Proceedings of 2017 IEEE International Conference on Mechatronics and Automation August 6 - 9, Takamatsu, Japan
Fault Tolerant Control Strategy Based on Actuation Switch Mechanism for More-electric Aircraft with Vertical Tail Damage Zhihan Zhou, Shaoping Wang, Xingjian Wang Department of Automation Science and Electrical Engineering Beihang University Beijing, China, 100191
[email protected] Abstract - This paper proposes a fault tolerant control Therefore, it reminds us to investigate the fault tolerant strategy with an actuation switch mechanism for different control strategy towards more-electric aircraft(MEA), which degrees of vertical tail damage of more-electric aircraft (MEA). A underlines the combination of the hydraulic power and the damage degree coefficient of vertical tail is introduced and the electrical power to drive the aircraft actuation systems, known relationship between lateral derivatives and damage degree is as dissimilar redundant actuation system (DRAS). Researches formulated. Benefit from the more-electric characteristics, a [10, 11] about the DRAS indicate that aircrafts with DRAS combination of electro-hydrostatic actuation (EHA) system and have a potential fault tolerant capability under some extreme engine differential thrust is proposed for serious vertical tail situations, which may assist the crew on the accident aircrafts damage to regain lateral-directional stability and mentioned above. Moreover, adopting the MEA framework manoeuvrability. Furthermore, the reconfigurable control law is carried out by the model reference control (MRC) combined with has plenty of advantages such as optimizing the aircraft linear quadratic regulator (LQR). Simulation results with the performance and decreasing operating and maintenance NASA generic transportation model (GTM) demonstrate the costs[12]. Therefore, it is meaningful to put effort on how to effectiveness of the proposed control strategy for the damaged design fault tolerant control strategy for MEA under such aircraft. severe conditions. Index Terms – Fault tolerant control, actuation switch This paper is organized to solve this problem. In section mechanism, vertical tail damage, more-electric aircraft. Ⅱ, the impact of different damage degree of vertical tail is formulated and the linearized model of the aircraft in normal I. INTRODUCTION and damage conditions is carried out. Section Ⅲ presents the With the increasing requirement of safety and reliability actuation switch mechanism design and reconfigurable control for civil aviation, lots of effort has been made to improve law design. In section Ⅳ, numerical simulation results are aircraft safety levels and reduce the risks that major failures given, followed by the conclusion in section Ⅴ. occur. Novel aircraft configurations such as software and II. DAMAGED AIRCRAFT MODELING AND ANALYSIS hardware redundancy hardware redundancy and power by wire (PBW) etc. have been addressed and corresponding fault A. Dissimilar redundant actuation system tolerant control strategies have been designed to achieve those Fig. 1 shows the detailed layout of DRAS, in which the safety goals. whole elevators, inboard ailerons, lower rudder, and spoilers However, those efforts are not enough to guarantee the 1,2,11 and 12 are equipped with the HA/EHA system. This absolute safety of the aircraft. Loss of Control (LoC) still kind of design can ensure that the aircraft can manipulate the remains a main cause of fatal accidents such as structural elevator, rudder and aileron in performance degradation damage[1]. Representative examples include the accident of condition with EHA even if all the hydraulic power supply Japan Airlines Flight JL123, whose whole vertical tail of this system fails. aircraft was blown off, together with components of all four Speed brakes Speed brakes independent hydraulic systems, and another accident of Roll surfaces Roll surfaces American Airlines flight 587 with the overuse of the rudder which made the vertical tail snapped off entirely. Spoilers Spoilers Ailerons Ailerons Lots of control strategies have been proposed for this case 7 8 9 10 11 12 6 1 5 2 3 4 of structural damage scenarios[2], such as model predictive control(MPC), H control, model reference adaptive control(MRAC), etc.[3-7] And a common way to compensate EHA, electro-hydrostatic actuator Upper the effect of vertical tail damage is the utilization of the engine HA, hydraulic actuator rudder differential thrust[8, 9]. However, according to those Lower Elevators rudder researchers, a fact has been neglected that all actuators would lose their efficiency while vertical tail is seriously damaged Fig. 1 The generic structure of DRAS accompanied with hydraulic loss.
