滑模变结构控制系统设计方法研究
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摘要
滑模变结构控制出现在50年代，由于变结构系统的滑动模态运动对系统的参数摄动、外界的扰动、系统不确定模态和模型不确定性具有不变性，也就是完全鲁棒性，滑模控制才引起了人们的极大关注。它的不足主要是当系统运动状态在到达滑动平面后，会在滑动平面附近产生高频抖振，同时系统的控制量也产生高频振荡。
本文对滑模变结构控制的设计方法进行了一些研究，针对滑模控制器设计目前存在的问题作了一些工作，仿真结果表明了能够取得较好的控制效果。具体工作主要有：
第一，比较全面查阅了关于滑模变结构控制的文献，总结了滑模变结构控制的发展历史和特点，详细介绍了连续系统和离散系统滑模变结构控制的基本概念、基本定义和设计方法；
第二，针对一类具有不确定性的单输入非线性系统，把滑模控制原理和模糊控制理论相结合，提出了一种新的模糊滑模设计方法。该方法将到达条件改为指数趋近律，并且通过模糊规则自适应调整切换函数的模糊量化因子。仿真结果表明，设计的模糊滑模系统进一步提高了到达滑动面的速度，在消除变结构控制系统固有的抖振的同时进一步改善了系统偏差，提高了控制精度。
第三，本文以最简单的单输入离散系统为模型，分析讨论了控制量延迟对离散变结构控制系统的影响，提出了基于系统状态预测值的离散变结构控制设计方法；仿真表明该方法设计的具有控制滞后的变结构系统避免了控制量延迟对系统动静态的不利影响，控制效果良好。还讨论了系统参数误差对按上述的基于预测值方法设计的离散滑模变结构控制系统的影响，提出了采用在线算法的变结构设计方法，达到了良好的控制效果。
The sliding mode variable structure control that is brought in 50's is attention- getting because of its ideal robustness. The sliding mode movement of variable structure system holds the invariance for the change of system parameters, outside disturbance, uncertain mode and model uncertainty of the system. Its flaw is that after the system state getting to the sliding plane, it will produce high frequency chattering around the sliding plane and the control variable of the system will also produce high frequency chattering.
The paper makes some research for the design method of sliding mode variable structure control, and does some works for the existent problems at present. The simulation shows that better control effect can be achieved. The main works are summarized as follows:
Firstly, this thesis relatively fully refers to the literature in the field of sliding mode variable structure control, and summarizes the development history and characteristics of sliding mode variable structure control, and particularly introduces the elementary concepts and elementary definitions and design method.
Secondly, based on the principle of sliding mode control and fuzzy control a new design method of fuzzy sliding mode control is put forward for a class of SISO nonlinear systems in the presence of uncertainties. The reaching condition of the method becomes exponent load-frequency and fuzzy measure gene of switch function is adaptively adjusted through fuzzy rules. Simulation results show that the fuzzy sliding mode system ulteriorly increases the speed to the sliding plane, and that the system
errors are improved ulteriorly and the control precision is advanced when avoiding the chattering phenomenon that is inherent to sliding mode variable structure systems.
Thirdly, with the simplest single-input discrete system as the model, we analyze and discuss the effects for control-delay on the discrete variable structure control systems, and bring forward the design method of discrete variable structure control based on the system state forecast; Simulations show that the above solution avoids adverse influences for Control-delay on the performance of variable structure control systems with control-delay, and control effect is fine. In addition, we discuss the effects for the errors of system parameters on the discrete sliding mode variable structure control systems that are designed by means of above solution based on the system state forecast, and put forward the variable structure design method with on-line arithmetic, and achieve favorable control effect.
本文对滑模变结构控制的设计方法进行了一些研究，针对滑模控制器设计目前存在的问题作了一些工作，仿真结果表明了能够取得较好的控制效果。具体工作主要有：
第一，比较全面查阅了关于滑模变结构控制的文献，总结了滑模变结构控制的发展历史和特点，详细介绍了连续系统和离散系统滑模变结构控制的基本概念、基本定义和设计方法；
第二，针对一类具有不确定性的单输入非线性系统，把滑模控制原理和模糊控制理论相结合，提出了一种新的模糊滑模设计方法。该方法将到达条件改为指数趋近律，并且通过模糊规则自适应调整切换函数的模糊量化因子。仿真结果表明，设计的模糊滑模系统进一步提高了到达滑动面的速度，在消除变结构控制系统固有的抖振的同时进一步改善了系统偏差，提高了控制精度。
第三，本文以最简单的单输入离散系统为模型，分析讨论了控制量延迟对离散变结构控制系统的影响，提出了基于系统状态预测值的离散变结构控制设计方法；仿真表明该方法设计的具有控制滞后的变结构系统避免了控制量延迟对系统动静态的不利影响，控制效果良好。还讨论了系统参数误差对按上述的基于预测值方法设计的离散滑模变结构控制系统的影响，提出了采用在线算法的变结构设计方法，达到了良好的控制效果。
The sliding mode variable structure control that is brought in 50's is attention- getting because of its ideal robustness. The sliding mode movement of variable structure system holds the invariance for the change of system parameters, outside disturbance, uncertain mode and model uncertainty of the system. Its flaw is that after the system state getting to the sliding plane, it will produce high frequency chattering around the sliding plane and the control variable of the system will also produce high frequency chattering.
