PID Controller Simulator
A PID tuning bench in your browser. Pick a process: cruise control, a water tank, an oven with dead time, a hovering drone or a DC motor. Then drag the proportional, integral and derivative gains and watch the closed loop respond live: setpoint, process variable and controller output on a scrolling chart, with the P, I and D contributions split out. Step the setpoint or hit the plant with a disturbance (a hill, an open oven door, a gust of wind) and read rise time, overshoot, settling time and steady-state error as they happen. Toggle actuator limits, integral anti-windup, derivative filtering and sensor noise to see why real controllers need them, or let the relay auto-tuner find the ultimate gain and apply Ziegler–Nichols settings for you.
Runs 100% in your browser — simulations are computed locally on your device.
Notes
- The controller is the textbook parallel form u = Kp·e + Ki·∫e dt + Kd·de/dt, evaluated every simulation step; the processes are small differential equations integrated with fourth-order Runge–Kutta.
- Proportional gain alone leaves a steady-state error on most processes; the integral term removes it but adds overshoot, and the derivative term damps the swing: the trade-off every tuning rule balances.
- Auto-tune runs an Åström–Hägglund relay experiment to find the ultimate gain Ku and period Tu, then applies the classic Ziegler–Nichols table (Kp = 0.6·Ku, Ti = Tu/2, Td = Tu/8): a starting point that is usually on the aggressive side.
- Runs 100% in your browser — simulations are computed locally on your device.
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