1 Pole Step Response

Cuthbert Nyack

The unit step response of 1 pole type 0 and 1 system is shown in the applet below. Two responses with different time constants are shown for comparison.
The open and closed loop transfer function for the type 0 system is
G(s) = K/(T1s + 1), C(s)/R(s) = K/(T1s + (1 + K)) with R(s) = 1/s
The offset of the type zero system tends to (1/(1 + K)) for large t while that of the type 1 system tends to zero for large t.
The closed loop poles for type 0 and 1 are shown on the applet.
eg parameters (2.0, 1.0, 0.5) show that type 0 offset is 1/(K + 1) = 1/3, (0.5, 0.6, 0.2) show that type 0 offset is 1/(K + 1) = 2/3.

Gif image below shows how applet should appear.

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