直线柔性二级倒立摆的LQR控制系统设计

Design of Linear Flexible Two Inverted Pendulum Control System Based on LQR

由于直线二级柔性倒立摆闭环系统是自不稳定的系统,而且柔性连接处的弹簧影响了系统的响应频率。先根据拉格朗日方程列出系统的状态方程,然后根据最优控制理论设计LQR控制器。利用MATLAB工具计算出系统的状态反馈向量。在MATLAB中将所得到的反馈向量反馈给状态方程,运行后分析仿真曲线达到了预期效果。最后编写MATLAB和VC两个版本的上位机控制程序,反复调试后实现了对倒立摆稳定控制的要求。

Since linear flexible double inverted pendulum closed loop system is unstable, and the spring of flexible joint has effect on the frequency response of the system. The flexible two inverted pendulum mathematical modeling was built based on Lagrange method. According to the optimal control theory, a system of optimal liner quadratic regulator was designed. Using MATLAB to calculate the state feedback vector and then feed back to the equation of state, the obtained simulation curve reached the desired effect. The compiled programs in MATLAB and VC succeed in achieving the stability of liner spring double inverted pendulum stability controlling.