New Switching and Nonswitching Type Reaching Laws for SMC of Discrete Time Systems

Abstract

In this brief a new switching type reaching law for sliding mode control of discrete time systems is proposed. The proposed reaching law is a refined version of an earlier approach (introduced in the seminal work of Gao et al.) which enforces constant plus proportional decrease rate of change of the sliding variable. In our method, the proportional term is modified, so that the rate is always bounded and decreases slower for smaller values of the sliding variable than in the original approach. The refined reaching law proposed in this brief, on the one hand, ensures faster convergence and better robustness of the controlled plant than the earlier approach, and on the other hand, it helps satisfy constraints of important signals in the system. Furthermore, in the latter part of this brief a new nonswitching type reaching law is introduced, and it is demonstrated that it results in further improvement of the system robustness without increasing the magnitude of the critical signals in the system. Index Terms-Constraints, discrete time sliding mode control, nonswitching sliding mode controller, reaching law approach, sliding mode control, switching sliding mode controller.

Discrete‐time higher‐order sliding mode control of systems with unmatched uncertainty

“…Since these discrete‐time systems are inherently discrete, the control techniques designed for continuous‐time systems cannot be applied in discrete‐time systems directly. Simultaneously, a considerable amount of research on discrete‐time sliding mode (DSM) controller design has been done . In the case of discrete‐time systems, the control input can be applied only at certain sampling instants.…”

“…sliding mode (DSM) controller design has been done. [19][20][21][22] In the case of discrete-time systems, the control input can be applied only at certain sampling instants. Due to finite-time sampling frequency, the system may not move on the sliding surface or may switch about the sliding surface at each sample.…”

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

“…The manifold around the sliding surface is called the band of quasi-sliding domain, expressed by Δ (Δ > 0). Bartoszewicz et al proposed a type of nonswitching reaching law in [26,31] based on the idea that the system states are not required to cross the sliding surface in each successive step. Qu et al [32] proposed a dynamic discrete-time SMC for uncertain systems with a disturbance compensator to alleviate chattering.…”

“…Although infinite-frequency switching is theoretically feasible from the robustness point of view, it is usually hard to achieve in practical systems because of physical constraints. In order to solve the inherent shortcoming of DSMC systems, many scholars proposed novel reaching laws; for example, Andrzej Bartoszewicz proposed some novel reaching laws [26,31] which are different from Gao et al [23]. These reaching laws are based on the idea that the system state is not required to cross the sliding surface in each successive control step, so they can alleviate undesired chattering; but for the nonswitching type reaching law, some advantages of QSM are also lost at the same time, such as the robustness of system.…”

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

“…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].…”