Model transformation based sliding mode control of discrete-time two-dimensional Fornasini–Marchesini systems

• Published in: Journal of the Franklin Institute Vol. 356; no. 5; pp. 2463 - 2473
• Main Authors: Yang, Rongni, Zheng, Wei Xing
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.03.2019; Elsevier Science Ltd
• Subjects: Asymptotic methods; Asymptotic properties; Closed loop systems; Control systems; Controllers; Discrete element method; Discrete time systems; Dynamic stability; Feedback control; Sliding mode control; State space models; Surface stability; Transformations; Two dimensional models
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2018.11.017

This paper investigates the problem of sliding mode control (SMC) for discrete-time two-dimensional (2-D) systems subject to external disturbances. Given a 2-D Fornasini–Marchesini (FM) local state space model, attention is focused on designing the 2-D sliding surface and sliding mode controller, which guarantees the resultant closed-loop system to be asymptotically stable. Particularly, this problem is solved using the model transformation based method. First of all, sufficient conditions are formulated for the existence of a linear sliding surface guaranteeing the asymptotic stability of the equivalent sliding mode dynamics. Based on this, a sliding mode controller is synthesized to ensure that the associated 2-D FM system satisfies the reaching condition. The efficiency of the proposed 2-D SMC law design is shown by a numerical example. This paper extends the idea of model transformation to the 2-D systems and solves the SMC problem of a more general 2-D model in FM type for the first time.