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arXiv · 2606.22217

Monotonic, Minimum-Settling-Time PI Tuning for First-Order-Plus-Dead-Time Plants: A Tangency Characterization

Senol Gulgonul
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Abstract

This paper studies PI tuning of a first-order-plus-dead-time (FOTD) plant for the fastest strictly monotone (zero-overshoot) setpoint step response, with monotonicity imposed on the plant output only. The minimizer is shown to be neither the pole-zero cancellation design nor the multiple real dominant pole (MRDP) design. It is a non-cancellation point at which the closed loop carries a slow real mode of small residue together with a faster underdamped complex pair, with the controller zero placed near the dominant real pole. The analytical centerpiece is a single tangency identity, tan(omega tau_star + alpha) = (a - b)/omega, which states that the monotonicity boundary is the locus where the secondary complex mode just fails to drive the output slope below zero. From this identity the design reduces to nested scalar conditions, realized at three levels of fidelity: an explicit closed-form rule, an exact response-based reduction, and a simulation-free transcendental system whose only non-elementary step is a fourth-order polynomial root. Relative to the critically damped Lambert-W cancellation rule the design reduces the 2% settling time by 14 to 52 percent and lowers the load integrated absolute error by 5 to 38 percent. We report the full cost: for delay-dominated plants (T/L <= 0.55) the control stays one-pulse, so the design is itself admissible in Huba's sense and merely faster, but for larger lag ratios the control becomes two-pulse, and across the range the maximum sensitivity rises from 1.39 to between 1.44 and 1.62. The contribution is positioned not as a uniformly better tuning but as the exact characterization of a specific, well-defined operating point, with an honest multi-metric comparison against established rules.

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Senol Gulgonul. 2026-06-20. Monotonic, Minimum-Settling-Time PI Tuning for First-Order-Plus-Dead-Time Plants: A Tangency Characterization. https://arxiv.org/abs/2606.22217

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