Closed Loop Response for 3 Real Poles

Cuthbert Nyack

This applet shows the Nyquist plot(red), the closed loop frequency response(light green and orange) and phase and gain margins(cyan, pink) of a 3 real poles system.
eg parameters (8.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.73) shows the gain and phase margins to be ~0(within the resolution of the applet). The system is oscillatory with an angular frequency of 1.73. The closed loop response reduces to a line in the left upper quadrant on the Nyquist plot.

The case (9.0, 1.0, 1.0, 1.0, 0.1, 3.0, 1.80) show an unstable case with -ve gain and phase margins, the peak of the closed loop response is in the upper right quadrant.

Parameters (7.0, 1.0, 1.0, 1.0, 0.1, 3.0, 1.66) show a case with +ve gain and phase margins, the peak of the closed loop frequency response is in the lower left quadrant.

(3.3, 0.34, 1.0, 1.0, 1.0, 2.0, 1.6), phase margin ~45°, gain margin ~10dB, the peak of the closed loop frequency response is on the -ve imaginary axis.
(2.4, 0.34, 0.2, 2.4, 2.0, 3.0, 1.5), phase margin ~90°, gain margin ~20dB, the peak of the closed loop frequency response is in the lower right quadrant..
(5.8, 0.24, 8.2, 6.4, 1.0, 7.0, 0.32), phase margin ~45°, gain margin ~20dB, the peak of the closed loop frequency response is in the lower right quadrant.
(10.0, 0.2, 0.2, 5.6, 2.0, 1.0, 1.62), phase margin ~60°, gain margin ~15dB, the peak of the closed loop frequency response is in the lower right quadrant.

Gif image below shows how applet should appear.

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