跷跷板系统的智能滑模控制
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摘要
跷跷板系统具有严重非线性、强耦合性、高阶次、对干扰敏感、模型较复杂等特点。由于跷跷板系统的控制策略和算法与航行船舶的平衡控制、机器人的行走控制、两轮平衡小车的平衡控制、飞行器姿态的调整方法非常相似,而且许多控制理论概念,如系统稳定性和系统抗干扰能力等等,都可以通过跷跷板系统实验直观地表现出来,因此对跷跷板系统的研究具有十分重要的理论和实践意义。
本文在总结和归纳了跷跷板系统的研究现状后,对智能控制及滑模变结构控制方法的原理、特性、抖振产生原因及削弱方法进行了简要的阐述。
首先,在分析了跷跷板系统的结构和工作原理基础上,利用拉格朗日方程建立了系统的数学模型;
其次,将模糊控制和滑模控制理论相结合,得出一种基于模糊切换增益调节的滑模控制方法,通过模糊控制器的模糊逻辑运算功能来在线调整滑模控制的切换增益值,从而很好地解决了滑模控制切换过程带来的系统抖振问题;
接着,结合神经网络和自适应控制的优点,设计一种神经网络自适应滑模控制器,利用神经网络的自学习能力来逼近系统的等效控制律,自适应控制算法来计算系统切换控制律的增益,该方法既保留了滑模控制所具有的较强的鲁棒性,又使控制系统滑动模态的品质得到保证和改善,并能很好地削弱了系统的抖振;
最后,利用Quanser公司提供的Wincon软件及跷跷板系统实验平台,将滑模变结构控制算法应用于实际的控制系统中,实验结果也进一步验证了所使用的控制算法是有效可行的。
Seesaw system has the characteristics of serious non-linear, strong coupling, higher-order, sensitive to disturbance, and complicated model, etc. As the control strategies and algorithms are similar to the methods of boat balance control, biped robot walking upright control, two wheel self-balanced vehicle balance control, the position adjustment of spacecraft, and many abstract control theories and concepts, such as stability of systems, controllability and anti-jamming capability, etc, can be visually displayed through the seesaw system experiments, Therefore, it is of great significance in theory and applications to do systematic research on the seesaw.
In this paper, the present research situations of seesaw system are summarized, and the theory of intelligent control and sliding mode control is described comprehensively.
Firstly, according to the analysis of the structure and basis principle of the system, Lagrange theory is used to establish a mathematical model of seesaw system.
Secondly, switching gain adjustment based on fuzzy sliding mode control scheme is proposed by incorporating the fuzzy control and sliding mode control. The switching gain of sliding mode control is tuned on-line through the corresponding fuzzy logic operation, so the chattering problem of the system can be solved.
Thirdly, with the advantages of neural networks and adaptive control, a neural network adaptive sliding-mode controller is designed. Neural network is used to approximate the equivalent control of sliding mode control, and adaptive controller is used to achieve the compensation control of the system. The method not only retains the strong robustness of system, but also guarantees and improves the quality of the sliding-mode. Chattering of the system is eliminated at the same time.
Finally, the software (Wincon) and seesaw system experimental platform are used to study the sliding mode variable structure control strategy based on index reaching law, the experimental results also further illustrate that the proposed control algorithm is effective and feasible.
本文在总结和归纳了跷跷板系统的研究现状后,对智能控制及滑模变结构控制方法的原理、特性、抖振产生原因及削弱方法进行了简要的阐述。
首先,在分析了跷跷板系统的结构和工作原理基础上,利用拉格朗日方程建立了系统的数学模型;
其次,将模糊控制和滑模控制理论相结合,得出一种基于模糊切换增益调节的滑模控制方法,通过模糊控制器的模糊逻辑运算功能来在线调整滑模控制的切换增益值,从而很好地解决了滑模控制切换过程带来的系统抖振问题;
接着,结合神经网络和自适应控制的优点,设计一种神经网络自适应滑模控制器,利用神经网络的自学习能力来逼近系统的等效控制律,自适应控制算法来计算系统切换控制律的增益,该方法既保留了滑模控制所具有的较强的鲁棒性,又使控制系统滑动模态的品质得到保证和改善,并能很好地削弱了系统的抖振;
最后,利用Quanser公司提供的Wincon软件及跷跷板系统实验平台,将滑模变结构控制算法应用于实际的控制系统中,实验结果也进一步验证了所使用的控制算法是有效可行的。
Seesaw system has the characteristics of serious non-linear, strong coupling, higher-order, sensitive to disturbance, and complicated model, etc. As the control strategies and algorithms are similar to the methods of boat balance control, biped robot walking upright control, two wheel self-balanced vehicle balance control, the position adjustment of spacecraft, and many abstract control theories and concepts, such as stability of systems, controllability and anti-jamming capability, etc, can be visually displayed through the seesaw system experiments, Therefore, it is of great significance in theory and applications to do systematic research on the seesaw.
