Abstract
This paper presents a proportional parallel distributed compensation (PPDC) design to the robust stabilization and tracking control of the nonlinear dynamic system, which is described by the uncertain and perturbed Takagi–Sugeno (T-S) fuzzy model. The proposed PPDC control design can greatly reduce the number of adjustable parameters involved in the original PDC and separate them from the feedback gain. Furthermore, the process of finding the common quadratic Lyapunov matrix is simplified. Then, the global asymptotic stability with decay rate and disturbance attenuation of the closed-loop T-S model affected by uncertainties and external disturbances are discussed using the H∞ synthesis and linear matrix inequality (LMI) tools. Finally, to illustrate the merit of our purpose, numerical simulation studies of stabilizing and tracking an inverted pendulum system are presented.
Highlights
During the last decade, the fuzzy logic control has attracted rapidly growing attention from both the academic and industrial communities [1,2,3]
The Takagi–Sugeno (T-S) fuzzy model has been extensively used to investigate nonlinear control systems [4, 5]. is model is described by a set of fuzzy If- rules with fuzzy sets in the antecedents and linear dynamics models in the consequent [6,7,8]. e overall model of the complex system is achieved by fuzzy interpolating these linear models through nonlinear fuzzy membership functions
The stability study of this class of systems has been usually based on the use of the Lyapunov direct method. e obtained stability conditions are in general given in terms of linear matrix inequalities (LMI), which can efficiently be solved by convex programming techniques [9,10,11]. e overall controller of the T-S fuzzy model used the parallel distributed compensation (PDC) approach which used multiple linear state feedback controllers corresponding to the local models via fuzzy rules [12, 13]
Summary
The fuzzy logic control has attracted rapidly growing attention from both the academic and industrial communities [1,2,3]. H∞ state feedback synthesis and reference model tracking control schemes are expanded to include nonlinear systems described as uncertain and disturbed the T-S fuzzy model by using the PPDC approach. We consider both the stability problem of satisfying the decay rate and the disturbance attenuation. (i) Compared with the existing results obtained with the normal PDC approach [9, 13, 22, 23, 28,29,30,31], our control design is carried out based on the T-S fuzzy model via the PPDC scheme, which can significantly reduce the number of parameters in PDC. A simulation example is considered in Section 4 to illustrate the merit of the designed H∞ controllers
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