Robust discrete-time nonlinear sliding mode controller with plant uncertainties

Abstract

This paper addresses the new control algorithm, by designing the asymptotically stable nonlinear sliding surface with investigation of the states. This proposed algorithm leads to solve the problem of unstable systems, by proving the asymptotic stability of a class of uncertain discrete-time systems. A particular linear transformation is being defined to transform the discrete-time system and asymptotic stability is proved for designed nonlinear sliding surface, which leads to show stability of the system. The states of the plant's will be brought down on a proven asymptotic stable nonlinear sliding surface by the proposed control law and they will be remained on stable nonlinear sliding surface for all future times. This proposed technique will be more useful for enhancing the stability of the real world nonlinear systems. The application of proposed algorithm in magnetic tape drive-servo motors and avionic systems, where the parametric uncertainties are occurring frequently.

A Novel Method for the Design of Switching Surfaces for Discretized MIMO Nonlinear Systems

“…However, the control law u (k) must be designed such that some reaching law must be fulfilled considering these uncertainties, mostly when the matching conditions are not achieved (Furuta, 1990;Gao et al, 1995;Kim et al, 2000;Sira-Ramírez, 1991;Yu et al, 2000;Yadav and Singh, 2012;Mondal et al, 2012;Qu et al, 2014). This part of the design of DVSC controllers is not directly carried out during switching the surface design phase.…”

Discrete second-order sliding mode control based on optimal sliding function vector for multivariable systems with input-output representation

“…In order to reduce the reachability phase, sliding mode control uses the technique of LMIs, thanks to their effectiveness in the choice of coefficients of the sliding function . In this context, a robust sliding mode control using a linear sliding function based on the LMIs was proposed in .…”

“…In order to reduce the reachability phase, sliding mode control uses the technique of LMIs, thanks to their effectiveness in the choice of coefficients of the sliding function [11][12][13][14][15]. In this context, a 3808 H. ROMDHANE, K. DEHRI AND A. S. NOURI with S.k C d / as the sliding function vector in the case of classical sliding mode control.…”

“…One of the problems of the synthesis of sliding mode control is the choice of the coefficients of the sliding function. Therefore, several methods have been developed in order to determine these coefficients such as the pole placement method and the linear matrix inequalities (LMIs) approach .…”

“…Simulation results prove good performances in terms of reduction of the reachability phase.OPTIMAL SLIDING FUNCTION VECTOR 3807 robust sliding mode control using a linear sliding function based on the LMIs was proposed in [11]. An algorithm for designing a nonlinear sliding function for a class of uncertain discrete-time systems was presented in [12]. Also, a sliding function using the technique of pole placement in the LMI region was developed in [13].…”