离散系统滑模变结构控制研究
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摘要
变结构控制自产生以来,因其对参数摄动和外界干扰的不敏感性,受到了控制界的广泛关注。近年来,随着计算机技术的发展和工业自动化领域的实际需要,控制算法的实现经常利用数字计算机,但当采用数字计算机实现变结构控制算法时,由于采样过程的限制,离散系统变结构控制中的切换不再是连续光滑的,而只是一个准滑动模态。同时,在离散的情况下,滑动模态的性质、存在条件及其到达条件都已经改变,因此研究离散时间系统变结构控制方法对降低抖振具有重要的理论价值和实际意义。
本文首先介绍了变结构控制的历史及现状及存在的问题。而后给出了离散时间系统变结构控制的有关概念,分析了离散时间系统滑动模态的到达条件、存在条件和稳定性问题。
着重讨论了利用离散趋近律设计离散时间系统的变结构控制问题,在衰减控制的基础上,针对衰减变速趋近律的抖振问题,给出了两种改进方案。而后利用全程滑模变结构控制理论,提出了基于衰减控制的全程滑模变结构控制器,充分利用了全程滑动模态鲁棒性强的优点,并分别给出了每种方案的数例仿真,仿真结果表明所提方案是有效的可行的。最后,针对不确定性问题,分别利用干扰观测器和利用时延性估计未知干扰的方法设计了两种鲁棒性控制器,通过数例仿真验证了其良好的鲁棒性。
Variable structure control (VSC) is well known for its robustness to system parameter variations and external disturbances.VSC has been widely used in many applications.In recent years,with the development of microcomputer technology and the needs of industrial automation,we use computer to realize the control algor- ithm.But during the time of realizing the VSC,because of the limits of sampling, the ideal sliding mode does not exist,and the switching control is not smooth any more,it is only a quasi-sliding mode.It is significant to study discrete-time VSC (DVSC) to reduce chattering of sliding mode.
Firstly,in this dissertation,a detailed analysis of the history and current situation of study on variable structure and a discussion about the discrete-time systems VSC are stressed.Secondly,the related definitions of DVSC are proposed. After analyzing the arrival condition,the existence condition and stabilization of sliding mode in DVSC.
It is discussed that the design of variable structure control for discrete time system using discrete reaching law.Based on the he attenuating variable rate and the attenuating power reaching law,two improved discrete reaching law are developed. Using global sliding mode variable structure control theory,a global sliding mode variable structure controller based on the attenuating power reaching law is developed.It used the advantage for robustness of the sliding mode. The simulation results show that the approach is effective.Finally,A discrete-time variable structure controller with a decoupled disturbance compensator its application to a CNC servomechanism is designed.And another kind of controller is designed by applying delay characteristic to estimate the uncertainty on-line.Both theory analysis and simulation can prove the validity of these methods.
本文首先介绍了变结构控制的历史及现状及存在的问题。而后给出了离散时间系统变结构控制的有关概念,分析了离散时间系统滑动模态的到达条件、存在条件和稳定性问题。
着重讨论了利用离散趋近律设计离散时间系统的变结构控制问题,在衰减控制的基础上,针对衰减变速趋近律的抖振问题,给出了两种改进方案。而后利用全程滑模变结构控制理论,提出了基于衰减控制的全程滑模变结构控制器,充分利用了全程滑动模态鲁棒性强的优点,并分别给出了每种方案的数例仿真,仿真结果表明所提方案是有效的可行的。最后,针对不确定性问题,分别利用干扰观测器和利用时延性估计未知干扰的方法设计了两种鲁棒性控制器,通过数例仿真验证了其良好的鲁棒性。
Variable structure control (VSC) is well known for its robustness to system parameter variations and external disturbances.VSC has been widely used in many applications.In recent years,with the development of microcomputer technology and the needs of industrial automation,we use computer to realize the control algor- ithm.But during the time of realizing the VSC,because of the limits of sampling, the ideal sliding mode does not exist,and the switching control is not smooth any more,it is only a quasi-sliding mode.It is significant to study discrete-time VSC (DVSC) to reduce chattering of sliding mode.
Firstly,in this dissertation,a detailed analysis of the history and current situation of study on variable structure and a discussion about the discrete-time systems VSC are stressed.Secondly,the related definitions of DVSC are proposed. After analyzing the arrival condition,the existence condition and stabilization of sliding mode in DVSC.
