Assessment Study of the State of the Art in Adaptive Control and its Applications to Aircraft Control

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Assessment Study of the State of the Art in Adaptive Control

and its Applications to Aircraft Control

by Howard Kaufman ECSE Department Rensselaer Polytechnic Institute Troy, NY 12180 email: kaufmh@rpi.edu Tel: 518 276 6081 Fax: 518 276 6261 FINAL REPORT to NASA GRANT NAG-I-2075 1 May 1998 to 31 December 1998

Summary

Many papers relevant to reconfigurable flight control have appeared over the past fifteen years. In general these have consisted of theoretical issues, simulation experiments, and in some cases, actual flight tests. Results indicate that reconfiguration of flight controls is certainly feasible for a wide class of failures.

However many of the proposed procedures although quite attractive, need further analytical and experimental studies for meaningful validation. Many procedures assume the availability of failure detection and identification logic that will supply adequately fast, the dynamics corresponding to the failed aircraft. This in general implies that the failure detection and fault identification logic must have access to all possible anticipated faults and the corresponding dynamical equations of motion. Unless some sort of explicit on line parameter identification is included, the computational demands could possibly be too excessive. This suggests the need for some form of adaptive control, either by itself as the prime procedure for control reconfiguration or in conjunction with the failure detection logic.

If explict or indirect adaptive control is used, then it is important that the identitied models be such that the corresponding computed controls deliver adequate performance to the actual aircraft.

Unknown changes in trim should be modelled, and parameter identification needs to be adequately insensitive to noise and at the same time capable of tracking abrupt changes.

If however, both failure detection and system parameter identification turn out to be too time consuming in an emergency situation, then the concepts of direct adaptive control should be considered. If direct model reference adaptive control is to be used (on a linear model) with stability assurances, then a positive real or passivity condition needs to be satisfied for all possible configurations. This condition is often satisfied with a feedforward compensator around the plant.

This compensator must be robustly designed such that the compensated plant satisfies the required positive real conditions over all expected parameter values. Furthermore, with the feedforward only around the plant, a nonzero (but bounded error) will exist in steady state between the plant and model outputs. This error can be removed by placing the compensator also in the reference model. Design of such a compensator should not be too difficult a problem since for flight control it is generally possible to feedback all the system states.

It is also important to note that multiple model based approaches are very attractive in terms of their potential speed of response to abrupt changes and/or failures. However unless some tuning is present, an extraordinary number of models may be required.

In view of the advantages offered by direct adaptive control and multiple model based control, it is anticipated that the combination of these methods should be very effective for reconfigurable

flight control systems. Associatedwith eachof the multiple modelswould be a controller and

possiblya reference model.Suchcontrollerswould bedesigned apriori sothatthe response of the

correspondingcontrol loop would display desiredhandlingqualities and at the sametime be

relativelyrobustovera reasonable rangeof plantuncertainty. Differentreference modelsassociated

with eachaircraft configurationmodel would allow the specificationof changedperformance

requirements in the presence of failures.Theadaptation procedurecanthen eitherbe designedto

retunethe controllersbecause of mismatchbetweenthe selectedaircraft model and the actual

dynamics,or theadaptivecontrollermightbedesigned to adjustthe inputappliedto theclosedloop

definedby the aircraft andthe selected controller.With enoughselectable modelsandassociated tunablecontrollersthatareadequately robust,it is anticipated thattheresultingreconfigurationwill be implementable, adequately fastandsuchthattheperformance goalsaresatisfied.

1.0 Introduction Adaptive controllers have the capability for both recognition of the occurrence of a system change and the appropriate modification to the controller itself so that the response characteristics are preserved. Adaptive control has been studied extensively in the past for flight control applications by many investigators. However such applications have for the most part considered adaptation of the controllers to account for system modeling uncertainties, nonlinearities, and the dynamic effects caused by changes in mach number and altitude. In these cases, the scenarios did not consider an abrupt change in system configuration that might without immediate intervention, lead to instability.

The importance of being able to maintain acceptable control in the presence of such changes is evident from the activities of NASA's Intelligent Damage Adaptive Control System (IDACS) program and the recent workshops on Reconfigurable Systems for Tailless Fighter Aircraft (RESTORE) held at Wright Patterson Air Force Base (WPAFB). A description of the RESTORE program and its accomplishments may be found in the 1998 AIAA paper by Brinker and Wise [11].

