New Time-Varying Sliding Surface for Switching Type Quasi-Sliding Mode Control

Katarzyna Adamiak,Andrzej Bartoszewicz

doi:10.3390/en14133811

Abstract

This study considers the problem of energetical efficiency in switching type sliding mode control of discrete-time systems. The aim of this work is to reduce the quasi-sliding mode band-width and, as follows, the necessary control input, through an application of a new type of time-varying sliding hyperplane in quasi-sliding mode control of sampled time systems. Although time-varying sliding hyperplanes are well known to provide insensitivity to matched external disturbances and uncertainties of the model in the whole range of motion for continuous-time systems, their application in the discrete-time case has never been studied in detail. Therefore, this paper proposes a sliding surface, which crosses the system’s representative point at the initial step and then shifts in the state space according to the pre-generated demand profile of the sliding variable. Next, a controller for a real perturbed plant is designed so that it drives the system’s representative point to its reference position on the sliding plane in each step. Therefore, the impact of external disturbances on the system’s trajectory is minimized, which leads to a reduction of the necessary control effort. Moreover, thanks to a new reaching law applied in the reference profile generator, the sliding surface shift in each step is strictly limited and a switching type of motion occurs. Finally, under the assumption of boundedness and smoothness of continuous-time disturbance, a compensation scheme is added. It is proved that this control strategy reduces the quasi-sliding mode band-width from O(T) to O(T3) order from the very beginning of the regulation process. Moreover, it is shown that the maximum state variable errors become of O(T3) order as well. These achievements directly reduce the energy consumption in the closed-loop system, which is nowadays one of the crucial factors in control engineering.

Highlights

The term sliding mode has first appeared in the theory of variable structure systems [1]and referred to a characteristic form of nonlinear, discontinuous, feedback control, as described in [2,3]
This paper proposed a new discrete-time sliding mode control method based on the time-varying sliding surface concept
The pre-generated reference profile manifests all the properties required from the actual system, so it converges to zero in finite time and exhibits the zigzagging motion around the equilibrium point

Summary

Introduction

Referred to a characteristic form of nonlinear, discontinuous, feedback control, as described in [2,3] This comprehensive control scheme may be successfully applied to both linear [4] and nonlinear systems [5,6]. The so-called reaching phase, the system’s state is driven to a predefined surface in the state space. The so-called sliding phase, the representative point of the system slides along this surface until it reaches the equilibrium point. Enforcing faster convergence often requires large magnitudes of the control input and consumes more energy. This observation resulted in the development of time-varying sliding planes

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Methods

Conclusion