McGraw-Hill Book

understood. Therate limitingproblem occurred atfre-

Co., New York, 1986.

quencies higher thantherange used by apilotinhan-

dlingqualities tasks.Theexperiment showed thata

7 IMSL Library Reference Manual, 8th ed., Vol. II,

vehiclewiththehighlevelof staticinstability of the

IMSL LIB-0008, 1MSL, Inc., Houston, 1980.

X-29Acanbe madeto performwith accelerations

Table1.X-29Aphysical characteristics.

27.2ft

Wingspan

185 ft 2

Wingarea

29.3 °

Wingleading-edge sweep (forward)

7.2 ft

Mean aerodynamic chord

14,000 lb

Vehicle empty weight

4,000 lb

Maximum fuelcapacity

Maximum thrust 16,000 Ib

37 fl 2

Canard area

/-Wing flap _Canard _ _._ Strake flap_ -.,I 48 ft 1 in. - --- F.5A Rudder -_ t-.i--- nose ._ section / 14 tt 9.5 in.

' Strake flap J __X

_ St rake flap J 27 ft 2.44 in. --_.-i Fig. 1 X-29A airplane.

Lateral I Command _,_ Proportional J _ i stick shaping end int(,gral filter position J J Bank angle 'l IH='°""°n,:.o,,.,.

"_ Feedback J_ ;la';;;;;rl--LaterVa_"=*"ation Rudder / Command shaping pedal -_ filter _'_ compensation position J ID13_ Fig. 2 Simplified lateral-direclional conlrol law block diagram.

Longitudinal I stick shaping forward Symmetric flap = I

Comman F.f

filter compensation Strake flap position I I i X-29A ; Ytc I I Feedback J_: Pitch rate compensation IX Normat acceleration ___ I_ Canard position P Fig. 3 Simplified longitudinal control law block diagram.

Compensator X-29A _a Aircraft aircraft plus pitch control Desiredpitch _+ _" J K e'0"3s [ "cpls - _-_ system attitude-I [ p ,_:1) ttitude Fig. 4 Block diagram of closed-loop pitch attitude tracking task.

• Predicted, design point 1 • Predicted, design point 2 <_ Flight, design point 2 * Desired point Level 2 peak, 0 dB -2 Resonant 2 i_ -4 I I t 1 I I\ I -3O -20 -10 0 10 20 30 40 50 6O Pilot lead, deg =41 Fig. 5 Heal-Smith analysis on original gains comparing predicted and flight test results.

Flight date Linear prediction % :--_ 15 _ High frequency

'0_m _

5 erg gain margin, Amplitude 8,5 dB 10,0 dB ratio, 0 _ .----4-1- dB -5 _ -..--4-1- -10 _ -15 ........ _........ _.._ II -20 _ ----LI- ----12 '..

I I I I

iiiii ;_

_-1.o ........ ........

shift, -180 : : _'d'Phas' maral141 .ff ........... _ -200 _-: : : :

"° II__

................... i.l.1; :i

: i i!: -240 i .1 1 10 Frequency, rad/sec Fig. 6 Open-loop frequency response transfer function.

l "1 q_

J

8 _ j.q

8p j _ ;_

]

Yt c _ ._.

r- 1 n: I

L J

n% 8co i_ _ % L2 Fig. 7 Longitudinal control law block diagram showing subsystem transfer functions.

Flight data ...... Linear prediction Angle of atlack, deg Pitch rate, deg/sec -4 -6 Pitch attitude, deg Normal acceleration g's I I I I I 1 2 3 4 5 Time, sec _, -- Flight data ..... Linear prediction Canard -2 position, -4 deg -6 -8 Symmetric flap position, deg -1 Slrake flap -1 position, -2 deg -3 -4 Longitudinal stick position, In, 0 1 2 3 4 5 Time, aec Fig. 8 Response of vehicle to pitch doublet compared with linear model.

-- Flight data ...... Linear prediction

so 40 ...... i'

30 _ i iii_l Amplitude ! I _:::; ratio, dB 10 ...... _.-..-I---,'-_'-,-_ "_

i:i

-i ........ _ ...... ..%.." ....

i _ i t

-lO i 1ii!i -160 : " " i -18o _ T_ -200 ........ _-..-,. '--_"+ ......j. _ ':? ..:-_-; i iiii -220 ....... _ '-_ ........ _ ....... i 'i? .... ,"_'_'_.

