Experimental analysis of a fractional-order control applied to a second order linear system

This paper presents the application of a PDD^1/2 fractional order controller to a purely inertial second order system, with the aim of deepening the study of the half-derivative contribution on control performances, in particular on settling time and settling energy of a step response. An approximation of the half-derivative term is proposed for a discrete time version of the controller. The choice is justified by the results obtained by an analysis of order and sampling time influence on accuracy and computation time of a discrete-time fractional derivative. Afterwards, simulation results, all obtained in dimensionless form, are extended to the physical case by means of experimental tests on a rotary axis. In the end it is shown that the half-derivative approximation still allows to improve the system dynamics if compared with a conventional PD controller.