Refinements of the Ziegler–Nichols tuning formula

TLDR

The Ziegler‑Nichols tuning formula’s accuracy is examined for PID and PI autotuning. The study aims to refine the formula for PID and PI autotuning by showing that set‑point weighting can reduce overshoot, is superior to conventional methods, and that the formula must be modified for undershoot and PI control. The refinements rely on using the process’s normalized gain or dead‑time to apply set‑point weighting and modify the tuning formula. Incorporating these heuristic refinements appreciably improves autotuner performance.

Abstract

The accuracy of the Ziegler-Nichols tuning formula is reviewed in the context of PID and PI autotuning. For PID autotuning, it will be shown that, for excessive overshoot in the set-point response, set-point weighting can reduce the overshoot to specified values, and the original Ziegler-Nichols tuning formula can be retained. It will also be shown that set-point weighting is superior to the conventional solution of reducing large overshoot by gain detuning or set-point filtering. However, for excessive set-point undershoot, the tuning formula will have to be modified. For PI autotuning, it will be shown that the Ziegler-Nichols tuning formula is inadequate and has to be completely revised. The application of set-point weighting and the modification of the tuning formula can be based simply on the knowledge of the normalised gain or normalised dead-time of the process. These heuristic refinements, when incorporated, will give appreciable improvement in the performance of autotuners.