LQR self-adjusting based control for the planar double inverted pendulum

Firstly, the mathematical model of planar double inverted pendulum was established by means of analytical dynamics method. Based on the linear quadratic optimal theory, LQR self-adjusting controller was presented with optimize factor. Further the output of LQR controller is refined through optimize factor which is the function of the states of planar pendulum, and on account of that, control action exerted on the pendulum is improved. Simulation results together with pilot scale experiment verify the efficacy of the suggested scheme. The results show that the controller designed is simple and real-time is good in the lab. Moreover it can ensure fast response, good stability and robustness in the different operating conditions.