Bode Plot and Step Response for 4 Real Poles

Cuthbert Nyack
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.

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COPYRIGHT 2006 Cuthbert Nyack.