Controlling of inverted pendulum system by using PI-PD controller

Inverted pendulum is one of the most common benchmarks used in areas of control engineering and robotics. The inverted pendulum system is a well-known example of singleinput multiple-output (SIMO) system in the literature. In this study, modelling of a cart-inverted pendulum system and controlling it by using PI-PD controller were carried out. The PI-PD controller is a type of controller that gives better results than PID controller for controlling of integrating or unstable systems. In the study done, the system was modeled by using both physical laws and Matlab system identification tool. The transfer functions obtained for pendulum angle and cart position by using the Matlab system identification tool are lower order than those obtained by using physical laws. Therefore, the transfer functions found by using the Matlab system identification tool were used in controller design. In the cart-inverted pendulum system, the transfer function of the cart position has integrator and the transfer function of the pendulum angle in the upright position (inverted pendulum) is unstable. The tuning parameters of the PI-PD controllers used for balancing the pendulum in the upright position and controlling the cart position were obtained with the standard form approach. It was demonstrated in both pendulum angle and cart position real time implementation results that the PI-PD controller is better than the PID controller for controlling the cart-inverted pendulum system.