Original title: Model-Free PID Tuning by Step-Response Inspection
Daniel Pachner, Pavel Otta, Jiří Dostál, Vladimír Havlena · September 2026
Factories use PID controllers to keep systems steady, like holding a constant temperature. Engineers still tune these controllers by hand: they change a target setting, watch the system react, and adjust the knobs. This paper introduces an algorithm named SPIN that automates this manual task. SPIN watches a single routine step response and creates three special motion graphs called phase portraits from the error signal. It counts how many times the curve loops around its stopping point on each graph. These loop counts are independent of step size and time, and they reveal which control band rings too much. A rule then cuts the gain of the faulty band and raises the others. The process uses no math model, works during normal operation, and can safely start from unstable settings. Tests show it drives controllers right to the edge of well-damped behavior while letting operators see every choice.
Imagine adjusting the water temperature in a shower. You nudge the handle, wait, and watch whether the water overshoots and swings back and forth. If it swings a lot, you turn the handle down a bit; if it barely moves, you turn it up. Now suppose you had three separate handles — one for hot, one for cold, one for pressure — and each swing pattern told you which handle was causing the rocking. In this paper the method watches one reaction, counts how many times the temperature winds around the target for each of the three handles, and turns down only the handle that is clearly causing the rocking while gently raising the others.
PID loops are everywhere in factories, and most are still tuned by hand. SPIN automates the exact step-and-look procedure, so a loop can be retuned while it keeps running, with no model and no optimization. That means less downtime and tuning decisions an operator can actually see.
The abstract doesn't say how sensitive SPIN is to the fixed step size and dimensionless constants used in validation. It also doesn't report comparisons with other tuning methods or proof of global optimality. The method's assumptions — stable, self-regulating process with gain and phase falling with frequency, and a controller with integral action — define its scope.
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Model-Free PID Tuning by Step-Response Inspection — Daniel Pachner, Pavel Otta, Jiří Dostál et al.
Abstract licence: CC0
Explanation generated by Synthesis from the abstract — it is not the original paper. This is a preprint, so it hasn't necessarily been peer reviewed.