模糊控制在二级倒立摆系统中的应用研究
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摘要
倒立摆为典型的快速、多变量、非线性、绝对不稳定系统,对倒立摆系统的稳定性研究在理论和方法上均具有深远意义。它不但是验证现代控制理论方法的典型实验装置,而且其控制方法和思路对处理一般工业过程亦有广泛的用途。
本文首先分析和综述了近年来国内外二级倒立摆系统控制的新理论和新方法,如模糊控制、神经网络控制、混合控制等。其次推导了二级倒立摆系统的数学模型,分析了系统的稳定性、能控性和能观性,并在此基础上给出了线性最优控制器的设计,实现了运用现代控制理论对二级倒立摆的控制。但是二级倒立摆系统抗干扰能力较差,鲁棒性较弱,所以本文运用模糊控制方法对二级倒立摆进行控制,引入了综合误差和综合误差率的概念,减少了模糊控制器的输入变量个数,从而简化了模糊控制器的控制规则,使控制器的控制规则更简单、有效。最后通过对二级倒立摆系统的仿真,验证了模糊控制器具有抗干扰能力较强,鲁棒性较好的特点。
Inverted pendulum system is a typical model of multi-variable, nonlinear, essentially unsteady system, and researching stability of inverted pendulum system has the profound meaning in theory and methodology. The method and thought of inverted pendulum system's control can be extensively used to deal with the industry course.
The paper analyzes and summarizes new theories and ideas overseas in recent years such as fuzzy control, neural networks control, hybrid control and so on firstly. Secondly, the paper derives the model of the double inverted pendulum and the state-space expression. Analyzes the stability, controllability and observables and designs the linear regulator, realizes the control of the double inverted pendulum. Because abilities of anti-jamming and robustness of these methods and weak, the author uses fuzzy control to control the double inverted pendulum. The paper introduces synthetic error and synthetic error variety, and reduces the input varieties of fuzzy control, thus reduces the control rule of fuzzy controller, and makes the fuzzy controller simple and effective. Because human factors affect the designs of fuzzy controller, the author introduces a kind of adaptive genetic algorithms, which can optimize the parameters of fuzzy control. Finally, a simulation of the double inverted pendulum system demonstrates the performance of the model and controller.
本文首先分析和综述了近年来国内外二级倒立摆系统控制的新理论和新方法,如模糊控制、神经网络控制、混合控制等。其次推导了二级倒立摆系统的数学模型,分析了系统的稳定性、能控性和能观性,并在此基础上给出了线性最优控制器的设计,实现了运用现代控制理论对二级倒立摆的控制。但是二级倒立摆系统抗干扰能力较差,鲁棒性较弱,所以本文运用模糊控制方法对二级倒立摆进行控制,引入了综合误差和综合误差率的概念,减少了模糊控制器的输入变量个数,从而简化了模糊控制器的控制规则,使控制器的控制规则更简单、有效。最后通过对二级倒立摆系统的仿真,验证了模糊控制器具有抗干扰能力较强,鲁棒性较好的特点。
Inverted pendulum system is a typical model of multi-variable, nonlinear, essentially unsteady system, and researching stability of inverted pendulum system has the profound meaning in theory and methodology. The method and thought of inverted pendulum system's control can be extensively used to deal with the industry course.
The paper analyzes and summarizes new theories and ideas overseas in recent years such as fuzzy control, neural networks control, hybrid control and so on firstly. Secondly, the paper derives the model of the double inverted pendulum and the state-space expression. Analyzes the stability, controllability and observables and designs the linear regulator, realizes the control of the double inverted pendulum. Because abilities of anti-jamming and robustness of these methods and weak, the author uses fuzzy control to control the double inverted pendulum. The paper introduces synthetic error and synthetic error variety, and reduces the input varieties of fuzzy control, thus reduces the control rule of fuzzy controller, and makes the fuzzy controller simple and effective. Because human factors affect the designs of fuzzy controller, the author introduces a kind of adaptive genetic algorithms, which can optimize the parameters of fuzzy control. Finally, a simulation of the double inverted pendulum system demonstrates the performance of the model and controller.
