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access icon free Equivalent-input-disturbance-based repetitive tracking control for Takagi–Sugeno fuzzy systems with saturating actuator

© The Institution of Engineering and Technology
Received 12/01/2016, Accepted 03/06/2016, Revised 07/05/2016, Published 15/06/2016

This study investigates the output tracking problem for a class of Takagi–Sugeno fuzzy systems subject to periodic signals and actuator saturation via equivalent-input-disturbance (EID) technique. In particular, to ensure the periodic signals tracking, a state-space repetitive control structure is considered. Further, the EID technique is utilised to improve the disturbance rejection performance without any prior knowledge of the disturbance and inverse dynamics of the plant. By constructing a suitable Lyapunov–Krasovskii functional and using the Wirtinger-based integral inequality, a new set of sufficient conditions is derived in terms of linear matrix inequalities (LMIs) which ensures the stability of the addressed system. In addition to that by using a Lyapunov level set, saturation-dependent Lyapunov function captures the real-time information on the severity of actuator saturation and leads to less conservative estimate of the domain of attraction, which is based on the solution of an LMI optimisation problem. Moreover, the designed fuzzy repetitive controller is reliable in the sense that the stability and the satisfactory performance of the closed-loop system are achieved not only under normal operation, but also in the presence of any actuator faults, saturation and dead zone. Finally, the proposed method is validated through two numerical examples to illustrate the effectiveness and superiority of the developed controller design.

Inspec keywords: position control; stability; fuzzy systems; actuators; closed loop systems; control system synthesis; fault tolerant control; fuzzy control; linear matrix inequalities; Lyapunov methods

Other keywords: Takagi-Sugeno fuzzy systems; saturation-dependent Lyapunov function; stability; closed-loop system; Wirtinger-based integral inequality; dead zone; disturbance dynamics; periodic signals tracking; inverse dynamics; LMI optimisation problem; real-time information; fuzzy controller design; EID technique; LMI; saturating actuator; equivalent-input-disturbance-based repetitive tracking control; state-space repetitive control structure; Lyapunov level set; Lyapunov-Krasovskii functional; linear matrix inequalities; actuator faults; disturbance rejection performance

Subjects: Algebra; Control system analysis and synthesis methods; Fuzzy control; Spatial variables control; Actuating and final control devices; Stability in control theory

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