PI and PID Tuning of Plants up to Third Order for a Monotonic Minimum Settling Time Solution

Summary

arXiv:2606.02868v1 Announce Type: new Abstract: A unified, closed-form analytical PI/PID tuning method is presented for all-pole plants up to third order that yields a strictly monotonic (zero-overshoot) step response with minimum settling time. The design target is the binomial closed loop p^n/(s+p)^n, which is monotonic with robustness depending only on the order n. Because adding a left-half-plane zero to a fixed pole pattern only slows the response, the minimum-settling solution requires the controller zeros to be cancelled, which forces the controller numerator to divide the plant denominator.