Abrupt system changes can result from failures, weather effects, and pilot inattention. Aircraft accidents have in the past, resulted from the failure of one or more actuators and/or sensors and from sudden changes in the aerodynamic characteristics. Actuator failures might be caused by electrical and/or mechanical problems, hydraulic line damage caused by debris breaking away from the aircraft, fatigue, and air flame structural damage. Sensor failures might be caused by device failures.

Aerodynamic changes might be caused by icing, engine failures, physical engine separation, and structural damage.

In many such cases, it is probable that the aircraft remains controllable, although with response characteristics unfamiliar to the pilot. Thus it is important that some type of control compensation be incorporated that can assist the pilot to safely maneuver the damaged aircraft. In some cases, it may even be desirable to have the controller override the pilot's commands. The feasibility of such a procedure was demonstrated in 1997 by Burken and Burcham [ 12] who discussed results of flight tests on a large civilian multi-engine transport, the MD- 11 in which only engine thrust would serve as backup to the primary flight control system. Results showed that this thrust backup system could be used in the presence of certain major failures (eg hydraulic pressure loss), for landing the airplane without the aid of the aerodynamic control surfaces.

Therefore it is of interest to develop a system that quickly recognizes and then compensates for a sudden change in the aircraft capabilities and/or a change in the response characteristics. This recognition should be followed by a damage assessment in terms of controllability, a development of requirements with respect to mission changes (e.g., to an immediate landing), specification of changes in the actuator armamentarium, designation of useable sensors, and appropriate modifications to the control algorithms.

Relevant to these requirements are the concepts of reconfigurable control and reconstructable control [51 ]. Although in many cases these terms have been and are being used interchangeably,

therearedistinctionsbased uponthedegree ofpre-planning.Whenthe controlsaredesigned apriori

to accommodate anticipatedfailures,thenthesearedesignated as reconfigurable;however,if the

controlsareto accommodate unanticipated failures,thenthetermreconstructable is appropriate.

With regardto the needfor suchcontrolmodifications,manyinvestigators haveconsidered

thefeasibilityof theaccommodation to specifictypesof damage or failuresandthepotentialof using somesort of adaptivecontrol for the implementation. Both explicit (or indirect) and implicit (or direct)adaptivecontrollershavebeenconsidered. Explicit adaptivecontrollersrequiretheuseof an (explicit) onlineparameter identifierfor trackingtheactualaircraftparameter changes. Suchonline trackingis of course subjectto thetradeoffs between theneeds for a shortmemoryfor rapidtracking

andalongmemoryfornoisereduction. Implicit adaptive controllersmonitorthesystem behaviorand

directly adjustthecontrollerparameters (gains)withoutthe explicit useof a parameter identifier.In both casesthe adaptation needsto be sufficientlyrapid in orderto maintaindesiredperformance specifications duringthe failure accommodation.

In manycases,input hasbeenincludedfrom a higherlevel fault diagnosis and/or failure

detection andidentificationsystem thatbothrecognizes theexistence of a problemandidentifiesthe

sourceof the problem(eg from a suddensensorand/oractuatorfailure). This would immediately

designate the needto considera revisedsetof actuators and/orsensors andthus avoid the slower processof ofiline identification.

Validation of the variousproposed reconfigurationcontrolalgorithmshasbeenperformed

usinglinearmodels,nonlinearmodels,andin somecases actualflight tests.Clearlyresponse time

is animportantfactorfor successful controllerreconfiguration.

Taking into accountthe needfor rapid controlleradjustment in response to failuresand/or

rapid parameter variations,it is importantto considerandto assess the potentialrole of adaptive control.In fact in a recentpaper,PachterandChandler[53] statethat"adaptivecontrolaffordsthe accommodation of a high level of uncertainty."Theythengoonto statethatreconfigurable control shouldbe usedin thepresence of dynamicandabruptunknownparameter changes.To this effect,

a review of the existing literature on reconfigurablecontrolsis containedin Section2.0. An

evaluationof this previouswork is presentedin Section3.0, andvalidation procedures arethen

presented in Section4.0.Finally conclusions andrecommendations for future research effortsare discussed in Section5.0.

