滑模变结构控制理论在飞行器姿态控制系统中的应用研究
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摘要
滑模变结构控制由上世纪50年代前苏联学者Emelyanov首先提出。由于滑模变结构控制对系统参数摄动和外界扰动的不变性，即完全鲁棒性，这一突出优点引起了人们的极大关注。经过50多年的发展，滑模变结构控制已广泛地应用于机器人、工业控制、航空航天等控制领域。但是滑模变结构控制也有其固有的缺点，就是当系统的运动状态到达滑动平面后，会在滑动平面附近产生高频抖振。该抖振对于控制是极其有害的。
本文对滑模变结构控制理论进行了一些研究，主要针对滑模变结构控制律的设计及其抖振进行了探讨，并总结了控制律设计的步骤及削弱抖振的方法。通过对飞行器姿态的参数化描述方法的研究，得出了基于单位四元数的飞行器姿态动力学方程和运动学方程。同时，对飞行器的姿态控制系统进行了研究，并成功地将滑模变结构控制理论应用到飞行器姿态控制系统中。本文将飞行器姿态控制分为：姿态稳定和姿态跟踪两种情况加以研究。利用Lyapunov直接法设计、推导出了两种姿态稳定控制器，并对其进行了证明，结果表明这两种控制器都能使系统在有限的时间内达到稳定平衡状态。
最后，本文利用滑模变结构控制理论推导、设计出了一种基于误差四元数的滑模变结构控制(Variable Structure Control with Sliding Mode，VSS)飞行器姿态跟踪控制律，并对其进行了实例仿真。仿真结果显示，该控制律对系统参数摄动及外部干扰具有较强的鲁棒性，动态性能良好。
Variable structure control with sliding mode (VSS) was firstly proposed by Emelyanov, a Soviet researcher, in the 1950s. It was gotten most attention because of its excellent invariance to the change of system parameters ,external disturbance, namely complete robustness. During the 50 years, it has been applied in all sorts of controlling fields such as robot, technical control, Aeronautics & Astronautics etc. However, it has its own disadvantage that after the system state getting to the sliding surface, it will produce high frequency chattering around the sliding surface. The chattering is very harmful to the control.
The paper makes some research of VSS, especially the controller and the chattering. We summarize the design step of the controller and the methods of the weakening chattering. The paper reasons the dynamic equation and the kinematic equation of the attitude based on the unit quaternion by means of the description of the attitude parameter. The paper also makes research of aerocraft attitude controlling system and applies VSS to it. The aerocraft attitude control is divided into two parts: attitude stabilization and attitude track. We designed two controllers of the attitude stabilization using the Lyapunov's direct method. The two controllers were proved correct.
Finally, the paper designed an aerocraft attitude tracking controller with VSS based on error quaternion. We make simulation to the controller. Simulation results show that the controller has excellent robustness to the system uncertainties and the external disturbance and perfect dynamic performance.
本文对滑模变结构控制理论进行了一些研究，主要针对滑模变结构控制律的设计及其抖振进行了探讨，并总结了控制律设计的步骤及削弱抖振的方法。通过对飞行器姿态的参数化描述方法的研究，得出了基于单位四元数的飞行器姿态动力学方程和运动学方程。同时，对飞行器的姿态控制系统进行了研究，并成功地将滑模变结构控制理论应用到飞行器姿态控制系统中。本文将飞行器姿态控制分为：姿态稳定和姿态跟踪两种情况加以研究。利用Lyapunov直接法设计、推导出了两种姿态稳定控制器，并对其进行了证明，结果表明这两种控制器都能使系统在有限的时间内达到稳定平衡状态。
最后，本文利用滑模变结构控制理论推导、设计出了一种基于误差四元数的滑模变结构控制(Variable Structure Control with Sliding Mode，VSS)飞行器姿态跟踪控制律，并对其进行了实例仿真。仿真结果显示，该控制律对系统参数摄动及外部干扰具有较强的鲁棒性，动态性能良好。
Variable structure control with sliding mode (VSS) was firstly proposed by Emelyanov, a Soviet researcher, in the 1950s. It was gotten most attention because of its excellent invariance to the change of system parameters ,external disturbance, namely complete robustness. During the 50 years, it has been applied in all sorts of controlling fields such as robot, technical control, Aeronautics & Astronautics etc. However, it has its own disadvantage that after the system state getting to the sliding surface, it will produce high frequency chattering around the sliding surface. The chattering is very harmful to the control.
