Tuning of fractional PID controllers with Ziegler–Nichols-type rules

In this paper two sets of tuning rules for fractional PIDs are presented. These rules are quadratic and require the same plant time–response data used by the first Ziegler–Nichols tuning rule for (usual, integer) PIDs. Hence no model for the plant to control is needed—only an S-shaped step response is. Even if a model is known rules quickly provide a starting point for fine tuning. Results compare well with those obtained with rule-tuned integer PIDs.