Table Of Content!c)2000American InstituteofAeronautics &Astronautics orPublishedwithPermission ofAuthor(s) and/orAuthor(s)' Sponsoring Organ_zataon
AIAA Guidan_. Navigation, and
Contm( Conference and Exhll_t
14-17 August 2000 Denver, CO
A00-37004
AIAA 2000-3942
A Reconfiguration Scheme for Ae_:ommodating Actuator Failures in Multi-lnput, Multi-Output
Flight Control Systems
W. Siwakosit' and R.A. Hess 2
Dept. of Mechanical and Aeronautical Engineering
University of California
Davis, CA 95616
Abstract
A multi-input, multi-output requirement, reconflgurable flight control is an
reconfigurable flight control system design active research area, see for example Refs 1-8.
utilizing a robust controller and an adaptive filter
is presented. The robust control design consists The research to be described will focus
of a reduced-order, linear dynamic inversion on the problem of recovering performance in the
controller with an outer-loop compensation matrix presence of actuator failures. The methodology to
derived from Quantitatitve Feedback Theory be described will allow continuous pilot control
(QFT). A principle feature of the scheme is during reconfiguration, a significant improvement
placement of the adaptive filter in series with the over some of the approaches that have preceded
QFT compensator thus exploiting the inherent it, i.e., gels. 6 and 8. In addition, reconfiguration
robustness of the nominal flight control system in in the presence of significant nonlinearities
the presence of plant uncertainties. An example of stemming fi'om actuator amplitude and rate
the scheme is presented in a pilot-in-the-loop limitations will be demonstrated as will the
computer simulation using a simplified model of handling qualities and pilot-induced oscillation
the lateral-directional dynamics of the NASA F- (PIO) prediction technique offered in Refs. 9 and
18 High Angle of Attack Research Vehicle 10.
(HARV) that included nonlinear anti-windup
logic and actuator limitations. Prediction of Considering the type of damage that can
handling qualities and pilot-induced oscillation accrue in aircraft, particularly combat aircraft,
tendencies in the presence of these nonlinearities focusing upon actuator damage/failures alone may
is included in the example. seem an unwarranted simplification. However,
the control effectors that are actuated by these
Introduction devices are powerful aerodynamic/propulsive
Damage to the actuators driving the force and moment producers. Thus, a design
control effectors of a modem aircrafi can methodology capable of accommodating actuator
adversely affect the performance and stability of failures may also be a candidate for handling
the vehicle. Indeed, the design of future, high- other type of damage, e.g., that associated with
performance aircraft will likely include some the airfi'ame, itself.
ability to automatically reconfigure the aircraft
flight control system in the presence of failure or Methodology
damage to the actuators. Because of this evolving The proposed flight control system will
be designed based on a Quantitative Feedback
=Graduate Student
zProfessor and Vice Chairman, AssociateFellow AIAA
Copyright © by W. Siwakosit and R.A. Hess. Published bythe American Instituteof Aeronautics and
Astronautics, Inc.with permission.
1
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Theory/Pre-Design Technique (QFT/PDT) _ and the presence of plant uncertainties. In some
a reduced-order, linear, dynamic inversion cases, aformal QFT design may not be necessary
(RLD[) controller. 12'13Although reconfigurable if the PDT provides satisfactory results. The
control was not the goal in the study summarized design of the QFT/PDT controller will be based
in Ref. 13, the QFT/PDT and RL'DI controllers upon the dynamics of undamaged aircraR and will
developed therein were shown t._provide stability ensure satisfactory handling qualities with no
and performance robustness to significant pilot-induced oscillation (PIO) tendencies. Its
uncertainties in the vehicle model. This structure will not be altered during
robustness made the controllers ideal candidates reconfiguration.