It is discussed that the design of variable structure control for discrete time system using discrete reaching law.Based on the he attenuating variable rate and the attenuating power reaching law,two improved discrete reaching law are developed. Using global sliding mode variable structure control theory,a global sliding mode variable structure controller based on the attenuating power reaching law is developed.It used the advantage for robustness of the sliding mode. The simulation results show that the approach is effective.Finally,A discrete-time variable structure controller with a decoupled disturbance compensator its application to a CNC servomechanism is designed.And another kind of controller is designed by applying delay characteristic to estimate the uncertainty on-line.Both theory analysis and simulation can prove the validity of these methods.
引文
[1] Y. Dote,R. G. Hoft.Microprocessor based sliding mode controller for DC motor drives. In:Presented at the Ind. Applic. Soc. Annu Meeting,Cincinnati,1980.
[2] S. Z. Sarpturk,Y. Istefanopulos,O. Kaynak. On the stability of discrete-time sliding mode control system. IEEE Transaction on Automation Control,1987,32(10):930～932
[3] K. Furuta. Sliding mode control of a discrete system. System & Control Letters,1990,14(2):145～152
[4] 高为炳.离散时间系统的变结构控制.自动化学报,1995,21(2):154～160
[5] W. B. Gao, Y. F. Wang,A. Homaifa.Discrete-time variable structure control systems.IEEE Transactions on Industrial Electronics,1995,42(2):117～122
[6] 姚琼荟,黄继起,吴汉松.变的结构控制系统.重庆:重庆大学出版社,1997.
[7] 姚琼荟,宋立忠,温 洪.离散变结构控制系统得比例-等速-变速控制.控制与决策,2000,15(3):329～332
[8] 翟长连,吴智铭.不确定离散系统得变结构控制器设计.自动化学报,2000,26(2):184～191
[9] 周靖林, 肖雁鸿等. 离散变结构系统的衰减变速控制,基础自动化,2001,8(5):16～18
[10] Y. D. Pan.K. Furuta.Discrete-time VSS Controller Design.International Journal of Robust and Nonlinear Control,1997,7(4):373～386
[11] A. J. Koshkouei,A. S. I. Zinober.Sliding mode control of discrete-time systems. Journal of Dynamic Systems,Measurement,and Control,2000,122:793～802
[12] J. H. Kim,Oh. S. H,D. I. Cho,etc.Robust discrete-time variable structure control methods.Joural of Dynamic Systems,Measurement,and Control, 2000,122:766～775
[13] S. V. Emelyanov,S. K. Korovin,I. G.. Mamedov.Variable Structure ControlSystems:Discrete and Digital.Mir Publishers,Moscow,2000.
[14] Y. S. Lu,J. S. Chen.Design of a global sliding-mode controller for a motor drive with bound control.International Journal of Control,1995,62(5):1001 ～1019
[15] 肖雁鸿,葛召炎,周靖林等.全滑模变结构控制系统.电机与控制学报,2002, 6(30): 233～236
[16] 米 阳,李文林,井元伟等. 线性多变量离散系统全程滑模变结构控制.控制与决策,2003,18(4):460～464
[17] 谢胜利,周凤歧. 不确定系统的变结构鲁棒自适应控制及其在机械手控制中的应用.控制理论与应用,1992,9(2):116～123
[18] 王孙安.离散变结构控制的新方法及其在液压伺服系统中的应用.西安交通大学学报,1996,30(6):75～81
[19] 刘迎树.高速磁悬浮机床主轴的离散变结构控制.控制理论与应用,2002,19(2):304～310
