New PID Tuning Method Guarantees Zero-Overshoot with Minimum Settling Time

Control systems engineer Senol Gulgonul has published a paper on arXiv detailing a unified, closed-form analytical method for tuning PI and PID controllers. The method applies to all-pole plants up to third order and achieves a strictly monotonic (zero-overshoot) step response while minimizing settling time. The design target is a binomial closed-loop transfer function of the form p^n/(s+p)^n, which inherently provides robust stability with margins dependent only on the order n. A key insight is that for minimum settling time, controller zeros must cancel with plant denominator factors, forcing the controller numerator to divide the plant denominator. This principle yields exact real-gained solutions for stable plants up to second order with PI and third order with PID controllers.

Gulgonul derives explicit gain formulas for various plant configurations: first-order plants (PI), second-order plants with real or complex poles (PI and PID), and third-order plants with three real poles or a real pole plus a complex pair (PID). The second-order PI case is treated fully as the lowest-order example. The monotonicity property guarantees Mt = 1, which implies Ms < 2, phase margin above 60°, and gain margin above 6 dB—tightening to universal constants for the binomial family. Numerical verification confirms the results. This work simplifies PID tuning for industrial applications, offering a direct path to stable, fast-responding control without overshoot.