Reconfigurable Flight Control During Actuator Failures Using Predictive Control

RECONFTGURABLE FLIGHT CONTROL DURING ACTUATOR FAIL...

14th World Congress oflFAC

Copyright (C) 1999 IFAC 14th Triennial World Congress. Beijing, P.R. China ChiRFATL...

P-8a-02-5

RECONFIGURABLE FLIGHT CONTROL DURING ACTUATOR FAILURES USING PREDICTIVE CONTROL 11lI. Huzmezan *,1 J.M. Maciejowski '

• Cambridge University Engineering Dep(utment, Trumpin.l}ton St., Cambridge, CB2 lPZ, UK.

Abstract. This paper descrihes a scheme for fault-tolerant control of an aircraft with a high angle of incidence. The scheme is an example of a generic scheme proposed in (Maciejowski, 1997), adapted to the particular needs of this application. Details of the predictive control technique when employed for rcconfiguration are given. The paper also contains a discussion of various scenarios for possible actuator faults. The performance of the proposed fault-tolerant scheme in the presence of severe failures of control surfaces is examined in simulation with an High Incidence R esearch Model (IIIRM). Copyright:l:) 1999 !FAC Keywords. Reconfigurable Flight Control, Predictive Control, Optimisation, Fault Tolerant Control

1. INTROD1.:CTIOS

This paper is concerned with fa.ult. tolerant control. In previous work (Huzmezan and ~laciejowski, 1998a; Maciejowski, 1997; Huzmczan and Maciejowski, 1998b) we addressed the methodology used to cope with actuator and structural failures. In this paper we apply this methodology and report simulation results for the essent.ial problem of actuator failures. The fault tolerant method suggested is based on the assumption that accurate and almost instantaneous Fault Detection a.nd Isola.tion (FDI) is performed by a d edicated system outside of the control algorithm.

1 ,,-mail: {mh 2, jmm}@eng.cam.ac.uk, tel:+44-1223-332732. vVe would like to acknowledge Pembroke College Cambridge , Lun d gren Pund, Cambridge Oversea~ Trusl and C T Taylor Pund by which .Mihai Huzmezan i3 ~ upportcd. \Vc a cknowledge the assistance given by the DERA - Bed ford in support of the work covered in this paper.

Our experience t.o date shows that accuracy of the FOI system is more crucial than its speed in determing the failure. As various incidents proved, it is often enough t.ime between the fault occurrence and the moment when this is transformed into a catastrophic failure, that is the time when a pilot loses control of the aircraft. In this paper we describe a control strat.egy exhibi t-ing actuator fault tolerance for the longitudinal channel of the High Incidence Research Model (HIR~f). \Ve owe the development of t.he model to the authors of (Magni et al., 1997; WilIcox, 1997). This model has redundant motivators, a taileron and a. canard, in the longitudinal channel. The highfidelity model developed in the case of this aircraft is regarded as being sufficiently accurate to reflect a wide class of failures detected and isolated by the FDI system of which only actuator failures are considered in this paper. Before going into details we give the reader a. broad

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RECONFIGURABLE FLIGHT CONTROL DURING ACTUATOR FAIL...

14th World Congress ofIFAC

outline of our strategy for control reconfiguration which is based Oil four system components: the high fidelit.y modelling, fault detection and isolation, model approximation/simplification and constrained Model Based Predictive Control (A1 BPC). These techniques work toget.her as follows in order to provide ~chedlll­ ing and reconfiguration for the HIRM aircraft:

Development Space" (Huzmezan and lVlaciejowski, 1997) and the aerodyna.mics and engines model of the HIRM model CMagni et al., 1997; \Villcox, 1997).

2. THE AIRCRAFT :\lODEL AND FAILURE SCE~ARIOS

(1) When a failure occurs the FDI system pinpoint.s the nature of it. If t.he failure is structural, parameters in the high fidelity model are modified (specifically, aerodynamic coefficients are modified) whereas in the case of actuator failures, such as jamming or reduced movement, information is passed dinc:ctly t.o the j\.f BPC controller as modifications of input and input rate constraints. The latter type of failure will be considered in the paper. (2) A linear time-invariant. (LTI) model is obtained at; each st.ep, techniques used in accomplishing this step being reported in (Huzmezan and ),faciejow:;ki, 1998a; Maciejowski, 1997; Huzmezan and Ivlaciejowski, 1998b). This is t.he LTI mod"l used by the .M BPC controller as its internal modc"l. In this paper our focus is not on the model update. (3) The constrained J.1.;f BPC controller computes appropriate control inputs to the plant. Giving it c'J1ough degrees of freedom (a large enough set of control inputs) enables it to keep the plant dose to the required trajectory: under t.he as:-mmption that any failures arc compatible with this.

