A New Method for PID Tuning Including Plants Without Ultimate Frequency

The classical relay feedback method for tuning proportional-integral-derivative (PID) controllers cannot be applied to plants whose Nyquist diagrams do not cross the negative real axis; these are customarily tuned based on the reaction curve experiment. In this brief, we propose a tuning method based on a modified relay feedback experiment. In this experiment, a transfer function of constant phase in an arbitrarily large range of frequencies is inserted in the loop. The proposed methodology thus unifies the Ziegler-Nichols-like tuning methods, by allowing PID tuning based on relay feedback for a class of plants without ultimate frequency.