# 3 Real Poles 0, 1 and 2 Real Zeros Step Response

Cuthbert Nyack
The step response of 3 pole systems with 0, 1 and 2 zeros is shown in the applet below.
The open and closed loop transfer function for the system is
no zero G(s) = K/(s(T1s + 1)(T2s + 1)), C(s)/R(s) = K/(s(T1s + 1)(T2s + 1) + K))
with 1 zero G(s) = K(T3s + 1)/(s(T1s + 1)(T2s + 1)), C(s)/R(s) = K(T3s + 1)/(s(T1s + 1)(T2s + 1) + K(T3s + 1)))
with 2 zeros G(s) = K(T3s + 1)(T4s + 1)/(s(T1s + 1)(T2s + 1)), C(s)/R(s) = K(T3s + 1)(T4s + 1)/(s(T1s + 1)(T2s + 1) + K(T3s + 1)(T4s + 1)))

Since this is a 3 pole system then instability is possible. The parameter values (2.0, 1.0, 1.0, 0.4, 0.7, 2.0) shows the step response when the system without a zero is unstable.
With a zero the values (>10.0, 1.0, 1.0, 0.4, 0.7, 2.0) show instability.
With 2 zeros the values (2.9-14.3, 3.3, 2.0, 0.4, 0.4, 5.0), show instability.
The effect of the zeros on the unstable system is shown by the parameters (2.0, 1.0, 1.0, 1.4, 0.4, 1.0).

Gif image below shows how applet should appear. Return to main page
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COPYRIGHT ę 2006 Cuthbert Nyack.