3 Real Poles Type 0 Step and Impulse Response

Cuthbert Nyack

The impulse and step response of a 3 pole type 0 system is shown in the applet below.
The open and closed loop transfer function for the system is
G(s) = K/((T1s + 1)(T2s + 1)(T3s + 1)), C(s)/R(s) = K/((T1s + 1)(T2s + 1)(T3s + 1) + K))
Since this is a 3 pole system then instability is possible.
The parameter values (8.0, 1.0, 1.0, 1.0, 2.0, 1.0),
(14.4, 1.0, 1.0, 5.0, 2.0, 1.0),
(9.0, 1.0, 1.0, 0.5, 1.0, 1.0),
shows the step response when the system with poles at -1/T1, -1/T2, -1/T3 is unstable.
It is easier to understand these numbers if the closed loop transfer function is written as
C(s)/R(s) = (K/T1T2T3)/((s + 1/T1)(s + 1/T2)(s + 1/T3) + K/T1T2T3))
Impulse response of second order is included for comparison.

Gif image below shows how applet should appear.

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