PID Loop Tuning

Quick pick (TL;DR)

Do a bump test to get the process gain K, time constant τ and dead time θ (FOPDT model).
Then tune: e.g. Ziegler-Nichols open-loop PI gives Kc = 0.9τ/(K·θ), Ti = 3.33θ.
Use PI for flow & pressure (fast, noisy — no derivative); add derivative (PID) only on slow temperature loops.
The ratio θ/τ tells controllability — below ~0.2 is easy, above ~1 is hard (consider feedforward/dead-time compensation).

Step 1 — Identify the process

Parameter	From bump test	Meaning
K	ΔPV / ΔOP	Process gain
τ	63% response time	Speed
θ	Initial delay	Hardest part

Step 2 — Worked tuning

Flow loop: K 2.0, τ 40, θ 8

Z-N open-loop PI Kc = 0.9 · τ / (K · θ) Ti = 3.33 · θ Given K = 2.0 , τ = 40 s , θ = 8 s Step 1 — Controllability θ/τ = 8/40 = 0.20 → easy to control Step 2 — Gain Kc = 0.9 × 40 / (2.0 × 8) Kc = 36 / 16 = 2.25 Step 3 — Integral Ti = 3.33 × 8 = 26.6 s Answer → PI: Kc 2.25, Ti 26.6 s (no derivative)

Z-N is a starting point; θ/τ=0.2 = easy loop. PI for flow; add Td≈0.5θ on slow temp loops.

Step 3 — PI vs PID

Flow/pressure → PI only.
Temperature → PID.
Level → loose PI.
Anti-windup; feedforward for high dead time.

Ziegler-Nichols tuning calculator

PI & PID settings from K, τ, θ

Open-loop tuning from a bump test; θ/τ shows controllability.

Process gain K

τ (s)

θ (s)

Controller

Z-N = starting point; no derivative on noisy loops; high θ/τ needs feedforward.

Common mistakes

Derivative on noisy loops.
Tuning without measuring dead time.
Over-tight gain → oscillation.

Requisition & datasheet

Variable, K, τ, θ.
Mode, Kc, Ti, Td, method.

Frequently asked questions

What should I know about PID Loop Tuning?

Do a bump test to get the process gain K, time constant τ and dead time θ (FOPDT model). Then tune: e.g. Ziegler-Nichols open-loop PI gives Kc = 0.9τ/(K·θ), Ti = 3.33θ. Use PI for flow & pressure (fast, noisy — no derivative); add derivative (PID) only on slow temperature loops. The ratio θ/τ tells controllability — below ~0.2 is easy, above ~1 is hard (consider feedforward/dead-time compensation).

Which standards or codes apply?

ISA 5.1 (instrumentation symbols), Ziegler-Nichols & Cohen-Coon tuning rules, Lambda/IMC tuning, vendor DCS tuning guides.

Standards — ISA 5.1; Ziegler-Nichols; Cohen-Coon; IMC.