to serve as a base-line nominal controller for the
reconfigurable system to be described. The only Adaptive Filtering
modification of the design of Ref. 13 was the The reconfiguration scheme will utilize
inclusion of adaptive filtering in series with the the Widrow-Hopf Least Mean Square (LMS)
QET/PDT compensator. As such, the design can algorithm t4in an adaptive form called the filtered-
be thought of as an adaptive QFT system. Figure E:LMS algorithm, js This algorithm resembles a
I shows the general topology of the feedback model-reference adaptive control scheme that
system just described. minimizes the square of the difference between
the output of the system and the output of the
Failure detection is not addressed in the selected model. Figure 2 shows the structure of
discussion to follow. It is assumed that the the adaptive filter and Fig. 3 shows the filtered-I;
reconfiguration logic is operating at all times and LMS algorithm. Analyses of stability, rate of
adjusting to performance degradations arising convergence, and noise effects in the weights for
from actuator failures. The system could, of the filtered- g LMS algorithm shown in Fig. 3 are
course, be employed in conjunction with a failure discussed in Ref. 15.
detection algorithm that activates the
reconfiguration logic upon identification of a The algorithm for updating the filter
failure. The reconfiguration logic does not, weights has the following structure,
however, require identifying which actuator(s)
has failed. Wk,I = W_ +2pXk_r k (1)
where I1
RLDI
For undamaged aircraft, the QFT/PDT
procedure can produce unacceptably high-gain
X -1
controllers when applied across the entire flight Xk = k. ,
envelope. This tendency will be eliminated by
gain scheduling a RLDI. This technique can
[.Xk-LJ
provide desired input-output dynamics over the
flight envelope including approximate decoupling ' Iwokl
of the control channels. The gain scheduling /->,/
process is straightforward and the formulation of
RLDI has already been demonstratedJ 2 After W k = :
design of the RLDI, the QFT/PDT compensation
LWLkJ
provides additional performance robustness lost
due to uncertainties in the vehicle model use to
obtain the RLDI. In addition, the QFT/PDT and E;k= dk _XkWkr =d k_W krXk
compensator can provide at least stability
dk= desired response
robustness in the presence of a classof actuator
L+I = number of weights
failures. 6
xk= input to an adaptive filter
Qb'_r/PDT Wik i=0,1,2,...,L --adaptive weights
The Quantitative Feedback Theory
Yk = output from an adaptive filter =
(QFT) Pre-Design Technique (PDT) was
introduced and fully discussed in Ref. 11. The XkrWk = wrx_
PDT will give an estimation of a QFT controller
that will satisfy the performance specifications in
2
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Equation I is the LMS algorithm. =''=_In this form, " The aircraft with a nominal control structure that
the LMS algorithm can be implemented in a meets these criteria will be reconfigurable using
practical system with simplicity. It can be shown the proposed scheme.
that convergence of the weight vector is obtained
by appropriate selection of _ and L inEq. 1.=4'=_ Simulation of Pilot-in-the-Loop Control
The ability to function under continuous
The filtered-g LMS" algoritlLrn can be pilot control is an important attribute of the
proposed reconfiguration scheme. To
applied to multi-input, multi-output (MIMO)
demonstrate this attribute, a Structural Pilot
systems, is As can be seen from Fig. 3, estimation
Model 9is utilized to as part of a pilot-in-the-loop
of the inverse plant model, I_-I is required in
tracking task with the pilot dynamics are based
order to implement this scheme. Off-line
upon the undamaged "effective vehicle" (aircraft
estimation of 13-1 can be accomplished with
plus control system). The Structural Model is
inverse plant modeling, but may not be possible in
shown in Figure 4. An interactive computer
-son= situations, e.g. in the reconfigurabie flight program I° is used to determine the pilot model.
control problem. However, the exactness of the This program can also be used in assessing the
13-) is not critical to the convergence of the performance of the damaged vehicle with and
adaptive filter in Fig. 3. As will be demonstrated, without reconfiguration. Actuator dynamics
an approximation to f,-I can be employed with no including amplitude and rate limits are included in
off-line or on-line inverse modeling of the plant. the simulation. In addition, the program of Ref.
