- Email: [email protected]
Design and Analysis of Helicopter Fault-Tolerant Flight Control System
Copyright © IFAC Automatic Control in Aerospace, Saint-Petersburg, Russia, 2004
ELSEVIER
IFAC PUBLICATIONS www.elsevier.comllocatelifac
DESIGN AND ANALYSIS OF HELICOPTER FAULT-TOLERANT FLIGIIT CONTROL SYSTEM Mo F. AI-Malki and D.-W. Gu
Control and Instrumentation Research Group Department of Engineering University of Leicester, Leicester LEI 7RH, UK e-mails:[email protected]@le.ac.uk
Abstract: In this paper we present a fault-tolerant, reliable flight control scheme for Bell205 Helicopter for the lateral dynamics case. The scheme is featured by integration of an Artificial Neural Network (ANN) based fault detection, isolation, and accommodation (FDIA) system and an Hoc mixed-sensitivity robust controller. The delay problem caused by the computational overhead of ANNs is addressed in the design. The robustness of the system is analyzed using Small Gain Theorem and J.L analysis Copyright ©2004 IFAC Keywords: fault-tolerant, fault detection, fault isolation, H-infinity, stability robustness
1. INTRODUCTION
describes the whole fault tolerant flight control system (FfFCS) and analysis of its stability and performance. Conclusions are drawn and future work is highlighted in the last section.
The reliability of a flight control system (FCS) is of prime importance. Even though modern aircrafts are equipped with advanced sensors and actuators, still there are possibilities of occurrences of faults. Airframe damages could happen as well. Such scenarios can cause catastrophic results if they are not detected and compensated in time. Naturally faults and their impacts should be taken into consideration as much as possible during the design stage. Design of flight control systems which tolerate certain flight faults and thus improve flight safety is possible, though usually with degraded performance. In our work reported here, we focus on sensor failures in a Bell-205 helicopter. The work shows that an FDIA system together with a robust control system can accommodate the sensor faults with reasonably well maintained performance. Furthermore, the stability and performance of the overall system are analysed with the consideration of fault scenarios. The paper is organised as follows. Next section describes briefly the lateral dynamics of the Bell-205 helicopter. Section-3 gives an outline of the ANN-based FDIA which was detailed in a previous paper (Al-Malki and Gu, 2003). Section-4 introduces the design of a robust controller. Section-5
2. LATERAL DYNAMICS OF BELL 205 Bell-205 helicopter is an advanced experimental flyby-wire (FBW) helicopter operated by the NRC, Canada. The input-output structure of the Bell 205 is similar to other helicopters, though as an experimental vehicle it is equipped with additional sensors which will not be considered in this research. The helicopter has four actuators (with reference signals given by the pilot inceptors): main rotor collective (mainly influences vertical motion), longitudinal cyclic (mainly influences pitching motion), lateral cyclic (mainly influences rolling motion), and tail rotor collective (mainly influences yawing motion). It is intuitive to mention that coupling among the axis cannot be avoided where a command in one axis causes a transformation in another axis. The measured outputs in lateral channels are numerous. However, not all of them are of major importance 885
o o o
to controller design and performance. Only those used in feedback loops are considered here, namely, roll attitude (
B=
0 0 0
0
0
o
0
-2.1098
0 7.0991
o
Two models of Bell-205 are available. One is a set of linear models produced by NASA and the other is a collection of a nonlinear model and a set of linearized models produced by DERA. Details on these models can be found in (DERA, 1998) and (Heftly et al., 1978). This research is based on the DERA linearized model. The following summaries the inputs, outputs and states concerned.
C=
1000000) 0010000 ( 0100000
D~(m
The inputs to the helicopter are the lateral cyclic (FDA), longitudinal cyclic (FDE), and tail rotor collective (FDR). The Main Rotor (MR) collective is not part of the flight control system. The states are: the roll attitude (
3. ANN-BASED FDIA Fault-tolerance control (FTC) system design has been discussed in many recent papers and reports. In Figure- 1, a conceptual design ofFTC is shown which consists of three major subsystems:
1'-"'·"" .:.