引文
[1] MEIER H., FARWIG.Z and UNBEHAUEN H: Discrete computer control of a triple-inverted pendulum. Opt, Connt.App&Methods, 1990, 11,pp. 157-171
[2] Mori Shozo, H .Nishihara and K .Furuta. Control of unstable mechanical system Control of pendulum [J], Int.J. of Controll 976, 23(5):673-692
[3] K. Furuta, Katsuhisa, H. Kajiwara and K.Kosuge. Digital control of a double inverted pendulum on an inclined rail [J],Int.J. of Control 1980,32(5):907-924
[4] J. W. Watts. Control of an inverted pendulum, ASEE Annual Conference, session 2527, 1984,706-710
[6] K. Furuta, M. Yamakita and S. Kobayashi, Swing-up control of inverted pendulum using pseudo-state feedback [J], J. of Systems and Control Engineering 1992,206:263-269
[7] A.L.Fradkov, P.Y Guzenko, D.J. Hill and AX Pogromsky. Speed gradient control and passivity of nonlinear oscillators [C]. Proc. of IFAC symposium on Control of Nonlinear Systems, Lake Tahoe.1995, 655-659
[8] Wiklund, Magnus, Anders Kristenson and K.J.Astrom. A new strategy for swing up an inverted pendulum[C].In preprints IFAC 12th world congress. Sydney, Australia. 1993, 151-154
[9] M.Yamakita, M.Iwashiro, Y Sugahara and K.Furuta. Robust swing-up control of inverted pendulum [C], Proc. of the American Control Conference, Seattle, Washington, 1995, 290-294
[10] T.H.Hung, M.F.Yeh and H.C.Lu. API-like fuzzy controller implementation for the inverted pendulum system, IEEE ICIPS 97, Beijing, China, 1997 ,pp. 218-222
[11] Tzuu-Hseng S.Li, Chin-Yin Tsai. Parallel fuzzy sliding mode control of the cart-pole system IEEE International Conference on Industrial Electronics, Control and Instrumentation, 1995,2: 1468-1473
[12] 张乃尧, C.Ebert, R.Belschner, H.Strahl. 倒立摆的双闭环模糊控制．控制与决策, 1996,11(1):85-88
[14] F. Bouslama, A. Ichikawa. Application of neural network to fuzzy control, Neural Networks, 1993, 6:791-799
[15] S.Mori, H.Nishihara, K .Furuta. Control of unstable mechanical system control of pendulum, International Journal of Control,1976,23(5):673-692
[16] K.J. Astrom. Swing up a pendulum by energy control. In I FAC 13th world Congress, San Francisco, California, 1996, F: 301-306
[17]S.A.Bortorff.Robust swing-up control for a rational double pendulum,In IFAC13th world Congress.San Francisco.California.1996.F:413-419
[18]李祖枢、陈庆春,倒立摆系统的智能控制研究及其发展动向,第二届全球华人智能控制与智能自动化大会论文集(上卷),PP.14-19
[19]曾馅.小车-二级摆摆起倒立的仿人智能控制研究,重庆大学硕士学位论文,2001年,
[20]王加银.基于变论域自适应模糊控制的倒立摆仿真与实物实现.北京师范大学博士学位论文2002.5.
[21]C.W Anderson.Learning to control an inverted pendulum using neural networks,IEEE Control Systems Magazine,1989,9(3):31-37
[22]I.Hayashi,H.Nomura,N.Wakami.Artificial neural network driven fuzzy control and its application to the learning of inverted pendulum system,Proceedings of the 3rd IFSA Congress,Seatle,1989:610-613
[23]D.Yah,M.Saif Neural networks based controllers for non-linear systems.Control and computers,1995,23(3)
[24]朱江滨.二级倒立摆的摆起控制.系统仿真学报,2003,15(7):1043-1045
[25]史晓霞,张振东,李俊芳,杨屹.二级倒立摆系统数学模型的建立及意义.河北工业大学学报.2001,10.30(5):48-51
[26]李岩,姚旭东.二级倒立摆控制系统分析.沈阳工业学院学报,1999,6.18(2):86-92
[27]宋君烈,肖军,徐心和.倒立摆系统的Lagrange方程建模与模糊控制.(自然科学版),2002.4,23(4):333-336
[28]陈文良,洪嘉振,周鉴如,等分析动力学[M].北京:清华大学出版社1994.158-276
[29]杜继宏,解学书,慕春棣.自动控制原理(下)清华大学出版社,1992
[30]吴麟主编.自动控制原理清华大学出版社,1990
[31]胡寿松主编.自动控制原理(第三版).国防工业出版社,1994.
[32]张冬军,丛爽,秦志强.倒立摆控制系统研究综述.固高科技研究生论文集第一辑,非线性复杂系统的智能控制.
