A ROBUST POLE ASSIGNMENT ALGORITHM USING LINEAR QUADRATIC REGULATOR APPLIED TO AN INVERTED PENDULUM

摘要

This paper describes the method for stabilizing and trajectory tracking of Self Erecting Single Inverted Pendulum (SESIP) using Linear Quadratic Regulator (LQR). An important advantage of LQR is that it gives a robust system by guaranteeing stability margins, and this property is used to develop an algorithm for locating the robust poles according to the controller specifications. A robust weight selection algorithm is proposed in this paper to determine the appropriate weighting matrices Q and R of LQR to assign the eigen values at the desired locations. When the desired poles lie outside the allowable LQR region, the achievable poles inside the region that are closest to the desired poles are determined by minimizing the eigen value cost difference function. The solution requires a gradient search technique to minimize the difference of weighted eigen value cost function. The steady state and dynamic characteristics of the proposed controller are investigated by conducting experiments on benchmark linear inverted pendulum system. Experimental results prove that the proposed LQR controller can guarantee the inverted pendulum a faster and smoother stabilizing process with less oscillation and better robustness than a conventional PID controller.