Process Model & Simulation

FOLPD, SOPTD and standard 2nd-order step response and frequency response. Exact closed‑form formulas running locally in your browser — no server, no downloads.

Parameters

Gain K: 2.0

Time Constant T (s): 5.0

Dead Time L (s): 1.0

Derived Metrics

Gain:2.0

Rise Time:5.0 s

Dead Time:1.0 s

L/T:0.20

Bandwidth ωbw:0.20 rad/s

Gain:2.0

T₁:3.0 s

T₂:2.0 s

Dead Time:1.0 s

Damping ζ:1.02

Bandwidth ωbw:0.33 rad/s

Gain:1.0

Damping ζ:0.50

ωn:2.0 rad/s

Poles:complex conj.

Bandwidth ωbw:2.47 rad/s

Transfer Function

$$G(s)=\frac{K}{Ts+1}\,e^{-Ls}$$ First-order lag plus dead-time (FOLPD). Commonly used for PID tuning rules.

$$G(s)=\frac{K}{(T_1s+1)(T_2s+1)}\,e^{-Ls}$$ Second-order with two real poles plus dead-time (SOPTD). T₁ and T₂ are independent time constants.

$$G(s)=\frac{K\,\omega_n^{\,2}}{s^2+2\zeta\omega_n s+\omega_n^{\,2}}$$ Standard second-order system. ζ controls damping; ωn is the undamped natural frequency.

Process Model & Simulation

Parameters

Derived Metrics

Transfer Function

Step Response

Bode — Magnitude

Bode — Phase

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