An approximation to f,-= will not be changed 10 can be employed to predict handling qualities
during adaptation and can be a very rough levels with the nominal, damaged and the
estimate of the dynamics of the damaged reconfigured vehicle.
aircraft. =_ In linear systems, the adaptive
algorithm will converge to an absolute minimum. Example
If the system in question is nonlinear, System Design
convergence of Eq. I to an absolute minimum is For the purpose of demonstrating the
not guaranteed, i.e., only a relative minimum may reconfiguration technique a MIMO system will be
be obtained. analyzed. A simple model of the lateral-
directional dynamics of the NASA F-Ig High
Herein, the reference model selected in Angle of Attack Research Vehicle (HARV) l_will
the reconfiguration scheme will have the desired he used to demonstrate the methodology. As
dynamics of the decoupled system as obtained shown in Fig. 5 the vehicle has redundant
from the dynamic inversion of the nominal effectors for both roll control (differential tail
system. In this way, the adaptive filter will be (DT), aileron (AI), and roll thrust vector (RTV))
attempting to recreate the dynamics prescribed by and sideslip control (rudder (RU) and yaw thrust
the RLD[ when operating with the nominal vector (YTV)). The base-line controller design
vehicle. Recall also that the adaptation does not (PDT and ALDI) is obtained for an undamaged
have to be exact, since the robust QFT/PDT
vehicle for the 18 flight conditions shown in Fig.
controller will accommodate imperfections 6. The flight condition chosen for the
(uncertainty) in the inner-loop reconfiguration. reconfiguration example is also indicated in Fig.
Finally, the proposed scheme doe not require 6. This flight condition is the most challenging
detection of the failed actuators since the for the control system because of the low dynamic
modified filtered-t; scheme does not need
pressure.
identification of the failed system.
Figures %8 show the magnitude plots for
Conditions for Successful Reconfiguration thetracking transfer f_nctions p/pc and 13/[_=for all
Successful reconfiguration depends upon 18 flight conditions, including random variations
the following conditions being met: in the elements of the vehicle dynamic model
1.) The dynamic inversion loop remains stable (elements of the A and B state space matrices) of
after actuator failure occurs. a maximum ± 20%. The pilot-in-the-loop
2.) In the presence of actuator failures, the tracking task is shown in Fig. 9. Note that no
aircraft will still be controllable by virtue of
pilot input in the sideslip loop is assumed, i..e.,
redundant effectors. the task is"feet on the floor" for the pilot. The
upper and lower tracking bounds on the p/p=
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magnitude plots were evaluated for handling algorithm to be utilized in the examples. Design
qualities and PIO tendencies using the computer parameters of the PDT module and the RLDI are
program of Ref. 10. The handling qualities given in Table I. As discussed in the preceeding,
prediction is based upon the "handling qualities the plant inverse is approximate and is based upon
sensitivity function" (HQSF) defined as the desired dynamics of the decoupled system
(referred to as the "reference model" in Table 1).
I
1 UM . (2) All parameters are shown in Table I. The pilot
(J )l
HQSF =_ model is determined from the PDT/RLDI control
structure in the roll loop for the undamaged
where UMand C are two signals in the Structural aircra_. For an evaluation of tracking
Pilot Model shown in Fig. 4. The predicted performance, acrossover frequency of 1.5 rad/sec
handling qualities levels as defined on the was utilized in the pilot/vehicle tracking loop, a
Cooper-Harper rating scale of Fig. 10 are based value representative of pilot/vehicle crossover
upon.whether the HQSF penetrates specified frequency in tracking, e.g, Ref. 19.
bounds on a linear HQSF vs frequency plot. 9:°
Likewise PIO "levels" defined on the PIO Rating Figure 15 illustrates the adaptive filters,
(PIOR) scale of Fig. 11 are also predicted by FII, F12, F21, and F22, for the 2 by 2 MIMO
plotting the power spectral density of the signal system pertinent to the example. Each filter has
UM when a command C with a specified power the same structure as in Fig. 2 except that the
spectral density is applied. 9:0 Figure 12 shows error (;k is replaced by a corresponding filtered
results for the upper and lower tracking p/pc error (filtered-t; .) An input signal x k for each
bounds indicating level 1 handling qualities with
filter isjust the corresponding command from the
no PIO tendencies. Note that these predictions
PDT module. Each filter has its own set of
were based upon a linear vehicle model.
weights and each set and adaptation step size can
be chosen independently for each filter element.
