| Fuzzy control which is based on fuzzy set and fuzzy logic is an important branch ofintelligent control. Fuzzy control is effective to deal with the systems which are nonlinear,complicable and vaiable. Variable universe fuzzy control is a current research focuse in thefield of fuzzy control. With the adjustment of a group of nonlinear contraction-expansionfactors, the domain of fuzzy control can adaptively change with error to achieve highadaptivity. Practice results shows that the contraction-expansion factors play an importantrole in the variable universe fuzzy controller, not only affect the dynamic quality ofcontrol system, but also affect the stability of the control system and approximation ofcontroller. Therefore, the study of contraction-expansion factors has a certain significanceof variable universe fuzzy control.Combine the variable universe fuzzy controller’s features and its theoretical researchstatus. The following four works are discussed in this paper:(1)An improved function-type contraction-expansion factor is designed in this paper.Optimization criterion rules of contraction-expansion factor are designed by analyzing thechanging relationship between the input signals of fuzzy controller andcontraction-expansion factor. On this basis, an improved contraction-expansion factor isdesigned to optimize the structure and improve the control quality of the system.(2) Based on Lyapunov stability theory, the stability of variable universe fuzzy controlsystem with designed contraction-expansion factor is proved. Firstly, variable universefuzzy control system of a class of nonlinear dynamic object is constructed; Then, thedesign method of variable universe fuzzy control system is obtained based onLyapunov stability analysis method; Finally, the simulation results show that the design ofvariable universe fuzzy control method can effectively improve system stability.(3) The universal approximation and convergence of variable universe controller with improved contraction-expansion factor is proved in this paper. Firstly, from theperspective of a universal approximation, this kind of fuzzy controller can approximateany nonlinear continuous function in arbitrary precision. Which explain the reason of highaccuracy of variable universe fuzzy controller from the mathematical point of view. Then,the influence of membership function’s shape to controller’s approximation is discussed.The conditions to be met in dividing the domain are obtained according to theapproximation error sufficient condition for convergence. Finally, the simulation resultsshow the validity of the conclusions.(4) The designed variable universe fuzzy controller with improvedcontraction-expansion factor is applied in servo control of four wheels smart car. Theexperiment results demonstrate the effectiveness of the designed controller by comparingnormal fuzzy controller and PD controller. |
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