978-1-5090-6759-6/17/$31.00 ©2017 IEEE
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Then a degree parameter 0,1 is introduced indicating
B. Nominal Aircraft Modeling The aircraft dynamic models have been well developed. Practically, the aircraft model is linearized around a certain steady flight operating point. According to the previous research[13], the traditional linearized state-space equation for the aircraft lateral-directional motion is: x = Ax + Bu y = Cx
the damage degree of vertical tail. It is defined as the percentage of the lost part in the whole effective areas of vertical tail, as shown in Fig. 2. =0 means no damage to the vertical tail while =1 means the complete damage of the vertical tail. According to[5], the relationship between the damage degree parameter and the damaged vertical tail derivative
(1)
where the state variable vector x
C y is expressed as:
p r , in which is the sideslip angle, p is the roll rate, r is the yaw rate, is the roll angle. The corresponding matrices are: Y Yp (Yr u0 ) / V0 L i N L i N Lr ix N r p x p x 1 ix iz 1 ix iz 1 ix iz A N i L N i L N x p x p r ix Lr 1 i i 1 ix iz 1 ix iz x z 0 1 0 0 Y r 1 0 0 0 . L L B a r , C N N 0 0 0 1 24 a r 0 0 4 2
T
g 0 cos 0 / V0 0 0 44 0
Here the control input vector u a
Sout (1 ) d 2 A 1.07 1 ( S S ) S (1 ) b b out out ref C y A2 2 tan 2 max t 2 4 1 2 2
2
(2)
where 2 =1-Ma2 with Ma the Mach number; b is the height
,
of the vertical tail, b b is the remaining height and d is the fuselage diameter; Sref
is the reference area and
1 ct cr b is the exposed area, with ct and cr the 2 vertical tail tip chord length and the vertical tail root chord length respectively; A is the aspect ratio of the damaged Sout
vertical tail; max t is the vertical tail sweep of string position of airfoil thickness and is the efficiency of airfoil. The vertical tail characteristics of NASA GTM is used and the relationship between and C y can be obtained and shown in Fig. 3.
r is provided by ailerons and rudders respectively. The sideslip angle and roll angle are the system output. The corresponding T
4.5
derivatives and variables in A and B can be found in NASA report CR-2144. vertical tail derivative C y
4
C. Vertical tail damage analysis and modeling In order to analyse the impact of the damage degree of the vertical tail, an assumption is made as follows: Assumption 1. The shape of vertical tail is a regular trapezium and the part of vertical tail is fractured regularly.
3.5 3 2.5 2 1.5 1
ct
0.5 0
b
ct
0
0.1
0.2
0.3
0.4 0.5 0.6 0.7 vertical tail damage degree
Fig. 3 The relationship between
b
and
0.8
0.9
1
C y
Besides, the lateral-directional derivatives that related with the vertical tail can be obtained：
cr
CN
Fig. 2 The regular damage and parameters of vertical tail
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l CYr 2 CY b( ) d CN f V CL 1 d
(3) (4)
l C Nr 2V CL b CLr
The structure of the overall fault-tolerant control strategy is shown in Fig.4. The baseline controller is designed for the normal condition. In this situation, the aircraft dynamics is kept by the HA system. When the aircraft suffers from vertical tail damage, it is assumed that the failure can be determined precisely by the FDI system. Therefore, based on the information from FDI system, the control switch decides whether or not to change the baseline control law into reconfigurable control law. Meanwhile, depends on the damage degree, the control allocation mechanism decides whether or not to change HA system into the EHA system and whether or not to launch engine differential thrust control. The steps to design the AFTC strategy are shown in this section.
(5)
l z CL 2 CY 4 b b
(6)
where l is the distance from the vertical tail center to the
d is the change in side wash angle to d change in sideslip angle. aircraft gravity center;
D. Damaged Aircraft Modeling The nominal aircraft model, however, is simplified and cannot reflect the available control surfaces in real flight conditions. Therefore, we need to build up a more-electric aircraft model which allows independent control of all actuators. The lateral-directional control inputs of this model are defined as: The inboard aileron is ain and the outboard aileron is aout . The upper rudder is rup and lower rudder is rlow .
A. Actuation switch mechanism In this subsection, an actuation switch mechanism is designed corresponding to the damage degree of the vertical tail. When damage degree is small, the effect to directional derivatives is small and the dual-redundancy HA system can work properly in this situation. When the damage degree is higher, the HA system may malfunction and EHA system should be launched immediately; when the damage becomes severe, the rest part of the vertical tail cannot provide the required yawing moment and then engine differential thrust should be adopted.
