MaximaLabsOpen app

Controller Auto-Tuning

Maps a first-order-plus-dead-time (FOPDT) process model to PID gains via three established open-loop tuning rules — Ziegler-Nichols, Cohen-Coon, and IMC/lambda tuning — computed deterministically, never guessed by the AI.

controltuningfopdtimc
Concept

Given a first-order-plus-dead-time (FOPDT) process model — gain K, time constant τ, dead time θ — three established open-loop tuning rules map it to PID gains. The AI may recommend a method or a λ value; the gains themselves are always computed deterministically here, never guessed by a model (principle #9).

The math
Show the governing equations
τ dydt=K u(t−θ)−y(the FOPDT model being tuned against)\tau\,\frac{dy}{dt} = K\,u(t-\theta) - y \quad \text{(the FOPDT model being tuned against)}
Ziegler-Nichols (1942) — classic, aggressive reaction-curve rules. Cohen-Coon (1953) — better for larger dead-time-to-lag ratios. IMC/lambda tuning (Rivera-Morari-Skogestad, 1986) — the robust modern default, with one knob (the closed-loop time constant λ) trading speed for robustness.
Execution
POST /api/dynamics/identify-fopdt   # fit K, tau, theta from step-test data
POST /api/dynamics/tune-pid         # map an FOPDT model -> Kc, tauI, tauD