3 Real Poles Step Response

Cuthbert Nyack

The step response of a 3 pole system is shown in the applet below.
The open and closed loop transfer function for the system is
G(s) = K/(s(T1s + 1)(T2s + 1)), C(s)/R(s) = K/(s(T1s + 1)(T2s + 1) + K))
Since this is a 3 pole system then instability is possible.
The parameter values (1.5, 1.0, 1.0, 2.0, 4.0) shows the step response when the system with poles at 0, -1/T1, -1/T3 is oscillatory. Unstable for K > 1.5.

Values (2.0, 1.0, 1.0, 2.0, 4.0) show oscillation with poles at 0, -1/T1, -1/T2. Unstable for K > 2.0.

Values (9.0, 1.0, 1.0, 2.0, 2.0) show oscillation of type 0 with poles at -1/T1, -1/T2, -1/T3. Unstable for K > 9.0.

Gif image below shows how applet should appear.

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