In this paper, the present research situations of seesaw system are summarized, and the theory of intelligent control and sliding mode control is described comprehensively.
Firstly, according to the analysis of the structure and basis principle of the system, Lagrange theory is used to establish a mathematical model of seesaw system.
Secondly, switching gain adjustment based on fuzzy sliding mode control scheme is proposed by incorporating the fuzzy control and sliding mode control. The switching gain of sliding mode control is tuned on-line through the corresponding fuzzy logic operation, so the chattering problem of the system can be solved.
Thirdly, with the advantages of neural networks and adaptive control, a neural network adaptive sliding-mode controller is designed. Neural network is used to approximate the equivalent control of sliding mode control, and adaptive controller is used to achieve the compensation control of the system. The method not only retains the strong robustness of system, but also guarantees and improves the quality of the sliding-mode. Chattering of the system is eliminated at the same time.
Finally, the software (Wincon) and seesaw system experimental platform are used to study the sliding mode variable structure control strategy based on index reaching law, the experimental results also further illustrate that the proposed control algorithm is effective and feasible.
引文
[1] Chia-Ju Wu. Quasi Time-Optimal PID Control of Multivariable Systems: A Seesaw Example [J]. Journal of the Chinese Institute of Engineers, 1999, 22(5):617-625.
[2] Lon-Chen Hung, Hung-Yuan Chung .Decoupled Control Using Neural Network-based Sliding-mode Controller for Nonlinear Systems [J]. Expert Systems with Applications, 2007, 32(12): 1168–1182.
[3] Jeng-HannLI, Tzuu-Hseng S. Li and Ting-Han Ou. Design and Implementation of Fuzzy Sliding-Mode Controller for a Wedge Balancing System [J]. Journal of Intelligent and Robotic Systems 2003, 37(4): 285–306.
[4] Chun-Hsien Tsai, Hung-Yuan Chung. Neuro-Sliding Mode Control with Its Applications to Seesaw Systems [J]. IEEE Transactions on Neural Networks, 2004, 5(1): 124-134.
[5]牛宏侠.基于拉格朗日方程的小车跷跷板状态反馈控制研究[J].兰州交通大学学报, 2008, 27(4):99-101.
[6]韩江.跷跷板系统变结构控制研究[D].西安电子科技大学,2006.
[7]崔燕.基于动态模糊控制的不稳定体“跷跷板”的控制研究[D].西安电子科技大学, 2006.
[8] Alexander M. Meystel, James Sacra Albus. Intelligent Systems: Architecture, Design, and Control [M].New York, NY, 2000: 20-34.
[9] Meng Qingjin, Xing Baoling, Yu Hongliang. The application of intelligent control to combustion control system of CFB boiler [J]. 2009 9th International Conference on Hybrid Intelligent Systems, 2009: 163-167.
[10] Wang Wu, Wang Hongling. Study on Integrated Intelligent Control with Hierarchical Structure [J]. International Symposium on Computer Science and Computational Technology, ISCSCT 2008: 63-65.
[11] Mitrishkin Yuri V, Guerra Rodolfo Haber. Intelligent hierarchical control system for complex processes: Three levels control system [J]. ICINCO 2009-6th International Conference on Informatics in Control, Automation and Robotics, Proceedings, v1 ICSO, 2009: 333-336.
