模糊滑模控制方法研究
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摘要
二十世纪五十年代，前苏联学者Emelyanov首次提出变结构的概念，然后Utkin和Itkis等人进一步发展了变结构系统理论。七十年代，变结构系统以其独特的优点和特性引起了西方学者的广泛重视。众多学者从不同的理论角度，运用各种数学手段，对变结构控制进行了深入研究，使变结构控制理论逐渐发展成为一个独立的研究分支。变结构拧制是一种十分有效的鲁棒控制策略。近年来，随着鲁棒控制、自适应控制和模糊控制等理论研究领域的不断发展，变结构控制理论得到了快速的发展。
根据变结构理论发展的研究现状以及实际应用对变结构控制理论研究所提出的新要求，本文针对变结构控制中面临的一些问题，进行了深入的研究，并最终给出了相应的研究结果。本文的主要研究工作概括如下：
1、提出基于T-S模糊神经网络的变结构控制方法。选择误差及其各阶导数的线性集结作为切换面，用趋近律方法设计变结构控制律，引入T-S模糊神经网络，使实际输出始终跟踪给定值。运用T-S模糊神经网络自组织自调节功能，隶属度的各项参数在线调整，来满足期望的控制效果。
2、基于积分变结构控制提出模糊积分变结构控制方法，综合了积分变结构稳态误差小和模糊控制自组织的特点：同时加入了灰色模型，对参数摄动等不确定部分进行辨识，并引入补偿控制，改善控制效果。
3、根据模糊积分变结构控制方法，对三阶倒立摆模型进行仿真研究，基本思想是对倒立摆模型在工作点附近进行线性化，将线性化过程中忽略的各个量全部看作不确定项，根据不确定项的大小实时调整控制律中符号函数的系数，保证系统稳定。
最后是全文的总结和展望。
In the 1950s, Sovist researcher-Emelyanov first proposed the conception of variable structure. Furthermore, the theory of variable structure system(VSS) was developed by Utkin and Itkis etc. In the 1970s, the VSS got extensive attention of the western researchers for its distinct features. It has been deeply studied from the different aspects with many mathematic methods. Now the VSS already becomes a relative independence research branch. Variable structure control(VSC) is an effective robust control strategy. In the recent years, with the development of all kinds of control theory, such as robust control, adaptive control and fiizzy control etc, the theory of VSC has also obtained development rapidly.
Based on the study status of VSS and the new requirements from the practice for the theory of VSC, some ways are put forward to resolve the problems existed in VSC, also the corresponding results are given. The main contents are as follows:
1. A variable structure control method based on T-S fuzzy neural network (FNN) is brought forward. The linear combination of the error and its derivative are selected as switch surface, and then the tendency law method is used to design VSC control law. T-S FNN is imported, so that the actual output can trail the given value. The self-organize and self-regulate ability of T-S FNN is utilized to adjust some parameter of the subjection function online, so that the anticipant control purpose can be satisfied.
2. A fuzzy integral VSC method based on integral VSC method is put forward. The characteristic of integral VSC method and the fuzzy control is integrated. Synchronously the uncertainties such as parameter change are estimated by affiliating gray model, control impact is improved by import compensate control.
3. Some research on three-order inverted pendulum has been done based on the fuzzy integral VSC method above. The essence thought is to get the linear model near the work point
from the nonlinear model, look upon all the items ignored during linear course as uncertainties, the stabilization of the system is guaranteed by adjusting the coefficient of the sign function online according to the uncertainties.
The summarization and prospect are given in the end of the paper.
根据变结构理论发展的研究现状以及实际应用对变结构控制理论研究所提出的新要求，本文针对变结构控制中面临的一些问题，进行了深入的研究，并最终给出了相应的研究结果。本文的主要研究工作概括如下：
1、提出基于T-S模糊神经网络的变结构控制方法。选择误差及其各阶导数的线性集结作为切换面，用趋近律方法设计变结构控制律，引入T-S模糊神经网络，使实际输出始终跟踪给定值。运用T-S模糊神经网络自组织自调节功能，隶属度的各项参数在线调整，来满足期望的控制效果。
2、基于积分变结构控制提出模糊积分变结构控制方法，综合了积分变结构稳态误差小和模糊控制自组织的特点：同时加入了灰色模型，对参数摄动等不确定部分进行辨识，并引入补偿控制，改善控制效果。
3、根据模糊积分变结构控制方法，对三阶倒立摆模型进行仿真研究，基本思想是对倒立摆模型在工作点附近进行线性化，将线性化过程中忽略的各个量全部看作不确定项，根据不确定项的大小实时调整控制律中符号函数的系数，保证系统稳定。
最后是全文的总结和展望。
In the 1950s, Sovist researcher-Emelyanov first proposed the conception of variable structure. Furthermore, the theory of variable structure system(VSS) was developed by Utkin and Itkis etc. In the 1970s, the VSS got extensive attention of the western researchers for its distinct features. It has been deeply studied from the different aspects with many mathematic methods. Now the VSS already becomes a relative independence research branch. Variable structure control(VSC) is an effective robust control strategy. In the recent years, with the development of all kinds of control theory, such as robust control, adaptive control and fiizzy control etc, the theory of VSC has also obtained development rapidly.
