LQR based Optimal Tuning of PID Controller for Trajectory Tracking of Magnetic Levitation System

In this paper, we consider the stabilization and trajectory tracking of magnetic levitation system using PID controller whose controller gains are determined via Linear Quadratic Regulator (LQR) approach. Firstly, the nonlinear mathematical model of the system is obtained from the first principles. Then by applying Taylor's series, the non linear equation of motion is linearized around the equilibrium point to implement the stabilizing controller. Finally, the gains of the PID controller to achieve the desired response are determined using the LQR theory. Based on the natural frequency and damping ratio of the closed loop system, a new criterion for selecting the weighting matrices of LQR is proposed in this paper. Experiments are conducted on a Quanser magnetic levitation system to evaluate the performance of the proposed methodology and the experimental results prove that the proposed control strategy is effective not only in stabilizing the ball but also in rejecting the disturbance present in the system.