[12] Chen Gang, Zhang Weigong, Gong Zongyang, Sun Wei, Zhao Maquan. Coordinated control of multiple manipulators for vehicle robot driver [J]. Yi Qi Yi Biao XueBao/Chinese Journal of Scientific Instrument, 2009, 30(9):1836-1840.
[13] Ping He, Min Li, Yuheng Qian. A study of expert control system of oil pump energy-saving based on genetic neural network [C]. 2009 Chinese Control and Decision Conference, 2009: 5441-5444.
[14]杨宇,倪云峰等.基于专家控制器的空气预热器漏风控制系统[J].华南理工大学学报, 2004, 32(8): 25-28.
[15]张勇,王介生等.专家控制方法在浮选过程中的应用[J].控制与决策, 2004, 19(11):1271-1274.
[16] Weiping Guo, Diantong Liu. Adaptive Sliding Mode Fuzzy Control for a Class of Underactuated Mechanical Systems[C].Springer Berlin/Heidelberg.2007, 4681: 345-354.
[17] Liu Cheng, Peng Jin-Feng, Zhao Fu-Yu. Design and optimization of fuzzy-PID controller for the nuclear reactor power control [J]. Nuclear Engineering and Design, 2009, 239(11): 2311-2316.
[18] Ahmad Bagheri, Jalal Javadi Moghaddam. Decoupled adaptive neuro-fuzzy (DANF) sliding mode control system for a Lorenz chaotic problem [J]. Expert Systems with Applications, 2009, 36: 6062–6068.
[19] Peng Dong, Feng Dai, Ningxia Li. Adaptive optimization control based on improved genetic algorithm and fuzzy neural network [C]. 2009 International Conference on E-Business and Information System Security, 2009:1-4.
[20] Ashraf S, Muhammad E, AI-Habaibeh A. Self-learning control systems using identification-based adaptive iterative learning controller [J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2008, 222(7): 1177-1187.
[21] Bo Liu, Huiguang Li, Tihua Wu. Neural network identification method applied to the nonlinear system [C]. Proceedings of the 2009 WRI Global Congress on Intelligent Systems, 2009, 4: 120-124.
[22] Wei Wei, Xu Sheng-Hui, Guo Xin-Chao. Method on hybrid sliding-mode variable structure control of induction motor [J]. Dianji yu Kongzhi Xuebao/Electric Machines and Control, 2009, 13(3): 458-463.
[23] Morsy M.A.A, Moteleb M.S.A, Dorrah H.T. Fuzzy variable structure control strategy for stable nonlinear dynamic system [C]. IEEE EUROCON 2009, 2009: 942-947.
[24] Navid Noroozi, Mehdi Roopaei . M. Zolghadri Jahromi Adaptive fuzzy sliding mode control scheme for uncertain systems [C]. Commun Nonlinear Sci Numer Simulat 2009, 14:3978–3992.
[25]赵红超,范绍里等.弹道导弹的自适应模糊滑模控制研究[J].航天控制, 2009, 27(1):49-52.
[26]刘姗梅,马迁.自适应模糊滑模控制在PMSM中的应用[J].微电机,2009,42(5):43-46.
[27] H.F. Ho, Y.K. Wong, A.B. Rad. Adaptive fuzzy sliding mode control with chattering elimination for nonlinear SISO systems [J]. Simulation Modelling Practice and Theory 2009, 17: 1199–1210.
[28]林雷,任华彬等.基于模糊神经网络的机器人滑模自适应控制[J].控制工程, 2007, 14(5): 532-534.
[29] Lon-Chen Hung, Hung-Yuan Chung. Decoupled sliding-mode with fuzzy-neural network controller for nonlinear systems [J]. International Journal of Approximate Reasoning2007, 46: 74–97.
[30] Ping Guan, Xiangjie Liu, Jizhen Liu. Adaptive fuzzy sliding mode control for flexible satellite [J]. Engineering Applications of Artificial Intelligence 2005, 18: 451–459.
[31]孙泓.两轮自平衡小车的模糊滑模研究[D].西安电子科技大学, 2008.
[32] H.F. Ho, Y.K. Wong. Adaptive fuzzy sliding mode control with chattering elimination for nonlinear SISO systems [J]. Simulation Modelling Practice and Theory, 2009, 17: 1199–1210.
