Robust Control of Electromagnetic Levitation System

Abstract

Nonlinear ${H}_{\infty }$ control is a promising way of attenuating negative effects of external disturbances in nonlinear systems and is robust against uncertainties of the plant. However, partial differential equation (PDE) obtained from this method rarely can be solved analytically. Thus, some sort of approximation is required. Furthermore, produced controllers by this method using Taylor series approximation (especially higher order controllers) are complicated and hard to implement. In this paper, a robust and nonlinear controller is introduced which combines linear ${H}_{\infty }$ controller and feedback linearization technique. First, a nonlinear state transformation is applied to the nonlinear system such that the resulting system is linear. Next, a linear ${H}_{\infty }$ controller is designed for the feedback linearized system. By this method, approximation is not required in designing ${H}_{\infty }$ controller because for linear systems, resulting PDE is simplified to a Riccati equation. Proposed approach has been applied to a Magnetic Levitation (Maglev) system, and its performance is compared with third-order nonlinear ${H}_{\infty }$ controller to verify the effectiveness and robustness of new method. Simulation results show that proposed controller attenuates external disturbance much better than nonlinear ${H}_{\infty }$, and simultaneously has less control effort.