PID Controller Simulator

About this tool

Drag the Kp, Ki, and Kd sliders to see exactly how each PID term reshapes a system's response to a step change in setpoint, redrawn live on the chart. The controller drives a fixed, generic second-order process — the same kind of textbook plant used to teach PID tuning — so you can isolate the effect of each gain without also having to account for a changing system.

Proportional (Kp) reacts to the current error and speeds up the response, but on its own it settles below the setpoint — a pure-P controller always leaves some steady-state error on this plant. Integral (Ki) accumulates past error over time and drives that steady-state error to zero, at the cost of extra overshoot and a slower approach if it's too aggressive. Derivative (Kd) reacts to the rate of change of the output (not the error, to avoid a "derivative kick" when the setpoint jumps) and damps oscillation, trading a bit of speed for a cleaner settle.

Frequently asked questions

What process is being controlled?

A fixed second-order transfer function, G(s) = 1 / (s² + 10s + 20) — a standard illustrative plant (equivalent to a mass-spring-damper system) used in many PID tuning tutorials. It's open-loop stable but, without integral action, a proportional-only controller can't fully eliminate steady-state error on it.

Why does the response start moving before Kp, Ki, or Kd are "big"?

The chart always simulates a unit step in setpoint (from 0 to 1) at t = 0, so you're seeing the closed-loop step response for whatever gains the sliders are set to — including the default starting values.

Why is derivative action based on the output instead of the error?

This is "derivative on measurement," the standard real-world implementation. Differentiating the error directly causes a huge instantaneous spike (a "derivative kick") the moment the setpoint changes, since the error itself jumps abruptly — differentiating the measured output instead avoids that spike while damping oscillation just as effectively.

What do overshoot, rise time, settling time, and steady-state error mean?

Overshoot is how far the output peaks above the final setpoint, as a percentage. Rise time is how long it takes to go from 10% to 90% of the setpoint. Settling time is when the output finally stays within ±2% of the setpoint for good. Steady-state error is the remaining gap between the output and the setpoint at the end of the simulated window.

Why does increasing Ki sometimes make things worse before they get better?

Integral action keeps accumulating error until it's driven to zero, which is great for eliminating offset but can overshoot and oscillate if it's too aggressive relative to Kp and Kd — this is the classic "PI without enough D" tuning tradeoff the sliders let you feel directly.