2.0 Literature Review

2.1 Overview Over the past 15 years, many investigators have studied various aspects of reconfigurable and/or reconstructable aircraft control systems. Many of these control procedures used adaptive algorithms for alleviating the effects of failures and rapid parameter changes. In general these adaptive procedures used online explicit parameter identification or model following principles for fault accommodation. As an alternative, other approaches have utilized explicit fault diagnosis and/or failure detection and identification logic for defining the new model structure and/or parameter set, which would subsequently be used for control redesign. In many cases, the fault diagnosis and adaptation functions have been combined through the use of a bank of multiple models, or through the use of fuzzy logic, intelligent control, and/or neural networks.

The importance and feasibility of reconfigurable control was pointed out in 1995 by Wise [64], who cited three main problems to be considered; namely, real time identification, real time control computation, and digital implementation. He also discussed successful flight tests conducted under the joint Air Force and NASA program, Self Repairing Flight Control System (SRFC.S). These tests showed the potential of reconfigurable/damage adaptive flight control laws for recovery from failures. He also cited the ongoing work at Barron Associates [46,63], where adaptive algorithms were being evaluated by flight test for a variety of simulated failures (e.g. missing flaperon, missing half tail surface, partially missing rudder, missing half tail and rudder).

Also of importance to the overall issue of validation ofreconfigurable aircraft controls, is the 1997 paper by Burken and Burcham [ 12]. They report on flight test results on a large civilian multi- engine transport, the MD-11. The control system for this aircraft was modified so that only engine thrust would serve as backup to the primary flight control system. Results showed that the backup system could be used in the presence of certain major failures (e.g. hydraulic pressure loss), for landing the airplane without the aid of the aerodynamic control surfaces.

An overview of research on various aspects ofreconfigurable flight control is presented in the next four sub-sections. Section 2.2 considers procedures that directly require some sort of explicit fault diagnosis and/or failure detection and identification procedure in conjunction with a control algorithm. Because of the large number of possible faults that can arise, a comprehensive fault detection scheme can be computationally prohibitive. Thus as an alternative to using fault diagnosis logic, sections 2.3 and 2.4 respectively discuss literature relevant to the usage of explicit (indirect) adaptive control procedures and implicit (direct) adaptive control procedures. Section 2.5 then discusses multiple model based procedures that in a sense combine rapid failure detection with adaptive control. Finally Section 2.5 presents reconfigurable controllers that have been designed with neural nets, fuzzy concepts and/or intelligent control procedures.

2.2 Reconfiguration using failure detection/fault diagnosis Reconfiguration procedures have been proposed that are dependant upon having available some higher level fault diagnosis/failure detection and identification logic that defines a model tbr the aircraft dynamics following some abrupt physical change. A general survey of procedures for detecting changes is given by Basseville in [5]. It is of interest to note that in some cases this logic is coupled with some sort of system parameter identification. More recently in 1998, Gopisetty and Stengel [27] presented parity space and parameter estimation methods for detection and identification of sensor and actuator failures in flight control systems.

A study of the potential of using reconfigurable controls to accommodate failures was presented by Ostroff and Hueschen [52] in 1984. In 1988 Caglayan et. al. [13,14] described a hierarchical failure detection, identification, and estimation (FDIE) algorithm for use in a self- repairing flight control system. Coupling of such FDIE procedures with a procedure for adjusting the controls accordingly defines a reconfignrable control system. Since 1985 various papers have appeared that discuss controllers that might be coupled to such an FDIE system for flight control reconfiguration.

A paper by Ostroff [51] in 1985 showed how reconfiguration might be accomplished by coupling failure detection with least squares matching of the closed loop system transfer functions.

This required the pseudo inverse of the control and output matrices. Although this procedure was validated using nonlinear simulation tests, no supporting analytical stability results were presented.

In 1988, Caglayan and his co-investigators [13,14] also discussed a pseudo-inverse based re- adjustment of control gains so that the closed loop matrices would be preserved in a least squares sense. Their algorithm was evaluated using a nonlinear simulation ofa Grumman CRCA with stirface damage. Although results were positive, stability was not guaranteed, and problems could result from saturation effects. A stability analysis of such pseudo-inverse based procedures was presented by Gao and Antsaklis [24] in 1991. They proposed a new approach valid for a certain class of structured uncertainties; however, no extensive flight control evaluation studies were presented. In [21,24], Dhayagude, Gao, and Antsaklis evaluated the validity of applying pseudo-inverse methods with model following procedures in the presence of aircraft changes. However they did not include any results corresponding to a coupling of fault diagnosis with their control restructuring procedure.