Figure 13 shows the RLDI in more
The weight sets Wkll, Wkl2, Wk21, and Wk22
detail. In Fig. 13, K is a control distribution
belong to FIl, F12, F21, and F22, respectively.
matrix that distributes the two pseudo-control
For simplicity, the same number of weights and
signals emanating from the dynamic inverter to
adaptation step size are utilized for all filters.
the five actuators. K is implemented with only a
Figure 16 shows the 2 by 2 MIMO linear
single non-zero entry in any row. The non-zero
combiner composed of CI I, C12, C21, and C22.
element is proportional to the rate limit of the
Selection of the number of weights L+I was
actuator that it affects. This definition allows the
obtained here by trial and error. First an equal
use of "software rate limiters ''_= to improve the
number of weights were chosen for each of the
tracking performance of the nominal vehicle
four channels (CIi - C22). The number of
under actuator rate saturation if desired. These
weights was chosen as a large number that would
software limiters were not included in this study,
still allow reasonable computation times on the
however. G is the RLDI controller or dynamic
simulation computer (a desktop PC). Here, this
inverter. The actuators in Fig. 13 exhibit the rate
meant L+I = 50. The paramter p. was selected
and amplitude limits shown in Table 1.
according to the convergence criterion for single-
input, single output (SISO) systems of Refs. 15
Simple anti-windup logic has been
and 16as
implemented in the PDT module for both cases to
cope with actuator saturation in the nominal
design. This logic was created in each channel by 1
removing an integrator from the PDT module in
l<P<(L J--+l-E'i)k [ 2- (3)
each control channel and simply replacing it with
a limiting integrator. The upper and lower limits
of the limiting integrator were obtained by trial
and error using the computer simulation and are Proof of convergence for MIMO systems has yet
given in Table i. to be derived. The utility of the SISO criterion
lies in the approximate decoupling afforded by
Figure 14 is a detailed representation of the RLDI and PDT systems. In inequality (3),
the Adaptive Module called out in Fig. 13 and E[ik2] is the temporal average of the square of the
shows the proposed MIMO, modified, filtered- input power into the filter element, e.g., the roll-
4
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rate or sideslip commands indicated in Figs. 15 identically scaled. The shaded portions of the
and 16. This value was estimated m this figure are actually the time histories of 49 of the
application. [t is typical to select lato be less weights in the case ofWkl I and Wk22 and all 50
than one-tenth the upper value in inequality (3). weights in case of Wkl2 and Wk21. As can be
An example of the detailed structure of a linear seen from Fig. 20, filter adaptation converges in
combiner is shown in Fig. 17. approximately 20 sees. Of considerable
/ importance is the fact that the reconfiguration
Since four control channels are involved, logic operated in the presence of significant
four values of the parameter p.could be selected. nonlinearities, both from the anti-windup
However, no crosscoupling commands were integrators and the rate limited actuators.
involved, e.g., no 13/pcand there was no 13cin the
13-loop. Inequality (3) would thus imply Prediction of Handling Qualities and PIO
arbitrarily large values of _ for these channels. Susceptibility
The handling qualities and PlO
• - Instead, the _ value for the p-loop was used for all
prediction methodology of Refs. 9 and 10 were
four channels.
next applied to the healthy, damaged and
reconfigured vehicles. It should be emphasized
Computer Simulation of Pilot/Vehicle
that the latter evaluation was made on the
Performance
reconfigured vehicle, but not on the vehicle
For the majority of the flight conditions
and failures simulated the basic RLDI/QFT- during reconfiguration. The implementation of the
LMS filter as part of the flight control system
defined system was capable of providing
made it cumbersome to calculate of the P/Pc
acceptable performance without reconfiguration.
transfer function needed for the pilot modeling
However, one challenging flight condition and
technique of gefs. 9 and 10. This necessitated an
failure demonstrated the utility of the
identification of the P/Pc transfer function for the
reconfiguration scheme. This occurred when
damaged and reconfigured vehicles. This was
YTV was reduced to only 10% effectiveness at a
accomplished by fitting a transfer function to the
flight condition involving a trim angle of attack
p/pc Bode plot derived from a Fast Fourier
(AOA) = 29.7 degrees, a Math No. = 0.2, an
Transform identification technique. Figure 21
altitude = 10,000 feet with an aggressive roll
shows the results for the reconfigured vehicle.
tracking task presented to the simulated pilot.
