1 Real 2 Complex Conjugate Poles Impulse and Step Response

Cuthbert Nyack
The impulse and step response of a 3 pole system (1 real and 2 complex conjugate poles) is shown in the applet below.
The open and closed loop transfer function for the system is
type 1 G(s) = K/((T1s + 1)(s + x + jy)(s + x - jy)), C(s)/R(s) = K/((T1s + 1)(s + x + jy)(s + x - jy) + K))
Since this is a 3 pole system then instability is possible. The parameter values (10.0, 6.0, 0.1, 3.0, 1.0, 2.0) shows the impulse and step response consisting of contributions from the real pole(gradual rise to final value) and from the complex conjugate poles(oscillatory behaviour). One set of parameter values showing instability is (15.7, 2.0, 0.4, 3.0, 2.0, 1.0) another is (11.3, 1.0, 0.5, 3.0, 1.0, 1.0). If the complex conjugate poles are far to the left, then the dynamics is dominated by the real pole eg (18.3, 1.2, 5.0, 3.0, 1.0, 1.0).



Gif image below shows how applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.