Discrete time sliding mode control with reduced switching – a new reaching law approach

Abstract

Summary In this paper, a novel reaching law for discrete‐time variable structure systems is proposed. It ensures that the representative point (state) of the controlled plant approaches the switching plane in finite time and then crosses it in every subsequent step. Moreover, the proposed reaching law ensures that for the nominal plant the absolute value of the sliding variable asymptotically decreases to zero, and for the perturbed plant, it converges to a smaller interval around zero than with the application of previously proposed reaching laws. The control method proposed in this paper guarantees asymptotic stability of the nominal system and uniform ultimate boundedness of the perturbed one. Furthermore, the method ensures that the sliding variable rate of change (i.e. the difference between its values at any two subsequent sampling instants) is bounded by design parameters, which do not depend on the system initial conditions. This is a highly desirable property, as it results in a priori specified, ‘almost’ constant convergence rate of the sliding variable when the system state is far off the switching plane and helps enforce state constraints in the system. Copyright © 2014 John Wiley & Sons, Ltd.

The problem of state constraints in designing the discrete time sliding mode controller

“…Hence, the representative point arrives to the neighborhood of the sliding hyperplane in finite time and the parameter λ i is of the form (21). This ends the proof.…”

“…Originally, the reaching law method was introduced for continuous time systems [19], and then developed for discrete time ones [20]. Recently, a large number of new reaching laws were presented [21][22][23][24][25][26][27][28][29][30].…”

Discrete‐time systems sliding mode switching hyperplane design: A survey

“…2,16,17,42 Definition 2. Given (x, u), a discrete-time SISO linear system, whose dynamics are described in (9). The system is said to be represented in Frobenius or Luenberger canonical control form 57 or simply controller canonical form if the matrices Φ and Γ have the following structure:…”

Static output‐feedback sliding mode control under round‐robin protocol

“…In this section, an output-feedback SMC lawū(k) shall be designed to asymptotically stabilize the uncertain NCS (1)-(2) under round-robin protocol (4)- (5).…”

“…The following theorem presents a sufficient condition for guaranteeing the asymptotic stability of the closed-loop system (13) under the round-robin protocol (4)-(5). (1)-(2) with the round-robin protocol (4)- (5). Let the matrix F in sliding function (8) and the parameter in the token-dependent SMC law (11) be given.…”