| Summary: | 博士 === 國立中央大學 === 電機工程研究所 === 93 === In this dissertation, several novel Takagi-Sugeno (T-S) fuzzy control approaches are developed for nonlinear control problems. These design approaches can be separated into two parts: (i) Parallel Distribution Compensation (PDC) design and (ii) Fuzzy Region Compensation (FRC) one.
The first type of T-S fuzzy control approach is developed for single input fuzzy control systems, in which all sub-models are represented as a controllability canonical form. The controller structure is based on the PDC control structure and the synthesis is derived from the covariance control techniques. Unfortunately, these state feedback designs are very difficult to deal with the static output feedback fuzzy control problems because the extra constraints or assumptions have to be attached. To overcome this problem, this dissertation proposes the mixed GA/LMI algorithm, which combines a standard Genetic Algorithm (GA) with LMI solver.
Even if PDC-based design approaches are very popular and ripe, it still has the following serious disadvantages when the fuzzy controller involving many IF-THEN rules: (i) The design result is difficult to implement with some simple hardware or cheap microcontroller. (ii) The total number of Lyapunov stability conditions is rapidly increased. (iii) The modeling errors between a T-S fuzzy model and a nonlinear model could result in the instability or undesired performances when applying the T-S fuzzy controller to the nonlinear models.
To improve the above problems, the FRC control structure is developed in this dissertation. The design idea is to partition the fuzzy model into several regions, and each region is redefined as a polytopic model. In this dissertation, this kind of fuzzy model is named T-S fuzzy region model or TSFRM for short. The proposed fuzzy controller is called T-S fuzzy region controller (TSFRC), in which the controller rule has to stabilize the polytopic model of the fuzzy region and the original nonlinear model is asymptotically stable. The stability analysis and control synthesis are derived from Lyapunov stability criterion, which is considered the robust compensation and is expressed in terms of Linear Matrix Inequalities (LMIs). Comparing with PDC-based designs, TSFRC is easy to design and to implement with simple hardware or a cheap microcontroller. Even if the total number of controller rules of TSFRC is reduced, TSFRC is able to provide competent performances as well as PDC-based designs. By combining the region-based control structure and GA/LMI algorithm, we further shows that the proposed ideas in the field of T-S fuzzy control can be applied to design the static output feedback robust control problems.
It should be noted that the merit of this dissertation is to provide simple design procedures and realizable solutions for state and static output feedback designs when the original T-S fuzzy model is complicated. From the synthesis point of view, these design approaches can deal with various performance constraints without complex mathematical derivations. From the implementation point of view, the design results can be implemented with simple hardware or a cheap microcontroller.
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