Fault-tolerant control for a multi-propeller airship based on adaptive sliding mode method
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摘要: 針對多螺旋槳浮空器執行機構易發生故障的容錯控制問題，同時考慮系統所受到的未知外部擾動和螺旋槳輸入幅值的飽和約束，提出一種自適應滑模容錯控制方法。建立浮空器的四自由度運動模型，系統分析矢量螺旋槳的故障類型，分為輸出力的大小故障和矢量轉角故障，得到浮空器執行機構的故障模型。基于自適應和滑模控制理論，由跟蹤目標與系統當前狀態偏差設計積分滑模面。針對未知外部擾動和執行機構偏移故障，設計相應的自適應律進行處理；針對螺旋槳輸入飽和約束，應用Sigmoid函數設計跟蹤軌跡進行處理。由此設計一種自適應滑模容錯控制策略，利用Lyapunov穩定性理論證明了閉環系統的全局漸近穩定性能。以上海交通大學的多螺旋槳浮空器為模型，仿真驗證了故障容錯控制方法的有效性和魯棒性。Abstract: An airship is a kind of light-than-air vehicle, which is composed of a gas-filled cyst body and a propulsion system. The airship mainly flies in near-space, and because of the exposure to the lower temperature, solar radiation and long-term operation, it is difficult to avoid failure. Therefore, how to solve the failures of the airship and increase its safety has been a significant topic. The recent research on a fault-tolerant control system can be divided into two parts, active and passive fault-tolerant control. The active fault-tolerant control system requires a fault detection module to obtain the fault information, and then the reconfiguration control law will be reconstructed by the fault-tolerant control module. In this way, the design of the controller is very complicated and the parameters are more difficult to adjust. The passive fault-tolerant control develops a control system based on robust theory without changing the controller and system structure, which doesn’t need the fault information. In this paper, an adaptive sliding mode controller (ASMFTC) was developed for multi-propeller airship with the faults of actuators, where the external wind disturbances and control input saturation were also considered. A four-DOF dynamic model of the airship was established, and the novel fault model of the vectored propellers was designed. The fault system model of the multi-propeller airship was then built. Based on the sliding mode control theory, an integral sliding surface was presented with the residue between the trajectory and states of the airship, in order to deal with the problems of the offset faults and external disturbances, the adaptive law was designed. Thus, an adaptive sliding mode fault-tolerant control controller was proposed. The global asymptotic stability of the system is guaranteed by Lyapunov theory. The effectiveness and robustness of the controller are demonstrated by simulation results of a multi-propeller airship designed by Shanghai Jiao Tong University.
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圖 1 多螺旋槳浮空器與坐標系. （a）浮空器實物圖；（b）浮空器坐標系
Figure 1. Multi-propeller airship and coordinate system: (a) physical picture of airship; (b) coordinate system
圖 2 螺旋槳矢量推力分解示意圖
Figure 2. Orthogonal decomposition diagram of vector propeller’s force
圖 5 軌跡跟蹤狀態響應對比圖. （a）高度方向跟蹤響應；（b）偏航角跟蹤響應
Figure 5. Comparison of the trajectory tracking response: (a) hight tracking response; (b) yaw angle tracking response
圖 6 自適應滑模容錯控制螺旋槳響應. （a~d）螺旋槳推力變化；（e~h）螺旋槳轉角變化
Figure 6. Response of propellers under the ASMFTC: (a?d) propellers’ forces change; (e?h) propellers’ angles change
圖 9 軌跡跟蹤狀態響應比較. （a）高度方向跟蹤響應；（b）偏航角跟蹤響應
Figure 9. Comparison of the trajectory tracking response: (a) hight tracking response; (b) yaw angle tracking response
圖 10 自適應滑模容錯控制螺旋槳響應. （a~d）螺旋槳推力變化；（e~h）螺旋槳轉角變化
Figure 10. Response of propellers under the ASMFTC: (a?d) propellers’ forces change; (e?h) propellers’ angles change
表 1 矢量螺旋槳故障模型
Table 1. Fault model of the vectored propeller
Fault forms Fault types ${\varepsilon _i}\left( {i = 1 \ldots 4} \right)$ ${u_{{\rm{a}}i}}\left( {i = 1 \ldots 4} \right)$ The faults of ${{{f}}_i}$ Loss of effectiveness $0 < {\varepsilon _i} < 1$ ${u_{{\rm{a}}i}} = 0$ Offset fault ${\varepsilon _i} = 1$ ${u_{{\rm{a}}i}} \ne 0$ Stuck fault ${\varepsilon _i} = 0$ ${u_{{\rm{a}}i}} \ne 0$ Failure fault ${\varepsilon _i} = 0$ ${u_{{\rm{a}}i}} = 0$ The faults of $\,{\mu _i}$ Stuck fault ${\varepsilon _i} = 1$ ${u_{{\rm{a}}i}} \ne 0$ Offset fault ${\varepsilon _i} = 1$ ${u_{{\rm{a}}i}} \ne 0$ 
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表 2 多螺旋槳浮空器模型參數
Table 2. Parameters of multi-propeller airship
Parameters Values Parameters Values Mass/kg 72 Added mass,${m_{11}}$/kg 10.8147 Volume/m3 70 Added mass,${m_{22}}$/kg 10.8147 Area/m2 16.9850 Added mass,${m_{33}}$/kg 38.9521 Installation radius of propeller,${R_{\rm{p}}}$/m 2.81 Added mass,${m_{66}}$/kg 0.0 Barycentric coordinates,$\left( {{x_{\rm{G}}},{y_{\rm{G}}},{z_{\rm{G}}}} \right)/{\rm{m}}$ (0,0,2) Moment of inertia,${I_x}$/(kg?m2) 409.4260 Maximum thrust of propeller,${F_{\max }}$/N 150 Moment of inertia,${I_y}$/(kg?m2) 409.4260 Rotation angle of propeller,$\mu /{\rm{rad}}$ $ - {\text{π} } \sim {\text{π} }$ Moment of inertia,${I_z}$/(kg?m2) 34.5941
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