Manual PID Tuner and Simulator
Free-form closed-loop simulation for any process model. Pick FOLPD, SOPDT, or an arbitrary transfer function, dial in PID gains manually, and watch the step response and Bode plot update in real time. No auto-tuning — just explore.
Closed-Loop Setpoint Step Response
Process Output Setpoint Control Output
Closed-Loop Disturbance Step Response
Unit step disturbance d = 1 at process input, setpoint = 0.
Process Output y(t) Control Output u(t)
Open-Loop Bode Plot
Bandwidth ωgc
—
rad/s
Phase Margin
—
degrees
Gain Margin
—
dB
Process Model
PID Parameters
Plant Transfer Function
General form (FOLPD):
$$G(s) = \frac{K \, e^{-L s}}{T \, s + 1}$$
K = process gain
T = time constant (s)
L = dead time (s)
Current model:
DC gain = 2.00
Rise time (≈ 2.2T) ≈ 11.0 s
Controllability ratio L/T = 0.20
PID Controller Equations — Standard (Parallel) Form
Transfer function:
$$
G_c(s) = K_p + \frac{K_i}{s} + \frac{K_d \, s}{\tau_d \, s + 1}
$$
Ki = integral gain (Ki = Kp / Ti)
Kd = derivative gain (Kd = Kp · Td)
τd = derivative filter time constant
Time-domain:
$$
u(t) = K_p\,e(t) + K_i\!\int_0^t e(\tau)\,d\tau + K_d\,\frac{de}{dt}\bigg|_{\text{filtered}}
$$
P, I, and D terms add in parallel
Changing Ki or Kd affects only that term