Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Robust Sliding Mode Control of a Magnetic Levitation System: Continuous-Time and Discrete-Time Approaches

Version 1 : Received: 24 October 2021 / Approved: 27 October 2021 / Online: 27 October 2021 (13:33:34 CEST)

How to cite: Vernekar, P.; Bandal, V. Robust Sliding Mode Control of a Magnetic Levitation System: Continuous-Time and Discrete-Time Approaches. Preprints 2021, 2021100414 (doi: 10.20944/preprints202110.0414.v1). Vernekar, P.; Bandal, V. Robust Sliding Mode Control of a Magnetic Levitation System: Continuous-Time and Discrete-Time Approaches. Preprints 2021, 2021100414 (doi: 10.20944/preprints202110.0414.v1).

Abstract

This paper presents three types of sliding mode controllers for a magnetic levitation system. First, a proportional-integral sliding mode controller (PI-SMC) is designed using a new switching surface and a proportional plus power rate reaching law. The PI-SMC is more robust than a feedback linearization controller in the presence of mismatched uncertainties and outperforms the SMC schemes reported recently in the literature in terms of the convergence rate and settling time. Next, to reduce the chattering phenomenon in the PI-SMC, a state feedback-based discrete-time SMC algorithm is developed. However, the disturbance rejection ability is compromised to some extent. Furthermore, to improve the robustness without compromising the chattering reduction benefits of the discrete-time SMC, mismatched uncertainties like sensor noise and track input disturbance are incorporated in a robust discrete-time SMC design using multirate output feedback (MROF). With this technique, it is possible to realize the effect of a full-state feedback controller without incurring the complexity of a dynamic controller or an additional discrete-time observer. Also, the MROF-based discrete-time SMC strategy can stabilize the magnetic levitation system with excellent dynamic and steady-state performance with superior robustness in the presence of mismatched uncertainties. The stability of the closed-loop system under the proposed controllers is proved by using the Lyapunov stability theory. The simulation results and analytical comparisons demonstrate the effectiveness and robustness of the proposed control schemes.

Keywords

Chattering reduction; discrete-time sliding mode control; magnetic levitation system; multirate output feedback; robust control; sliding mode control (SMC)

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