Sliding mode control for non-linear systems by Takagi–Sugeno fuzzy model and delta operator approaches

• Published in: IET control theory & applications Vol. 11; no. 8; pp. 1205 - 1213
• Main Authors: Wang, Jiahui, Gao, Yabin, Qiu, Jianbin, Ki Ahn, Choon
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 12.05.2017
• Subjects: actuator faults; actuators; adaptive control; adaptive sliding mode control; closed loop systems; control system synthesis; delta operator method; discrete time systems; discrete‐time nonlinear systems; discrete‐time Takagi‐Sugeno fuzzy systems; Dynamical systems; external disturbances; Fault tolerance; fault tolerant control; fault‐tolerant control scheme; Fuzzy systems; linear matrix inequalities; linear matrix inequality constraint; Linear operators; Mathematical models; mathematical operators; nonlinear control systems; Nonlinear dynamics; reduced order systems; Sliding mode; Sliding mode control; Special Issue: Recent Developments on Sliding Mode Control and Its Applications for Complex Systems; T–S fuzzy models; uniform ultimately bounded closed‐loop system; variable structure systems; delta operator method; discrete time systems; actuator faults; linear matrix inequality constraint; adaptive sliding mode control; adaptive control; control system synthesis; mathematical operators; T–S fuzzy models; closed loop systems; discrete-time Takagi-Sugeno fuzzy systems; uniform ultimately bounded closed-loop system; actuators; discrete-time nonlinear systems; fault-tolerant control scheme; linear matrix inequalities; nonlinear control systems; reduced order systems; fuzzy systems; external disturbances; variable structure systems; fault tolerant control
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2016.0231

This study considers the problem of adaptive sliding mode control for discrete-time Takagi–Sugeno (T–S) fuzzy systems with actuator faults and external disturbances via the delta operator method. The delta operator approach is used to represent the discrete-time non-linear systems described by T–S fuzzy models. The actuator fault considered in this study is unknown and its fault-deviation is also unknown. A reduced-order system is utilised to design the sliding mode surface subject to linear matrix inequality constraint. By constructing the sliding mode surface, a novel adaptive sliding mode controller is designed to guarantee that the closed-loop system is uniformly ultimately bounded. Finally, two practical examples are presented to show the effectiveness and applicability of the developed fault-tolerant control scheme.