Bode Plot and Step Response for 5 Real Poles

Cuthbert Nyack
Applet shows the Bode plot and step response for a 5 real pole system.
The magnitude(red) starts with a slope of 0 and ends with a slope of -100dB/decade. The phase(green) starts from zero and ends at -2.5p. 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 (0.8, 1.0, 1.0, 1.0, 1.0, 0.14, 5.0) oscillates at ~0.497rad/s.
(2.89, 1.0, 1.0, 1.0, 1.0, 1.0, 3.0) oscillates at ~0.727rad/s.
(4.29, 1.0, 1.0, 1.0, 1.0, 1.46, 3.0) oscillates at ~0.78rad/s.
(9.43, 1.0, 1.0, 1.0, 1.0, 2.95, 3.0) oscillates at ~0.866rad/s.
(17.1, 1.0, 1.0, 1.0, 1.0, 5.0, 3.0) oscillates at ~0.913rad/s.
Phase margin of 0 at 0.01rad/s means phase margin is undefined.



Gif image below shows how applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.