A: """-11 ... _ _
The linearized model of the lateral dynamics is given by the following generic equations:
Fig. 1. Fault-Tolerant Control System Architecture
x=Ax+Bu
(1)
y=Cx+Du
(2)
• Fault Detection and Isolation (FDI). The FDI scope covers sensors, actuators and plant components. In the case of sensor failures, the plant stability and control derivatives (A and B matrices) are not affected. However, the output matrix (C matrix) does change. • Decision Logic Module (DLM) which is the supervisor of the system that examines the signals and decides actions to be taken. • Controller which is designed using either classical or modem techniques. In this study, the controller is designed using the sub-optimal Hoc> method.
where:
-0.0000
1.0000 -2.4732 -0.2716 32.1742 -4.8115 0.4075 -32.9361 o 0 o 0
o o
A=
o -0.0157 0.0284 -0.0494 -0.5458
o o
-0.0005 -0.0006 -0.6943 -9.1062 -0.0359 0 0
0 -20.3127 -2.1174 -32.4426 -21.6488 -12.5786 0
0 -0.0182 0.0176 -0.0502 -0.2338 0 0
There are essentially two standard approaches to the fault tolerant control problem. The first approach relies on integration of an FDIA system with a flight control system while the other one relies on an adaptive scheme. We have followed the first approach, i.e. the control system is a fixed structure controller. This approach requires an accurate fault detection and isolation (FDI) scheme and a robust controller. The FDI system we have designed uses well trained artificial neural networks (ANN).
0 4.6427 -13.4637 18.1631 0 0 -25.0000 886
e.g. (Smerlas, 1999), (postelthwaite et aI., 1999) and (Turner, 2000». In the present work, a standard Sover-KS design configuration is employed.
The ANN fault detection and isolation scheme developed for the lateral dynamics of the Bell-205 helicopter has a master ANN to model all sensors' readings collectively as a multi-input-multi-output (MIMO) system and three multi-input-single-output (MISO) ANNs for those three measured outputs, the roll attitude, the yaw attitude and the roll rate « ), (r), and (p), respectively). All the ANNs are with timedelays to reflect the dynamic nature of the system. The ANNs are trained, verified and tested using real flight data, which makes the FDI system more robust.
The objective of the design is to minimize:
where S = (I - G K) -1 is the sensitivity function and K is the controller to be designed. W 1 and W 2 are two frequency dependent weighting functions,
Details of the architecture of all those neural network models, threshold selections, simulation results as well as property analysis can be found in (Al-Malki and Gu, 2003). In order to implement our fault tolerant scheme, an accurate bound on the possible errors between the measured (healthy sensors) outputs and the estimated outputs from the ANNs is essential. After extensive tests conducted both on individual ANNs that models individual sensor's reading and on the ANN that is responsible for the overall output dynamics, an error bound 6. (represented in Figure- 2) is derived.
W2
=
0
[WFDA
o
]
WFDR
After several trials, the weighting functions are chosen as below: with
la4>l:::; 1.141 larl :::; 0.9879 lapl :::; 0.0929
W =0.5 s+0.6 4> s + 0.005
(3)
Wr = 0.5 s + 0.6 s + 0.001 Wp=O.OOl
while
W
-0 2 s + 0.005
+ 20 0 1 s + 0.005
FDA - .
Fig. 2. Closed-Loop with FDIA Model
W
FDR-
·
S
s+20
4. ROBUST CONTROLLER DESIGN Design of Hoo controllers for helicopters has been a subject of numerous research papers. The Control and Instrumentation Research Group at Leicester University has been engaged in designing various controllers for Bell-205 and Lynx helicopters (see
With these weighting functions, an H 00 controller is designed which gives frequency and time responses of the closed-loop system in Figure- 3 and Figure- 4.
887
at the corresponding sensor. Such failures could be a sensor stuck at a fixed level or a deviation from healthy output values, or other cases «AI-Malki and Gu, 2001) and (Al-Malki and Gu, 2003)). In the simulation, the above system has been tested with two faults. The first one is a step signal of size 2 that happens at t=O.5 second in the roll attitude
. . . ·•.. ..·
---
Ir=~: m.'m 1 ·"L.==; . .. . . ·. j ~~i.;E~;1~2:i:::~~Y:~~~~~~
•
.40,
.,
~l
~.
J~,
"
_.
,.
right-hand-side part in Figure- 5. However, with successful implementation of fault detection, isolation, and accommodation, the outputs of the system are
,
~_y_
~
shown in the left-hand-side part which are the same
;~
.. in the fault-free c.,e.
~? L ~l
;,_, , : .
~
Fig. 3. Mixed-sensitivity Hoc Controller Frequency Response
12'r-~"':.:..:-r=-=""=Rwp:~----,
'. r--..