[33] Mehdi Roopaei, Mansoor Zolghadri, Sina Meshksar. Enhanced adaptive fuzzy sliding mode control for uncertain nonlinear systems [J]. Commun Nonlinear Sci Numer Simulat, 2009, 14: 3670–3681.
[34] A.Sabanovic, K. Jezernik, and M. Rodic, Neural network application in sliding mode control systems, in Proc [J]. 1996 IEEE International Workshop on VSS’96, 1996, 143–147.
[35]宋佐时,易建强,赵冬斌.基于神经网络的一类非线性系统自适应滑模控制[J].电机与控制学报, 2005, 9(5):481-485.
[36]谢宗武,刘子龙,刘宏.直流电机神经自适应滑模位置跟踪控制[J].系统仿真学报, 2005, 17(10):2476-2478.
[37]王伟,易建强,赵冬斌.一种新型神经网络滑模控制器的设计[J].电机与控制学报, 2005, 9(6): 603-606.
[38]李鸿儒,顾树生.基于神经网络的PMSM(永磁同步电机)自适应滑模控制[J].控制理论与应用, 2005, 22(3): 461-464.
[39]王贞艳,张井岗,陈志梅.基于神经网络的全局滑模变结构控制[J].系统仿真学报, 2007, 19(11): 2523-2526.
[40] Niu Jianjun, Fu Yongling, Qi Xiaoye. Design and Application of Discrete Sliding Mode Control with RBF Network-based Switching Law [J]. Chinese Journal of Aeronautics, 2009, 22: 279-284.
[41] J. Javadi-Moghaddam, A. Bagheri. An adaptive neuro-fuzzy sliding mode based genetic algorithm control system for under water remotely operated vehicle [J]. Expert Systems with Applications, 2010, 37: 647-660.
[42]程利荣.拉格朗日-麦克斯韦方程在旋转电机动态建模中的运用[J].青岛大学学报, 2000, 13(4):59-62.
[43]安延涛,马汝建.机械系统的拉格朗日建模与仿真[J].系统仿真技术, 2007, 3(4):206-210.
[44]肖立龙,彭辉.基于拉格朗日建模的单级倒立摆起摆与稳定控制[J].控制理论与应用, 2007, 26(4):4-7.
[45] M. Roopaei, M. Zolghadri Jahromi. Chattering-free fuzzy sliding mode control in MIMO uncertain systems [J]. Nonlinear Analysis, 2009, 71: 4430_4437.
[46]孙逊,章卫国,张金红,杨婷婷.一种改进的自适应模糊滑模大包线飞行控制方法[J].系统仿真学报, 2008, 20(5): 1262-1264.
[47]王猛.基于遗传算法优化模糊神经网络的倒立摆智能控制[J].自动化博览, 2008: 84-86.
[48] J. Javadi Moghaddam, M.H. Farahani, N. Amanifard. A neural network-based sliding-mode control for rotating stall and surge in axial compressors [J]. Applied Soft Computing, 2010:1-8.
[49] Wincon User Guide [M]. Quanser Company Press. 2003: 522-530.
[2] Lon-Chen Hung, Hung-Yuan Chung .Decoupled Control Using Neural Network-based Sliding-mode Controller for Nonlinear Systems [J]. Expert Systems with Applications, 2007, 32(12): 1168–1182.
[3] Jeng-HannLI, Tzuu-Hseng S. Li and Ting-Han Ou. Design and Implementation of Fuzzy Sliding-Mode Controller for a Wedge Balancing System [J]. Journal of Intelligent and Robotic Systems 2003, 37(4): 285–306.
[4] Chun-Hsien Tsai, Hung-Yuan Chung. Neuro-Sliding Mode Control with Its Applications to Seesaw Systems [J]. IEEE Transactions on Neural Networks, 2004, 5(1): 124-134.
[5]牛宏侠.基于拉格朗日方程的小车跷跷板状态反馈控制研究[J].兰州交通大学学报, 2008, 27(4):99-101.
[6]韩江.跷跷板系统变结构控制研究[D].西安电子科技大学,2006.
