Stabilization of the cart pendulum system by fractional order control with experimental realization

Abstract

This paper deals with stability problem of cart inverted pendulum system controlled by a fractional order controller. Inverted pendulum is an underactuated mechanical system with one control input and two degrees of freedom. Detailed mathematical model of pendulum is derived using the Rodriguez method. Stabilization of pendulum around its unstable equilibrium point is achieved by using the fractional order PDα controller, in combination with partial feedback linearization technique. Since fractional order control law includes non-rational functions, an efficient method for numerical evaluation of this type of functions is used in this paper. The performance of the proposed method is demonstrated with experimental verification of the stabilization control of the cart pendulum system.