[33]李士勇编著,模糊控制神经控制和智能控制论.哈尔滨工业大学出版社.1996
[34]戎月莉编著,计算机模糊控制原理与应用.北京航空航天大学出版社.1995
[35]范醒哲,张乃尧,陈宁.三级倒立摆的二种模糊串级控制方案,2002,6,the 3rd World Congress on Intelligent Control and Automation.Hefei.P.R China 1721-1726
[36]Shuliang Lei,Reza Langari,Hierarchical Fuzzy Logic Control of a Double Inverted Pendulum.C2000 IEEE,1074-1077
[37]程福雁,钟国民,李友善.二级倒立摆的参变量模糊控制.信息与控制,1995,24(3):189-192
[38]Fuyan Cheng,Guomin Zhong,Youshan Li,Zhengming Xu.Fuzzy control of a double inverted pendulum,Fuzzy Set sand Systems,1996,79(3):315-321
[39]Bryson A E,Luenberger D G.The Synthesis of Regulator Logic Using Variable Control[C].Proceeding of the IEEE,1970,58(11)
[40]黄圣乐.智能调整型模糊控制器的研究.同济大学学报.1996,6,24(3):331-335
[41]Weigent T J,Tsal Jingpha,Liu Xuhua.Fuzzy operator logic and fuzzy resolution,Journal of Automated Reasoning,1993,10(1):59-78
[42]陆春晖,翁正新,李和贵等.一种新型智能模糊控制器的研究,计算机仿真.2003,9,20(9):95-97
[43]刘春生,吴庆宪,邹新生等.量化因子对二级倒立摆模糊控制器性能的影响.模式识别与人工智能.2000,12,13(4):404-406
[44]张志勇等编著.精通MATLAB6.5版.北京航空航天大学出版社,2003
[49]楼顺天,于卫编著.基于MATLAB的系统分析与设计-控制系统.西安电子科技大学出版社,1998
[50]姚俊,马松辉.Simulink建模与仿真.西安电子科技大学出版社,2002
[51]王沫然编著.MATLAB工程应用丛书Simulink4建模及动态仿真.电子工业出版社,2002
[52]吴晓莉,林哲辉等编著.MATLAB辅助模糊系统设计.西安电子科技大学出版社,2002
[53]Karl J.Astrom Bjorn Wittemark.Computer-controlled Systems Theory and Design(Third Edition),Prentice Hall.
[54]王锦标编著.计算机控制系统.清华大学出版社,2004
[55]薛定宇.控制系统计算机辅助设计-MATLAB语言与应用(第二版).清华大学出版社,2006.3
[56]李国用.智能控制及其MATLAB实现[M].电子工业出版社,2005.194-256
[2] Mori Shozo, H .Nishihara and K .Furuta. Control of unstable mechanical system Control of pendulum [J], Int.J. of Controll 976, 23(5):673-692
[3] K. Furuta, Katsuhisa, H. Kajiwara and K.Kosuge. Digital control of a double inverted pendulum on an inclined rail [J],Int.J. of Control 1980,32(5):907-924
[4] J. W. Watts. Control of an inverted pendulum, ASEE Annual Conference, session 2527, 1984,706-710
[6] K. Furuta, M. Yamakita and S. Kobayashi, Swing-up control of inverted pendulum using pseudo-state feedback [J], J. of Systems and Control Engineering 1992,206:263-269
[7] A.L.Fradkov, P.Y Guzenko, D.J. Hill and AX Pogromsky. Speed gradient control and passivity of nonlinear oscillators [C]. Proc. of IFAC symposium on Control of Nonlinear Systems, Lake Tahoe.1995, 655-659
[8] Wiklund, Magnus, Anders Kristenson and K.J.Astrom. A new strategy for swing up an inverted pendulum[C].In preprints IFAC 12th world congress. Sydney, Australia. 1993, 151-154
[9] M.Yamakita, M.Iwashiro, Y Sugahara and K.Furuta. Robust swing-up control of inverted pendulum [C], Proc. of the American Control Conference, Seattle, Washington, 1995, 290-294
[10] T.H.Hung, M.F.Yeh and H.C.Lu. API-like fuzzy controller implementation for the inverted pendulum system, IEEE ICIPS 97, Beijing, China, 1997 ,pp. 218-222
[11] Tzuu-Hseng S.Li, Chin-Yin Tsai. Parallel fuzzy sliding mode control of the cart-pole system IEEE International Conference on Industrial Electronics, Control and Instrumentation, 1995,2: 1468-1473
[12] 张乃尧, C.Ebert, R.Belschner, H.Strahl. 倒立摆的双闭环模糊控制．控制与决策, 1996,11(1):85-88
[14] F. Bouslama, A. Ichikawa. Application of neural network to fuzzy control, Neural Networks, 1993, 6:791-799
[15] S.Mori, H.Nishihara, K .Furuta. Control of unstable mechanical system control of pendulum, International Journal of Control,1976,23(5):673-692
[16] K.J. Astrom. Swing up a pendulum by energy control. In I FAC 13th world Congress, San Francisco, California, 1996, F: 301-306
[17]S.A.Bortorff.Robust swing-up control for a rational double pendulum,In IFAC13th world Congress.San Francisco.California.1996.F:413-419
[18]李祖枢、陈庆春,倒立摆系统的智能控制研究及其发展动向,第二届全球华人智能控制与智能自动化大会论文集(上卷),PP.14-19
[19]曾馅.小车-二级摆摆起倒立的仿人智能控制研究,重庆大学硕士学位论文,2001年,
[20]王加银.基于变论域自适应模糊控制的倒立摆仿真与实物实现.北京师范大学博士学位论文2002.5.
