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 s

The poles of the closed loop transfer function with a is shown in the applet.

As plotted the amplitude is K/w

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.

COPYRIGHT © 2006 Cuthbert Nyack.