Development of a new linearizing controller using Lyapunov stability theory and model reference control

Abstract

One of the most challenging aspects in the nonlinear control of a magnetic levitation (Maglev) system is to find an efficient control algorithm to achieve the stability and accuracy of the closed-loop system. The challenge is then to develop a linearizing control algorithm to maintain a steel ball at a desired position. In this paper, a novel linearizing control algorithm is proposed, which consists of the Lyapunov direct method (LDM) and the model reference control (MRC). The Lyapunov function is developed using the nonlinear equations of the magnetic levitation system, and the reference model is a linear second order system. Two control methods are developed to guarantee system robustness and output stability. Firstly, a new integral linear quadratic regulator (ILQR) is designed for the reference model. Then, an additional innovative proportional gain is combined with the linearizing controller to make the nonlinear control signal stronger. The simulation results indicate that the proposed linearizing controller has excellent set-point tracking, no time delay, fast rising and settling times, and achieves states stability.