0..1
·r ....... .
,
i
i ··
1
. .
... .. 40
eo
eo
100
120
.
O~
.(
O~
, ..
o.
,
20
Fig. 5. Successful FDIA with the Hoc Controller in the loop
12.--~Y-:.:..:-;::=-=AMpoo:r="'----
I
0..
-020
We now further discuss a few issues concerning the closed-loop system with the FTFCS. As described earlier, the lateral channel FDIA consists of four ANNs. Each ANN is of multilayer structure, and each layer is with several neurons. Furthermore, every ANN has a TIme-Delay Line (IDL) concerning its inputs and outputs in order to properly match the system dynamics. All the above leads to some computational delays which happen in the implementation of the scheme. The delay is quite natural as ANNs in general are parallel in nature while the computation is carried over on sequential machines. Two approaches can be used to deal with this problem.
....•. ; .... . .. .
,
I
Fig. 4. Mixed-sensitivity Hoc Controller Step Response
• Use a computational machine with parallel processors which is suitable for neural networks computation. These are available nowadays. The cost is not high while the benefit is tremendous. • Use Smith Predictor approach. This has been tried in the present study. A second order Pade approximation of the delay is used. This approach slightly improves the performance of the system.
5. FTFCS FOR LATERAL DYNAMICS We can now integrate the controller described in the previous section with the ANN-based FDI system described in Section-3. More details on ANN-based FDIA can be found in (Al-Malki and Gu, 2001). The helicopter measured outputs (i.e. the feedback signals) will be replaced by the estimated outputs from the ANN FDI scheme once a decision has been made that a failure has occurred
For the original closed loop system, the plant (i.e. the Bell-205 Helicopter) is not stable but the closed loop is stabilized by the controller (K) which was designed using Hoc mixed-sensitivity approach. After
888
~
140
Small Gain Theorem, the closed loop remains stable if the following holds for all possible ~:
integrating the FOIA with the controller, the overall system is represented by Figure- 6. In Figure- 6, the FOIA breaks the feedback loop and receives the plant measured outputs (Ym). The ANNs produce estimates for the three outputs (~,p, and f). The ANN-based FOIA checks the signals to find out if a single or multiple fault occurs. If that happens, the FOIA would replace the faulty value(s) by the estimate(s). In that case, a stability problem of the closed-loop system may arise, due to the discrepancy between the estimated outputs and the (healthy) measured outputs. It could be argued that this discrepancy has been taken care of in the design of controller since the sensitivity function minimization is included which may be interpreted as consideration on the output disturbance. However, since we have the estimation of error bounds for ANNs (equation- 3), we may analyze the stability more explicitly.
Lr-;(~I_~G;:K ;-~":"!-[" (G;:K 1- - .J
Legend, DLM; Decision Losic Module FDI ; Fault Detection and Isolation
Fig. 7. Closed-Loop with FOIA Model - SGT view K
Fig. 6. Fault-Tolerant Control System - Fixed Controller Case
However, the norm calculation shows that
0.99827 ~ IITA io 1100 ~ 0.99927
Given the original closed loop system, the plant is stabilized using the Hoo mixed-sensitivity controller K . We need to show if the closed loop in Figure- 2, which is a re-drawn of Figure- 6, is still stable with the same controller.
While the perturbation block ~ has a norm of 1.141, the above reveals clearly that this designed controller does not give robust stability of the closed-loop system. In reality, it means that for some sensor faults the closed-loop system may become unstable if the measured output is replaced by estimated signals from the ANNs. The above consideration is, however, under the assumption that the uncertainty ~ is unstructured. In our case, the uncertainty block actually represents the possible error at output channels between healthy sensor measurements and estimations generated by ANNs, and is thus highly structured. It is therefore much more appropriate to discuss robust stability of the system using ",-analysis. It turns out that the bound of '" value of the corresponding interconnected system, over the frequency range of 1O-3 ra d/ s to 1Q3 ra d/ s, is less than 0.61 (see Figure- 8). That result means the robust stability has been indeed attained. The highly structured uncertainty in this system leaves scope for further improvement of controller design. The ",-synthesis would be an obvious choice. The controller design using the J.L-synthesis is currently being conducted. Initial results show indeed that J.L controllers are better than Hoo controllers.
