Fuzzy-logic control of an inverted pendulum on a cart

The inverted pendulum on a cart is an under actuated, unstable non-linear system that is used as a benchmarking problems in control theory. The non-linear nature of the system makes linear controllers, such as the proportional integral derivative (PID) controllers, possibly unfeasible as they only guarantee stability of a linear system. A fuzzy-logic controller provides many different stable controllers applicable to inverted pendulum on a cart. In this paper, the fuzzy parallel distributed compensation (PDC) controller is introduced and implemented on an unstable system, and the performance is demonstrated in MATLAB Simulink. The fuzzy PDC controller is dependent on the Takagi-Sugeno (TS) fuzzy model to obtain the state feedback gains required by solving the linear matrix inequalities (LMI). The LMI produced satisfactory results for all initial pendulum positions simulated even under uniformed disturbance. Our results have been compared against two other works to reveal the effectiveness of the proposed model.