The mathematics behind stability are crystal clear. I am very confused, however, as to how these measurements are taken in a real system. Specifically, say I have a power supply. How would one measure the power supply stability including gain margin and phase margin. I am interested in a controlled way, what kind of probes, etc.
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\$\begingroup\$ What kind of stability? \$\endgroup\$– MarioFeb 24, 2016 at 23:53
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\$\begingroup\$ @Mario I hope my edit clarifies a little. \$\endgroup\$– mcmilnFeb 25, 2016 at 0:04
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There are ways to measure the transfer function of a given system. However, just to judge the stability a good way is to look at the step response. The overshoot (or the lack thereof) can be used to determine the phase margin of a system.
Often systems can be approximated by a second order transfer function and almost every (basic) book on control theory covers the theory of these systems and the relationship between step response and phase margin.
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\$\begingroup\$ I've heard the step response idea thrown around, but I'm curious how accurate this really is. What changes in a real environment and what kind of accuracy would you expect? \$\endgroup\$– mcmilnFeb 25, 2016 at 0:27
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1\$\begingroup\$ As the phase margin goes towards zero the overshoot can reach 100 percent. For 45 degrees its above 20 percent. \$\endgroup\$– MarioFeb 25, 2016 at 0:38
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\$\begingroup\$ The step response is every bit as reliable a measure of stability as phase margin. If you don't have some reason why you actually need to know the phase margin, I would suggest that you not worry about it as such, and just observe the step response. \$\endgroup\$– mkeithFeb 25, 2016 at 3:54
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\$\begingroup\$ Well if this is truly the method everyone uses then I can accept that, but what accuracy equipment am I generally looking for? \$\endgroup\$– mcmilnFeb 25, 2016 at 17:19