(A) new simple design methodology for fuzzy logic controllers and its stability analysis

Abstract

Since the fuzzy logic was first introduced by Lotfi A. Zadeh and its application to automatic control areas had been addressed by E. H. Mamdani, the fuzzy logic controller(FLC) has emerged as one of the most active and fruitful areas in the application of fuzzy set theory. In general, the FLC is suitable for many nontraditionally modelled industrial processes such as linguistically controlled devices and systems that 1) cannot be precisely described by mathematical formulations, 2) have significant unmodeled effects and uncertainties, and 3) even contain contradictory conditions. The FLC is also said to be superior to their corresponding linear controllers to control linear and nonlinear processes. In spite of many advantages of the fuzzy logic, the FLC has still some problems: It has many tuning parameters as follows: 1) Tuning of rules, 2) Tuning of membership functions, and 3) Tuning of scaling factors. Also, although the FLCs are succeeded in many practical applications, it does not attract popular attention to some control scientists because it has not been viewed as a rigorous science due to a lack of formal synthesis techniques such as stability analysis. And the FLC does not have the self adjusting capability of control parameters. In this thesis, above problems of the FLC are partially resolved. In most cases, FLCs use only the error and the change-of-error as fuzzy input variables regardless of the complexity of the controlled processes. These FLCs often generate a control input or an incremental control input. Such conventional FLCs are frequently suitable for simple second order plants. The case of complex higher order processes may require some more input variables. In this case, the FLC requires a huge number of control rules. Then the number of tuning parameters is greatly increased. And it makes difficult to establish control rules for the good control performance. Hence, most FLCs use only the error and the change-of-error as fuzzy input vari...