Abstract
The paper proposes a new design method based on linear matrix inequalities (LMIs) for tracking constant signals (regulation) considering nonlinear plants described by the Takagi‐Sugeno fuzzy models. The procedure consists in designing a single controller that stabilizes the system at operation points belonging to a certain range or region, without the need of remaking the design of the controller gains at each new chosen equilibrium point. The control system design of a magnetic levitator illustrates the proposed methodology.
Highlights
In recent years the design of tracking control systems for nonlinear plants described by Takagi-Sugeno fuzzy models 1 has been the subject of several studies 2–10
In 4 is proposed a design method for tracking system with disturbance rejection applied to a class of nonlinear systems using fuzzy control
A similar study is presented in 7, where a robust reference-tracking control problem for nonlinear distributed parameter systems with time delays, external disturbances, and measurement noises is studied; the nonlinear distributed parameter systems are measured at several sensor locations for output-feedback tracking control
Summary
In recent years the design of tracking control systems for nonlinear plants described by Takagi-Sugeno fuzzy models 1 has been the subject of several studies 2–10. This paper proposes a new control methodology for tracking constant signals for a class of nonlinear plants This method is based on LMIs and uses the Takagi-Sugeno fuzzy models to accurately describe the nonlinear model of the plant. The project considers that the change from an operating point to another occurs after large time intervals, such that in the instants of the changes the system is practically in steady-state This new methodology allows the use of well-known LMIs-based design methods, for the design of fuzzy regulators for plants described by the Takagi-Sugeno fuzzy models, for instance presented in 11, 14, 15, 24–28 , which allows the inclusion of the specification of performance indices such as decay rate and constraints on the plant input and output. Gij Ai − BiFj , 2.6 can be written as follows: rr xt αi x t αj x t Gij x t
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