Step Response for Minimum and Non Minimum Phase

Cuthbert Nyack

The Applet below show the step response of
(1) a second order type 0 system.(orange)
G(s) = K/((T1s + 1)(T2s + 1)), C(s)/R(s) = K/(((T1s + 1)(T2s + 1)) + K))

(2) a second order type 0 system with a zero to the left of the imaginary axis.(cyan)
G(s) = K(1 + Tns)/((T1s + 1)(T2s + 1))), C(s)/R(s) = K(1 + Tns)/(((T1s + 1)(T2s + 1)) + K(1 + Tns))

(3) a second order type 0 system with a zero to the right of the imaginary axis(nonminimum phase).(red)
G(s) = K(1 - Tns)/(((T1s + 1)(T2s + 1))), C(s)/R(s) = K(1 - Tns)/(((T1s + 1)(T2s + 1)) + K(1 - Tns))

The eg parameters (5.0, 1.0, 2.0, -0.4, 2.0) show that while a zero to the left of the imaginary axis damps out transient oscillations, a zero to the right of the axis enhances it.
The eg parameters (7.5, 1.0, 2.0, -0.4, 2.0) show that a zero to the right of the imaginary axis can make a second order system unstable.
eg parameters (3.75, 1.0, 2.0, -0.8, 2.0), (15.0, 1.0, 2.0, -0.2, 2.0) show that the system becomes unstable for smaller K when the zero moves closer to the imaginary axis.

Gif image below shows how applet should appear.

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