Fuzzy control is one of the important branches of intelligent control, and so far it has been the advanced international focus. As the essential part of fuzzy control systems, the research on fuzzy controllers is soundly meaningful both in theory and in practice. In this paper, new structures of fuzzy controllers have been studied in detail. The main work can be concluded in the following two aspects: 1. The paper investigates into the features of one-to-many mapping fuzzy PID controllers. This kind of controllers, possessing the merits of fuzzy logic control and PID control, has simple structure and clear-cut physical meaning. Furthermore, it eliminates common problems build-in the popularly used fuzzy controllers such as rule explosion, gain dependency. The proposed fuzzy controller is compared with others through various simulation experiments. Simulation results state that under the same condition, the proposed controller can obtain more satisfactory results than the others. This is because the suggested controller can adjust its control gain individually; thus it can produce more flexible nonlinear output than others. The simulation results also prove that a simple method does not mean it can not achieve the best outcome. If the parameters and rules can be adjusted effectively, this method can lead to the best result as well. Meanwhile, the Simple Genetic Algorithm is modified to search optimum in simulations. The partitions of parameter space and variable mutation rate have been applied to the procedure. Simulation result proves that this method is effective to avoid being trapped into the local optimum. 2. This paper extends the logical equivalent relation between the Intersection-Rule Configuration (IRC) and Union-Rule Configuration (URC) to nonlinear equivalent relation. The URC approach proposed by Combs and Andrews is very useful to lessen the combinatorial rule explosion difficulties of fuzzy systems. Their research is focused on the logical equivalency between the two methods. However, the logical equivalency is not sufficient to produce an identical relationship from the perspective of fuzzy systems' function, as a universal approximator. Stimulated by this thought, this paper studies this issue and proposes the sufficient condition for the existence of nonlinear identical transition and gives out the proof as well. The research also discovers that ingeneral, there does not exist a nonlinearly equivalent transition of fuzzy systems from the IRC to URC if other types of inference schemes are used. Thus the research on IRC controllers is still meaningful and necessary.
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