The technique of Refs. 9 and 10 also requires a
The 10% effectiveness implies that the "gain",
crossover frequency of 2.0 rad/sec the tracking
rate and amplitude limits of the actuator are only
10% of the nominal values. The roll command to loop being investigated. This was not achievable
with the damaged vehicle, as instability resulted.
the pilot consists of a series of filtered steps of 5
This is synonymous with predicted level 3
see duration and varying amplitude, with some
handling qualities. For the handling qualities and
commanded changes as large as 40 deg. The
PIO analysis for both the damaged and
reconfiguration is initiated with a failure
reconfigured vehicles, the pilot model was
occurring at t = 0 see. The number of weights and
changed from that indicated in Table 1. This was
adaptation step size (p.) for each filter are 50 and
an absolute necessity since the methodology of
Ixl0 "6,respectively. For purposes of evaluating
Refs. 9 and 10 were predicated upon a pilot
tracking performance, the pilot model given in
model properly tuned to the vehicle dynamics at
Table 1 for the nominal vehicle was used for
hand.
nominal, damaged and reconfigured vehicles.
For handling qualities evaluations, the pilot model
Figures 22-23 show the predicted
for the damaged and reconfigured vehicle was
handling qualities and PIO levels for the nominal
tuned to the altered vehicle dynamics as will be
and damaged vehicles using the program of Ref.
described.
i0. The nominal vehicle shows a violation of the
level I boundary. This is attributable to the
The roll angle responses of the healthy
aggressive nature of the roll attitude command of
(undamaged or nominal), damaged and
Fig. 18. Note that the reconfigured vehicle has
reconfigured vehicles are plotted in Fig 18.
retained predicted level I handling qualities with
Sideslip responses are compared in Fig. 19.
minimal PIO tendencies. Figure 24-25 show the
Adaptive filter weight time histories are shown in
amplitude and rate limiting that was occurring
Fig. 20. For comparison purposes, the ordinates
during and after reconfiguration as compared to
of each of the plots in Fig. 20 have been
5
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that of the damaged vehicle. This limiting is Reconfigurable Flight Control," IEEE
attributable both to the challenging nature of the Transactions on Control Systems Technology,
flight condition, and to the reconfigurable control Vol.5, No.2, 1997, pp. 217-229
scheme attempting to recapture performance lost 6Hess, R.A., Siwakosit,W., and Chung.
due to the failure in the thrust vectoring nozzle. J., "Accommodating A Class of Actuator Failures
The nonlinearities did not, however, inhibit the in a Flight Control System, Journal of Guidance,
reconfiguration. Control, and Dynamics, to appear.
7Burken, J., Lu, P. and Wu, Z,
Conclusions "Reconfigurable Flight Control Designs with
A methodology for MIMO Application to the X-33 Vehicle, AIAA Paper No.
reconfigurableflightcontroldesignutilizinga 99-4134, AIAA Guidance, Navigation and
robustcontrollerand adaptivefilterhas been Control Conference, 9-11 Aug., 1999, Portland,
proposed. The demonstrationofthe proposed OR.
_systme shows significanitmprovement intracking 8Hess, R. A., and McLean, C.,
performance as compared to the same vehicle "Development of a Design Methodology for
withoutreconfigurationinachallengingexample Reconfigurable Flight Control Systems," AIAA
from one of the 18 flight conditions in the flight Paper No. 99-4134, AIAA Guidance, Navigation
envelope for which the nominal system was and Control Conference, 9-11 Aug., 199,
designed. The reconfiguration was characterized Portland, Or.
by fast adaptation times during which the •less, R.A., "A Unifed Theory for
simulated pilot retained control. Application to a Aircraft Handling Qualities and Adverse Pilot-
system with nonlinear effects supports the utility Vehicle Coupling," Journal of Guidance,
of the proposed concept. Control and Dynamics, Vol. 20, No.6, 1997, pp.