In Figure- 2, the FOIA subsystem is enclosed by a dashed box. The output of the FOIA subsystem is thus represented by:
Y! = (1 + .6.)Ym
where Y! is the FOIA output and Ym is the sensor measurements (the roll attitude
The closed-loop system can be re-drawn as in Figure7 for robust stability analysis. From the well-known
889
Heffly, R. K., W. Jewell, J. Lehman and R. Winkle (1978). A Compilation and Analysis of Helicopter Handling Qualities Data. Volume one: Data Compilation. NASA Scientific and Technical Information Branch. Postelthwaite, I., A. Smerlas and D. J. Walker (1999). hoc Control of the NRC Bell 205 Fly By Wire Helicopter. Journal of The American Helicopter Society pp. 276-284. Smerlas, A. (1999). Robust Multivariable Control of Helicopters: From Mathematical Models to Flight Tests .. PhD thesis. Leicester,UK. Turner, M. C. (2000). Robust control of Systems Subject to Input Nonlinearities with Application to High Performance Helicopter. PhD thesis.
Fig. 8. J.L Analysis Robust Stability Output Before leaving this subject, we must point out that the estimation error is high in one of the channels. That is the result of the ANN being trained with the available, limited flight data set. Should better flight data set be availed and used for the training, the result could be much better.
6. CONCLUSION In this paper we reported a complete design case of a fault-tolerant flight control system for the lateral sensor dynamics of Bell 205 helicopter. The FIFCS consists of an ANN-based FDIA system and a robust controller. The same approach has been applied for the longitudinal dynamics as well (not reported here due to space limit). Successful simulations have been observed. In this approach, the sensor failures may be considered as uncertainties on the plant outputs. Due to the structured nature of such uncertainties, our research has now moved to design robust controllers using J.L-analysis and synthesis procedure. In addition, we are exploring the advantages of using adaptive schemes to deal with fault occurrences in flight vehicles.
REFERENCES Al-Malki, M. F. and Da-Wei Gu (2001). An ANNBased Sensors' Fault Detection, Isolation, and Accommodation for Bell-205 Helicopter. Al-Malki, M. F. and Da-Wei Gu (2003). Sensors fault detection, isolation with application to high performance helicopter. International Conference on Simulation and Modelling, Marbella, Spain. DERA (1998). Configuration of the DERA HEIUSIM Model to represent the flight dynamics ofthe NRC Bell-205 Helicopter (U). DERA, UK.
890
ELSEVIER
IFAC PUBLICATIONS www.elsevier.comllocatelifac
DESIGN AND ANALYSIS OF HELICOPTER FAULT-TOLERANT FLIGIIT CONTROL SYSTEM Mo F. AI-Malki and D.-W. Gu
Control and Instrumentation Research Group Department of Engineering University of Leicester, Leicester LEI 7RH, UK e-mails:[email protected]@le.ac.uk
Abstract: In this paper we present a fault-tolerant, reliable flight control scheme for Bell205 Helicopter for the lateral dynamics case. The scheme is featured by integration of an Artificial Neural Network (ANN) based fault detection, isolation, and accommodation (FDIA) system and an Hoc mixed-sensitivity robust controller. The delay problem caused by the computational overhead of ANNs is addressed in the design. The robustness of the system is analyzed using Small Gain Theorem and J.L analysis Copyright ©2004 IFAC Keywords: fault-tolerant, fault detection, fault isolation, H-infinity, stability robustness
1. INTRODUCTION
describes the whole fault tolerant flight control system (FfFCS) and analysis of its stability and performance. Conclusions are drawn and future work is highlighted in the last section.
