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Fuzzy Nonlinear Adaptive Internal Model Control (FNAIMC)

In this paper, it is proposed to apply Fuzzy Nonlinear Adaptive Internal Model Control (FNAIMC) for dealing with stable nonlinear systems. The developed strategy consists in including a Takagi-Sugeno fuzzy model of the plant within the control structure. In this way, the controller design simply results in a fuzzy model inversion. In this framework, the originality of the presented work lies in the use of a fuzzy model and its inversion. In order to be able to implement the control structure, two crucial points have to be solved in the considered fuzzy context, on the one hand the model identification, and on the other, the model inversion. A method is proposed to handle these two tasks when considering Takagi-Sugeno fuzzy formalism. As the structure of the fuzzy model (number of rules and rule premise) is assumed to be known, the fuzzy model identification is restricted to parameter identification (singleton consequence of the rules). Based on input-output process data, an online adaptive identification method is developed. The stability and convergence of the proposed recursive algorithm is guaranteed according to a Lyapunov synthesis. The model inversion strategy is viewed as a rulebase inversion problem. According to a linguistic interpretation of the model rulebase, each rule is directly inverted. By doing so, exact inversion is obtained and offset-free performances are ensured. In order to impose a desired regulation dynamic behavior and ensure the robustness of stability of the control system, the fuzzy controller is cascaded with a robustness filter. The potential of the proposed method is demonstrated by simulation examples.