Applet shows the Bode plot and step response for a 4 real pole system.

The magnitude(red) starts with a slope of 0 and ends with a slope of -80dB/decade. The phase(green) starts from zero and ends at -2p. The step response is in pink and the magnitude vs phase plot in yellow.

In this case the system is stable for small K and unstable for large K when the closed loop poles move to the right of the s plane. The value of K which places the poles on the imaginary axis depends on the pole locations.

eg (1.0, 1.0, 1.0, 1.0, 0.05, 2.0) oscillates at ~0.61rad/s.

(2.0, 1.0, 1.0, 1.0, 0.43, 2.0) oscillates at ~0.82rad/s.

(4.0, 1.0, 1.0, 1.0, 1.0, 2.0) oscillates at 1rad/s.

(5.0, 1.0, 1.0, 1.0, 1.24, 2.0) oscillates at ~1.07rad/s.

(8.64, 1.0, 1.0, 1.0, 2.0, 2.0) oscillates at ~1.18rad/s.

(14.23, 1.0, 1.0, 1.0, 3.0, 2.0) oscillates at ~1.29rad/s.

Gif image below shows how applet should appear.

COPYRIGHT © 2006 Cuthbert Nyack.