FOLPD, SOPTD and standard 2nd-order step response and frequency response.
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Parameters
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.