A servo amplifier's loop gain has three poles

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Feedback, operational amplifiers and analogue signal processing · Signals, systems, control and digital signal processing

Electronics for Measurement, Ch Transfer functions, poles and the stability of a loop

Problem

A servo amplifier's loop gain has three poles, at

f_1 = 15\,\mathrm{Hz}

f_2 = 400\,\mathrm{kHz}

and

f_3 = 1.2\,\mathrm{MHz}

. A network analyser sweep shows the loop gain magnitude crossing unity at

f_c = 370\,\mathrm{kHz}

. For a near-second-order loop the step overshoot is about

9\%

23\%

42\%

and

66\%

for phase margins of

60^\circ

45^\circ

30^\circ

and

15^\circ

respectively. ((a)) Predict the phase margin at

f_c

, from the sum of the three arctangent phase lags. ((b)) Predict the overshoot of the closed loop's step response. ((c)) A technician plans to raise the controller gain until this margin is used up entirely. Predict the frequency at which the loop would then begin to oscillate.

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