Analytical And Limiting Structures Of Typical Fuzzy Controllers

The analytical and limiting structures of fuzzy controllers is an important research issue,because it can reveal the essential character of fuzzy controllers and the relationship between fuzzy controllers and classical PID(Proportion Integral Derivative) controllers. It makes the fuzzy controllers more comprehensive and operable in practice. However, the existing achievements accompany with this issue all are based on Single-Implication algorithm(single-I for short) for fuzzy inference. This algorithm uses another compound algorithm, and deviates from the framework of the semantic implication. specially, the single-implication algorithm is not a reductive method, so it can not represent the relationship of the rules. These reasons make the results obtained by this method not the best and also make the understanding to fuzzy controllers difficult to deepen through this method. At the same time, this method needs the membership function using the full overlap, triangular, uniform distribution. Consequently, all fuzzy rules have to share the same importance degree. This is not true in practice. In order to overcome this problem, the full implication triple I algorithm is used in fuzzy controllers as a fuzzy inference method. Triple I algorithm based on fuzzy logic has a strong generalized ability and reductive ability, so it has achieved remarkable results. However, so far the triple I algorithm can not contribute to the analytical and limiting structures research. Thus this paper focus on this research.The main contribution of this paper is as follows:1) In the framework of single-I algorithm, analytical and limiting structures of the typical controllers with different fuzzy rules with different membership are studied. The obtained results show that, the output response of fuzzy controllers with single-input and single-output is a section of a P-regulator; the output response of fuzzy controllers with two-input and single-output is slices of a PD (or PI)- regulator.2) The response characteristics obtained by triple I algorithm of fuzzy controllers with single-input single-output or two-input single-output are also researched. On this basis a new fuzzy controller was proposed in this paper. The analytical and limiting structures of the new controller are studied by triple I algorithm. The conclusion show: a typical single-input single-output fuzzy controller with countable rules is equivalent to a global two-dimensional multi-valued relay and a local nonlinear PI controller. 3) Using triple I algorithm to approximate the fuzzy system through simulation examples. The simulations on two-dimensional function show that the new fuzzy controller having good performance and qualities are confirmed.