Optimized fuzzy PDC controller for nonlinear systems with T-S model mismatch

In this paper, a heuristic method based on Genetic Algorithms (GA) is proposed to improve the performance of Fuzzy Logic Controllers (FLCs) designed for Takagi-Sugeno (T-S) model of nonlinear plants by Parallel Distributed Compensation (PDC) technique. Generally, T-S models might not represent the dynamics of nonlinear plants accurately. Due to this mismatch, sometimes the response of the controlled nonlinear plant is not as desirable as the response of the corresponding T-S model controlled by the same FLC. Despite the fact that there is a flurry of research on the stability of FLCs applied to T-S model of nonlinear systems, the stability matters of FLCs applied to nonlinear systems is still a challenge. It is obvious that the performance of FLCs is entirely affected by the characteristics of membership functions. Thus, by tuning the type or parameters of fuzzy controller's membership functions using GA, the drawbacks caused by model mismatch can be decreased. In fact, the proposed method concerns the applicability of fuzzy PDC controllers to nonlinear plants and does not confide itself to dealing with T-S models. Thus, the improved fuzzy PDC controller is a fine-tuned PDC controller that can compensate the nonlinear plant as well as the corresponding T-S model. In order to verify the introduced strategy, the problem of balancing and swing up of an inverted pendulum on a cart is considered as a nonlinear case study. The simulation results demonstrate the effectiveness of the improved PDC.