2.1 The longitudinal model dynamics In this paper we restrict our attention to the longitudinal channel of the HIRM. 'Ve can assume that the ::;ideslip angle as well 1l.S the roll and yaw rates are zero. The model Inotion:

based on the following equations of

(~.) cos(r) + C7~') + C:~,

i =-

)

sin(a)

a=q--y

(~) J

q=M

-

ZATPF

1I

r>= -gsinh) -

if =

(~)

+

(~)

Vsinh)

where;, Q, q, V, If denote vertical flight path angle, angle of attack, pitch rate, airspeed, and altitude, respectively. The variables m, C, J1/ are constants denoting, respectively, the aircraft mass, t.he reference mean aerodynamic chord, and the pitch IliOIIlent of inertia.

Our claim is that this strategy provides two layers of fault tolerant control

The expressions of the aerodynamic drag (D), lift (L) and pitch moment ("'-'I) expressed in body axes are:

• the reconfiguration of control activities which occurs if there are actuator failures which are consist.ent with maintenance of t.he requil'eu fiight conditions • the implicit re-design of the control Ia.w which occurs if there ale structural failures, as a consequence of changes in the int.ernal modeL A brief outline of the paper is as follows. First the paper briefiy surveys the aircraft model. Then an exposition of possible ~ceIlarios for actuator failures and their implementation in simulation follows. Next the overall controller structure, and the design cycle are descrihed. Simulation result.s \vith the aircraft being subjected to several RCfmarios are shown (of course due to space limitations only some of t.he most relevant results arc included in the paper). All these results were produced using IVlatlab Simulink software which comhined our" fl1 B PC

IS

+ OX",::o (et, 6T5 )6C5]

LJ = qS [CXJTS (a, 6TS)

L

= qS

[CZ'TS (et, 6TS)

,

+ CZ'cs (n, OTS)OCS+

QC]

+ C z .] (0, Scs) 2V

11.1 = qSc [CM"TS (a, 6TS)

+

,

+ C/rvI.,cs {a, OTS)OCS+

qC]

CMq (a, 60S) 2V

where (j = bp(H) v 2 is the dynamic pressure and p(H) the ai; density, which varies as a function of altitude. In the ahove eqnations the meaning of F, 6TS: 6cs is: t.hrust vector, symmetrical taileron deflection, and symmetrical canard deflection, respectively. These are t.he three control inputs. The con-

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ISBN: 008 0432484

RECONFIGURABLE FLIGHT CONTROL DURING ACTUATOR FAIL...

14th World Congress ofIFAC

twlled outputs are: the pitch rate (q) and the airspeed CV).

Another important aspect of these failure scenarios is the ability of the FDI system t.o deliver information about t.he fault. Three different situations can be imagined: no informa.tion about the failure, a significant delay in determining the fault and almost instantaneous delivery of the data concerning the failure.

The non dimensional coefficients in these equations: C Xors (a, tiTS), CX'cs (a, tics), CZ'rs (a, tiTS), C ZOC5 (0:, tics), C z" (0, rles) , C MJTS ((X, tiTS); CMijC8 (0, clCS) , CM" (0, clc:s) are given in look-up tables obtained as 11 result of wind tunnel tests (:'Iagni et al., 1997; \Villcox, 1997). In the on board high fidelity model their values are computed hy linearly interpolating between the values stored as functions of the variable 0: and the corresponding surface deflection.

The simulation results presented in Section '1 contain several of these scenarios.

3. THE CONTROLLER ARCHITECTURE AND TUNING

The way the aerodynamics forces, together with the engine thrust, act upon t.he 6-DOF nonlinear simulation model is defined based on wind tunnel data and simple first order actuator models which also include delays. The model is programmed in C using thp. MatJah Simulink S-function template ami run as compiled code.

