3 Real Poles 1 Real Zero Step Response

Cuthbert Nyack
The step response of 3 pole systems with and without a zero 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 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))) Since this is a 3 pole system then instability is possible. The parameter values (2.0, 1.0, 1.0, 0.3, 2.0) shows the step response when the system without a zero is unstable. With a zero the values (5.0, 1.0, 1.0, 0.3, 2.0) show instability.
The effect of the zero on the unstable system is shown by the parameters (2.0, 1.0, 1.0, 1.6, 2.0)



Gif image below shows how applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.