Single Input General Type-2 Fuzzy PD Controller for Ball and Beam System

The footprint of uncertainty for a general type-2 fuzzy (GT2) system consist of type-1 sets. Consequently, the GT2 system is more adept at handling higher-order uncertainties, disturbances, and parameter uncertainties compared to the interval type-2 fuzzy (IT2) system. In this study, we design a single-input general type-2 fuzzy PD (SGT2-FPD) controller for a ball and beam system. The SGT2-FPD controller integrates the conventional PD controller with the GT2 fuzzy system. In the design of the SGT2-FPD controller, three triangular general type-2 membership functions are employed for the input variable, while three singleton membership functions are utilized for the output variable. The performance of the SGT2-FPD controller is evaluated against the single-input interval type-2 fuzzy PD (SIT2-FPD) controller and the conventional PD controller under various conditions, including nominal conditions, disturbances, and parameter uncertainties. Simulation results indicate that the SGT2-FPD controller outperforms other controllers, demonstrating superior robustness.