PID-type controller tuning for unstable first order plus dead time processes based on gain and phase margin specifications

The control of unstable first-order plus dead-time (UFOPDT) processes using proportional-integral (PI) and proportional-integral-differential (PID) type controllers is investigated in this brief. New tuning rules based on the exact satisfaction of gain and phase margin specifications are proposed. The tuning rules are given in the form of iterative algorithms, as well as in the form of accurate, analytical approximations. Moreover, several specific functions, related to the crossover frequencies of the Nyquist plot and to the feasible design specifications for a given process, are derived. These functions, which are particularly useful for the general design of PI- and PID-type controllers for UFOPDT processes are accurately approximated, in order to simplify the tuning procedure. With the proposed approximations, the tuning rules reported in this brief require relatively small computational effort and are particularly useful for online applications