Comparison of PDD1/2 and PDu Position Controls of a Second Order Linear System

Luca Bruzzone and Pietro Fanghella


Control, Simulation, Fractional calculus


This paper compares the application of the PDD1/2 and PDu fractional-order control schemes to position control of a purely inertial, second order system. The PDD1/2 control is a PD control with the addition of the half-derivative term, while the PDu scheme, with non-integer derivative, is the most common approach to fractional-order control synthesis. The comparison between PDD1/2 and PDu is performed using nondimensional variables and parameters for generality. Simulations analyse the dynamic behaviour of the closed-loop system for tunings of the two control schemes which are characterized by equal settling energy in case of unit step input. The results demonstrate that, with the considered hypotheses, the PDD1/2 control is more profitable than PD and PDu controls in improving the control readiness, with the drawback of a limited increase of the overshoot.

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