The reliability of a flight control system (FCS) is of prime importance. Even though modern aircrafts are equipped with advanced sensors and actuators, still there are possibilities of occurrences of faults. Airframe damages could happen as well. Such scenarios can cause catastrophic results if they are not detected and compensated in time. Naturally faults and their impacts should be taken into consideration as much as possible during the design stage. Design of flight control systems which tolerate certain flight faults and thus improve flight safety is possible, though usually with degraded performance. In our work reported here, we focus on sensor failures in a Bell-205 helicopter. The work shows that an FDIA system together with a robust control system can accommodate the sensor faults with reasonably well maintained performance. Furthermore, the stability and performance of the overall system are analysed with the consideration of fault scenarios. The paper is organised as follows. Next section describes briefly the lateral dynamics of the Bell-205 helicopter. Section-3 gives an outline of the ANN-based FDIA which was detailed in a previous paper (Al-Malki and Gu, 2003). Section-4 introduces the design of a robust controller. Section-5
2. LATERAL DYNAMICS OF BELL 205 Bell-205 helicopter is an advanced experimental flyby-wire (FBW) helicopter operated by the NRC, Canada. The input-output structure of the Bell 205 is similar to other helicopters, though as an experimental vehicle it is equipped with additional sensors which will not be considered in this research. The helicopter has four actuators (with reference signals given by the pilot inceptors): main rotor collective (mainly influences vertical motion), longitudinal cyclic (mainly influences pitching motion), lateral cyclic (mainly influences rolling motion), and tail rotor collective (mainly influences yawing motion). It is intuitive to mention that coupling among the axis cannot be avoided where a command in one axis causes a transformation in another axis. The measured outputs in lateral channels are numerous. However, not all of them are of major importance 885
o o o
to controller design and performance. Only those used in feedback loops are considered here, namely, roll attitude (
B=
0 0 0
0
0
o
0
-2.1098
0 7.0991
o
Two models of Bell-205 are available. One is a set of linear models produced by NASA and the other is a collection of a nonlinear model and a set of linearized models produced by DERA. Details on these models can be found in (DERA, 1998) and (Heftly et al., 1978). This research is based on the DERA linearized model. The following summaries the inputs, outputs and states concerned.
C=
1000000) 0010000 ( 0100000
D~(m
The inputs to the helicopter are the lateral cyclic (FDA), longitudinal cyclic (FDE), and tail rotor collective (FDR). The Main Rotor (MR) collective is not part of the flight control system. The states are: the roll attitude (
3. ANN-BASED FDIA Fault-tolerance control (FTC) system design has been discussed in many recent papers and reports. In Figure- 1, a conceptual design ofFTC is shown which consists of three major subsystems:
1'-"'·"" .:.
A: """-11 ... _ _
The linearized model of the lateral dynamics is given by the following generic equations:
Fig. 1. Fault-Tolerant Control System Architecture
x=Ax+Bu
(1)
y=Cx+Du
(2)
• Fault Detection and Isolation (FDI). The FDI scope covers sensors, actuators and plant components. In the case of sensor failures, the plant stability and control derivatives (A and B matrices) are not affected. However, the output matrix (C matrix) does change. • Decision Logic Module (DLM) which is the supervisor of the system that examines the signals and decides actions to be taken. • Controller which is designed using either classical or modem techniques. In this study, the controller is designed using the sub-optimal Hoc> method.
where:
-0.0000
1.0000 -2.4732 -0.2716 32.1742 -4.8115 0.4075 -32.9361 o 0 o 0
o o
A=
o -0.0157 0.0284 -0.0494 -0.5458
o o
-0.0005 -0.0006 -0.6943 -9.1062 -0.0359 0 0
0 -20.3127 -2.1174 -32.4426 -21.6488 -12.5786 0
0 -0.0182 0.0176 -0.0502 -0.2338 0 0
There are essentially two standard approaches to the fault tolerant control problem. The first approach relies on integration of an FDIA system with a flight control system while the other one relies on an adaptive scheme. We have followed the first approach, i.e. the control system is a fixed structure controller. This approach requires an accurate fault detection and isolation (FDI) scheme and a robust controller. The FDI system we have designed uses well trained artificial neural networks (ANN).
0 4.6427 -13.4637 18.1631 0 0 -25.0000 886
e.g. (Smerlas, 1999), (postelthwaite et aI., 1999) and (Turner, 2000». In the present work, a standard Sover-KS design configuration is employed.
The ANN fault detection and isolation scheme developed for the lateral dynamics of the Bell-205 helicopter has a master ANN to model all sensors' readings collectively as a multi-input-multi-output (MIMO) system and three multi-input-single-output (MISO) ANNs for those three measured outputs, the roll attitude, the yaw attitude and the roll rate « ), (r), and (p), respectively). All the ANNs are with timedelays to reflect the dynamic nature of the system. The ANNs are trained, verified and tested using real flight data, which makes the FDI system more robust.
The objective of the design is to minimize:
where S = (I - G K) -1 is the sensitivity function and K is the controller to be designed. W 1 and W 2 are two frequency dependent weighting functions,
Details of the architecture of all those neural network models, threshold selections, simulation results as well as property analysis can be found in (Al-Malki and Gu, 2003). In order to implement our fault tolerant scheme, an accurate bound on the possible errors between the measured (healthy sensors) outputs and the estimated outputs from the ANNs is essential. After extensive tests conducted both on individual ANNs that models individual sensor's reading and on the ANN that is responsible for the overall output dynamics, an error bound 6. (represented in Figure- 2) is derived.
