基于卡尔曼滤波的二级倒立摆LQR控制方法

LQR Control Method for Double-Inverted Pendulum System Based on Kalman Filter

针对二次型最优控制调节器难以实现对二级倒立摆系统的最优控制问题,本文建立了倒立摆数学模型,并对直线二级倒立摆(线性二次型控制器)(linear quadratic regulator,LQR)进行设计,同时采用卡尔曼滤波对系统的输出做出最优估计,并利用Matlab对未经卡尔曼滤波的调节器系统与前置卡尔曼滤波器的调节器系统进行仿真比较分析,仿真结果表明,应用基于前置Kalman滤波器的控制,比单独用线性二次型最优控制效果更加有效可行:未经滤波时,系统输出受扰动影响大;采用卡尔曼滤波后,系统输出波动小,稳定性好。该研究可以消除噪声给系统带来的抖动影响,具有一定的实用性。

In order to solve the optimal control problem of the quadratic optimal control regulation to the double inverted pendulum system, this paper establishes the mathematical model of the inverted pendu lum, and designs linear quadratic regulator（LQR）to the linear double inverted pendulum system. This pa- per adopts Kalman filter to make the optimal estimation for the output of the system, and uses Matlab to compare the system which without Kalman filter regulator with the system which has the front Kalman fil ter regulator. Simulation results indicate that the proposed control method is effective： the output of the system is affected by disturbance without filter; after using Kalman filter, the output of the system has a small wave and a good stability. This study can eliminate the jitter effect on the system, and it has a certain practicality.