On the use of inversion formulae for the synthesis of discrete PID controllers

Abstract

This paper presents a new set of formulae for the design of discrete proportional-integral-derivative (PID) controllers under requirements on steady-state performance and robustness specifications, such as the phase and the gain margins, as well as the gain crossover frequency. The proposed technique has the advantage of avoiding trial-anderror procedures or approximations connected to an a posteriori discretisation. This method can also be implemented as a graphical design procedure in the Nyquist plane.