Control of the cart pendulum system by using a fractional order PD controller

Abstract

This paper deals with stability problem of cart inverted pendulum controlled by a fractional order PD controller. Inverted pendulum is an underactuated mechanical system because it has one control input and two degrees of freedom. Mathematical model of cart pendulum system is derived and fractional order PD controller is introduced in order to stabilize it. Control strategy consists of two parts, a swing up controller and stabilizing controller. Problem of asymptotic stability of closed loop system is solved using the D decomposition approach. Stability regions in control parameters space are calculated using this method, and tuning of the fractional order controller can be carried out.