Phase -240 _ -+ shift, deg -280 -300 ........ _..)_ l._._.:.:

........... i ........ i i/il

-320 ' ' ' 1 10 100 .1 Frequency, rad/sec _._ Fig. 9 Pitch rate due to e transfer function.

-- Flight data ..... Linear prediction .i.i ................. i.........

"x, "_'_ .................. i..........

Amplitude ratio, ...... :..4.

dB ;i':': .......... !'" '"¢'"" iil -10 -20 -30

.2,0 l ll_

-260 _ _'_ -->" i?i_ ...... _"'" :'"'_'" _"

.280 ........... l.-i\t--

Phase ........ ,,_ :;; ._' ..:.....;.

shift, -300 ..............

deg -320 --_,--_r---_- .3,0 Z.: I_, _ .............. _1 i'il _:_ iil ii

._oo J_

10 100 .1 1 Frequency, rad/sec o._ Fig. 10 Normal acceleration due to e transfer function.

-- Flight data ..... Linear prediction

i i iliii! i i i

303s_4° i __ii!i!

...-+.*-*+_-_; ............ _---i--i-, • Predicted, original gains, design point 1 Amplitude • " Predicted, new gains, design point 1 ratio, ..... _.' *.H*!*........... *.-_--i.

41, Predicted, original gains, design point 2 dB .... _.-,_-_,-_-:_ ......... $.-i.-i.

_' Predicted, new gains, design point 2 c/" Flight, new gains, design point 1 <_ Flight, original gains, design point 2 .... _-._._.i-i_ .......

Flight, new gains, design point 2 5 * Desired point -60

6 E

Level 2 -80 - 1 O0 2 Resonant Phase peak,

!

shift, -120 dB deg -140 Level._: 1;___ B.

-2

!

- 160

1 t

I I I I I\1

-180 -4 .1 1 10 100 -30 -20 -10 10 20 30 40 5O 60 Frequency, rad/sec I147 Pilot lead, deg ,_*= Fig. 11 Canard position due to e transfer function.

Fig. 12 Neal-Smith analysis comparing the modified gains with the original gains for both predicted and flight test results.

New gains ..... Original gains Amplitude ratio, dB -10 -20 I I IIIIIll I I lllllll I I lkl.4']lll -30 -120 --

.16o - ," i i

Pshift,deghaSe -240"200 - I II i?tl;_;; '/; ' '! :'' ' .1 1 10 100 Frequency, rad/sec Fig. 13 Open-loop frequency response comparison between the new and original gains.

New gains ..... Original gains

Angle of ;F

attack, 5h /.," _,,.

deg 4 ...... "'-.

,I- i" i z i i_--_

Pitch rate, 2 deg/sec 0 -2 -4 Pitch acceleration, 0 -, deg/sec -20 -4o f I f Normal 1,8 acceleration, g's 1.0 .6 0 1 2 3 4 5 6 Time, sec New gains ..... Original gains Canard position, -2 deg -4 -6 -8 Symmetric flap position, deg Strake flap -5 position, deg -7 -9 Longitudinal ,4 stick position, II1.

.2

It L

I 1 I I 0 1 2 3 4 5 6 Time, sec Fig. 14 Response of linear model to a pitch step input and other parameters.

Flight data ..... Linear prediction 4 °" Angle of attack, deg Pitch attitude, dog Normal acceleration, 1.6 g'a 1.2 .8 4 5 0 1 2 3 Time, sac ,t,,, Right data ..... Linear prediCtion -2 I "" ..........

Canard -3 position, -4 deg Symmetric 1 flap position, deg 0 .1 Strake flap -1 position, .2 deg -3 -4 .4 Longitudinal .3 2 stick position, in. .1 I +J 0 1 2 3 4 5 "Time, sac ms_D Response of vehicle and linear model to pitch step with new gains.

Fig. 15 -- Flight data ...... Linear prediction ............. i..;.*-: _-!.

H tt ii Ji

Amplitude |iHigh frequency Low frequency i , ratio, " "_•i gain margin, ...... gain margin, 'i .....

dB 8.SdB

.?0.Vs

-5 -10 I I I I -140 [ -160 /Ph ;e I Phase -180 t 3.', : ......

shift,

,y

deg -200 ---- -220 -240 .1 1 10 100 Frequency, _d/_c Fig. 16 Open-loop frequency response transfer func- tion after gain change.