[21]C.W Anderson.Learning to control an inverted pendulum using neural networks,IEEE Control Systems Magazine,1989,9(3):31-37
[22]I.Hayashi,H.Nomura,N.Wakami.Artificial neural network driven fuzzy control and its application to the learning of inverted pendulum system,Proceedings of the 3rd IFSA Congress,Seatle,1989:610-613
[23]D.Yah,M.Saif Neural networks based controllers for non-linear systems.Control and computers,1995,23(3)
[24]朱江滨.二级倒立摆的摆起控制.系统仿真学报,2003,15(7):1043-1045
[25]史晓霞,张振东,李俊芳,杨屹.二级倒立摆系统数学模型的建立及意义.河北工业大学学报.2001,10.30(5):48-51
[26]李岩,姚旭东.二级倒立摆控制系统分析.沈阳工业学院学报,1999,6.18(2):86-92
[27]宋君烈,肖军,徐心和.倒立摆系统的Lagrange方程建模与模糊控制.(自然科学版),2002.4,23(4):333-336
[28]陈文良,洪嘉振,周鉴如,等分析动力学[M].北京:清华大学出版社1994.158-276
[29]杜继宏,解学书,慕春棣.自动控制原理(下)清华大学出版社,1992
[30]吴麟主编.自动控制原理清华大学出版社,1990
[31]胡寿松主编.自动控制原理(第三版).国防工业出版社,1994.
[32]张冬军,丛爽,秦志强.倒立摆控制系统研究综述.固高科技研究生论文集第一辑,非线性复杂系统的智能控制.
[33]李士勇编著,模糊控制神经控制和智能控制论.哈尔滨工业大学出版社.1996
[34]戎月莉编著,计算机模糊控制原理与应用.北京航空航天大学出版社.1995
[35]范醒哲,张乃尧,陈宁.三级倒立摆的二种模糊串级控制方案,2002,6,the 3rd World Congress on Intelligent Control and Automation.Hefei.P.R China 1721-1726
[36]Shuliang Lei,Reza Langari,Hierarchical Fuzzy Logic Control of a Double Inverted Pendulum.C2000 IEEE,1074-1077
[37]程福雁,钟国民,李友善.二级倒立摆的参变量模糊控制.信息与控制,1995,24(3):189-192
[38]Fuyan Cheng,Guomin Zhong,Youshan Li,Zhengming Xu.Fuzzy control of a double inverted pendulum,Fuzzy Set sand Systems,1996,79(3):315-321
[39]Bryson A E,Luenberger D G.The Synthesis of Regulator Logic Using Variable Control[C].Proceeding of the IEEE,1970,58(11)
[40]黄圣乐.智能调整型模糊控制器的研究.同济大学学报.1996,6,24(3):331-335
[41]Weigent T J,Tsal Jingpha,Liu Xuhua.Fuzzy operator logic and fuzzy resolution,Journal of Automated Reasoning,1993,10(1):59-78
[42]陆春晖,翁正新,李和贵等.一种新型智能模糊控制器的研究,计算机仿真.2003,9,20(9):95-97
[43]刘春生,吴庆宪,邹新生等.量化因子对二级倒立摆模糊控制器性能的影响.模式识别与人工智能.2000,12,13(4):404-406
[44]张志勇等编著.精通MATLAB6.5版.北京航空航天大学出版社,2003
[49]楼顺天,于卫编著.基于MATLAB的系统分析与设计-控制系统.西安电子科技大学出版社,1998
[50]姚俊,马松辉.Simulink建模与仿真.西安电子科技大学出版社,2002
[51]王沫然编著.MATLAB工程应用丛书Simulink4建模及动态仿真.电子工业出版社,2002
[52]吴晓莉,林哲辉等编著.MATLAB辅助模糊系统设计.西安电子科技大学出版社,2002
[53]Karl J.Astrom Bjorn Wittemark.Computer-controlled Systems Theory and Design(Third Edition),Prentice Hall.
[54]王锦标编著.计算机控制系统.清华大学出版社,2004
[55]薛定宇.控制系统计算机辅助设计-MATLAB语言与应用(第二版).清华大学出版社,2006.3
[56]李国用.智能控制及其MATLAB实现[M].电子工业出版社,2005.194-256