Based on the study status of VSS and the new requirements from the practice for the theory of VSC, some ways are put forward to resolve the problems existed in VSC, also the corresponding results are given. The main contents are as follows:
1. A variable structure control method based on T-S fuzzy neural network (FNN) is brought forward. The linear combination of the error and its derivative are selected as switch surface, and then the tendency law method is used to design VSC control law. T-S FNN is imported, so that the actual output can trail the given value. The self-organize and self-regulate ability of T-S FNN is utilized to adjust some parameter of the subjection function online, so that the anticipant control purpose can be satisfied.
2. A fuzzy integral VSC method based on integral VSC method is put forward. The characteristic of integral VSC method and the fuzzy control is integrated. Synchronously the uncertainties such as parameter change are estimated by affiliating gray model, control impact is improved by import compensate control.
3. Some research on three-order inverted pendulum has been done based on the fuzzy integral VSC method above. The essence thought is to get the linear model near the work point
from the nonlinear model, look upon all the items ignored during linear course as uncertainties, the stabilization of the system is guaranteed by adjusting the coefficient of the sign function online according to the uncertainties.
The summarization and prospect are given in the end of the paper.
引文
[1] Palm R. Robust control by fttzzy sliding mode. Automatica. 1994, 30(9): 1429～1437.
[2] Now acki Z, et al. On the robustness of fuzzy control of an overhead crane. IEEE int. sym p. on industrial electronics. 1996, 1: 433～437.
[3] Wu J C, Liu T S . Fuzzy control stabilization with applications to motorcycle control. IEEE trans, on systems, man and cybemetics, part B. 1996, 26(6): 836～847.
[4] Wang W J, Lin H R. Fuzzy control design for the trajectory tracking on uncertain nonlinear systems, IEEE Trans. on fuzzy systems. 1999, 7(1): 53～62.
[5] Hwang G C, Cheng S . A stability approach to control design for nonlinear systems. Fuzzy sets and systems. 1992, 48(3): 279～287.
[6] Kung C C, Liao C C. Fuzzy-sliding mode controller design for tracking control of nonlinear system. Proc. of american control conference. 1994, 180～184.
[7] Kung C C, Lai W C. GA-based design of a region-wise fuzzy sliding mode controller. Proc. of IEEE canadian conf. on electrical and computer engineer. 1999: 971～976.
[8] 李少远，席裕庚．模糊滑动模态控制系统的性质分析．控制理论与应用．2000，17(1)：14～18．
[9] Wal R J, Lin F J . Fuzzy neural network sliding-mode position controller for in. uction servo motor drive. IEE proc..Electronics power application. 1999, 146(3): 297～308.
[10] Tamai Y J, Akhmetov D et al. Novel fuzzy-neural network with general pa?meter learning applied to sliding mode control systems. Proc. of IEEE int. conf. on sys ems, man and cybernetics. 1999., 1: 376～379.
[11] Hwang K S, Lin C S Self-organizing fuzzy CMAC for sliding mode control. proc. ofIEEE int. workshop on variable structure control. 1996, 133～138.
[12] Lin F J, Hwang W J et al. A supervisory fttzzy neural network control system for tracking periodic inputs. IEEE trans, on fuzzy systems. 1999, 7(1): 41～52.
[13] 孙增祈，张再兴，邓志东．智能控制理论与技术．北京：清华大学出版社和广西科学技术出版社，1997．
[14] 高为炳．变结构控制理论基础．北京：中国科科学技术出版社，1995．
[15] Wang J D, Lee T L, Juang Y T. New methods to design an integral variable structure controller. IEEE transactions on automatic control. 41(1): 104～143.
