Research On Fuzzy Control Algorithm Based On Granular Function

Fuzzy control is an important application of fuzzy information theory in the field of control, and it is the main method in the field of intelligent control. The method of fuzzy control is to rely on imitation of expert control experience, the fuzzy conditional statements instead of fuzzy rules. The mapping relation of the control system is represented by the method of language description, which makes the system has strong robustness and plays a very good control in the nonlinear and time varying systems. However, fuzzy control still faces two problems: The first, it is too difficult to realize the more fuzzy rules of high dimensional fuzzy controller. The second, in order to simplify the fuzzy control algorithm, currently we can only eliminate the defuzzification step in the process of fuzzy control. The fuzzification step still cannot be eliminated.This paper proposes a new algorithm to improve the problems in the two aspects mentioned above.This paper combined with the granular computing theory and fuzzy information granulation method put forward the concept of granular function. Several representation methods of granular function are defined. From the point view of granular function, this paper showed the essence of the fuzzy control is the realization control of the response function which is the granular function constraint of satisfy human experience the response function of the control. The interpolation mechanism of single input single output and double input single output fuzzy controller is proved by the formula. Meanwhile, this paper point out the control system model of fuzzy control algorithm based on granular function.The main idea of this algorithm is as follows: The fuzzy input and fuzzy output for granulating get the fuzzy information granule. The mapping relationship of grain sample points is obtained by human experience to fit out the granular function. Recording a function mapping relationship by tracing point method fit out a function. This function as the point response function of the fuzzy controller is used to control. The original source of the point response function is dependent on human control experience. This kind of control algorithm belongs to the fuzzy control algorithm which does not use the fuzzy logic.This algorithm has the following advantages: first, the point response function can replace the high dimensional fuzzy controller to control. The result solve the problem that high dimensional fuzzy controller is too difficult to be modeled. And it can avoid the “fuzzy rules explosion”. Second, Mamdani fuzzy control system requires the steps of fuzzification and defuzzification, T-S fuzzy control system eliminates defuzzification in the process of control. It still need the step of fuzzification. The fuzzy control system model designed by this algorithm can eliminates fuzzification and defuzzification step in the process of fuzzy control, greatly simplified the process of fuzzy control. Third, stability analysis is always a major problem for fuzzy control system. A point function as the response function of the fuzzy control system will contribute to the stability analysis of fuzzy control system.To analysis the simulate results of the single inverted pendulum, the fuzzy control algorithm based on granular function has a certain control effect. When the maximum term of the point response function is 2, inverted pendulum system in about 8 seconds reach the balance, when the maximum term of the point response function is 3, as with the series of fuzzy control, reach balance in about 4 seconds. When the maximum term of the point response function is 4, inverted pendulum system in about 3.5 seconds reach the balance. Therefore, the series of fuzzy algorithm and traditional fuzzy control function of the particle control algorithm based on the comparison superiority, obtained by this algorithm point response function. The highest number of items it is higher, the better the effect of the control system.