PID Gains
Proportional Gain Kp
Integral Time Ti (s)
s
Larger Ti = weaker integral. Use the checkbox below to disable I.
Derivative Time Td (s)
s
Setpoint SP
Simulation Time (s)
s
Presets
Performance Metrics
Results
—
90% arrival time (s)
—
Settling time ts (s)
—
Overshoot %
—
End-of-run error %
—
IAE
—
ITAE
Process Variable y(t) and Setpoint
Controller Output u(t)
U
Process variable y(t)
Setpoint SP
Control output u(t)
Theory & Key Formulas
$$u(t)=K_p\!\left[e(t)+\frac{1}{T_i}\!\int_0^t\!e\,d\tau+T_d\frac{de}{dt}\right]$$
ZN step response tuning:
$K_p=1.2\,\tau/(K\cdot L),\quad T_i=2L,\quad T_d=0.5L$
$K_p=1.2\,\tau/(K\cdot L),\quad T_i=2L,\quad T_d=0.5L$
Results
0.70
Setpoint SP
0.000
Current value PV
0.700
Error e
0.00
Control output u
0.0%
Overshoot
—
Rise time
—
Settling time
0.700
Steady-state error
0.000
Ki=Kp/Ti
0.00
Kd=Kp·Td
PV (liquid level)
SP (setpoint)
e (error)
u (inflow = control output)
Proportional Gain Kp1.50
Integral time Ti (s)8.0
Derivative time Td (s)0.00
Target liquid level SP0.70
Process time constant τ (s)5.0
Changing Kp/Ki/Kd visibly shifts the closed-loop response from sluggish → responsive → oscillatory → unstable. For a first-order plant, P-only control leaves a steady-state error = 1/(1+Kp·K); adding the I term drives the error → 0.