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

TL;DR

This paper develops and compares continuous-time and discrete-time sliding mode controllers for magnetic levitation systems, demonstrating improved robustness, reduced chattering, and better disturbance rejection through novel control strategies and multirate output feedback.

Contribution

It introduces a new PI sliding mode controller and a robust discrete-time SMC with multirate output feedback, enhancing robustness and reducing chattering in magnetic levitation control.

Findings

PI-SMC outperforms existing controllers in convergence and settling time.

Discrete-time SMC reduces chattering but slightly compromises disturbance rejection.

MROF-based discrete-time SMC achieves high robustness and stability under uncertainties.

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.