The unit step response of a 1 pole 1 zero system is shown in the applet below. Since the power of s in the numerator and denominator is the same, then the transfer function contains a constant term which appears as a "jump" at the origin of the step response.

The open and closed loop transfer function is

G(s) = K(Tzs + 1)/(Tps + 1)

C(s)/R(s) = K(Tzs + 1)/((Tps + 1) + K(Tzs + 1)), C(s)/R(s) = (sKTz + K)/(s(Tp + KTz) + (1 + K))

Note:- (as + 1)/(bs + 1) = a/b + (1 - a/b)/(bs + 1)

Gif image below shows how applet should appear.

COPYRIGHT © 2006 Cuthbert Nyack.