Study On Petri Net Modeling And Stability Of Fuzzy Control Systems

The stability is one of the most important performance properties of controlsystems. Therefore, during analyzing and constructing a fuzzy control system, thedesigner is firstly concerned with the investigation of the stability of the system,because a control system that is unstable can not be applied in practice. It is difficult toanalyze the stability of fuzzy control systems. This is because these systems areessentially nonlinear. The construction and stability analysis of fuzzy control systemshave always been an important subject of research on fuzzy control theory, manyscholars have done a lot of work in this area, and have got a number of theoreticalresearch results, but it has not yet formed a complete theoretical system, as well asmanytheoreticalissuesremaintobefurtherstudied.Since Petri nets can be used to represent not only the flow of control flow but alsothe flow of data, these make it possible to analyze the stability of the fuzzy controlsystems. In this stability analysis, all transitions in the Petri nets have clearcorrespondences with actions of the controller and the controlled object. The behaviorofthecontrolsystemiseasytounderstand.This paper firstly introduces the basics of fuzzy control and Petri nets; then it usesPetri nets as a fuzzycontrol system modeling tools, and gives modeling methods of thefuzzycontrollerandstabilityanalysistheoremofthefuzzycontrolsystems basedonthePetri nets model. The necessaryand sufficient conditions under which the fuzzycontrolsystem is stable were derived by applying the Petri nets model. Finally, The Petri netmodels of the fuzzycontrol systems of balancing an inverted pendulum, controlling thecurrent in a circuit, and controlling a two-order object have been built.The simulationanalysis is given to verify Petri net Modeling and stability theory of fuzzy controlsystems, and the simulation results demonstrate the validity of modeling methods andstabilitytheorempresentedinthispaper.