Refinements of the Ziegler–Nichols tuning formula

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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.

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