W2
=
0
[WFDA
o
]
WFDR
After several trials, the weighting functions are chosen as below: with
la4>l:::; 1.141 larl :::; 0.9879 lapl :::; 0.0929
W =0.5 s+0.6 4> s + 0.005
(3)
Wr = 0.5 s + 0.6 s + 0.001 Wp=O.OOl
while
W
-0 2 s + 0.005
+ 20 0 1 s + 0.005
FDA - .
Fig. 2. Closed-Loop with FDIA Model
W
FDR-
·
S
s+20
4. ROBUST CONTROLLER DESIGN Design of Hoo controllers for helicopters has been a subject of numerous research papers. The Control and Instrumentation Research Group at Leicester University has been engaged in designing various controllers for Bell-205 and Lynx helicopters (see
With these weighting functions, an H 00 controller is designed which gives frequency and time responses of the closed-loop system in Figure- 3 and Figure- 4.
887
at the corresponding sensor. Such failures could be a sensor stuck at a fixed level or a deviation from healthy output values, or other cases «AI-Malki and Gu, 2001) and (Al-Malki and Gu, 2003)). In the simulation, the above system has been tested with two faults. The first one is a step signal of size 2 that happens at t=O.5 second in the roll attitude
. . . ·•.. ..·
---
Ir=~: m.'m 1 ·"L.==; . .. . . ·. j ~~i.;E~;1~2:i:::~~Y:~~~~~~
•
.40,
.,
~l
~.
J~,
"
_.
,.
right-hand-side part in Figure- 5. However, with successful implementation of fault detection, isolation, and accommodation, the outputs of the system are
,
~_y_
~
shown in the left-hand-side part which are the same
;~
.. in the fault-free c.,e.
~? L ~l
;,_, , : .
~
Fig. 3. Mixed-sensitivity Hoc Controller Frequency Response
12'r-~"':.:..:-r=-=""=Rwp:~----,
'. r--..
0..1
·r ....... .
,
i
i ··
1
. .
... .. 40
eo
eo
100
120
.
O~
.(
O~
, ..
o.
,
20
Fig. 5. Successful FDIA with the Hoc Controller in the loop
12.--~Y-:.:..:-;::=-=AMpoo:r="'----
I
0..
-020
We now further discuss a few issues concerning the closed-loop system with the FTFCS. As described earlier, the lateral channel FDIA consists of four ANNs. Each ANN is of multilayer structure, and each layer is with several neurons. Furthermore, every ANN has a TIme-Delay Line (IDL) concerning its inputs and outputs in order to properly match the system dynamics. All the above leads to some computational delays which happen in the implementation of the scheme. The delay is quite natural as ANNs in general are parallel in nature while the computation is carried over on sequential machines. Two approaches can be used to deal with this problem.
....•. ; .... . .. .
,
I
Fig. 4. Mixed-sensitivity Hoc Controller Step Response
• Use a computational machine with parallel processors which is suitable for neural networks computation. These are available nowadays. The cost is not high while the benefit is tremendous. • Use Smith Predictor approach. This has been tried in the present study. A second order Pade approximation of the delay is used. This approach slightly improves the performance of the system.
5. FTFCS FOR LATERAL DYNAMICS We can now integrate the controller described in the previous section with the ANN-based FDI system described in Section-3. More details on ANN-based FDIA can be found in (Al-Malki and Gu, 2001). The helicopter measured outputs (i.e. the feedback signals) will be replaced by the estimated outputs from the ANN FDI scheme once a decision has been made that a failure has occurred
For the original closed loop system, the plant (i.e. the Bell-205 Helicopter) is not stable but the closed loop is stabilized by the controller (K) which was designed using Hoc mixed-sensitivity approach. After
888
~
140
Small Gain Theorem, the closed loop remains stable if the following holds for all possible ~:
integrating the FOIA with the controller, the overall system is represented by Figure- 6. In Figure- 6, the FOIA breaks the feedback loop and receives the plant measured outputs (Ym). The ANNs produce estimates for the three outputs (~,p, and f). The ANN-based FOIA checks the signals to find out if a single or multiple fault occurs. If that happens, the FOIA would replace the faulty value(s) by the estimate(s). In that case, a stability problem of the closed-loop system may arise, due to the discrepancy between the estimated outputs and the (healthy) measured outputs. It could be argued that this discrepancy has been taken care of in the design of controller since the sensitivity function minimization is included which may be interpreted as consideration on the output disturbance. However, since we have the estimation of error bounds for ANNs (equation- 3), we may analyze the stability more explicitly.
