Sliding mode control for magnetic levitation systems with mismatched uncertainties using multirate output feedback

This paper presents two sliding mode control (SMC) strategies for a magnetic levitation system. First, a state feedback-based discrete-time sliding mode controller (DSMC) is designed using an improved reaching law to counteract the matched uncertainties with reduced chattering. However, the disturbance rejection ability is compromised to some extent due to the quasi-sliding mode (QSM) motion of the state trajectory and the finite switching frequency. Next, to enhance the robustness without compromising the chattering reduction benefits of the state feedback-based DSMC, a robust multirate output feedback (MROF)-based DSMC strategy is proposed. This strategy utilizes a novel sliding surface, a modified reaching law, an integrated MROF-based state estimator, and an augmented nonlinear feedback linearization controller to reject the mismatched disturbances. With this technique, it is possible to realize the effect of full-state feedback with superior robustness features while preserving the properties of an ideal continuous-time SMC as much as possible. Quantitative and qualitative comparative analyses of the proposed controllers and different state-of-the-art control techniques are done using standard performance criteria. The simulation results and comparative studies demonstrate that the MROF-based DSMC performs much better than the other advanced control strategies in terms of superior disturbance rejection ability, better steady-state performance, smaller width of the QSM band, and reduced chatter under mismatched uncertainties. A rigorous stability analysis of the closed-loop system for the proposed controllers is performed using the Lyapunov stability theory. Furthermore, the benefits and drawbacks of some recently explored control strategies for a magnetic levitation system are elaborated.