PDD1/2 Control of Purely Inertial Systems: Nondimensional Analysis of the Ramp Response

Luca Bruzzone and Giorgio Bozzini


Control, Simulation, fractional calculus, PDD1/2 control


The paper discusses the ramp response of a second-order (purely inertial) linear system controlled by means of a fractional-order PDD1/2 scheme. The PDD1/2 is an extension of the classical PD scheme, characterized by the introduction of the half derivative term: a third gain multiplies the half-derivative of the error. As shown in previous works, in case of step response the proper combination of the half-derivative and derivative terms reduces the settling time under the conditions of finite control output and null overshoot. In the present paper the ramp response of the system, tuned using the same criterion, is analyzed, exploiting a nondimensional approach for the sake of generality. The results show that the PDD1/2 control reduces the settling time with respect to the PD scheme also in case of ramp setpoint.

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