倒立摆线性二次型最优控制方法研究

Research on Control Method of Linear Quadratic Regulator with Inverted Pendulum

为优化倒立摆控制性能,提高系统响应的快速性和稳定性,研究了线性二次型最优控制方法。应用动力学分析方法建立单级倒立摆线性状态空间模型,设计线性二次型控制器(LQR);应用Matlab软件中LQR函数,确定倒立摆闭环控制系统状态反馈向量及最优控制目标函数,完成线性二次型状态反馈控制系统设计。时间响应分析及动态仿真结果表明,基于LQR函数设计的线性二次型状态反馈控制系统,阶跃响应上升时间<2 s,调节时间<5 s,实现了单级倒立摆快速、稳定控制。

To optimize the controlling performance and improve the time response performance of the inverted pendulum system,the control method of the linear quadratic regulator is studied.The linear state-space model of single stage inverted pendulum is built by the dynamic analysis and the linear quadratic regulator(LQR)is designed.The state feedback vector of closed-cycle control system and the objective function of optimum controlling of the inverted pendulum system are determined with LQR function in Matlab software.Its state feedback controlling system is designed.The result shows that its step rising time is less than 2 s and the regulating time is less than 5 s.This system meets the requirements of the fast and stable controlling.