基于LQR最优调节器的二级倒立摆控制系统

Coutrol System of Double Inverted Pendulum Based on the LQR Optimal Regulator

倒立摆是一个典型的快速、多变量、非线性、绝对不稳定系统,对倒立摆系统的稳定性研究在理论上和方法上具有深远的意义。本文建立了二级倒立摆的数学模型,并推导出模型的状态空间表达式,分析了系统的稳定性,能控性和能观性,利用了线性二次型最优调节器(LQR)方法实现对二级倒立摆的最优控制,MATLAB仿真结果表明了该方法的有效性。

Inverted pendulum is a system of a typical model of multi-var/able,non-linear, essentially unsteady.It has profound meaning in theory and methodology to study the stability of inverted pendulum system. In the paper we establish the model of double inverted pendulum system and deduce an expression state-space. We also analyze its stability,controllability. By the use of LQR we get an optimal control for the double inverted pendulum system and turn it to be effective by the MATLAB-simulated experiments.