[16] 姚琼慧，黄继起，吴汉松．变结构控制系统．重庆：重庆大学出版社，1997．
[17] Sivaramakrishnan A Y, et al. Design of variable-structure load frequency cont?oller using pole assignment technique. Int. J. contr.. 1984, 40(3): 487～498.
[18] Murty A S R, Parameswaran S, Ramar K. Design of variable structure stabilizer usin? pole assignment technique. Electric machines and power systems. 1998, 26:185～206.
[19] Hsu Y Y, Chan W C. Optimal variable-structure controller for DC motor speed control. IEE Proc. pt. D.. 1984, 131(6): 233～237.
[20] Utkin V I. Variable structure system with sliding modes. IEEE Trans. automat. Contr.1997, AC(22).
[21] El-Ghezawi O M E, Zinober A S I,Billings S A. Analysis and. design of variable stru. cture systems using a geometric approach. Int. J. contr.. 1983, 38(3): 657～671.
[22] Young K K D. Design of variable structure model-following control systems. IEEE ?rans. automat, contr.. 1978, AC(23).
[23] Dorling C M. Two approaches to hyper-plane design in multivariable structure c?ntrol systems. Int. J. contr.. 1986, 44(1). 65～82.
[24] Young K D, Ozugener U. Frequency shaping compensator for sliding mode . lnt.J. contr. 1993, 57(5):1005～1019.
[25] Koshkouei A J, Zinober A S I. Robust frequency shaping sliding mode control IEE proc. control theory appl.. 2000, 147(3): 312～320.
[26] 贾志勇，林延圻，朝嵩伟．一种基于频率整形的滑模变结构控制器设计．工业仪表与自动化装置．1999，145(1)：3～5．
[27] 冯勇，安澄全，李涛．采用双滑模面减少一类非线性系统的稳态误差．控制与决策．2000，(3)：361～364．
[28] Shyu K K, et al. A modified variable structure controller. Automatica .1992, 28(6): 1209～1213.
[29] Shyu K K, Shieh H J. A new switching surface sliding mode speed control for induction mo tor drive system. IEEE trans, power electron. 1996, 11: 666～667
[30] Lee J J, Xu Y S. A new method of switching surface design for multivariable variable system. IEEE trans, on automatic control. February., 1994, 39(2).
[31] 夏伯第，李冶．具有随机量测噪声的变结构控制．控制与决策．1994，9(3)：226～229．
[32] Guider J, Utkin V I. Tracking the gradient of artificial field sliding mode control for mobile robots. Int. J. contr.. 1996, 64: 417～432.
[33] Ackermann J, Utkin V I. Sliding mode control based on Ackerma?n's formula. Proc. IEEE conference on decision and control. 1994, 4: 3622～3627.
[34] Park K B, Lee J J . Variable structure controller for robotic mani?ulators using time- varying sliding surface. Proc. of 1993 IEEE conference on robotic s and automation.1993, 1: 89～93.
[35] Choi S B, Park D W. Moving sliding surface for fast tracking control of second orde? dynamic systems. ASMEjoumal of dynamic systems, measurement and control. 1994,116:154～158.
[36] Ha Q P, Rye D C, Durrant-Whyte H F. Fuzzy moving sliding mode control with application to robotic manipulators. Automatica, 1999, 35: 607～616.
[37] Bartoszewicz A . Time-varying sliding modes for second order systems. IEEE proc. control theory appl..1996, 143(5): 455～462.
[38] Choi S B, heong C C, Park D W. Moving switching surface for robust control of second order variable structure systems. Int. J. Contr.. 1993, 58: 229～247.
[39] Dong W P, Seung B C. Moving sliding surface for high-order variable structure systems. Int.J. Contr.. 1999, 72: 960～970.
