Control Track · Hands-on

The PID Tuning Trainer

You can read about P, I and D forever — tuning only clicks when you feel the loop fight back. This is a live closed-loop: a real first-order process with deadtime, controlled by a PID you tune with three sliders. Step the setpoint, kick it with a disturbance, and watch overshoot, settling and steady-state error move as you turn each knob. Break it on purpose, then make it beautiful.

📈 live loop🎚️ tune Kp·Ki·Kd💥 disturbance📐 Z–N method
01 · The three terms, fast

What each knob actually does

The controller looks at error = setpoint − process value, and sums three responses. Each has one job — and one failure mode if you overdo it.

🟦 P — Proportional (Kp): push in proportion to the present error. More Kp = faster & stronger, but too much = oscillation. P alone leaves a permanent offset.

🟩 I — Integral (Ki): accumulate past error until it's gone — this is what kills the offset. Too much = sluggish overshoot and windup.

🟨 D — Derivative (Kd): react to the rate of change — anticipate and damp. Calms overshoot, but amplifies noise, so it's used sparingly (often zero).

➕ Output = Kp·e + Ki·∫e + Kd·(de/dt), clamped to 0–100%. The art is balancing the three so the process reaches setpoint fast, flat and stable.

02 · The trainer

🎛️ Tune a live loop

The grey line is your setpoint; the orange line is the process value chasing it; the faint blue is the controller output. Drag the knobs and watch the response redraw live. Try a preset, then hit Step setpoint or Disturbance to test it.

present error → strength
past error → kills offset
rate → damps overshoot
target value
Overshoot
—
Settling
—
SS error
—
Verdict
—
Drag a knob or pick a preset. Watching how the orange line misbehaves teaches you more than any rule of thumb.
03 · The method

How to tune it on purpose

Don't twiddle randomly. The classic manual recipe gets you 90% there in minutes:

  1. Set Ki = 0, Kd = 0. Raise Kp until the loop just starts to oscillate steadily — note that gain.
  2. Back Kp off to about half that value. Now it's responsive but stable.
  3. Add Ki slowly until the steady-state offset disappears — but stop before overshoot grows.
  4. Add a little Kd only if you need to damp overshoot — and only if the signal isn't noisy.
  5. Test with a disturbance, not just a setpoint step. A loop tuned only for steps can be terrible at rejecting upsets.
  6. Re-check after any process change (load, temperature, product) — tuning is not "set once."

📐 Ziegler–Nichols formalises step 1: find the ultimate gain Ku (where it oscillates) and period Tu, then for a classic PID set Kp = 0.6·Ku, Ki = 1.2·Ku/Tu, Kd = 0.075·Ku·Tu. It's aggressive — a great starting point, rarely the final answer.

04 · The traps

Three gotchas that bite everyone

📈 Integral windup

When the output saturates (100%), the integral keeps piling up — so when you finally reach setpoint it massively overshoots. Fix: clamp the integral (anti-windup) when the output is maxed.

⚡ Derivative kick

A step change in setpoint makes de/dt spike, slamming the output. Fix: compute D on the process value, not the error ("derivative on measurement").

📻 Noise amplification

D multiplies high-frequency noise into a jittery output that wears valves. Fix: filter the input or keep Kd small/zero on noisy signals.

05 · Field kit

PID in one screen

  1. error = SP − PV · out = Kp·e + Ki·∫e + Kd·(de/dt)
  2. P = speed/strength · I = removes offset · D = damps (anticipates)
  3. Tune order: Kp first, then Ki, then a little Kd.
  4. P-only always leaves an offset; that's the I term's job.
  5. Clamp the integral (anti-windup) when output saturates.
  6. Take the derivative on PV, not error, to avoid set-point kick.
  7. Keep Kd small or zero on noisy signals; filter the input.
  8. Always test disturbance rejection, not just setpoint steps.