基于趋近律的直线倒立摆滑模控制
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摘要
直线倒立摆是一个高度非线性系统,具有强耦合和复杂不稳定的特点,在已建立的倒立摆数学模型的基础上,针对常规滑模控制方法容易使系统出现高频抖振,导致系统稳定性差的问题,以直线倒立摆为被控对象,采用指数趋近律、饱和函数趋近律和连续函数趋近律等控制方法对直线倒立摆进行控制,应用Lyapunov理论证明了控制系统的稳定性。仿真结果表明,三种控制方法均能实现对直线倒立摆的稳定控制,并且后两种方法能明显的削弱系统的抖振,为直线倒立摆稳定性设计提供了依据。
A line inverted pendulum is a class of complicated,unstable system with nonlinear and strong coupled character. On the basis of the known inverted pendulum mathematical model,taking into consideration that there exists chattering in the traditional sliding mode control which may affect the stability of closed-loop system,this paper investigated the sliding mode control of line inverted pendulum based on exponential reaching law,boundary layer method and continuous function reaching law,respectively. The stability of the control system was proved by Lyapunov theory. Simulation results show that the proposed three strategies can provide effective control of line inverted pendulum and the later two reaching laws can reduce chattering more effectively.
A line inverted pendulum is a class of complicated,unstable system with nonlinear and strong coupled character. On the basis of the known inverted pendulum mathematical model,taking into consideration that there exists chattering in the traditional sliding mode control which may affect the stability of closed-loop system,this paper investigated the sliding mode control of line inverted pendulum based on exponential reaching law,boundary layer method and continuous function reaching law,respectively. The stability of the control system was proved by Lyapunov theory. Simulation results show that the proposed three strategies can provide effective control of line inverted pendulum and the later two reaching laws can reduce chattering more effectively.
引文
[1]陈志梅,王贞艳,张井岗.滑模变结构控制理论及应用[M].北京:电子工业出版社,2012:8-12.
[2]阮晓钢,程怀玉,于乃功,左国玉.一级直线倒立摆匀速行走的模糊控制研究与实现[J].计算机测量与控制,2009-1.
[3]解晶,张丽香,张晶.二级倒立摆变结构控制改进方案的对比研究[J].计算机仿真,2012-4.
[4]孔凡国,刘锡林,钟廷志.平面一级倒立摆的滑模控制研究[J].机械设计与制造,2011.
[5]解晶.直线倒立摆的变结构稳定控制研究[D].山西大学,2012.
[6]刘金琨.滑模变结构控制MATLAB仿真[M].北京:清华大学出版社,2005:30-45.
[7]高为炳.变结构控制理论基础[M].北京:中国科学技术出版社,1990.
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[2]阮晓钢,程怀玉,于乃功,左国玉.一级直线倒立摆匀速行走的模糊控制研究与实现[J].计算机测量与控制,2009-1.
[3]解晶,张丽香,张晶.二级倒立摆变结构控制改进方案的对比研究[J].计算机仿真,2012-4.
[4]孔凡国,刘锡林,钟廷志.平面一级倒立摆的滑模控制研究[J].机械设计与制造,2011.
[5]解晶.直线倒立摆的变结构稳定控制研究[D].山西大学,2012.
[6]刘金琨.滑模变结构控制MATLAB仿真[M].北京:清华大学出版社,2005:30-45.
[7]高为炳.变结构控制理论基础[M].北京:中国科学技术出版社,1990.
[8]高为炳.非线性系统导论[M].北京:科学出版社,1988.