基于两轮自平衡小车的H_∞和LQR控制方法对比研究
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摘要
基于两轮自平衡小车平台,针对目前欠驱动系统较成熟的控制方法对比缺乏的问题,应用仿真对比、实物验证的方法,对目前较为理想的H_∞控制和LQR控制两种控制方法进行了理论上的对比,证明了H_∞控制策略在理论上是更具实际意义的控制系统。通过在相同的初始条件和控制结构下进行联合对比仿真,对仿真结果的角度、角速度、位置、速度四个指标进行了对比分析。最后用实物实验进行了验证,得出了"针对欠驱动系统H_∞控制优于LQR控制"这一结论,对以后欠驱动系统的控制具有一定的参考价值。
This paper is based on thesystem of Self-balancing Two-wheeled cart,in view of the lack of comparison among the mature control methods of underactuated systems,the methods of simulation comparison and object verification are applied,with the compared theories of the suitable H_∞ control and LQR control,H_∞ control strategy was proved to be the control system with more practical significance theoretically. Through the comparison joint simulation in the same initial conditions and control structure,the four indexes of the angle,palstance,position and velocity of the simulation results are compared and analyzed,Physical experiments were also carried out. it came to the conclusion that H_∞ control is better than LQR control,which has a certain reference value for the later control of underactuated systems.
This paper is based on thesystem of Self-balancing Two-wheeled cart,in view of the lack of comparison among the mature control methods of underactuated systems,the methods of simulation comparison and object verification are applied,with the compared theories of the suitable H_∞ control and LQR control,H_∞ control strategy was proved to be the control system with more practical significance theoretically. Through the comparison joint simulation in the same initial conditions and control structure,the four indexes of the angle,palstance,position and velocity of the simulation results are compared and analyzed,Physical experiments were also carried out. it came to the conclusion that H_∞ control is better than LQR control,which has a certain reference value for the later control of underactuated systems.
引文
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[2]朱建公,张俊俊.变参数PID控制器设计[J].西北大学学报:自然科学版,2003(4):397-400.(Zhu Jian Gong,Zhang Jun-jun.Design of variable parameter PID controller[J].Journal of Northwestern University:Natural Science Edition,2003(4):397-400.)
[3]王宏楠.基于RBF神经网络二级倒立摆系统的PID控制[J].辽宁石油化工大学学报,2010,30(2):58-61.(Wang Hong-nan.PID control of two inverted pendulum system based on RBF neural network[J].Journal of Liaoning Shihua University,2010,30(2):58-61.)
[4]Yue,Ming,Wei,Xing,Li,Zhi-jun.Zero-dynamics-based adaptive sliding mode control for a wheeled inverted pendulum with parametric friction and uncertain dynamics compensation[J].Transactions of the Institute of Measurement and Control,2015,37(1).
[5]王强,陈炜,赵新华.直线倒立摆的快速起摆与稳摆控制研究[J].机械设计与制造,2013(5):74-77.(Wang Qiang,Chen Wei,Zhao Xin-hua.Research on fast pendulum and pendulum control of linear inverted pendulum[J].Mechanical Design and Manufacture,2013(5):74-77.)
[6]刘金琨.先进PID控制MATLAB仿真[M].北京:电子工业出版社,2016:474-485,494-502.(Liu Jin-kun.Advanced PID Control MATLAB Simulation[M].Beijing:Publishing House of Electronics Industry,2016:474-485494-502.)
[7]周克敏.鲁棒与最优控制[M].北京:国防工业出版社,2002:28-29.(Zhou Ke-min.Robust and Optimal Control[M].Beijing:National Defence Industry Press,2002:28-29.)
[8]曾林森.倒立摆的鲁棒LQR最优控制[D].成都:西南交通大学,2014.(Zeng Lin-sen.Robust LQR optimal control of the inverted pendulum[D].Chengdu:Southwest Jiaotong University,2014.)
[9]李洋,梁义维.基于PID与LQR的两轮平衡小车控制算法的仿真研究[J].机械工程与自动化,2011(6):7-8+10.(Li Yang,Liang Yi-wei.Simulation research on control algorithm of two wheel balancing car based on PID and[J].Mechanical Engineering and Automation,2011(6):7-8+10.)
[10]李洋.基于LQR算法两轮自平衡小车的系统设计与研究[D].太原:太原理工大学,2011.(Li Yang.System design and research of self-balancing two-wheeled cartsystem vehicle based on LQR algorithm[D].Taiyuan:Taiyuan University of Technology,2011.)