Tuning of PI controllers based on gain and phase margin specifications

The authors examine a class of tuning formula associated with the relay auto-tuning, cross correlation auto-tuning and other self-tuning PI/PID controllers. These methods measure the ultimate gain, ultimate period, simplified process model parameters e.g. gain, time constant and dead-time or some related frequency response data e.g. a point on the Nyquist curve. The estimates are then used in the tuning formulae. It has been found from extensive simulation that the modified Ziegler-Nichols formulae give good responses over a wide range of process dynamics. A more general approach is to use the combined phase and gain margins approach. However, the method to date could only achieve a compromise in phase and gain margins by designing to move the compensated Nyquist curve to pass through a specified design point. The performance of this tuning formula, however, is found to be too conservative especially when the dead time is large. The authors propose an analytical method to tune/design the PI controller to pass through two design points and the Nyquist curve as specified by separate gain margin (A_m) and phase margin