Inversion formulae for the design of PIDF controllers

This paper introduces a set of closed-form formulae for the design of PIDF (i.e., PID + filter) controllers to exactly satisfy steady state requirements and standard frequency-domain specifications on the stability margins (i.e., phase and gain margins) and the gain crossover frequency. This design methodology is an extension of the so called Inversion Formulae method for the design of classical Lead, Lag, Notch and PI/PD/PID controllers. PIDF controllers are useful because, differently from standard PID controllers, they are described by a proper transfer function. In this paper we also show that the further degree of freedom introduced in the transfer function of the PIDF controller can be exploited to satisfy further specifications, compared to the classic PID controller.