Optimal contro. 1based procedures have also been considered for reconfignration assuming the existence of a higher level failure detection and identification algorithm. In 1985, Looze et. al. [40], proposed a procedure for re-adjusting the performance index weights so as to maintain system specifications even in the presence of a failure. Their evaluation used a linear simulation of a 737 with rudder failure. More extensive simulations however should be considered for this approach with different surface failures as well as sensor failures. In 1989, Moerder et. al. [45] used failure detection in conjunction with linear quadratic gaussian controllers on linear simulations of the AFTI F 16 with a variety of failed surfaces. Although results were favorable, more validation is needed on nonlinear models. The adjustment of performance index weights was also considered in 1990 by Huang and Stengel [29], who considered the optimization of model following indices. With linearized lateral F4 motion, they were able to show that such weight modification was feasible in the presence of aileronsurfacelossanddecrease in controleffectiveness. Howeverthis wasnot testedwith any

fault detectionor adaptationlogic. Anotherlinear optimal procedurewas proposedin 1991by

Ahmed-Zaidet.al.[2]. Although failureswereconsidered, the procedure wasprimarily for single input singleoutputsystems.

Various other procedures havealsobeenproposedfor use in conjunctionwith a failure

detectionandidentification algorithm.An eigenstructure procedureto accountfor changes from

operatingconditionswaspresented in 1994by Jiangin [31]. Because failureswerenot explicitly

considered, it is difficult to assess stabilityandtiming problemsthat may arise.In 1995Wu [66] appliedfuzzysets with Mu-synthesis toalinearpitchaxiscontrollerin thepresence of canard failure.

Howeverthis studywasvery limited in scope andwasmoreof theoretical interest.Finally in 1998,

Huzmezan andMaciejowski[30]considered modelbased predictivecontrolwith fault detectionfor

singleinputsingleoutputmissiledynamics. Althoughtheydid not consideraircraftdynamics,their

approach might berelevantif timing is not anissue.More recentlyShearer andHeise[57] applied

modelpredictivecontrolto a simulationof the nonlineardynamicsof an F-16aircraft.Although

resultswerepromising,moreresearch is needed to address topicssuchastuning,adaptation, model simplification,andpilot modelling.

2.3 Reconfiguration using explicit or indirect adaptive control As an alternative to using some type of failure detection logic, the concept of online parameter identification offers the possibility of tracking both continuous and sudden changes in the system dynamics. As these changes are identified, the adaptive control logic is used online for appropriate modification of the controller parameters (e.g.. gains) so that acceptable handling qualities are preserved even in the presence of failures. With the use of explicit parameter identification, it is often necessary to provide adequate external excitation in order to insure acceptable parameter estimates.

This excitation needs to be acceptable to the pilot and at the same time large enough to counteract the effects of noise. A further concern is the need to identify a system under closed loop control.

Without sufficient excitation and/or previous knowledge, such closed loop identification be only be capable of computing estimates of parameter combinations rather than individual estimates. These problems might be somewhat alleviated by recent results presented by Elgersma, Enns, and Shald on signal injection [22], and by some recent results on closed loop identification by Feng et. al. [23].

Chandler et.al. [ 16,17,18,19] and Pachter et.al. [54,55] have published many papers that deal with various aspects of online aircraft parameter identification for reconfigurable controls. They evaluated moving window based identifiers and coupled them with linear quadratic regulators, predictive controllers, and even online optimizing Hopfield networks. These adaptive controllers were then applied to linear simulations of an F-16 with disturbed trim and 50% loss in horizontal tail area. Results to date indicate that the proposed identification procedures should be very effective for tracking aircraft changes. Some work in combining identification with feedback linearization has been reported by Ochi and Kanai [50]. Although their paper lacks details concerning the algorithm, the results on a six degree of freedom nonlinear fighter model look very promising. Bodson et. al.

[7,8,28] have considered model following control with a modified sequential least squares based online identifier that combines a fading factor with a penalty on parameter changes. A constant

disturbance termwasalsoidentifiedto modelunknowntrim changes. Very goodresultshavebeen

reported for simulations with nonlineardynamics and a locked left horizontal tail. Because

reconfigurable controllersmustaccountfor constraints on actuatorratesandpositionsBodsonand

Pohlchuckin 1998 presentedfour approaches for limiting the commandsto a reconfigurable

controller [6]. In view of the excellenttrackingdeliveredby Bodson'smodified sequentialleast squares identifier, it alsohas beenusedby Ward et.al. [46,63] with a recedinghorizonpredictive controller.Thesestudies, possiblythemostextensive todate,consisted of simulationstudies, piloted simulationstudies, andactualflight tests. Failures includedtheleft horizontaltail, theright horizontal flaperon,partially missingrudder,andmissinghalf tail andrudder. Resultsshowedthe feasibility of using explicit adaptivecontrolfor reconfiguration andimprovedaircraft survivability.

