On the Discrete-Time Integral Sliding-Mode Control

Abstract

Abstract-A new discrete-time integral sliding mode control (DISMC) scheme is proposed for sampled-data systems. The new control scheme is characterized by a discrete-time integral switching surface which inherits the desired properties of the continuous-time integral switching surface, such as full order sliding manifold with eigenvalue assignment, and elimination of the reaching phase. In particular, comparing with existing discrete-time sliding mode control, the new scheme is able to achieve more precise tracking performance. It will be shown in this work that, the new control scheme achieves O(T 2 ) steadystate error for state regulation with the widely adopted delaybased disturbance estimation. Another desirable feature is, the proposed DISMC prevents the generation of overlarge control actions, which are usually inevitable due to the deadbeat poles of a reduced order sliding manifold designed for sampled-data systems. Both the theoretical analysis and illustrative example demonstrate the validity of the proposed scheme.

Enhanced discrete‐time sliding mode strategy with application to piezoelectric actuator control

“…Generally, the DSMC can be categorised into state-based and output-based methods. The former is developed based on the system state or state error [16][17][18], whereas the latter is realised on the base of the system output or output error [19,20]. Usually, the implementation of both methods requires the state feedback of the system.…”

“…However, in majority of practical situations, only the position information of a piezoelectric actuator system is provided by the displacement sensor. Hence, a state observer is indispensable for the practical realisation of DSMC [16,[18][19][20], which complicates the control design procedure. Furthermore, an improperly designed state observer may cause instability of the system.…”

Discrete time integral sliding mode control for systems with matched and unmatched uncertainties

“…Wang, Yu and Chen reported about discretisation of normal sliding mode systems in [10]. In 2007, K. Abidi, J. Xu and X. Yu reported the design of discrete time ISMC [11]. They worked on a sampled data system whose continuous counterpart contains a matched uncertainty.…”

Robust tracking and model following of uncertain dynamic systems via discrete-time integral sliding mode control

“…Hence, SMC is an effective robust control approach for uncertain systems, and widely applied to many practical control systems. Several design methods of SMC for discrete-time uncertain systems have been proposed in the literature [18][19][20][21][22][23][24][25][26][27]. The objective of this paper is to develop a discretetime integral SMC scheme for uncertain linear systems to track dynamic inputs of a non-delay reference model.…”