Nyquist Plot for 1, 2 and 3 Real Poles

Cuthbert Nyack
Applet shows the Nyquist plot and step response for 1(yellow,blue), 2(orange,cyan) and 3(red,green) real pole system. Since all systems are type 0, then plots start on the +ve real axis.
First order plot occurs in the first quadrant(phase from 0 to -90°), second order starts in the first and ends in the second quadrant(phase from 0 to -180°). Both systems are always stable.
Third order plot starts in the first and ends in the third quadrant(phase from 0 to -270°). In this case the system is stable for small K and unstable for large K when the Nyquist plot moves outside the -1 point.
eg parameters (4.0, 0.4, 1.0, 1.0, 1.0, 2.0, 1.35) show 3rd order oscillatory at ~1.35rad/s, plot passes over -1 point.
(4.3, 0.4, 1.0, 1.0, 1.0, 2.0, 1.39) show 3rd order unstable at ~1.39rad/s, plot passes around the -1 point.
(1.9, 0.4, 1.0, 1.0, 1.0, 2.0, 1.16) show 2nd order has a phase margin of 60° at ~1.16rad/s.
(1.0, 0.4, 1.0, 1.0, 1.0, 2.0, 0.61) show 3rd order has a phase margin of 60° at ~0.61rad/s.




Gif image below shows how applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.