Model reference discrete‐time variable structure control

Abstract

This paper presents a new reaching law-based model reference quasi-sliding mode control strategy for discrete-time dynamical systems. The strategy ensures the quasi-sliding mode attributes defined in the seminal paper of Gao et al, but at the same time, it offers essentially improved system robustness. In particular, it is demonstrated that the application of the reference model results in the decreased width of the quasi-sliding mode band and guarantees smaller errors of all state variables. KEYWORDS discrete-time systems, model reference sliding mode control, reaching law 1440

Model Reference DSMC With a Relative Degree Two Switching Variable

“…As a result, the desired trajectory of the system can become distorted at any stage of the control process. To remedy this issue, a recent work [33] proposed the use of a disturbance-free reference model of the plant. The new approach uses the reference model of the plant to obtain a desired trajectory of its representative point, and then, drives the state of the original plant alongside that trajectory, thus eliminating the residual effect of past perturbations on the motion of the system.…”

“…In this article, we introduce a new discrete-time reaching-law-based sliding mode control strategy using a reference model of the plant and apply it to the system subject to unmatched uncertainties. Contrary to the approach from [33] where Gao's classic reaching law [18] has been applied to the model, in our article, a more sophisticated reaching law is considered. In particular, we use generalization of Gao's reaching law for sliding variables with relative degree two [32].…”

Discrete‐time sliding mode output tracking control for a class of nonlinear perturbed systems

“…This effect can be suppressed by implicit Euler discretization of the discontinuous term 10,11 as well as by the time variation of the discontinuous term parameter 12,13,22 or by increasing the relative degree and, accordingly, the order of the sliding mode. 14,15,23 To avoid the chattering problem, continuous DT reaching controllers have been proposed in , including equivalent-control-based 7,20 and adaptive 24,25 SM algorithms. However, as a result of the lack of unknown perturbation for calculating the equivalent control, the sliding manifold reaches a boundary layer ( ) with as the sampling period.…”

“…To avoid the chattering problem, continuous DT reaching controllers have been proposed in References 16‐19, including equivalent‐control‐based 7,20 and adaptive 24,25 SM algorithms. However, as a result of the lack of unknown perturbation for calculating the equivalent control, the sliding manifold reaches a boundary layer with as the sampling period.…”

A Novel Reaching Law for Sliding Mode Control of Uncertain Discrete-Time Systems

“…One is to assume a certain control algorithm and demonstrate that this algorithm ensures stability of the sliding motion on the hyperplane; another approach is to apply the reaching law approach. The reaching law approach was first proposed by Gao and Hung [22], based on the equality type of reaching conditions [23][24][25][26][27]. The control of discrete-time systems via using the reaching law approach has been used in many significant studies [28][29][30].…”