| Recently, fuzzy control technology has been developing rapidly, and been approved as an effective method for solving the modeling and control problems of a variety of complex systems. The earlier design approaches of fuzzy controllers mainly relied on the experiences of the designer and lacked an efficient mathematical analysis of system performance. However, by using an analytical approach, many mature methods of traditional and modern control theories can be applied in the analysis and design of fuzzy control systems. Therefore, using analytical methods to anlayze and design a fuzzy contol system is an important approach to developing fuzzy control theory. In this dissertation, the analytical design and stability analysis methods of fuzzy controllers are systematically investigated, and applied to ship fin stabilizer control.Stability analysis and systematic design are two important issues in the study of fuzzy control theory. In this dissertation, the standard fuzzy partition (SFP) and two-overlapped fuzzy partition (TFP) are well defined by summarizing the common characteristics of premise variable membership functions of most fuzzy systems. The properties of fuzzy systems with SFP or TFP inputs are investigated in detail. A new method for stability analysis of Takagi-Sugeno (T-S) fuzzy control systems with SFP or TFP inputs by constructing a discontinuous piecewise Lyapunov function is proposed. The new condition makes full use of the structural information of the rule's promises, and only requires a common positive-definite matrix in each maximal overlapped-rules group to be found. It both relaxes the stability conditions and reduces the computation load in checking the stability of T-S fuzzy systems. Using the methods of parallel distributed compensation (PDC) and linear matrix inequalities (LMI), a new stability analysis approach for a closed-loop T-S fuzzy control system and systematic design methods of fuzzy state feedback controllers and output feedback controllers are presented.The interpolation models of typical single-input single-output (SISO) and double-input single-output (DISO) Mamdani fuzzy controllers are deduced, which can be extended to typical T-S fuzzy controllers. The input variables of typical Mamdani fuzzy controllers employ full-overlapped triangular normal membership functions, and their outputs employ singleton membership functions. From these interpolation models,some of the essential character of typical fuzzy controllers is revealed. The analytical interpolation models can be used to design and optimize this kind of fuzzy controller, and to develop a fast and precise control algorithm for practical use.In order to solve the problems which include "to design a fuzzy controller whose performance is better than conventional PID controllers", "the simplicity of fuzzy control" and "systematic design approach of fuzzy controllers", the TS-PID fuzzy controller is constructed by employing PID expressions in the rule's consequents of a T-S fuzzy controller. TS-PID controllers are a kind of composed contoller with wide application potential, and utilize the advantages of both fuzzy and PID controllers. The interpolation models of typical TS-PID fuzzy controllers are deduced in detail, and the essential characteristic of this class of fuzzy controller is further proven to be a nonlinear PID controller. The analytical models of typical TS-PID fuzzy controllers have great application potential in developing a fast and precise control algorithm in both practical use and optimal design. Using the passivity theorem, sufficient conditions for 10 stable closed-loop systems in which TS-PID fuzzy controllers are applied to several typical control plants are obtained. These conditions provide a new more simplified approach for the systematic design and stability analysis of TS-PID fuzzy controllers. In order to get an optimal or near-optimal performance, the full procedure of using genetic algorithms to design a TS-PID fuzzy controller was also investigated in detail.The fin stabilizer is an effective device widely used in reducing ship's rolling. At the present time, fm-angle-feedback-control and lift-feedback-control are two methods commonly adopted in fin stabilizer control systems. Conventional PID controllers are widely used in fin stabilizer control systems. However, the control effect of a conventional PID controller is limited since its parameters are always the same in the control process for all hydrodynamically environmental conditions. In this dissertation, fuzzy controllers were designed for the two control methods respectively, and the simulation results show that these fuzzy controllers are effective.(1) Based on the Conolly linear model of ship's rolling, the stability analysis and optimal design methods of TS-PID fuzzy controllers for the fin-angle-feedback fin stabilizer control systems were studied in this dissertation. The analytical model of typical TS-PID fuzzy controllers was used in design to solve the realtime problem ofcontrol algorithms. Using the passivity theorem, a sufficient condition of the 10 stable closed-loop system in which TS-PID fuzzy controllers are applied to ship fin stabilizer control is obtained. The genetic algorithm is used to optimize the parameters of a TS-PID fuzzy controller.(2) In lift-feedback ship fin stabilizer control systems, nonlinearity is mainly due to ship's rolling. In this dissertation, we firstly propose a T-S fuzzy model to approximate the nonlinear model of ship's rolling, then the fuzzy controller of a ship's lift-feedback-fin stabilizer is designed by using the method of PDC. The stability analysis and design approaches of T-S fuzzy control systems with SFP inputs are applied during the design process.Since fuzzy controllers have the advantages of easy application, high robustness, suitability to many nonlinear or uncertain systems, etc., they can be widely used in many process control applications of several fields including marine engineering. In this dissertation, to reinforce the practical engineering applicability, the stability analysis and design approaches were studied based on analytical methods. The results investigated in this dissertation can not only be used in ship's lift-feedback-fin stabilizer control systems, but also widely applied to other fields of ship motion and marine engineering.
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