2.4 Reconfiguration using implicit or direct adaptive control Although to date most of the research in adaptive control for aircraft controller reconfiguration, has considered indirect methods that require explicit on line parameter identification, some consideration has been given to direct procedures which in a sense directly estimate or adjust the controller gains without the use of explicit aircraft parameter estimates. In general these procedures are based upon the use of a forced reference model whose output is to be tracked by the process (aircraft) output. If all the states of the plant are to track all the states of the reference model, then the so called conditions for perfect model following must be satisfied [34]. All states must then be available for feedback or an observer must be incorporated. If however, only the plant output (usually of lower dimension than the state vector) is to track the model output, then the less restrictive so-called command generator tracker procedure may be used to develop the adaptive controller [34].

Although the controller is easily implemented, certain positivity or passivity conditions must be satisfied to assure stability. Procedures based upon feedforward compensators have been developed to alleviate these conditions [34].

The attractiveness of this approach for reconfigurable controls was pointed out by Morse and Ossman [47]. They used a simulation of linearized AFTI/F-16 dynamics in the presence of single surface failures (horizontal tail, rudder, flaperon), double sided failures (double flaperon, rudder and canard, double horizontal tail, same side flaperon and horizontal tail) as well as some triple and quadruple failures. Results were very encouraging and certainly indicative of the potential for applying direct adaptive control to aircraft reconfigurable control systems. However, additional work is needed to address some of the more recent theory related to the alleviation of the passivity conditions [32,33] required for stability assurance. Incorporation of feedforward compensation around both the aircraft and the reference model should enable the satisfaction of these passivity conditions and at the same time ensure perfect output tracking [34]. Further testing should also consider the use of more representative nonlinear aircraft equations of motion.

2.5 Reconfiguration using multiple model based procedures Adaptive flight control based upon a bank of switchable models was proposed by Athans et.

al. [3] in 1977 as a means for improving the transient response of adaptive systems especially in the presence of abrupt variations. The control was computed as the weighted sum of the linear-quadratic guassian controllers corresponding to each of the models. The weights were the associated conditional probabilities as computed by Kalman filters. More recently in 1994, Narendra and Balakrishnan [49] considered the problem of multiple model based model reference adaptive control.

They used multiple adaptive identification models to identify a plant and then the adaptive controller corresponding to the identified plant with the smallest performance index. In 1997, Narendra and Balakrishnan [48], proposed further switching and tuning schemes that combined both fixed and adaptive controllers. Their favored approach consisted of a bank of fixed models, with one free running adaptive model and one reinitialized adaptive model With regard to recent applications of multiple model controllers to flight systems, Maybeck et.al. [41,42,44] used multiple models with no adaptation for alleviating the effects of hard and soil actuator and sensor failures. They considered a nonlinear simulation of a Vista F-16 with failures in the stabilators, flaperons, rudder and sensors for velocity, angle of attack, pitch rate, normal acceleration, roll rate, yaw rate, and lateral acceleration. This approach required many models and was very effective for hard failures. Results for soft failures were best when effectiveness had been reduced below 50%. Rauch in [56] considered a reconfiguration using multiple models and fuzzy logic. However, this was mainly an idea tried out for ship motion without any attention given to aircraft. More recently Boskovic et. al. [9,10] and Mehra et. al [43] combined multiple model switching with adaptive model following control principles and considered simulations of a tailless advanced fighter aircraft with wing damage and control effector failures. Results did indeed demonstrate the effectiveness of this procedure. Because all states of the plant were forced to follow all states of the reference model, it was necessary to assume the validity of the so called conditions for perfect model following and to use observers for estimating the full state vector. This need for observers should be alleviated through the use of a bank of output model reference adaptive controllers.

