Paper Title
Backstepping-Based Control of A Magnetic Levitation System

Abstract
Magnetic levitation systems are highly nonlinear and unstable systems and their efficacy depends on a well-designed controller to stabilize the system as well as to track the desired reference signal. This work focuses on the design of a back stepping-based controller (BC) for the maglev levitation system under parameter uncertainty and external disturbance. Firstly, the nonlinear mathematical model is obtained and the back stepping control law is obtained based on the model and Lyapunov’s theory. Then, the parameters of the designed controller are optimally tuned by minimizing the integral of absolute error and control performance criterion using the particle swarm optimization algorithm. For comparison purpose, the optimal linear quadratic regulator (LQR) is also designed. A set of simulation works are carried out to verify both tracking and disturbance rejection performances of the proposed controller. The BC scheme outperforms the LQR by reducing the settling time by 28.8 and 27.7%, rise time by 26 and 26.7%, and IAEU by 26.1 and 25.3%, for upward and downward stepwise reference signals, respectively. The disturbance rejection performance of the BC is tested using load variations of up to 40% mass change. In the 40% load change, the BC gives 0.129sec, 0.193sec, and 0.183 of rise time, settling time, and IAEU, which are smaller in comparison with those of the LQR, respectively. Keywords - Magnetic Levitation System, Back Stepping Control, Optimization, PSO, LQR.