The 1st to the 12th spoilers are from sp1 to sp12 .
four Engine differential thrusts are from T1 to T4 . It should be pointed out that most of the spoilers, except for spoilers 5 to 8, assist the ailerons in providing the rolling moment. Noting that the spoilers can only deflect upward, we can define that the deflection of the right-side spoilers is positive, providing right-rolling moment and vice versa. Consequently, the input vector can be expressed as: The
u ain
aout sp rup rlow T
T
Flight mission
Diagnosing and precalculating
(7) No
0
where
sp sp1,12 sp 2,11 sp3,10 sp 4,9 T T1 T2 T3 T4
Yes
, . Considering different damage degree of vertical tail, the damaged aircraft lateral-directional model can be expressed as: x = A x + B Wu (8)
Change into EHA system No
1
where A and B is the state space matrices related to
Yes
the damage degree . W =diag( w1 , w2 ,..., wm ) is a diagonal matrix where w1 ,… wm represent the effectiveness or the usage of the control inputs; m is the number of the control inputs. If wi 1 , it means that the corresponding i -th input is adopted and is in healthy state; if 0 wi 1 , the efficiency of
Using engine differential thrust
Corresponding controller Ce
i -th input is degraded; and when wi 0 means that the corresponding input is unused or failed.
Corresponding controller Cee
Corresponding controller C h
End
Fig. 4 diagram of the actuator switching mechanism
III. FAULT-TOLERANT CONTROL LAW DESIGN BASED ON THE ACTUATION SWITCH MECHANISM
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Reference model
+ FDI
Reconfigurable controller Input
-
Control switch
HA
Actuating Switch
Aircraft
EHA
Output
Baseline controller
Engine differential thrust
Fig.5 Structure of fault tolerant control strategy with actuator switch mechanism
Therefore, according to Fig. 3, we introduce two damage degree constants 0 and 1 that represent the threshold of using the EHA system and using the engine differential thrust respectively. The actuation switch process is shown in Fig. 4. In Fig. 4, C h is the baseline controller where only HA system is used; C e is the reconfigurable controller where only
The reference model is a closed-loop system augmented with a control variable xc = r - y and controlled by the baseline controller using LQR method. The system matrices are deduced as:
A+ BK x Ar = -Bc C 1 Cr C 0
EHA system is used; Cee is the reconfigurable controller where EHA system and engine differential thrust control system is both used.
where xr = x
BK c 0 , Br = 42 , Ac 66 I 62 0 0 0 0 0 0 0 1 0 0 26
xc , ur = r = [r , r ]T and y [ , ]T . Similar to the reference model(9), we obtain the aircraft model under total hydraulic loss as follows: x p = Ap x p + B p1u p + B p 2 r (10) y p = C p x p
Remark 1: In practice, the choice of parameters in controller design should be in the light of a lot of simulations and experiments for a specific aircraft. In this paper, the damage degree threshold value is designed according to the flight condition, performance requirement, dynamic derivatives change and other associated factors.
T
Af 0 B T , B p1 = f , xc , Ap = -C 0 0 62 f 66 0 1 0 0 0 0 0 Bp 2 = 42 , C p C ， Af ， I 62 0 0 0 1 0 0 26 B f and C f are the matrices for the damaged aircraft.
B. Reconfigurable controller design The HA system would malfunction when the aircraft suffers from total hydraulic loss. Although the EHA system can be launched immediately, the baseline control law might not be robust enough to keep the required performance, or even cannot satisfy the flying requirement. Therefore, the controller should be reconfigured to stabilize the damaged aircraft and improve the survivability. We apply MRC method in this paper and the structure is shown in Fig. 6.
where x p x
Since the dimension of x r and x p is the same, we can apply MRC method to reconfigure the fault tolerant control law. The error between the state of reference model and damaged model can be defined as e = xm - x p , and the control input is chosen as:
up = K e e + K r xr
(11)
Then the differential of state error is written as:
e = xm - x p = Ap e + (Ar - Ap )xr + Br ur - B p1u p - B p 2 r = (Ap - B p1 K e )e + (Ar - AP - B p1 K r )xr
Fig.6 Structure of model reference control method
The reference model is expressed as follows:
xr = Ar xr + Br ur yr = C r x r
(12)
By selecting appropriate gain matrix K r R26 to satisfy the following equation:
(9)
Ar - AP - Bp1 K r = 0
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(13)
Thus the Eq. (13) becomes:
Remark 2. Stability proof: According to the NASA GTM model, as checked the controllability of ( Ap , B p1 ), it is
In Fig. 7, the lateral-directional response of the aircraft with the baseline controller is shown under the damage degree =0.3 . With the slight damage to the vertical tail, there is no need to use the engine differential thrust, so the corresponding term in matrix W is set to zero. Then the control input is
controllable and then there exists K e that assigns the poles of
u= ain
matrix Ap - Bp1 K e lie in the left side of plane, which
matrix W diag 1 1 1 1 1 0 . Here we can see that the
(14)
e = (Ap - Bp1 K e )e
T
and the weighing
T
guarantees that the error e = xr - x p tends to zero.
