Robust Output Feedback Stabilization of a Magnetic Levitation System Using Higher Order Sliding Mode Control Strategy

Abstract

This work studies the problem of robust output feedback stabilization of a Magnetic Levitation System using Higher Order Sliding Mode Control (HOSMC) strategy. The traditional (first order) sliding mode control (SMC) design tool provides for a systematic approach to solving the problem of stabilization and maintaining a predefined (user specified) consistent performance of a minimum-phase nonlinear system in the face of modeling imprecision and parametric uncertainties. Recently reported variants of SMC commonly known as Higher Order Sliding Mode Control schemes have gained substantial attention since these provide for a better transient performance together with robustness properties. In this work, we focus on design of an output feedback controller that robustly stabilizes a Magnetic Levitation System with an added objective of achieving an improvement in the transient performance. The proposed control scheme incorporates a higher-order sliding mode controller (HOSMC) to solve the robust semi-global stabilization problem in presence of a class of somewhat unknown disturbances and parametric uncertainties. The state feedback control design is extended to output feedback by including a high gain observer that estimates the unmeasured states. It is shown that by suitable choice of observer gains, the output feedback controller recovers the performance of state feedback and achieves semi-global stabilization over a domain of interest. A detailed analysis of the closed-loop system is given highlighting the various factors that lead to improvement in transient performance, robustness properties and elimination of chattering. Simulation results are included and a performance comparison is given for the traditional SMC and HOSMC designs employing the first and second order sliding modes in the controller structure.