1141-1148.
Acknowledgment '°Zeyada, Y., Hess, R.A., "PVDNL
This researchwas supportedby grants Pilot/Vehicle DynarnicsN._,== - An Interactive
from NASA Dryden FlightResearchCenterand Computer Program for Modeling the Human in
NASA Langley Research Center. The grant Single-Axis Linear and Nonlinear Tracking
technicalmanagers were John Burken and Ban Tasks," Dept. of Mechanical and Aeronautical
Bacon at NASA Dryden and NASA Langley, Engineering, University of California, Davis,
respectively. 1998.
'fHenderson, D.K. and Hess, R.A.,
References "Approximations for Quantitative Feedback
_Ostroff, A. J., and Hueshcen, R.M., Theory Designs," Journal of Guidance, Control,
"Investigation of Control Law Reconfiguration to and Dynamics, Vol.20, No.4, 1996, pp. 828-831
Accommodate a Control Element Failure on a t2Snell, A., "Decoupling Control Design
Commercial Aircraft," Proceeding of the 1984 with Applications to Flight," Journal of Guidanc,
American Control Conference, San Diego, CA, Control, and Dynamics, Vol.21, No.4, 1998, pp.
June, 1984 647-655
2Es[inger, R.A., and Chandler, P.R., J3Siwakosit,W., Snell, S. A., and Hess,
"Self-Repairing Flight Control System Program R.A., "Robust Flight Control Design with
Overview," Proceeding of IEEE National Handling Qualities Constraints Using Scheduled
Aerospace and Electronics Conference, 1988, pp. Linear Dynamic Inversion and Loop-Shaping,"
504-511 IEEE Transactions on Control Systems
3Chandler,P.R.,"IssuesinFlightControl Technology, Vol. g, No. 3, 2000, pp. 483-494.
DesignforRobustnesstoFailuresandDamages," t4Widrow, B., and Stearns, SD.,
Proceeding of IEEE International Conference on Adaptive Signal Processing, Prentice Hall, N.J.,
Control Applications, Jerusalem, Israel, paper ]985
WP-2-7, 1989 'sWidrow, B., and Wallach, E., Adaptive
4Kim, B.S., and Calise, A.J., "Nonlinear Inverse Control Prenctice Hall, N..L, 1996.
Flight Control Using Neural Networks," Journal =_Siwakosit, W., "Robust and
of Guidance, Control, and Dynamics, Vol.20, Reconfigurable Flight Control Design," Ph.D.
No.l, 1997, pp. 26-33 Dissertation, Dept. of Mechanical and
SBodson, M., and J. Groszkiewicz, Aeronautical Engineering, University of
"Multivariable Adaptive Algorithms for California, Davis, Sept., 2000.
American Institute of Aeronautics and Astronautics
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•." °
JTAdams, R.J., Buffington, ]M., Sparks, Control, and Dynamics, Vol. 21, No. 3, 1998, pp.
A.G., and Banda, S.S., "An Introduction to 361-367.
Multivariable Flight Control System Design," tgMitchell, D. G., Aponso, B. L., and D.
WL-TR-92-3110, Wright Laboratory, WPAFB, H., "Effects of Cockpit Lateral Stick
OH, 1992 Characteristics on Handling Qualities and Pilot
t=Snell, S.A., and Hess, R. A., "Robust Dynamics," NASA CR 4443, June, 1992.