baseline controller is robust to get over the slight damage. The damaged system performance is very close to the normal conditions with a little bigger sideslip and a bit longer raising time.
IV. SIMULATION RESULTS AND ANALYSIS In this section, simulations with the architecture described above were conducted for the scenarios of vertical tail damage and the simulations were based on the NASA GTM model which was trimmed at Mach 0.65 and 20,000 feet. Thus, we can get the detailed state space matrices in normal condition: -0.00558 0.0802 0.9968 0.0415 -3.05 -0.465 0.388 0 An 0.598 -0.0316 -0.115 0 0 1 0.0804 0
aout sp rup rlow T
15
Rolling angle(deg)
10 5 0
-5
-10 -15 0
M1:Normal M3:u=0.65 Input
10
20
30
Time(s)
40
50
60
5
,
4 3
Sideslip(deg)
0 0 0.00410.0032 0 0.268 0.3575 0.4469 0.126 0.027 Bn 0.0154 0.0193 0.0241 0.275 0.2 0 0 0 0 0
2 1
0
-1 -2 -3
M1:Normal M3:u=0.65 Input
-4 -50
The aim of the proposed control strategy is to stabilize the aircraft with vertical tail damage and to mimic the normal aircraft dynamics and track the given command. Here we set the damage degree constants as 0 =0.6 and 1 =0.8 , and give
10
20
30
Time(s)
40
50
60
Fig. 8 The response of system based on baseline controller when
=0.65
15
Rolling angle(deg)
10
the system a step command of coordinated turn as c =10 and
c 0 . Three different cases of vertical tail damage degree are considered: =0.3 , =0.65 and =1 . Simulation results
5 0
-5
-10
are given in Figs. 7-10.
-15 0
M1:Normal M4:driven by EHA Input
10
20
30
40
50
60
30
40
50
60
Time(s)
15 5
4
5
3
Sideslip(deg)
Rolling angle(deg)
10
0
-5
-10
-15 0
M1:Normal M2:u=0.3 Input
10
2
1 0 -1
-2
20
30
Time(s)
40
50
-3
60
-4
-5 0
10
20
Time(s)
5 4
Fig. 9 The response of system using reconfigurable controller when
3
Sideslip(deg)
M1:Normal M4:driven by EHA Input
=0.65
2
From Fig. 8 and Fig. 9, when the damage gets worse, that is, =0.65 , we can see that M3 represents the damaged system response with baseline control law and M4 is the damaged system response with reconfigurable control law. In this situation, according to the actuator switch mechanism, HA system would malfunction and EHA system was launched. It is
1 0 -1 -2 -3 -4 -5 0
M1:Normal M2:u=0.3 Input
10
20
30
Time(s)
40
50
60
Fig. 7 The response of system based on baseline controller when
=0.3
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notable that the EHA system suffers from the lower bandwidth and smaller stiffness compare d with HA system[12]. Therefore, it is assumed that the performance degradation of EHA system can be expressed with a first order delay system [5]: uEHA =e0.1t uHA And the corresponding weighing matrix becomes T W =diag 1 0 1 0 1 0 . As it is shown in Fig. 8 and Fig.
controller using LQR method, the reconfigurable controller can compensate the dynamic derivatives variation caused by the vertical tail damage, and the system had a better tracking performance. The utilization of engine differential thrust provided the momentum to compensate the effects caused by vertical tail loss and showed its effectiveness. Further study will put effort in post-damage landing control strategies to assist the pilot in executing a safe landing.
9, the response diverges which means the baseline controller cannot stabilize the damaged system. When switched to the proposed reconfigurable controller, the system can follow the rolling command very well while the sideslip angle has a larger fluctuation within a short period of time compared to the normal condition. This simulation result validates the effectiveness of the proposed reconfigurable control strategy.
