In this paper, discrete-time quasi-sliding-mode control systems are considered. A new definition describing the quasi-sliding mode as a motion of the system, such that its state always remains in a certain band around the sliding hyperplane, is introduced. Then, two novel reaching laws satisfying conditions of the definition are proposed and applied to the design of appropriate linear control strategies which drive the state of the controlled system to a band around the sliding hyperplane. Consequently, the undesirable chattering and high-frequency switching between different values of the control signal are avoided. The strategies, when compared with previously published results, guarantee better robustness, faster error convergence, and improved steady-state accuracy of the system. Furthermore, better performance of the system is achieved using essentially reduced control effort.

Discrete-time quasi-sliding-mode control strategies

This paper investigates the robust sliding mode control (SMC) problem for a class of uncertain nonlinear stochastic systems with mixed time delays. Both the sectorlike nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties and randomly occurring nonlinearities obey certain mutually uncorrelated Bernoulli distributed white noise sequences. The mixed time delays consist of both the discrete and the distributed delays. The time-varying delays are allowed in state. By employing the idea of delay fractioning and constructing a new Lyapunov-Krasovskii functional, sufficient conditions are established to ensure the stability of the system dynamics in the specified sliding surface by solving a certain semidefinite programming problem. A full-state feedback SMC law is designed to guarantee the reaching condition. A simulation example is given to demonstrate the effectiveness of the proposed SMC scheme.

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Robust Sliding Mode Control for Discrete Stochastic Systems With Mixed Time Delays, Randomly Occurring Uncertainties, and Randomly Occurring Nonlinearities

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 sliding manifold which inherits the desired properties of the continuous-time integral sliding manifold, such as full order sliding manifold with pole 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(T2) steady-state error for state regulation with the widely adopted delay-based disturbance estimation. Another desirable feature is, the proposed DISMC prevents the generation of overlarge control actions due to deadbeat response, which is usually inevitable due to the existence of poles at the origin for a reduced order sliding manifold designed for sampled-data systems. Both the theoretical analysis and illustrative example demonstrate the validity of the proposed scheme

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On the Discrete-Time Integral Sliding-Mode Control

Chattering-free discrete-time sliding mode control

Robust discrete-time chattering free sliding mode control

This paper presents a treatment of discrete variable structure control systems. The purpose is to lay a foundation upon which design of such type of systems can be made properly. Phenomena of switching, reaching, and quasi-sliding mode are investigated thoroughly. Terms pertaining to discrete variable structure control are defined. A method of quasi-sliding mode design is given. The inherently existing quasi-sliding mode band is analyzed. A recently introduced "reaching law approach" is conveniently used to develop the control law for robust control. Comments are given regarding chattering. The design technique is illustrated by a simulated system. >

Yufu Wang

Papers

Discrete-time variable structure control systems