2.2 P().£lll.re

3.1 The predictive control concept The defining feat.ure of Model Based Predictive Control Uvf BrG) is the repeated optimisation of a performance objective over a prediction horizon U'-'2). Given a set-point, a reference T(k + I) is produced and used within the cost function (1). Manipulating the control variable u( k + /), over the control horizon (IVIL ) , the algorithm drives t.he predicted output y( k+l), over the prediction horizon, towards the referencc. Thc futUre control movement over the control horizon (Nu) is determined by minimising the eost function:

.~cena'r1.08

Onc of the m.ost frequent failures encountered in practice is actuator failure. The reSUlting reduction of control authority leads to reduced performance, or even instability. In this section we define some failure scenarios for the longitudinal channel HIRM actuators. These scenarios assume level flight or transients when achieving a change in the air speed or pitch angle set-points. During these manoeuvres all [he actuators (taileron, canard and thrust) are em~ ployed either in trimming the aircraft for level flight or in the achievement of the Hew set-point and the required decoupling of the other channels. To a~·iSess the effects of actuator faults for the longitudinal aircraft channel all the above UlotivaT.ors have to be subjected to various rate and/or position rcst.r·ictions. The scenarios simllla.te various real wodd faults. For instance, an actuator which is stuck as 11 result of battle damage or a mechanical problem can be simulated by imposing constraints on its position (i. c equal limits for the minimllm and the maximum movement, values equal with the actuator position before the fault occurred). Alternativdy, a rate constraint can represent the effect of a h"ak in the hydraulic system. Such a failure does not modify t.he position constraints of the actuator. 'Ve also consider mixed rate and position failures.

]\l2

J(k) = ~

II(y(k + I)

- r(k

+ l)II~(l) + (1)

IVu - J

+

"L

II.c,u(k

+ i)II~(l)

1==0

subject to constraints on: • the input levels: Ul(l)~U(l)~uu(l), where kSISk + Nu - 1 • the input rates of change: D.llr(l) S.i')..u(l)SD.u,,(l), Vi here k"'2) Se k + .Vu - 1 • t.he output (and state) levels: YI (I)Sy(l) SYu(l) , where k + NI SISk + N2 In (1), Q(/) and R(l) arc weights independent of ~ 2 the time k and the norm II·II Qis defined as IlallQ := nTQo. It iR Clssumed that D.u.(l) = 0 for 12k + [·{u. The k1 BPC scheme works as follows: based on an internal model representing the plant t.he evolution of the sy::;tem is predicted into the futur·e and then these predictions involved in the co:-;t function (1) ,vhich is subject. to input (actuator) and output (Hight envelope) limitations. The optimisat.ion formulated i5 a quadratic program (QP) which is solved using a standarrl algorithm.

7981

Copyright 1999 IF AC

ISBN: 008 0432484

RECONFIGURABLE FLIGHT CONTROL DURING ACTUATOR FAIL...

14th World Congress ofIFAC

Only the first command increment .6.u(k) is implement.ed, and the optirnisation is re-solved B.t each step.

4. SIMULATION RESULTS 4.1 The modelling and implementation for simulation of actuator frw.lts

It is important to note that the optimisation constraints are modified on-line ba~ed on t.he new information available from the FDJ system. This is a straig;htforward mechanism which exploits the main feature of 11,01 BPC schemes used in our controller architecture.

3.2 Th!; flight

cont,,.oll(;~·

An important step in checking the behaviour of the YIBPC reconfigurable controller when facing actuator failures was their modelling. \Ve have modelled the actuator failures by defining for each inJlut channel a new Simulink block ,vhich receives the following inputs:

design

• current time, • failure t.ime, • delay time in detecting the failure (this has a zero value fOI' an iIl~taIltaIleous detection and great.er that 100 s for no information delivered to the controller about the fault), • rate and position constraints before and after failure (if miniIIlllm and maximum rate constraints after failure are both zero means that the corresponding actuat.or is stuck at the previous p()~iti()n before the fault).