Flight data new gains ..... Flight data original gains . • , .

Amplitude 20 ..... <..

ratio, dB 10 0 "-'"T-.

-10 -20 -160 -180 -200 -220 Phase shift, -240 deg -260 _ii -280 ....... I-_.I.-_,.L!.I_, -300

............ N iif

-320 .1 1 10 Frequency, Pad/sac Fig. 17 Pitch rate due to e transfer function before and after gain change.

-- Flight data new gains ..... Flight data original gains 4O 30 ............. _ _ _ L "_ iii :

iiii_

10 - ! ;: " Amplitude ratio, 0 ........ ,,_ ..................... i, _ ...... r dB -10 ........ ! I'" "_'* "_ ........ *-.'*.".'i- _......... _ -20 ........ I ................. ._..._..:.... _ .............

r liil i , -30 J : i " i_ _,ii _ : '"_ ,_\i_ _...i..L. : -290 ........ _.... _ , c_ ........... i ........ _.;, --.

Phase-330 ........ ,., ...... i_ _ _ ........ ...... _._i . I ........ ,_ ........ _ . _-"i "'"_'" deg -370 ....... "l i ................. _'"_"_" _" .......... " -45o I . i i i !iii .1 1 10 100 Frequency, tad/sac _N Fig. 18 Normal acceleration due to e transfer function before and after gain change.

Flight data new gains ...... Flight data original gains i i i :: • • : - .

Amplitude ratio, 20 - dB i _l i i :: 10 .- ..... •il_ ......... 17 ................. _ ......... .ii ;_'_.

[ I: _ ! -- • I -6O • 1 O0 Phase -140 shift, deg -180 -220 -260 .1 1 10 100 Frequency, tad/sac ilm Fig.

19 Canard position due to e transfer function before and after gain change.

i

Report Documentation Page

._oace A_r_,ao_ 3. Reciplent's Catalog No.

1. Report No. I 2. Government Accession No.

NASA TM-4142 4. Title and Subtitle 5. Report Date September 1989 A Design Procedure for the Handling Qualities Optimization 6. Performing Organization Code of the X-29A Aircraft 7. Author(s) 8. Performing Organization Report No.

H-1548 John T. Bosworth and Timothy H. Cox 10. Work Unit No.

RTOP 533-02-51 9. Performing Organization Name and Address 11. Contract or Grant No.

NASA Ames Research Center Dryden Flight Research Facility P.O. Box 273, Edwards, CA 93523-5000 13. Type of Report and Period Covered 12. Sponsoring Agency Name and Address Technical Memorandum 14. Sponsoring Agency Code National Aeronautics and Space Administration Washington, DC 20546 15. Supplementary Notes Prepared as AIAA paper 89-3428 for presentation at the Guidance, Navigation, and Control Conference, Boston, Massachusetts, August 14-16, 1989.

16. Abstract A design technique for handling qualities improvement was developed for the X-29A aircraft. As with any new aircraft, the X-29A control law designers were presented with a relatively high degree of uncertainty in their mathematical models. The presence of uncertainties, and the high level of static instability of the X-29A caused the control law designers to stress stability and robusmess over handling qualities. During flight test, the mathematical models of the vehicle were validated or corrected to match the vehicle dynamic behavior. The updated models were then used to fine tune the control system to provide fighter-like han- dling characteristics. A design methodology was developed which works within the existing control system architecture to provide improved handling qualities and acceptable stability with a minimum of cost in both implementation as well as software verification and validation.

18. Distribution Statement 17. Key Words (Suggested by Author(s)) Unclassified -- Unlimited Control system; Design procedure; Handling qualities; Neal-Smith criterion; Optimization; Stability; X-29A Subject category 08 22. Price 19. Security Classif. (of this report) 20. Security Clauif. (of this page) Unclassi fled A02 21. No. of pages ified NASA FORM 11126 OCT 86 For sale by the National Technical Information Service, Springfield, VA 22161-2171.

NASA-Langley, 1989 National Aerona.

Space Adminis' Code NTT-4 Washington, D.C.

20546-000!