The paper makes some research for the design method of sliding mode variable structure control, and does some works for the existent problems at present. The simulation shows that better control effect can be achieved. The main works are summarized as follows:
Firstly, this thesis relatively fully refers to the literature in the field of sliding mode variable structure control, and summarizes the development history and characteristics of sliding mode variable structure control, and particularly introduces the elementary concepts and elementary definitions and design method.
Secondly, based on the principle of sliding mode control and fuzzy control a new design method of fuzzy sliding mode control is put forward for a class of SISO nonlinear systems in the presence of uncertainties. The reaching condition of the method becomes exponent load-frequency and fuzzy measure gene of switch function is adaptively adjusted through fuzzy rules. Simulation results show that the fuzzy sliding mode system ulteriorly increases the speed to the sliding plane, and that the system
errors are improved ulteriorly and the control precision is advanced when avoiding the chattering phenomenon that is inherent to sliding mode variable structure systems.
Thirdly, with the simplest single-input discrete system as the model, we analyze and discuss the effects for control-delay on the discrete variable structure control systems, and bring forward the design method of discrete variable structure control based on the system state forecast; Simulations show that the above solution avoids adverse influences for Control-delay on the performance of variable structure control systems with control-delay, and control effect is fine. In addition, we discuss the effects for the errors of system parameters on the discrete sliding mode variable structure control systems that are designed by means of above solution based on the system state forecast, and put forward the variable structure design method with on-line arithmetic, and achieve favorable control effect.
引文
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[4] 张天平，冯纯伯，一类不确定动态系统的输出反馈模糊变结构控制，控制理论与应用，1996，13(4)：432-440
[5] Slotine J.E., Adaptive Sliding Controller Synthesis for Nonlinear Systems, Lnt. J.Control, 1996, .43 (6): 1631-1651
[6] 冯勇，李久胜，模型跟随变结构控制系统的滑模设计和控制策略研究，控制与决策，1996，11(1)：13-16
[7] 张天平，费树岷，基于模糊逻辑的分散自适应变结构控制，控制与决策，1997增刊：27-32
[8] SeungBok Choi, DongWon Park and Suhada Jayasuriya, A Time-Varing Sliding Surface for Fast and Robust Tracking Control of Second-Order Uncertain Systems, Automatica, 1994, 30 (5): 899-904
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[10] 朱志刚，周凤岐，不确定多变量系统的变结构最终滑动模态控制，控制与决策，1996增刊：49-53
[11] Yu Xinghuo, Man Zhihong, Multi-input uncertain linear systems with terminal sliding-mode control, AUTOMATICA, 1998, 34 (31:389-392
[12] 吴继伟，模糊滑模控制及其应用研究，硕士学位论文，同济大学，1999
[13] 傅春，谢剑英，模糊滑模控制研究综述，信息与控制，2001，30(5)：434-439
[14] Kung. C.C, Chen. TH, Fuzzy Sliding Mode Controller Design Based on Fuzzy Union Reasoning, Proc. of IEEE Int. Conf. On Systems, Man and Cybernetics, 1999, 3. 320-325
[15]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
[16]Wong. L.K, Leung.F.H.F, Combination of Sliding Mode Controller and PI Controller Using Fuzzy Logic Controller, Proc. of IEEE Int. Conf. on Fuzzy Systems, 1998, 1:296-301
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[18]A.Suyitno, F.Fujikawa, H.Kobayuashi and Y. Dote, Variable structured robust controller by fuzzy logic for servomotor, IEEE Trans. Ind. Electron., 1993, 40 (1): 80-88
[19]Buckley J.J., Fuzzy input-output controllers are universal approximators, FUZZY SET AND SYSTEMS, 1993, 58 (3): 61-67
[20]Wang L.X, Stable Adaptive Fuzzy Control of Nonlinear System, IEEE Trans. On Fuzzy Systems, 1993, 1: 146-155
[21]王灏，毛宗源，周其节，模糊变结构控制器的研究，控制理论和应用，1999，16(4)：550-557
[22]吴捷，钱来，杨金明，感应电动机锁相及模糊滑动模控制，控制理论与应用，2000，17(2)：198-203
[23]邱焕耀，毛宗源，采用模糊控制的感应电动机解耦变结构系统的研究，自动化学报，1998，24(3)：391-394
[24]Lao JiChang, Kuo YaHui, Decoupled Fuzzy Sliding-Mode Control, IEEE Transactions On Fuzzy Systems, 1998, 6 (3): 426-435
[25]贺爱玲，陈卫田，初学导，广义不确定系统的模糊滑模控制，控制理论与应用，1999，16(5)：677-681
[26]Hwang. G.C, Cheng S. A, Stability Approach to Control Design for Nonlinear Systems, Fuzzy Sets and Systems, 1992, 48 (3): 279-287
[27]Wu.J.C, Liu.T.S, A Sliding-Mode Approach to Fuzzy Control Design, IEEE TRANS. ON CONTROL SYSTEMS TECHNOLOGY, 1996, 4 (2): 141-151
[28]Kung.C.C, Liao. C.C, Fuzzy Sliding Mode Controller Design for Tracking Control of Non- linear System, Proc. of American Control Conference, 1994, 3: 180～184
[29]Lin.F.J, Fung. R.F, Sliding Mode and Fuzzy Control of Toggle Mechanism Using PM Synchronous Servomotor Drive, IEEE Proc. Control Theory Application, 1997, 144 (5): 393～402
[30]Ralph Gunter Berstecher, Rainer Palm, Direct Fuzzy Adaptation of A Fuzzy Controller, 13th IFAC, 1996, San Francisco, USA
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