The controller design followed the general procedure which we have developed for cOIlv(·mtional 111 BPC control (Huzmezan and Maciejowski, 1996). This involved tuning the M BPC controller for a plant model obtained by lilleari~ing the healthy high-fidelity model about an equilibrium point corresponding to level flight at Mach number M = 0.30 and height of H = 5000 jt with parametric uncertainties in l'vI of 3%. A sampling time of TB = 0.05 s provided a good approximation over the whole open-loop bandwidth (the smallest constant which appears in the model is on the transfer function from symmetrical taileroIl COTS) to pitch rate (q) and it has a cross-over of about 10 md/s). In order to speed up the proces~, the tuning was first performed for the unconstrained case. The control horizon wa.s chosen to be the same as the number of states iV." = 11, but the small sampling require a predict.ion horizon of N2 = .30 in order to be able to predict 1.5 s ahead. This was enough to ensure the achievement of the performance: criteria. The Af BrC eontrol weighting matrix had to be made relatively big: R = diag( [20000 15000 100J), a typical choice for the longitudinal channel of an aircraft. The .1\1 BPC trackill~ weighting matrix: Q = diag( [700 2J) leads to :-;atisfact.ory time response characteristics (rise time, settling time and overshoot) for the dosed loop system. These were obt.ained after sorne trial and enor, starting with unit values for both weighting matrices. The next step in the design, after checking the unconstrained dm;ed loop behaviour, was to enf(}n~e the constraints and check the constrained lv1 BPC performance. Due to space limitations, a detailed analysis of how the uncertainty contained in the aerodynamic coefficients is addressed hy the controller is not presented even though the A[ BPC design provides the requested degree of robustness in face of such mismodeling problems.

The outputs of the block that models the actuator failure are of two kinds: • the outputs simulating t.he FDr operat.ion which give details to the .'ViB PC controller about the fault in the corresponding actuator. • the scalar output repre:senting the input to the actuator, which respects the constraints on its output. It is possible to actuator model. the actuators is frequency of the

have this block lying outside the This is beeause the bandwidth of always bigger than the maximum output signal from our block.

4.2 Respon.~e!j of the Teconfig·uro.lile flight contmlle'r to actua.tor fa.nlts The simulation result shown in Figure 1 shows the system response when the canard actuator failed during a pitch rate (q) demand of 6" Is. The doublet in pitch rate demand occurred at time [) s followed by the failure, a limitation in the sYIIlmetrical canard actnator rate (from 80 /s to 30 0 /09) and position (from -20 to _6° and from +10~ to +3"), which occurred at time 12 s. A delay of 1 s for the FDI system to provide information about the failure was asommed. As discussed in the pr~vious section, this failure was represented by tightening the constraints on the allowed canard rate deflection in the 0

0

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Copyright 1999 IF AC

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RECONFIGURABLE FLIGHT CONTROL DURING ACTUATOR FAlL...

IvI BPC optimisation. Due to the M B PC feature of handling eOIlstrajnts explicitly, no other change was necessary in the structure of the controller. Figure 2 shows the behaviour of the canard actuator. Both figures show the nominal response, and the response after failure, with and without FDI. The sysll2111 rM:'JOI"ISe during doublet in Cl klr 3ew!lsl

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The canard was stuck at the position it had just before the failure. T h" iiystlllm r9~pon iOu during doubkJt in q lor ~Ve ta\ scerlo.rio.s

~nll~ios

· "---,---,----r---r-~~==~==~======~==l

Fif!;. 3. The pitch rate response with stuck canard during a pitch set-point doublet Thp. Cur d ~ ;(in g doub let in q fnr seifern' s-:enaros 8

Fig. 1. The pitch rate response with canard rate and position limitations during tramlients for a pitch set-point doublet

:r I

2-

~ I 0 rn

,

~

~

l

Ail~~'"

1

-2-

"

~""'-'-- ~-------I

-t

, I~

'., 1.1 H

-<,"

. l~

-Br

)

,f·

l

_10 L.._-'-_____- '____" - - _ - ' - _-'-_ >'!> 3(: 1O 15 0

~ .----L-------------.l

25

40

45

50

timlll5j

_6

-ll

o

.