The paper makes some research of VSS, especially the controller and the chattering. We summarize the design step of the controller and the methods of the weakening chattering. The paper reasons the dynamic equation and the kinematic equation of the attitude based on the unit quaternion by means of the description of the attitude parameter. The paper also makes research of aerocraft attitude controlling system and applies VSS to it. The aerocraft attitude control is divided into two parts: attitude stabilization and attitude track. We designed two controllers of the attitude stabilization using the Lyapunov's direct method. The two controllers were proved correct.
Finally, the paper designed an aerocraft attitude tracking controller with VSS based on error quaternion. We make simulation to the controller. Simulation results show that the controller has excellent robustness to the system uncertainties and the external disturbance and perfect dynamic performance.
引文
[1] ZHAO J,GOREZ R .WERTZ V. Synthesis of fuzzy control systems with desired performances[A], Proceedings of the 1996 IEEE International Symposium on Intelligent Control[C]. Dearbron, MI 1996:115-120
[2] TANAKA K, IKEDA T, WANG H O Fuzzy regulators and fuzzy observers:relaxed stability conditions and LMI-based designs[J]. IEEE Trans on Fuzzy Systems, 1998, 6(2):250-265
[3] Glower J.S.and Munighan J. Designing fuzzy controllers from a variable structure standpoint. IEEE Transactions on Fuzzy Systems, 1997, 5(1):138-144
[4] 邱焕耀，毛宗源．消除变结构系统中高频颤振的一种方法．全国控制理论与应用年会，1998，132-139
[5] Man Z.H., Yu X., Eshraghian K. and Palaniswami M. A robust adaptive sliding mode tracking control using an RBF neural network for robotic manipulators. IEEE International Conference on Neural Networks, 1995, 5:2403-2408
[6] Oucheriah S. Dynamic compensation of uncertain time-delay systems using variable structure approach. IEEE Transactions on Circuits and Systems:Fundamental Theory and Applications, 1995, 42(8):466-470
[7] Gouaisbaut F., Perruquetti W. and Richard J.P. A sliding mode control for linear systems with input and state delays.Proceedings of the 38th IEEE Conference on Decision and Control, 1999, 4:4234-4239
[8] Hu J.B. and Chu J., A new VSC design method based on LMI. IMC, Beijing, 1999, 302-305
[9] Lee Kang-Woong, Lee Sung-Jun and Choi Keh-Kun. A model following variable structure controller. IECON'89, 15th Annual Conference of IEEE Industrial Electronics Society, 1989, 2:330-334
[10] 李忠娟，张新政．变结构控制理论忠抖振问题的研究[J]．五邑大学学报(自然科学版)，2003，17(3)：66-70
[11] 罗宁苏，冯纯伯．消除变结构系统中高频颤振的一种方法．全国控制理论与应用年会，1988，132-139
[12] Davari A. and Zhang Z., Application of the three segments variable structure systems. Proc.American Control Conference, 1991:62-63
[13] Man Z.et al, A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators, IEEE Trans. On. Auto. Contr., 1994, 39:2464-2469
[14] Shuster M D. A survey of attitude representation. J. of Astronautical Sciences,
1993, 43:439-514
