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.

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COPYRIGHT 2006 Cuthbert Nyack.