[7]崔燕.基于动态模糊控制的不稳定体“跷跷板”的控制研究[D].西安电子科技大学, 2006.
[8] Alexander M. Meystel, James Sacra Albus. Intelligent Systems: Architecture, Design, and Control [M].New York, NY, 2000: 20-34.
[9] Meng Qingjin, Xing Baoling, Yu Hongliang. The application of intelligent control to combustion control system of CFB boiler [J]. 2009 9th International Conference on Hybrid Intelligent Systems, 2009: 163-167.
[10] Wang Wu, Wang Hongling. Study on Integrated Intelligent Control with Hierarchical Structure [J]. International Symposium on Computer Science and Computational Technology, ISCSCT 2008: 63-65.
[11] Mitrishkin Yuri V, Guerra Rodolfo Haber. Intelligent hierarchical control system for complex processes: Three levels control system [J]. ICINCO 2009-6th International Conference on Informatics in Control, Automation and Robotics, Proceedings, v1 ICSO, 2009: 333-336.
[12] Chen Gang, Zhang Weigong, Gong Zongyang, Sun Wei, Zhao Maquan. Coordinated control of multiple manipulators for vehicle robot driver [J]. Yi Qi Yi Biao XueBao/Chinese Journal of Scientific Instrument, 2009, 30(9):1836-1840.
[13] Ping He, Min Li, Yuheng Qian. A study of expert control system of oil pump energy-saving based on genetic neural network [C]. 2009 Chinese Control and Decision Conference, 2009: 5441-5444.
[14]杨宇,倪云峰等.基于专家控制器的空气预热器漏风控制系统[J].华南理工大学学报, 2004, 32(8): 25-28.
[15]张勇,王介生等.专家控制方法在浮选过程中的应用[J].控制与决策, 2004, 19(11):1271-1274.
[16] Weiping Guo, Diantong Liu. Adaptive Sliding Mode Fuzzy Control for a Class of Underactuated Mechanical Systems[C].Springer Berlin/Heidelberg.2007, 4681: 345-354.
[17] Liu Cheng, Peng Jin-Feng, Zhao Fu-Yu. Design and optimization of fuzzy-PID controller for the nuclear reactor power control [J]. Nuclear Engineering and Design, 2009, 239(11): 2311-2316.
[18] Ahmad Bagheri, Jalal Javadi Moghaddam. Decoupled adaptive neuro-fuzzy (DANF) sliding mode control system for a Lorenz chaotic problem [J]. Expert Systems with Applications, 2009, 36: 6062–6068.
[19] Peng Dong, Feng Dai, Ningxia Li. Adaptive optimization control based on improved genetic algorithm and fuzzy neural network [C]. 2009 International Conference on E-Business and Information System Security, 2009:1-4.
[20] Ashraf S, Muhammad E, AI-Habaibeh A. Self-learning control systems using identification-based adaptive iterative learning controller [J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2008, 222(7): 1177-1187.
[21] Bo Liu, Huiguang Li, Tihua Wu. Neural network identification method applied to the nonlinear system [C]. Proceedings of the 2009 WRI Global Congress on Intelligent Systems, 2009, 4: 120-124.
[22] Wei Wei, Xu Sheng-Hui, Guo Xin-Chao. Method on hybrid sliding-mode variable structure control of induction motor [J]. Dianji yu Kongzhi Xuebao/Electric Machines and Control, 2009, 13(3): 458-463.
[23] Morsy M.A.A, Moteleb M.S.A, Dorrah H.T. Fuzzy variable structure control strategy for stable nonlinear dynamic system [C]. IEEE EUROCON 2009, 2009: 942-947.
[24] Navid Noroozi, Mehdi Roopaei . M. Zolghadri Jahromi Adaptive fuzzy sliding mode control scheme for uncertain systems [C]. Commun Nonlinear Sci Numer Simulat 2009, 14:3978–3992.
[25]赵红超,范绍里等.弹道导弹的自适应模糊滑模控制研究[J].航天控制, 2009, 27(1):49-52.
[26]刘姗梅,马迁.自适应模糊滑模控制在PMSM中的应用[J].微电机,2009,42(5):43-46.