[15] Wen J-T and Kreutz-Delgdo,K. The attitude control problem.IEEE Trans. on Automatic Control, 1991, 36(10): 1148-1162
[16] Tsiotras P, Junkins J L, and Schaub H. Higher order Cayley transforms with application to attitude representation. J. of Guidance, Control, and Dynamics, 1997, 20:528-534
[17] 胡跃明编著．非线性控制系统理论与应用[M]．2002(1)，国防工业出版社，27-46
[18] Joshi S M, Kelkar A G and Wen J T Y. Robust attitude stabilization of spacecraft using nonlinear quaternion feedback. IEEE Trans Automatic Control, 1995, 40:1800-1803
[19] 谢树光．非线性模型预测控制(NMPC)在微型飞行器自适应控制中的应用．厦门大学硕士学位论文，2002．5
[20] Bartolini G , and Zolezzi T. Variable structure systems nonlinear in control laws.IEEE Trans. On Automatic Control, 1985, 30(7):681-684
[21] ZHAO J, GOREZ R. WERTZ V. Synthesis of fuzzy control systems with desired performances[a], Proceedings of the 1996 IEEE International Symposium on Intelligent Control[C]. Dearbron, MI. 1996:115-120
[22] TANAKA K, IKEDA T, WANG H O Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs[J]. IEEE Trans on fuzzy Systems, 1998, 6(2):250-265
[23] Utkin V. I. Variable structure systems with sliding modes. IEEE Trans on Auto. Contr., 1977, 22(2):212-222
[24] 李彦平．变结构控制理论及其应用．西北工业大学博士论文，1990
[25] 刘暾，赵钧编著．空间飞行器动力学[M]．2003(1)，哈尔滨工业大学出版社，154-161
[26] 袁子怀，钱杏芳编著．有控飞行力学与计算机仿真[M]．2001(1)，国防工业出版社，38-50
[27] B.T.Costic, D.M.Dawson, M.S.de Queiroz, and V.Kapila. A Quatemion-Based Adaptive Attitude Tracking Controller Without Velocity Measurements. Proceedings of the 39th IEEE Conference on Decision and Control, 2000, 12:2424 - 2429
[28] Tsiotras, P. A passivity approach to attitude stabilization using nonredundant kinematic parameterizations. Proceedings of the 34th IEEE Conference on Decision and Control, 1995, 1:515-520
[29] 梅生伟，申铁龙，刘康志编著．现代鲁棒控制理论与应用[M]．2003(1)，清华大学出版社，53-57
[30] 周宗锡，吴方向等．基于四元数的刚体姿态调节问题[J]．西安交通大学学报，2002，36(10)：37-40
[31] Weiss H. Quaternion-Based/Attitude Tracking Systems with Application to Gimbal Attitude Control. Journal of Guidance, Control and Dynamics, 1993, 16(4):609-616
[32] 耿云海，崔祜涛，崔海英，杨涤．挠性飞行器飞轮姿态控制系统设计[J]．系统工程与电子技术，2001，23(6)：55-58
[2] TANAKA K, IKEDA T, WANG H O Fuzzy regulators and fuzzy observers:relaxed stability conditions and LMI-based designs[J]. IEEE Trans on Fuzzy Systems, 1998, 6(2):250-265
[3] Glower J.S.and Munighan J. Designing fuzzy controllers from a variable structure standpoint. IEEE Transactions on Fuzzy Systems, 1997, 5(1):138-144
[4] 邱焕耀，毛宗源．消除变结构系统中高频颤振的一种方法．全国控制理论与应用年会，1998，132-139
[5] Man Z.H., Yu X., Eshraghian K. and Palaniswami M. A robust adaptive sliding mode tracking control using an RBF neural network for robotic manipulators. IEEE International Conference on Neural Networks, 1995, 5:2403-2408
[6] Oucheriah S. Dynamic compensation of uncertain time-delay systems using variable structure approach. IEEE Transactions on Circuits and Systems:Fundamental Theory and Applications, 1995, 42(8):466-470
[7] Gouaisbaut F., Perruquetti W. and Richard J.P. A sliding mode control for linear systems with input and state delays.Proceedings of the 38th IEEE Conference on Decision and Control, 1999, 4:4234-4239
