D-decomposition technique for stabilization of Furuta pendulum: fractional approach

Abstract

In this paper, the stability problem of Furuta pendulum controlled by the fractional order PD controller is presented. A mathematical model of rotational inverted pendulum is derived and the fractional order PD controller is introduced in order to stabilize the same. The problem of asymptotic stability of a closed loop system is solved using the D-decomposition approach. On the basis of this method, analytical forms expressing the boundaries of stability regions in the parameters space have been determined. The D-decomposition method is investigated for linear fractional order systems and for the case of linear parameter dependence. In addition, some results for the case of nonlinear parameter dependence are presented. An example is given and tests are made in order to confirm that stability domains have been well calculated. When the stability regions have been determined, tuning of the fractional order PD controller can be carried out.