Refinements of the Ziegler-Nichols tuning formula

The accuracy of the Ziegler-Nichols tuning formula is reviewed in the context of PID and PI autotuning. For PID autotuning, it is 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 is also 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 is 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 deadtime of the process. These heuristic refinements, when incorporated, will give appreciable improvement in the performance of autotuners