[8] Hu J.B. and Chu J., A new VSC design method based on LMI. IMC, Beijing, 1999, 302-305
[9] Lee Kang-Woong, Lee Sung-Jun and Choi Keh-Kun. A model following variable structure controller. IECON'89, 15th Annual Conference of IEEE Industrial Electronics Society, 1989, 2:330-334
[10] 李忠娟，张新政．变结构控制理论忠抖振问题的研究[J]．五邑大学学报(自然科学版)，2003，17(3)：66-70
[11] 罗宁苏，冯纯伯．消除变结构系统中高频颤振的一种方法．全国控制理论与应用年会，1988，132-139
[12] Davari A. and Zhang Z., Application of the three segments variable structure systems. Proc.American Control Conference, 1991:62-63
[13] Man Z.et al, A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators, IEEE Trans. On. Auto. Contr., 1994, 39:2464-2469
[14] Shuster M D. A survey of attitude representation. J. of Astronautical Sciences,
1993, 43:439-514
[15] Wen J-T and Kreutz-Delgdo,K. The attitude control problem.IEEE Trans. on Automatic Control, 1991, 36(10): 1148-1162
[16] Tsiotras P, Junkins J L, and Schaub H. Higher order Cayley transforms with application to attitude representation. J. of Guidance, Control, and Dynamics, 1997, 20:528-534
[17] 胡跃明编著．非线性控制系统理论与应用[M]．2002(1)，国防工业出版社，27-46
[18] Joshi S M, Kelkar A G and Wen J T Y. Robust attitude stabilization of spacecraft using nonlinear quaternion feedback. IEEE Trans Automatic Control, 1995, 40:1800-1803
[19] 谢树光．非线性模型预测控制(NMPC)在微型飞行器自适应控制中的应用．厦门大学硕士学位论文，2002．5
[20] Bartolini G , and Zolezzi T. Variable structure systems nonlinear in control laws.IEEE Trans. On Automatic Control, 1985, 30(7):681-684
[21] ZHAO J, GOREZ R. WERTZ V. Synthesis of fuzzy control systems with desired performances[a], Proceedings of the 1996 IEEE International Symposium on Intelligent Control[C]. Dearbron, MI. 1996:115-120
[22] TANAKA K, IKEDA T, WANG H O Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs[J]. IEEE Trans on fuzzy Systems, 1998, 6(2):250-265
[23] Utkin V. I. Variable structure systems with sliding modes. IEEE Trans on Auto. Contr., 1977, 22(2):212-222
[24] 李彦平．变结构控制理论及其应用．西北工业大学博士论文，1990
[25] 刘暾，赵钧编著．空间飞行器动力学[M]．2003(1)，哈尔滨工业大学出版社，154-161
[26] 袁子怀，钱杏芳编著．有控飞行力学与计算机仿真[M]．2001(1)，国防工业出版社，38-50
[27] B.T.Costic, D.M.Dawson, M.S.de Queiroz, and V.Kapila. A Quatemion-Based Adaptive Attitude Tracking Controller Without Velocity Measurements. Proceedings of the 39th IEEE Conference on Decision and Control, 2000, 12:2424 - 2429
[28] Tsiotras, P. A passivity approach to attitude stabilization using nonredundant kinematic parameterizations. Proceedings of the 34th IEEE Conference on Decision and Control, 1995, 1:515-520
[29] 梅生伟，申铁龙，刘康志编著．现代鲁棒控制理论与应用[M]．2003(1)，清华大学出版社，53-57
[30] 周宗锡，吴方向等．基于四元数的刚体姿态调节问题[J]．西安交通大学学报，2002，36(10)：37-40
[31] Weiss H. Quaternion-Based/Attitude Tracking Systems with Application to Gimbal Attitude Control. Journal of Guidance, Control and Dynamics, 1993, 16(4):609-616
[32] 耿云海，崔祜涛，崔海英，杨涤．挠性飞行器飞轮姿态控制系统设计[J]．系统工程与电子技术，2001，23(6)：55-58
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