S

•

1C

I -1S

~_'---

20

25 tiMe Is1

nomInal response response With FDr information

'.'P ons•

wilhoul FDI in!oHMli n

__ " - ----"

30

33

40

4S

Fig. 4. The canard response for various scenarios during the same failure as in Figure 3

' -1

,

The last test considers failure which is a. mixture of rate (from 80° /s to 30° ;.~) and position (from -40 0 to -20°) limitations for the taileron and simultaneously a stuck canard as in the previous simulation. All failures occurred at ~,ime 6 s . The results are shown in Figures)) and 6.

I

50

Fig. 2 . The canard response for various scenarios during the same failure as in Figure 1

It is important to note the way the lv[ BPC redistributes the control effort from the canard towards the taileron. SiIlce the control power delivered by the canard was severely limited by the failure, r edundancy in the corresponding input direction was required .

The second failure was a stuck canard that occurred at time 12 s during a similar manoeuvre as in the previo us case. The responses of both the uninformed and informed controller are shown in Figure 3. Figure 4 looks at the canard responses during this manoeuvre for all three scenarios stated in the legend.

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RECONFIGURABLE FLIGHT CONTROL DURING ACTUATOR FAlL...

For all cases, the delay of the FDI in providing the information about the failure is 1 s for the canard and 3 s for the taileron after the failure hClS occurred. ~ ate the performance of the controller in this case compared with the case of no information available. By looking at the performance criteria stated in the GARTEUR Design Challenge (l\[agni lOt al., 1997) , for this manoeuvre, we consider the controller performance in the presence of the severe failures to be satisfactory. All the results reportp.d in t.his section were obtained using a linearised model of the aireraft.

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5. CONCLUSIONS AND RECOMMENDATIONS The contribution of this paper is both at the coneeptual and practical level. \Ve have developed and tested in simulation a st rategy which provided r econfiguration of the ovcl'all cont.r oller during rate and position actuator failures. In t er ms of certification and real time implementation there is much more to be accomplished. The model chosen t o illu~trate t he algorithm was subjected to several realistic failure scenarios which showed the ability of the controller to meet the performance criteria mentioned in the GARTEUR d esign challenge. In this paper we h ave selected a sIIIall set of failures ,which we consider to be of most practical relevance.

Toosystf:l'f'1 ''''I5PMStI dlJ1K:9 dOlJblet in Q tor se'lleral.sc ellAn05

Given the results obtained, ami a .~suming that adequate hardware is available we consider this strategy as a potential future candidate for control reconfiguration.

6.

-3.0- .

REFERE~CES

,

Huzmezan, IVI. and J .M. ylaciejowski (1996). RCAM Design Challenge Presentation Do cument: The Model Based Predictive Control Approach. Technical Report TP-088-20. GARTEUR. Huzmezan, M. and .J.~I. :vlaciej ow~ki (1997). A development space for model hased predictive control. In: 7th Symposium on Computer Aided Contml System Des·ign, Ghent, Bdgium. IFAC. Huzmezan, M. and J.M. Mac:iejowfiki (1998a). Reconfiguration and Scheduling in Flight Using Quasi-LPV High-Fidelity Models and M BFC Control. In: American Contr'ol Conference. Huzmezan , M. and J .M. Maciejowski (1998b). Automatic Tuning for Model Based Predictive Control During Reconiiguration . In: Proceedings of AERO'9S, Seoul, Korea. IFAC . ~laciejowski, JM. (1997). Reconfigurable Control Using Const.rained Optimisation. In: Proceedings of ECC'97. Bruxelles, Belgium. Magni, JF., S. Bennani and J. Terlollw (1997). Robust Flight Control: A Design Challenge, GARTEUR. Chap. Chapter 27 - The HIRM Design Challenge Problem Description. Vo!. 224 of Lecture Notes in Control and Infor"mation Sciences. Springer-Verlag. Willcox, S.\V. (1997). Private communication, DERA. Technical report.

, ] "-.. o

-~----:':,----::---:':-----c::------!::----=---:~\----=--: 10

15

20

25

ao

35

.:10

-45

50

Imlii[sl

Fig. 5. Pitch rate response with a mixed rate and position taileron failure and stuck canard dllring a pitch set-point doublet

'f

-100'----~-lL C,--,L!~--2
Fig. 6. The taileron response for various scenar ios duL'ing the same failure as in Figure 5

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