Closed Loop response for 3 Real Poles

Cuthbert Nyack

This applet shows the Bode plot, the closed loop frequency response and phase and gain margins of a 3 real poles system.

The relation between the phase and gain margins and the closed loop frequency response.
eg parameters (8.0, 1.0, 1.0, 1.0, 0.7, 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 has a sharp peak ~50dB

The case (9.0, 1.0, 1.0, 1.0, 1.0, 3.0, 1.8) show an unstable case with -ve gain and phase margins. The closed loop peak is lower than for the oscillatory case ~25dB.

Parameters (7.0, 1.0, 1.0, 1.0, 1.0, 3.0, 1.66) show a case with +ve gain and phase margins. The closed loop peak is lower than for the oscillatory case ~23dB.

(3.3, 0.34, 1.0, 1.0, 1.0, 3.0, 1.6), phase margin ~45°, gain margin ~10dB, closed loop peak ~10dB.
(2.4, 0.34, 0.2, 2.4, 1.0, 3.0, 1.5), phase margin ~90°, gain margin ~20dB, no closed loop peak.
(5.8, 0.24, 8.2, 6.4, 1.0, 7.0, 0.32), phase margin ~45°, gain margin ~20dB, closed loop peak ~3.7dB.
(10.0, 0.2, 0.2, 5.6, 1.0, 1.0, 1.62), phase margin ~60°, gain margin ~15dB, closed loop peak ~0.75dB.

Gif image below shows how applet should appear.

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