ACKNOWLEDGMENT This work is supported by the National Natural Science Foundation of China (Grants No. 51620105010, No.51575019), the National Basic Research Program of China (973 Program) (Grant No.2014CB046402) and the Program 111 of China and China Scholarship Council (201406020021). REFERENCES [1] B. C. Airplanes, "Statistical summary of commercial jet airplane accidents, worldwide operations," 2016. [2] Y. Zhang and J. Jiang, "Bibliographical review on reconfigurable fault tolerant control systems," Annual Reviews in Control, vol. 32, pp. 229252, 2008. [3] R. E. Bavili, M. J. Khosrowjerdi, and R. Vatankhah, "Active Fault Tolerant Controller Design using Model Predictive Control," Control Engineering & Applied Informatics, vol. 17, pp. 68-76, 2015. [4] F. Moracamino and L. Zhong, "Neural Networks Based Aircraft Fault Tolerant Control," in Aiaa Aviation Technology, Integration, and Operations, 2012. [5] J. Wang, S. Wang, X. Wang, C. Shi, and M. M. Tomovic, "Active fault tolerant control for vertical tail damaged aircraft with dissimilar redundant actuation system," Chinese Journal of Aeronautics, vol. 29, pp. 1313-1325, 2016. [6] X. Wang, S. Wang, Z. Yang, and C. Zhang, "Active fault-tolerant control strategy of large civil aircraft under elevator failures," Chinese Journal of Aeronautics, vol. 28, pp. 1658-1666, 2015.B. Simpson, et al, “Title of paper goes here if known,” unpublished. [7] D. Sun, R. Choe, E. Xargay, and N. Hovakimyan, "An L1 Adaptive Backup Flight Control Law for Transport Aircraft with Vertical-Tail Damage," in AIAA Guidance, Navigation, and Control Conference, 2015. [8] Y. Hitachi, "Damage-tolerant Control System Design for Propulsioncontrolled Aircraft," School of Graduate Studies - Theses, vol. 28, pp. 551-554, 2015. [9] L. K. Lu and K. Turkoglu, "H ∞ Loop-Shaping Robust Differential Thrust Control Methodology for Lateral/Directional Stability of an Aircraft with a Damaged Vertical Stabilizer," in AIAA Guidance, Navigation, and Control Conference, 2016. [10] Y. Fu, Y. L. H. Pang, and L. Wang, "Design and working mode analysis of dissimilar redundant actuator system," Journal of Beijing University of Aeronautics & Astronautics, 2012. [11] C. Shi, X. Wang, S. Wang, J. Wang, and M. M. Tomovic, "Adaptive decoupling synchronous control of dissimilar redundant actuation system for large civil aircraft," Aerospace Science & Technology, vol. 47, pp. 114-124, 2015. [12] R. T. Naayagi, "A review of more electric aircraft technology," in International Conference on Energy Efficient Technologies for Sustainability, 2013, pp. 750-753. [13] C. Edwards, T. Lombaerts, and H. Smaili, Fault Tolerant Flight Control: Springer Berlin Heidelberg, 2010.
15
Rolling angle(deg)
10 5 0
-5
-10 -15 0
M5:driven by EHA and engine M6:driven only by EHA Input
10
20
30
40
50
60
30
40
50
60
Time(s)
5
4 3
Sideslip(deg)
2 1
0
-1 -2 -3
-4 -5 0
M5:driven by EHA and engine M6:driven only by EHA Input
10
20
Time(s)
Fig.10 The response of system using reconfigurable controller when
=1
When the vertical tail gets completely loss, there is no rudder to provide the yawing moment. Fig. 10 depicts the utilization of the engine differential thrust.M5 represents the system only driven by the EHA system and M6 represents the combination of EHA system and engine differential thrust. As it can be seen, M5 tracks the rolling command with an error of nearly 2 degrees and an obvious fluctuation appears for the opposite direction of rolling command; the sideslip angle gets oscillating with amplitude of 1.5 degrees. Compared with this, M6 performs much better and tracks the given command quickly. A conclusion can be made that the DRAS system combined with the engine differential thrust can improve the tracking performance. V. CONCLUSION Throughout this paper, the parameter of vertical tail damage degree and the effect of the different damage degree were introduced. Based on this, an actuator switch mechanism was designed for the vertical tail damage MEA. Then the MRC method was applied to the reconfigurable control strategy for the damaged MEA. Compared with the baseline 1899