Decoupled, Flight Control Design in with Rate
Saturating Actuators," Journal of Guidance,
Table 1 Vehicle, Pilot, and Control System Parameters
Aircraft Linearized Model
SOT
X=Ax+BA where x(t)=_p(t)l, _(t)=]SRu
y=cx+D Lr(t)j "
= angle of sideslip, deg; p = roll rate, deg/sec; r= yaw rate, deg/sec
5 DT = differential tail (DT), deg; 5AI = aileron (AI), deg; 5 RU = rudder (RU), deg
8RTV = roll thrust vector angle (RTV), deg; 5yT V = yaw thrust vector angle (YTV), deg
Example: (angle of attack = 29.73 deg, math = 0.2, altitude = 10,000 feet
-0.059 0.496 -0.868" I 0.006 0.006 0.004 0 0.090 ]
A _ -5.513 -0.939 0.665 B= 1 1.879 1.328 0.029 0.675 0.217 I
0.068 0.026 -0.104 L-O.109 -0.096 -0.084 0.007 -2.974j
Actuator Transfer Functions and Limits
302
DT: amplitude limit = +/-17.5 deg, rate limit = +/-60 deg/sec
s2 + 42.4s + 302
752
AI: amplitude limit = +/-27.5 deg, rate limit = +/-100 deg/sec
s2 +88.5s + 752
722
RU: amplitude limit = +/-30 deg, rate limit = +/-100 deg/sec
s2 +99.4s +722
202
RTV/YTV: amplitude limit = +/-30 deg, rate limit = +/-60 deg/sec
s2 +24s +20 2
PDT Controller
o
"197.33(s+5.15X_.0.97X$2+22.30s+355.4Xs2+102.70s+5070)
s(s+5896)3(s+438)(s2+2474s+50990)
G PDT = 216.16s(+O.97sX2+43.05s+896.302)+(8s725s+551600)
0
s(s+Sg96)3(s2+446?s+126600)
Anti-Windup limits at an integrator at each control channel =+/- 20 (deg/sec or deg)
7
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Table I, cont'd
= RLDI Controller
o1
G =[(A G -Hobs),[B G HobsI,CG,[DG 0 0 1
Ac = (A-BKE_F),B c = BKE_ I,C G =-E_IF,D G = E_ I
1
reference model for each channel = --
s+l
E = CBK, F= C+ CA; En"l= right inverse of E
Hob s = 1 K =
0 71
[.0,6
Pilot Model for Nominal Vehicle*(for tracking with nominal_ damaged and reconfigured vehicle)
3.139.105 units displacement
Pilot =
(s2 +7.027s +165.64)(s 2 +4!.97s + 754.6) tad
Pilot Model for Reconfigured Vehicle* (for handling qualities evaluation)
2.545.105 e-0.2s units displacemmt
Pilot =
(s2 + 4.Is+ i97.7)(s 2 +45s +837.7) rad
*Includes loop closure about force/feel system given by
252 units displacment
=
YFS s2 +35s+252 units force
Adaptive Filter
50 weights in each filter, adaptation step size /_= lx 10-6, sampling frequency = 50 He.
o]
reference model for filtered- E;algorithm = (s I)
(s + 1)
8
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o
[ _'-+-1t2 o
approximation ofplant inverse, /_-' =](s/_500+l)' (s+l)
.- L (_o +1)
Linear
Dynamic
Inversion
,opu_F--I +.. F-1 I----1 I-----11 i F---1 o_tp_
Pre-filter I QFT/PDT Acla_ptlve II II I
I Robust Fitter I StateFeedback I I
I c°ntr°ue'
Figure I Reconfigurable flight control scheme
Input Wok Desired
response
Wlk
,4 Output
d+_
--, _k
• Xk.t _Adaptive yk
elements
Unit delay +
w_t
(Weights)
Xk.L
Figure 2Adaptive filter inU'ansversal filter form
9
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(c)2000 American Institute ofAeronautics &AstronautiCs orPubhshed withPermission ofAuthor(s) and/or Author(s)' Sponsoring Organization
!
Xk
I Adap(tiCvoepyF)ilter
Plant with Dynamic
,"Controller Inversion Loop
!
Adaptive Filter I
Overall System
/
Filtered ck +
Error Error ?-
Estimation .4 Desired
of Pt Uk[ Resoonse
JReference /
"[ Model
Figure 3 Filtered-LMS algorithm
PILOT
r'- 1
! t VEHICLE
---_M
¾
vestibular feedback II
feedback
I
visual feedback II
I
_t
Figure 4 Structural model of human pilot
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AmericanInstituteofAeronauticsand Astronautics