[20] 宋立忠,陈少昌,姚琼荟.某型船舶电站离散准滑模有功分配控制器设计.电力系统自动化,2002,26(4):56～60
[21] 宋立忠,陈少昌,姚琼荟.自适应变结构控制及其在电力系统中的应用.中国电机工程学报,2002,22(12):97～100
[22] 翟长连,吴智铭.一种离散时间系统的变结构控制方法.上海交通大学学报, 2000,34(5):719～722
[23] 于双和,强文义,傅佩琛.无抖振离散准滑模控制.控制与决策,2001,16(3): 380～382
[24] 宋立忠,陈少昌,姚琼荟.多输入不确定性系统离散变结构控制设计.控制与决策,2003,18(4):468～471
[25] 晁红敏,胡跃明.动态滑模控制及其在移动机器人输出跟踪中的应用.控制与决策,2001,16(5):565～568
[26] S. H. Ryu,J. H. Park.Auto-tuning of sliding mode control parameters using fuzzy logic.America Control Science,2001,618～623
[27] 孙宜标,郭庆鼎,孙艳娜.基于模糊学习的交流直线伺服系统滑模变结构控制.电工技术学报,2001,16(1):52～56
[28] 达飞鹏,宋文忠.基于输入输出模型的模糊神经网络滑模控制.自动化学报,2000,26(1):136～139
[29] 林 岩,毛剑琴,操云甫.鲁棒低增益变结构模型参考自适应控制,自动化学报,2001,27(5):665～670
[30] 马克茂.离散时间系统变结构控制新方法.电机与控制学报.2001,5 (3): 181～184
[31] 庄开宇,苏宏业等.不匹配不确定时滞系统的自适应变结构控制.浙江大学学报,2002,32 (4):410～415
[32] 高为炳.变结构控制的理论及设计方法.北京:科学出版社,1996
[33] Xinghuo Yu. Discrete Variable Structure Control Systems, Int.J.Systems sci.1993,V01,24,No.2,273～386
[34] 张 科,周凤岐.不确定多变量系统的全程滑态变结构控制方案设计.控制理论于应用,1999,16(2):221～224
[35] 张克勤,苏宏业,庄开宇等.二阶不确定离散系统的时变滑模面变结构控制. 2002,36(4):416～420
[36] 李志楠,方一鸣,李志强等.一种离散全程滑模变结构控制方法.微处理机, 2006,4:53～55
[37] 李 俊,徐德民.不确定非线性系统的多模反演滑模控制.控制理论与应用,2001,18(5):801～804
[38] 逢海萍,刘成菊,刘爱忠.不确定时滞系统的滑模控制及其应用研究.系统仿真学报,2006,18:876～879
[39] 周景雷, 张维海.机器人机械臂的鲁棒最优控制.计算机工程与应用.2007,43(8):168～173
[40] 张益波,张井岗,陈志梅.一种不确定离散时间系统的变结构控制方法.控制与决策,2002,17:791～794
[41] 吴汉松,宋立忠,姚琼荟.离散变速趋近律抖振机理及鲁棒性研究.海军工程大学学报,2002,16(6):41～44
[42] 宋立忠,陈少昌,姚琼荟.单输入不确定系统离散变结构控制.海军工程大学学报,2003,15(2):35～40
[43] 于双和,傅佩琛,强文义.不确定离散时间系统的变结构控制.控制理论与应用,2000,17(1):85～88
[2] S. Z. Sarpturk,Y. Istefanopulos,O. Kaynak. On the stability of discrete-time sliding mode control system. IEEE Transaction on Automation Control,1987,32(10):930～932
[3] K. Furuta. Sliding mode control of a discrete system. System & Control Letters,1990,14(2):145～152
[4] 高为炳.离散时间系统的变结构控制.自动化学报,1995,21(2):154～160
[5] W. B. Gao, Y. F. Wang,A. Homaifa.Discrete-time variable structure control systems.IEEE Transactions on Industrial Electronics,1995,42(2):117～122
[6] 姚琼荟,黄继起,吴汉松.变的结构控制系统.重庆:重庆大学出版社,1997.
[7] 姚琼荟,宋立忠,温 洪.离散变结构控制系统得比例-等速-变速控制.控制与决策,2000,15(3):329～332
[8] 翟长连,吴智铭.不确定离散系统得变结构控制器设计.自动化学报,2000,26(2):184～191
[9] 周靖林, 肖雁鸿等. 离散变结构系统的衰减变速控制,基础自动化,2001,8(5):16～18
[10] Y. D. Pan.K. Furuta.Discrete-time VSS Controller Design.International Journal of Robust and Nonlinear Control,1997,7(4):373～386
[11] A. J. Koshkouei,A. S. I. Zinober.Sliding mode control of discrete-time systems. Journal of Dynamic Systems,Measurement,and Control,2000,122:793～802
[12] J. H. Kim,Oh. S. H,D. I. Cho,etc.Robust discrete-time variable structure control methods.Joural of Dynamic Systems,Measurement,and Control, 2000,122:766～775
[13] S. V. Emelyanov,S. K. Korovin,I. G.. Mamedov.Variable Structure ControlSystems:Discrete and Digital.Mir Publishers,Moscow,2000.
