Direct and exact methods for the synthesis of discrete-time proportional–integral–derivative controllers

This study 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 phase and the gain margins, as well as the gain crossover frequency. The proposed technique has the advantage of avoiding trial-and-error procedures or approximations connected to an a posteriori discretisation. This method can also be implemented as a graphical design procedure in the Nyquist plane. The plot of suitable regions can be used to check a priori if the problem leads to feasible values of the PID parameters.