Design And Stability Analysis Of Fuzzy Control System Based On Granular Function

The intelligent control system is the heated topic in the controlling field.In this field,the fuzzy control plays an import role.The traditional math method can't describe the model about fuzziness and uncertainty,because its object is the accurate model.However,the appearance of fuzzy mathematics solves this problem well,and presents the theoretical basis for the fuzzy control field.Fuzzy control system depends on the experience of expert and a large number of experiments.Comparing with the traditional control,fuzzy control is applied to the controlled object which is difficult to give accurate mathematical modeling.Although the fuzzy control system has the very mature control theory foundation,and the mathematics foundation,but in the industrial control field,experiments still face the two problems.The first is rule explosion that is caused by too many fuzzy conditional statements,which is the main reason for the high cost of the fuzzy control chip.The second is that the fuzzy control system are unable to effectively carry out the stability analysis of fuzzy controller and the whole system.In this paper,a new fuzzy control method is proposed to solve the two problems mentioned above.And,for stability analysis of fuzzy controller,a new experimental method is presented.In the end,the paper puts forward the fuzzy rules block granulation.The new experimental scheme is put forward and used in the experiment of inverted pendulum.This paper put forward the granulation structure is applied to the fuzzy conditional statement,and the original fuzzy inference process of fuzzy control system is replaced by granular function.The mapping relationship is obtained by the fitting of the regular particle points to obtain an accurate response function that is obtained by human logic.Therefore,this control method is a new idea.For the newly proposed algorithm,the particle response function solves the rule explosion problems.The rule explosion problem caused by too many fuzzy rules in fuzzy control system can be solved well by the granular function.Because the fuzzy controller is now controlled by the particle function,the stability analysis can be carried out according to the feedback state.In this paper,the fuzzy control of water level simulation experiment and fuzzy control of inverted pendulum simulation experiment are separately carried out.In the water tank level simulation experiment,the traditional fuzzy control system is contrasted to 3 order,5 order response function control system experiment.The experiment shows that the controller of water tank level control system,improved by granular function can achieve equilibrium level in demand.In the inverted pendulum simulation experiment,the fuzzy control of inverted pendulum system,5 order response function of the inverted pendulum system,2 order response function of the inverted pendulum system and 1 order response function of the inverted pendulum system are respectively compared with each other.The results show that inverted pendulum system based on granular function has the same control effect with the one based on traditional fuzzy control system.It effectively reduces the complexity,and also solves the rule explosion problem and can implement stability analysis.The innovation of this paper can be summarized in three points: 1.accurate response function based on granular function is used in fuzzy control system to achieve control,so effectively reduce the complexity.2.the application of granular function in this experiment solves the rule explosion problem.3.a new method for stability analysis in fuzzy control system based on granular function is obtained in paper.