Research On TS Fuzzy Model Based Simulation Of Double Inverted Pendulum System

The representation and control of the complicated nonlinear system has been one of the troubles in the realm of control theory all along. As an approach to describe and control the system, the fuzzy logic theory has been the common concerns of people. This paper introduces the Takagi-Sugeno(TS) fuzzy model based modeling and controller design theory of the nonlinear system. At first we introduce all kinds of TS model and their characteristic of approximation to arbitrary continuous function, which allows TS model approximate any physical nonlinear system within arbitrary accuracy. Then we introduce how to identify the TS model from sample data using fuzzy clustering algorithm and equivalent feedforward neural network. For identified first order TS model, we adopt a Sugeno type controller and a universal control design scheme which guarantees the stability of closed-loop system. And for identified statespace TS model, we utilize the parallel distributed compensate(PDC) technique to obtain a sufficient condition for the stability of closed-loop system, and further depict the latest research on the issue, for example, the relaxed stability condition and control scheme satisfying decay rate based on it. In the case of fluctuant parameter, a guaranteed cost control scheme is introduced which guarantees a minimum cost and robustness. When applying to the predictive control, a detailed realization of TS model based predictive control algorithm is proposed. In the end, a simulation of double inverted pendulum system demonstrates the performance of fuzzy modeling and variable control scheme.