Control of Inverted Pendulum System with Single Input Interval Type-2 Fuzzy PD Controllers

Single input type-2 fuzzy controllers gain increasing popularity for different control problems. In this study, a single input type-2 (SIT2) fuzzy control system is introduced for the control of an inverted pendulum system. The control system consists of two SIT2 fuzzy PD (SIT2-FPD) controllers for the control of the cart position and the pendulum angle. The SIT2-FPD controller is constructed by cascading a single input fuzzy controller with a classical PD controller. In the design of SIT2-FPD controllers, three triangular interval type-2 membership functions are assigned for the input variable error, and three singleton membership functions are used to define the output variable. In order to show the control and robustness performance of the SIT2-FPD control system, simulation studies are performed for different operating conditions and the performance results are compared with the performance of a classical PD control system. The performance comparison results show that the SIT2 fuzzy control system exhibits better control and robustness performance than the classical PD control system.