2 Poles 1 Zero Step Response

Cuthbert Nyack

The unit step response of 2 pole type 1 systems with and without a zero is shown in the applet below.
The open and closed loop transfer function for the system without a zero is
G(s) = K/(s(T1s + 1)), C(s)/R(s) = K/(s(T1s + 1) + K))
The open and closed loop transfer function for the system with a zero is
G(s) = K(T2s + 1)/(s(T1s + 1)), C(s)/R(s) = K(T2s + 1)/(s(T1s + 1) + K(T2s + 1))

The zero damps out the oscillations and reduces the rise and settling times.
eg parameters (5.0, 3.0, 2.2, 2.0) show the settling time for the system without a zero is ~15.6s while it is ~0.75s with the zero.

Gif image below shows how applet should appear.

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