[27] H.F. Ho, Y.K. Wong, A.B. Rad. Adaptive fuzzy sliding mode control with chattering elimination for nonlinear SISO systems [J]. Simulation Modelling Practice and Theory 2009, 17: 1199–1210.
[28]林雷,任华彬等.基于模糊神经网络的机器人滑模自适应控制[J].控制工程, 2007, 14(5): 532-534.
[29] Lon-Chen Hung, Hung-Yuan Chung. Decoupled sliding-mode with fuzzy-neural network controller for nonlinear systems [J]. International Journal of Approximate Reasoning2007, 46: 74–97.
[30] Ping Guan, Xiangjie Liu, Jizhen Liu. Adaptive fuzzy sliding mode control for flexible satellite [J]. Engineering Applications of Artificial Intelligence 2005, 18: 451–459.
[31]孙泓.两轮自平衡小车的模糊滑模研究[D].西安电子科技大学, 2008.
[32] H.F. Ho, Y.K. Wong. Adaptive fuzzy sliding mode control with chattering elimination for nonlinear SISO systems [J]. Simulation Modelling Practice and Theory, 2009, 17: 1199–1210.
[33] Mehdi Roopaei, Mansoor Zolghadri, Sina Meshksar. Enhanced adaptive fuzzy sliding mode control for uncertain nonlinear systems [J]. Commun Nonlinear Sci Numer Simulat, 2009, 14: 3670–3681.
[34] A.Sabanovic, K. Jezernik, and M. Rodic, Neural network application in sliding mode control systems, in Proc [J]. 1996 IEEE International Workshop on VSS’96, 1996, 143–147.
[35]宋佐时,易建强,赵冬斌.基于神经网络的一类非线性系统自适应滑模控制[J].电机与控制学报, 2005, 9(5):481-485.
[36]谢宗武,刘子龙,刘宏.直流电机神经自适应滑模位置跟踪控制[J].系统仿真学报, 2005, 17(10):2476-2478.
[37]王伟,易建强,赵冬斌.一种新型神经网络滑模控制器的设计[J].电机与控制学报, 2005, 9(6): 603-606.
[38]李鸿儒,顾树生.基于神经网络的PMSM(永磁同步电机)自适应滑模控制[J].控制理论与应用, 2005, 22(3): 461-464.
[39]王贞艳,张井岗,陈志梅.基于神经网络的全局滑模变结构控制[J].系统仿真学报, 2007, 19(11): 2523-2526.
[40] Niu Jianjun, Fu Yongling, Qi Xiaoye. Design and Application of Discrete Sliding Mode Control with RBF Network-based Switching Law [J]. Chinese Journal of Aeronautics, 2009, 22: 279-284.
[41] J. Javadi-Moghaddam, A. Bagheri. An adaptive neuro-fuzzy sliding mode based genetic algorithm control system for under water remotely operated vehicle [J]. Expert Systems with Applications, 2010, 37: 647-660.
[42]程利荣.拉格朗日-麦克斯韦方程在旋转电机动态建模中的运用[J].青岛大学学报, 2000, 13(4):59-62.
[43]安延涛,马汝建.机械系统的拉格朗日建模与仿真[J].系统仿真技术, 2007, 3(4):206-210.
[44]肖立龙,彭辉.基于拉格朗日建模的单级倒立摆起摆与稳定控制[J].控制理论与应用, 2007, 26(4):4-7.
[45] M. Roopaei, M. Zolghadri Jahromi. Chattering-free fuzzy sliding mode control in MIMO uncertain systems [J]. Nonlinear Analysis, 2009, 71: 4430_4437.
[46]孙逊,章卫国,张金红,杨婷婷.一种改进的自适应模糊滑模大包线飞行控制方法[J].系统仿真学报, 2008, 20(5): 1262-1264.
[47]王猛.基于遗传算法优化模糊神经网络的倒立摆智能控制[J].自动化博览, 2008: 84-86.
[48] J. Javadi Moghaddam, M.H. Farahani, N. Amanifard. A neural network-based sliding-mode control for rotating stall and surge in axial compressors [J]. Applied Soft Computing, 2010:1-8.
[49] Wincon User Guide [M]. Quanser Company Press. 2003: 522-530.