[14] Y. S. Lu,J. S. Chen.Design of a global sliding-mode controller for a motor drive with bound control.International Journal of Control,1995,62(5):1001 ～1019
[15] 肖雁鸿,葛召炎,周靖林等.全滑模变结构控制系统.电机与控制学报,2002, 6(30): 233～236
[16] 米 阳,李文林,井元伟等. 线性多变量离散系统全程滑模变结构控制.控制与决策,2003,18(4):460～464
[17] 谢胜利,周凤歧. 不确定系统的变结构鲁棒自适应控制及其在机械手控制中的应用.控制理论与应用,1992,9(2):116～123
[18] 王孙安.离散变结构控制的新方法及其在液压伺服系统中的应用.西安交通大学学报,1996,30(6):75～81
[19] 刘迎树.高速磁悬浮机床主轴的离散变结构控制.控制理论与应用,2002,19(2):304～310
[20] 宋立忠,陈少昌,姚琼荟.某型船舶电站离散准滑模有功分配控制器设计.电力系统自动化,2002,26(4):56～60
[21] 宋立忠,陈少昌,姚琼荟.自适应变结构控制及其在电力系统中的应用.中国电机工程学报,2002,22(12):97～100
[22] 翟长连,吴智铭.一种离散时间系统的变结构控制方法.上海交通大学学报, 2000,34(5):719～722
[23] 于双和,强文义,傅佩琛.无抖振离散准滑模控制.控制与决策,2001,16(3): 380～382
[24] 宋立忠,陈少昌,姚琼荟.多输入不确定性系统离散变结构控制设计.控制与决策,2003,18(4):468～471
[25] 晁红敏,胡跃明.动态滑模控制及其在移动机器人输出跟踪中的应用.控制与决策,2001,16(5):565～568
[26] S. H. Ryu,J. H. Park.Auto-tuning of sliding mode control parameters using fuzzy logic.America Control Science,2001,618～623
[27] 孙宜标,郭庆鼎,孙艳娜.基于模糊学习的交流直线伺服系统滑模变结构控制.电工技术学报,2001,16(1):52～56
[28] 达飞鹏,宋文忠.基于输入输出模型的模糊神经网络滑模控制.自动化学报,2000,26(1):136～139
[29] 林 岩,毛剑琴,操云甫.鲁棒低增益变结构模型参考自适应控制,自动化学报,2001,27(5):665～670
[30] 马克茂.离散时间系统变结构控制新方法.电机与控制学报.2001,5 (3): 181～184
[31] 庄开宇,苏宏业等.不匹配不确定时滞系统的自适应变结构控制.浙江大学学报,2002,32 (4):410～415
[32] 高为炳.变结构控制的理论及设计方法.北京:科学出版社,1996
[33] Xinghuo Yu. Discrete Variable Structure Control Systems, Int.J.Systems sci.1993,V01,24,No.2,273～386
[34] 张 科,周凤岐.不确定多变量系统的全程滑态变结构控制方案设计.控制理论于应用,1999,16(2):221～224
[35] 张克勤,苏宏业,庄开宇等.二阶不确定离散系统的时变滑模面变结构控制. 2002,36(4):416～420
[36] 李志楠,方一鸣,李志强等.一种离散全程滑模变结构控制方法.微处理机, 2006,4:53～55
[37] 李 俊,徐德民.不确定非线性系统的多模反演滑模控制.控制理论与应用,2001,18(5):801～804
[38] 逢海萍,刘成菊,刘爱忠.不确定时滞系统的滑模控制及其应用研究.系统仿真学报,2006,18:876～879
[39] 周景雷, 张维海.机器人机械臂的鲁棒最优控制.计算机工程与应用.2007,43(8):168～173
[40] 张益波,张井岗,陈志梅.一种不确定离散时间系统的变结构控制方法.控制与决策,2002,17:791～794
[41] 吴汉松,宋立忠,姚琼荟.离散变速趋近律抖振机理及鲁棒性研究.海军工程大学学报,2002,16(6):41～44
[42] 宋立忠,陈少昌,姚琼荟.单输入不确定系统离散变结构控制.海军工程大学学报,2003,15(2):35～40
[43] 于双和,傅佩琛,强文义.不确定离散时间系统的变结构控制.控制理论与应用,2000,17(1):85～88