2 Complex Conjugate Poles Impulse Response

Cuthbert Nyack
The unit impulse response of a 2 pole system is shown in the applet below. The poles are Complex Conjugate and are located at -a - jb and -a + jb. The applet shows 2 impulses for different a for comparison.
The open and closed loop transfer function for the system is
G(s) = K/((s + a + jb)(s + a - jb)), C(s)/R(s) = K/((s + a + jb)(s + a - jb) + K))
The denominator of the closed loop transfer function can be written as s2 + 2 wn zs + wn2
The poles of the closed loop transfer function with a is shown in the applet.
As plotted the amplitude is K/wn at the origin and decreases as e-wnzt.
q is the angle which the closed loop makes with the -ve real axis. eg parameters (8.4, 4.0, 1.0, 2.0, 0.5) show that to avoid undershoot, q should be < ~ 41°.

Gif image below shows how applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.