1 Pole Ramp Response

Cuthbert Nyack
The unit ramp response of 1 pole type 0 and 1 system is shown in the applet below.
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/s2
The offset of the type 1 system tends to a constant value(T/K) while of the type zero system decreases with K but increases with time t and T ie
t - (K/(K + 1))*(t - T/(K + 1)) = t/(K + 1) + K*T/(K + 1)2.
The offset at t = 1 for both type 0 and 1 is shown in the applet.
for eg parameters (4.0, 0.5) offset for type 1 should be 0.125 and for type 0 should be 0.28. Applet shows 0.12495 and 0.27999.



Gif image below shows how applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.