[40] 金耀初，蒋静坪．一类非线性系统的模糊变结构控制及应用．控制与决策，1992，7(1)：36～40．
[41] 达飞鹏，宋文忠．基于模糊神经网络的滑模控制．控制理论与应用，2000，17(1)：128～132．
[42] 王萧，任思聪．非线性系统模糊神经网络变结构自适应控制．控制与决策，1997，12(3)：208～212．
[43] 张天平，冯纯伯．一类非线性系统的自适应模糊滑模控制．自动化学报，1997， 23(3)：361～369．
[44] 高为炳．变结构控制的理论及设计方法．北京：科学出版社，1998．
[45] 王耀南．智能控制系统—模糊逻辑、专家系统、神经网络控制．长沙：湖南大学出版社，1996．
[46] 张飞舟，陈伟基，沈程智．拟人智能控制三级倒立摆机理的研究．北京航空航天大学学报，1999，25(2)：151～155．
[47] 朱江滨，易建强．二阶倒立摆的摆起控制．系统仿真学报，2003，1：(7)：1043～1045．
[48] 张克勤，苏宏业，庄开宇，褚健．三阶倒立摆系统基于滑模的鲁棒控制．浙江大学学报(工学版)，2002，36(4)：404～409．
[49] 于秀芬，段海滨，龚华军．基于人工神经网络BP算法的倒立摆控制研究．兵工自动化，2003，22(3)：41～44．
[50] 柏桂珍，梅晓榕，王述一．倾斜轨道上的三级倒立摆数学模型的建立与可控性研究．电机与控制学报，2003，7(2)：170～173．
[51] 李德毅．三级倒立摆的云控制方法及动平衡模式．中国工程科学，1999，1(2)：41～46．
[52] 宋君烈，肖君，徐心和．倒立摆系统的Lagrange方程建模与模糊控制．东北大学学报，2002，23(4)：333～336．
[2] Now acki Z, et al. On the robustness of fuzzy control of an overhead crane. IEEE int. sym p. on industrial electronics. 1996, 1: 433～437.
[3] Wu J C, Liu T S . Fuzzy control stabilization with applications to motorcycle control. IEEE trans, on systems, man and cybemetics, part B. 1996, 26(6): 836～847.
[4] Wang W J, Lin H R. Fuzzy control design for the trajectory tracking on uncertain nonlinear systems, IEEE Trans. on fuzzy systems. 1999, 7(1): 53～62.
[5] Hwang G C, Cheng S . A stability approach to control design for nonlinear systems. Fuzzy sets and systems. 1992, 48(3): 279～287.
[6] Kung C C, Liao C C. Fuzzy-sliding mode controller design for tracking control of nonlinear system. Proc. of american control conference. 1994, 180～184.
[7] Kung C C, Lai W C. GA-based design of a region-wise fuzzy sliding mode controller. Proc. of IEEE canadian conf. on electrical and computer engineer. 1999: 971～976.
[8] 李少远，席裕庚．模糊滑动模态控制系统的性质分析．控制理论与应用．2000，17(1)：14～18．
[9] Wal R J, Lin F J . Fuzzy neural network sliding-mode position controller for in. uction servo motor drive. IEE proc..Electronics power application. 1999, 146(3): 297～308.
[10] Tamai Y J, Akhmetov D et al. Novel fuzzy-neural network with general pa?meter learning applied to sliding mode control systems. Proc. of IEEE int. conf. on sys ems, man and cybernetics. 1999., 1: 376～379.
[11] Hwang K S, Lin C S Self-organizing fuzzy CMAC for sliding mode control. proc. ofIEEE int. workshop on variable structure control. 1996, 133～138.
[12] Lin F J, Hwang W J et al. A supervisory fttzzy neural network control system for tracking periodic inputs. IEEE trans, on fuzzy systems. 1999, 7(1): 41～52.
[13] 孙增祈，张再兴，邓志东．智能控制理论与技术．北京：清华大学出版社和广西科学技术出版社，1997．
[14] 高为炳．变结构控制理论基础．北京：中国科科学技术出版社，1995．
[15] Wang J D, Lee T L, Juang Y T. New methods to design an integral variable structure controller. IEEE transactions on automatic control. 41(1): 104～143.
[16] 姚琼慧，黄继起，吴汉松．变结构控制系统．重庆：重庆大学出版社，1997．
[17] Sivaramakrishnan A Y, et al. Design of variable-structure load frequency cont?oller using pole assignment technique. Int. J. contr.. 1984, 40(3): 487～498.
[18] Murty A S R, Parameswaran S, Ramar K. Design of variable structure stabilizer usin? pole assignment technique. Electric machines and power systems. 1998, 26:185～206.
[19] Hsu Y Y, Chan W C. Optimal variable-structure controller for DC motor speed control. IEE Proc. pt. D.. 1984, 131(6): 233～237.
[20] Utkin V I. Variable structure system with sliding modes. IEEE Trans. automat. Contr.1997, AC(22).
[21] El-Ghezawi O M E, Zinober A S I,Billings S A. Analysis and. design of variable stru. cture systems using a geometric approach. Int. J. contr.. 1983, 38(3): 657～671.
[22] Young K K D. Design of variable structure model-following control systems. IEEE ?rans. automat, contr.. 1978, AC(23).
