PID Tuner

Interactive closed-loop simulation with auto-tuning. Adjust PID gains and visualize step response in real time.

PID Tuning and Simulation

Interactive PID tuning and process control simulations. Adjust parameters in real time and visualize step responses and tuning rules.

PID Tuner — Closed-Loop Step Response

Process Output Setpoint Control Output

Process (FOLPD)

Gain K: 2.0

Time Constant T (s): 5.0

Dead Time L (s): 1.0

PID Parameters

Kp: 2.50

Ki: 0.50

Ti (s): 5.00

Kd: 1.25

Td (s): 0.50

Derivative Filter τd (s): 0.10

PID Controller Equations

Time-constant form (ISA / PID standard):

$$ u(t) = K_p \Bigl[ e(t) + \frac{1}{T_i}\!\int_0^t e(\tau)\,d\tau + T_d\,\frac{de}{dt} \Bigr] $$

Kp = proportional gain

Ti = integral time constant (s)

Td = derivative time constant (s)

Standard gain form:

$$ u(t) = K_p\,e(t) + K_i\!\int_0^t e(\tau)\,d\tau + K_d\,\frac{de}{dt} $$

Ki = Kp / Ti (integral gain)

Kd = Kp · Td (derivative gain)

Implementation: This simulator uses the standard gain form with anti-windup, derivative-on-measurement, and first-order derivative filtering (τd). See the relay-feedback tutorial → for derivation.

IMC Closed-Loop Time Constant τc (s): 1.0 (Smaller = faster/more aggressive; Larger = slower/more robust)

New to PID tuning? Read the Getting Started Tutorial →