Ziegler-Nichols method

The Ziegler-Nichols method is a heuristic procedure for tuning a PID controller, a feedback loop that combines proportional, integral and derivative terms. It was developed by John G. Ziegler and Nathaniel B. Nichols. The operator first sets the integral and derivative gains to zero and then raises the proportional gain from zero until the output of the control loop shows stable, sustained oscillations. The gain at that point is called the ultimate gain, and the period of the oscillation is the ultimate period. A table of rules then converts these two measured numbers into the proportional, integral and derivative settings for the type of controller wanted. The classic settings give a quarter wave decay response, which suits disturbance rejection but produces an aggressive gain and noticeable overshoot. Where overshoot must be small or absent, a separate row of rules, labelled no overshoot, gives gentler settings. The method needs no model of the process, only experiments on the running loop.