State Space Approach for Modelling of Fuzzy Control System

Abstract

Fuzzy modelling of dynamical systems provides a practical application in handling real-world problems. In this paper, the state space approach, which is based on the Takagi-Sugeno (TS) fuzzy model, is applied to solve a nonlinear control system. For this purpose, the state-space representation is considered, the fuzzy variables are defined and the fuzzification is employed to convert the nonlinear terms of the system, which is the crisp input, into fuzzy values. Then, the triangular membership functions are introduced to establish a set of fuzzy rules. On this basis, the fuzzy inference process is implemented in the system for which the related subsystems are constructed. Accordingly, the TS fuzzy controller is designed so that the solution of these subsystems can be obtained properly. After this, the defuzzification is addressed to convert the fuzzy values into the crisp output. For illustration, the rotary inverted pendulum and Rikitake system are studied. These systems are the nonlinear control examples in engineering studies. From the simulation results, it is noticed that the TS fuzzy controller provides a satisfactory result to the state trajectories for both nonlinear control systems. In conclusion, the efficiency of the TS fuzzy modelling in managing nonlinear control systems is verified apparently.