2.6 reconfiguration using neural networks, fuzzy concepts, and intelligent control Reconfigurable control can often be cast as a hierarchical problem requiring some sort of supervisory and/or intelligent control overseeing the detection and modifcation layers. Thus the use of intelligent control, neural networks, and fuzzy control has been considered for one or more of the reconfigurable functions. In [61,62], Stengel discussed intelligent fault tolerant control in general and specifically for flight control systems. Kwong et. al. [38] used fuzzy model reference learning control [39] for an F-16 simulation with failures in aileron or rudder. However there were no considerations given to timing, stability and robustness. A theoretical analysis of using fuzzy sets for controller selection was considered by Wu in [67]. However its application to flight control seems unclear. Copeland and Rattan [20] considered the use of fuzzy control as a supervisor for reconfigurable control. This paper however lacks details and does not address stability and timing issues. Barron in [4] considered the use of neural networks for fault detection using flight simulations; however, control reconfiguration was not considered. Rauch in [56] discussed reconfiguration using multiple models and fuzzy logic but for ship, not flight applications. Chandler et. al. [ 16] in 1993 reported on the use of Hopfield networks for optimizing a model following penalty

function given the identified parameterestimates;however, the procedureis at presenttoo

computationallyintensivefor realtime use.Finally in a recentpaper[ 15],Calise,Lee,andSharma discussed theuseof adaptiveneuralnetsfor modification(asopposed to theentirecomputation) of the control signalin the presence of failures.The neuralnetworkwasusedto compensate for the

inversionerrorbetweenthe baseline controllaw's model andthe true systemmodel.Differences

betweenthesemodelscanarisefromuncertainties and/orfailuresanddamage. Resultsto datehave

considered thesimulationof a taillessfighterwith lockedleft aft-bodyflap. Althoughtheseresults appearto bequitegood,moreevaluations areneeded for validation.

a transferfunction that satisfiesthe positivity conditions.Also baseduponthe work reportedby

Bodson[7,8], it is alsorecommended thata constant(butunknown)disturbance be includedin the

plantequations to accountfor unknowntrim.

Themultiplemodelbased approaches discussed in Section 2.5 areveryattractivein termsof

their potentialspeedof response to an abruptchangeand/orfailure. Howeverunlesssomeonline

tuning is present,an extraordinarynumberof modelsmay be required. With this in mind, the

procedures discussedby Boskovicet. al. [9,10] andMehraet. al. [43] seemvery promisingfor

reconfigurable controllers.This approach which combinesmultiple models,switching,andtuning

appears to berobustin thepresence of severe effectorfailures.Howeverasnotedin Section2.5, an observer is requiredsincefull statefeedback is required.Thusit is recommended thatdirectoutput modelfollowing beincorporated ( asdiscussed in Section 2.4)asthecontrolalgorithmtobecoupled with multiple modelbased switching.In additionit is suggested thatswitchingalsobeusedto select reference modeldynamics thataremorerepresentative of thefailed aircraftcapabilities. This follows

since a pilot aware of reducedcapabilitieswill not be as demandingin commandfollowing

expectation. It .isfurthersuggested thatthealgorithmalsobe extended to includesensorfailuresas well asactuatorfailures.

Finally with regardto reconfiguration usingneuralnetworks,fuzzyconcepts, andintelligent

control,neuralnetworkscould asin [ 15]beusefulfor generating a signalthatmodifiesthe control signalto accommodate toa change or failure.Because of stabilityissues, thisprocedure is preferable

to the directuseof a neuralnetfor computingtheentireactuatorcommand.Otherpossibleusesof

neuralnetworksarefor the detectionof failuresandin the development of onlinemodelsof the

aircraftdynamics.

, _ _ _ . ,'_ , :_ i ¸ 4.0 Validation Procedures To date the explicit adaptive control procedure described in [46] and [63] has received the most extensive validation. This has consisted of linear simulations, nonlinear simulations, piloted simulations, and actual fight tests. Various other procedures have been tested with only one or two simulated failures, while many others have been tested with a wide class of simulated sensor and actuator failures.

Because theoretical results have for the most part only addressed the stability of the algorithms as applied to linear aircraft motion with analytically modelled failures, it is very important that nonlinear simulation and/or analysis be considered. Recent results in the concept of backstepping might be considered for the stability analysis of the various reconfigurable algorithms when applied to nonlinear models.

In any event it is important that the controller be analytically shown as stabilizing for the linear models for the normal and for the various failed representations. This analysis should of course be followed by more representative simulation studies using nonlinear system models and then actual flight tests.

