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PID Controller Tuner — Live Step Response, Overshoot & Stability

A real PID loop, not an animation of one. Your gains drive an actual second-order plant G(s) = K/(τ²s² + 2ζτs + 1) integrated step by step, with derivative on measurement so a setpoint change produces no derivative kick, actuator saturation with conditional-integration anti-windup, and optional dead time. Overshoot, 2% settling time, 10–90% rise time, steady-state error and IAE are all measured from the resulting trajectory. The stability verdict is the exact Routh–Hurwitz criterion for this loop's characteristic polynomial — so when it says your gains are unstable, that is a theorem about your numbers, not a guess.

How to use PID Controller Tuner — Live Step Response & Stability Check

  1. Start from a preset — P only, PI, PID balanced, or deliberately too aggressive.
  2. Drag Kp, Ki and Kd and watch overshoot and settling time respond.
  3. Add dead time and see how quickly a good tuning falls apart.
  4. Tighten the actuator limit and toggle anti-windup to compare.

Frequently asked questions

Why does proportional-only control never reach the setpoint?
Because the loop settles exactly where the remaining error is big enough to produce the output you need — remove the error and you remove the drive. The offset lands on 1/(1 + Kp·K), so Kp = 4 leaves 20%. Raising Kp shrinks it without ever eliminating it, which is precisely why integral action exists: the integrator keeps accumulating until the error is genuinely zero.
What does the derivative term actually buy me?
Damping. D responds to how fast the process value is moving rather than how far off it is, so it starts braking before the setpoint is reached. Load the PID balanced preset and set Kd to 0: overshoot roughly quadruples on this plant. The cost is noise sensitivity, since differentiating a noisy measurement amplifies the noise — which is why real controllers filter the derivative.
What is integral windup, and what does anti-windup do?
When the actuator is saturated the error persists even though the controller cannot push any harder, so the integrator keeps accumulating a correction that has nowhere to go. When the output finally arrives, that stored-up integral drives a large overshoot. Anti-windup freezes the integrator while saturated and pushing further into the limit. Toggle it off with a tight actuator limit and overshoot appears where there was none: on the PID balanced preset at ±1.5 it goes from 0% to about 32%, and settling time nearly doubles.
How is the stability verdict computed?
For this plant the closed-loop characteristic polynomial is τ²s³ + (2ζτ + K·Kd)s² + (1 + K·Kp)s + K·Ki, and the Routh–Hurwitz condition reduces to (2ζτ + K·Kd)(1 + K·Kp) > τ²·K·Ki. The inequality with your current numbers is shown on the chart. It was checked against the simulation across a grid of gains and agreed in every case.
My unstable gains still show a bounded oscillation — why?
Because the actuator limit is holding it in. A linearly unstable loop with saturation settles into a limit cycle: a sustained oscillation of fixed amplitude that never decays no matter how long you wait. The tool says so explicitly when your gains fail the Routh test, because a bounded-looking trace is easy to mistake for a slow transient.
Why does dead time ruin a tuning that worked?
Every correction is computed from stale information, so it arrives out of phase with the error it was meant to cancel and can reinforce the oscillation instead. Transport lag is why real plants — long pipes, thermal masses, network round trips — need far more conservative gains than an ideal model suggests.

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