Lr-;(~I_~G;:K ;-~":"!-[" (G;:K 1- - .J
Legend, DLM; Decision Losic Module FDI ; Fault Detection and Isolation
Fig. 7. Closed-Loop with FOIA Model - SGT view K
Fig. 6. Fault-Tolerant Control System - Fixed Controller Case
However, the norm calculation shows that
0.99827 ~ IITA io 1100 ~ 0.99927
Given the original closed loop system, the plant is stabilized using the Hoo mixed-sensitivity controller K . We need to show if the closed loop in Figure- 2, which is a re-drawn of Figure- 6, is still stable with the same controller.
While the perturbation block ~ has a norm of 1.141, the above reveals clearly that this designed controller does not give robust stability of the closed-loop system. In reality, it means that for some sensor faults the closed-loop system may become unstable if the measured output is replaced by estimated signals from the ANNs. The above consideration is, however, under the assumption that the uncertainty ~ is unstructured. In our case, the uncertainty block actually represents the possible error at output channels between healthy sensor measurements and estimations generated by ANNs, and is thus highly structured. It is therefore much more appropriate to discuss robust stability of the system using ",-analysis. It turns out that the bound of '" value of the corresponding interconnected system, over the frequency range of 1O-3 ra d/ s to 1Q3 ra d/ s, is less than 0.61 (see Figure- 8). That result means the robust stability has been indeed attained. The highly structured uncertainty in this system leaves scope for further improvement of controller design. The ",-synthesis would be an obvious choice. The controller design using the J.L-synthesis is currently being conducted. Initial results show indeed that J.L controllers are better than Hoo controllers.
In Figure- 2, the FOIA subsystem is enclosed by a dashed box. The output of the FOIA subsystem is thus represented by:
Y! = (1 + .6.)Ym
where Y! is the FOIA output and Ym is the sensor measurements (the roll attitude
The closed-loop system can be re-drawn as in Figure7 for robust stability analysis. From the well-known
889
Heffly, R. K., W. Jewell, J. Lehman and R. Winkle (1978). A Compilation and Analysis of Helicopter Handling Qualities Data. Volume one: Data Compilation. NASA Scientific and Technical Information Branch. Postelthwaite, I., A. Smerlas and D. J. Walker (1999). hoc Control of the NRC Bell 205 Fly By Wire Helicopter. Journal of The American Helicopter Society pp. 276-284. Smerlas, A. (1999). Robust Multivariable Control of Helicopters: From Mathematical Models to Flight Tests .. PhD thesis. Leicester,UK. Turner, M. C. (2000). Robust control of Systems Subject to Input Nonlinearities with Application to High Performance Helicopter. PhD thesis.
Fig. 8. J.L Analysis Robust Stability Output Before leaving this subject, we must point out that the estimation error is high in one of the channels. That is the result of the ANN being trained with the available, limited flight data set. Should better flight data set be availed and used for the training, the result could be much better.
6. CONCLUSION In this paper we reported a complete design case of a fault-tolerant flight control system for the lateral sensor dynamics of Bell 205 helicopter. The FIFCS consists of an ANN-based FDIA system and a robust controller. The same approach has been applied for the longitudinal dynamics as well (not reported here due to space limit). Successful simulations have been observed. In this approach, the sensor failures may be considered as uncertainties on the plant outputs. Due to the structured nature of such uncertainties, our research has now moved to design robust controllers using J.L-analysis and synthesis procedure. In addition, we are exploring the advantages of using adaptive schemes to deal with fault occurrences in flight vehicles.
REFERENCES Al-Malki, M. F. and Da-Wei Gu (2001). An ANNBased Sensors' Fault Detection, Isolation, and Accommodation for Bell-205 Helicopter. Al-Malki, M. F. and Da-Wei Gu (2003). Sensors fault detection, isolation with application to high performance helicopter. International Conference on Simulation and Modelling, Marbella, Spain. DERA (1998). Configuration of the DERA HEIUSIM Model to represent the flight dynamics ofthe NRC Bell-205 Helicopter (U). DERA, UK.
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