A Generalized Backstepping Controller Design for a Second-Order Magnetic Levitation System

Abstract

This research tackles the control design challenge of stabilizing a second-order magnetic levitation system using a nonlinear control approach. The proposed controller is rooted in backstepping control theory, which ensures the asymptotic convergence of the system’s incremental state variables to the origin through a Lyapunov-based framework. A key advantage of this method is the generalized control input, expressed in a polynomial form with four adjustable control gains, allowing for precise tuning to achieve the desired dynamic performance. A major contribution of this study is the formal demonstration of stable performance provided by the generalized controller in second-order dynamic systems, with a particular emphasis on its application to magnetic levitation. Numerical simulations in Matlab/Simulink showcase the controller’s effectiveness across three different sets of control gains, enabling the system to realize critically damped, overdamped, and underdamped dynamic responses with respect to the desired position of the levitated metallic mass.