With regard to the types of failures to be considered, consideration should be given to flight control surface failures, damage to lifting surfaces, and sensor failures. Representative control surface failures should include locked and floating rudder, aileron, and elevator. Damage should be modelled as a reduction in control effectiveness for a wing flap and/or the rudder. Representative sensor failures should include those that measure velocity, angle of attack, pitch rate, yaw rate, lateral acceleration, and normal acceleration.

5.0 Conclusions and Recommendations Based upon the existing literature, it does indeed appear that it is possible to design and implement reconfigurable controllers for both commercial and military airplanes. This conclusion is based upon stability analysis, simulation experiments, and actual flight testing. It is also supported by the results in the 1997 paper by Burken and Burcham [ 12], who showed that a large civilian multi- engine transport, the MD-11 could be controlled with only engine thrust as backup to the primary flight control system. Results showed that this backup system could be used in the presence of certain major failures (e.g. hydraulic pressure loss), for landing the airplane without the aid of the aerodynamic control surfaces.

Common to much of the reported research in reconfigurable control design, is the use of controllers based upon model following principles, Such indices have been used for direct adaptive control [47], indirect adaptive control [6,7,8,28,46,63], multiple model control [9,10,43], variable structure control [35], and in neural network based control [ 15]. Thus it is recommended that the use of such indices be continued in subsequent research or at the very least be used as bench marks for comparative testing.

Taking into account that the allowable time for full control reconfiguration might be two to four seconds for a commercial airplane and fractions of a second for a military aircraft, it is important to stress those procedures that will be adequately fast with sufficient guarantees of stability. As stated in Section 2.0, Pachter and Chandler in a recent paper [53], recommend adaptive control in situations where there is a high level of uncertainty and when there are abrupt changes in unknown parameters.

In particular, Pachter and Chandler recommended the use of outer-loop explicit adaptive control as opposed to existing inner loop procedures. However since explicit adaptive controllers have already received considerable attention for reconfigurable control design, it is recommended that direct model reference adaptive controllers be considered in future research. Direct adaptive controllers have the potential of delivering a faster response to a configuration change compared with explicit adaptive controllers. This follows because no explicit online parameter identifier needs to be executed. The adaptive outer-loop recommendations of [53] can be accommodated if the inner-loop consists of the aircraft and an adequately robust control compensator. The direct adaptive algorithm would then be used as an outer-loop controller designed so that the inner-loop output tracks the reference model output. It is anticipated that satisfaction of the sufficiency conditions for this closed loop c6nfignration will be less demanding than for the open loop aircraft dynamics.

Furthermore, as previously noted, direct adaptive controllers can easily be combined with multiple model based procedures for even faster time response. Associated with each of the multiple models would be an adaptive controller and possibly a reference model. Such controllers would be designed apriori so that the response of the corresponding control loop would display desired handling qualities and at the same time be relatively robust over a reasonable range of plant uncertainty. Different reference models associated with each aircraft configuration model would allow the specification of changed performance requirements in the presence of failures. The adaptation procedure can either be designed to retune the controllers because of mismatch between the selected aircraft model and the actual dynamics, or the adaptive controller might be designed to adjust the inputappliedto theclosedloopdefinedby theaircraftandtheselected controller.In eitherevent,the

combination of a tunablecontrollerwith multiple modelbased switchingshouldreduce thenumber

of models thatwould beneeded if only fixed controllerswereto beused.With enoughselectable

modelsandassociated controllersthatareadequately robust[ 1 ], it is anticipated thatthe resulting reconfigurationwill be implementable, very rapid andwill meettheperformance goals.

Issues thatneedinvestigation include:

The inclusionof a constantplantdisturbance vectorto accountfor unknowntrim

The designof a representative bank of aircraft modelsthat allows rapid switching and

adequate control loop robustness

Thedesignof reference models thatareindicativeof performance goalsfor eac'h of thefailed

configurations

Developmentof procedures that assuresatisfactionof the passivity conditionsover all

anticipatedconfigurations

Development of robust-inner loopcompensators thatcanbeusedin conjunction with adaptive

outer-loopcontrollers.Of potentialinterestto sucha designarerecentresultsin

variablestructurecontrol for aircraft [35,58],linearmatrix inequality basedflight control

design[65], and H-infinity based fault tolerant design [26].

Although it should be possible to validate stability for the linear representations, it may be necessary to rely on simulation studies for more representative nonlinear models. However, recent results in the concept ofbackstepping [37] and its applications to aircraft control [60] might be useful for the stability analysis of certain nonlinear models controlled by the reconfiguration algorithms.

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