[23] Dorling C M. Two approaches to hyper-plane design in multivariable structure c?ntrol systems. Int. J. contr.. 1986, 44(1). 65～82.
[24] Young K D, Ozugener U. Frequency shaping compensator for sliding mode . lnt.J. contr. 1993, 57(5):1005～1019.
[25] Koshkouei A J, Zinober A S I. Robust frequency shaping sliding mode control IEE proc. control theory appl.. 2000, 147(3): 312～320.
[26] 贾志勇，林延圻，朝嵩伟．一种基于频率整形的滑模变结构控制器设计．工业仪表与自动化装置．1999，145(1)：3～5．
[27] 冯勇，安澄全，李涛．采用双滑模面减少一类非线性系统的稳态误差．控制与决策．2000，(3)：361～364．
[28] Shyu K K, et al. A modified variable structure controller. Automatica .1992, 28(6): 1209～1213.
[29] Shyu K K, Shieh H J. A new switching surface sliding mode speed control for induction mo tor drive system. IEEE trans, power electron. 1996, 11: 666～667
[30] Lee J J, Xu Y S. A new method of switching surface design for multivariable variable system. IEEE trans, on automatic control. February., 1994, 39(2).
[31] 夏伯第，李冶．具有随机量测噪声的变结构控制．控制与决策．1994，9(3)：226～229．
[32] Guider J, Utkin V I. Tracking the gradient of artificial field sliding mode control for mobile robots. Int. J. contr.. 1996, 64: 417～432.
[33] Ackermann J, Utkin V I. Sliding mode control based on Ackerma?n's formula. Proc. IEEE conference on decision and control. 1994, 4: 3622～3627.
[34] Park K B, Lee J J . Variable structure controller for robotic mani?ulators using time- varying sliding surface. Proc. of 1993 IEEE conference on robotic s and automation.1993, 1: 89～93.
[35] Choi S B, Park D W. Moving sliding surface for fast tracking control of second orde? dynamic systems. ASMEjoumal of dynamic systems, measurement and control. 1994,116:154～158.
[36] Ha Q P, Rye D C, Durrant-Whyte H F. Fuzzy moving sliding mode control with application to robotic manipulators. Automatica, 1999, 35: 607～616.
[37] Bartoszewicz A . Time-varying sliding modes for second order systems. IEEE proc. control theory appl..1996, 143(5): 455～462.
[38] Choi S B, heong C C, Park D W. Moving switching surface for robust control of second order variable structure systems. Int. J. Contr.. 1993, 58: 229～247.
[39] Dong W P, Seung B C. Moving sliding surface for high-order variable structure systems. Int.J. Contr.. 1999, 72: 960～970.
[40] 金耀初，蒋静坪．一类非线性系统的模糊变结构控制及应用．控制与决策，1992，7(1)：36～40．
[41] 达飞鹏，宋文忠．基于模糊神经网络的滑模控制．控制理论与应用，2000，17(1)：128～132．
[42] 王萧，任思聪．非线性系统模糊神经网络变结构自适应控制．控制与决策，1997，12(3)：208～212．
[43] 张天平，冯纯伯．一类非线性系统的自适应模糊滑模控制．自动化学报，1997， 23(3)：361～369．
[44] 高为炳．变结构控制的理论及设计方法．北京：科学出版社，1998．
[45] 王耀南．智能控制系统—模糊逻辑、专家系统、神经网络控制．长沙：湖南大学出版社，1996．
[46] 张飞舟，陈伟基，沈程智．拟人智能控制三级倒立摆机理的研究．北京航空航天大学学报，1999，25(2)：151～155．
[47] 朱江滨，易建强．二阶倒立摆的摆起控制．系统仿真学报，2003，1：(7)：1043～1045．
[48] 张克勤，苏宏业，庄开宇，褚健．三阶倒立摆系统基于滑模的鲁棒控制．浙江大学学报(工学版)，2002，36(4)：404～409．
[49] 于秀芬，段海滨，龚华军．基于人工神经网络BP算法的倒立摆控制研究．兵工自动化，2003，22(3)：41～44．
[50] 柏桂珍，梅晓榕，王述一．倾斜轨道上的三级倒立摆数学模型的建立与可控性研究．电机与控制学报，2003，7(2)：170～173．
[51] 李德毅．三级倒立摆的云控制方法及动平衡模式．中国工程科学，1999，1(2)：41～46．
[52] 宋君烈，肖君，徐心和．倒立摆系统的Lagrange方程建模与模糊控制．东北大学学报，2002，23(4)：333～336．