Determination of stability of a system - Page 1
Forum section: electronics / projects

author: sagnikbasu
author_rank: Contributor
timestamp: February 11, 2017, 12:39:27 pm
content: Why is it necessary to use the closed loop equation of transfer function to determine stability?

author: T3sl4co1l
author_rank: Super Contributor
timestamp: February 11, 2017, 05:15:39 pm
content: How would it be possible to do anything else?Tim

author: nctnico
author_rank: Super Contributor
timestamp: February 11, 2017, 05:22:38 pm
content: Build the circuit and feed it a step while watching on an oscilloscope?

author: Kleinstein
author_rank: Super Contributor
timestamp: February 11, 2017, 05:27:45 pm
content: One does not absolutely look at the loop gain, but this is standard method and works with most systems (e.g. if linear approximation works). In some cases one can look at different (though related) functions too.

author: MagicSmoker
author_rank: Super Contributor
timestamp: February 11, 2017, 06:28:29 pm
content: I think the key here is "closed loop"... While there certainly can be open-loop plants that are unstable, it generally takes closing a feedback loop to really mess things up.That said, the OP provided a startling lack of context for what otherwise appears to be a homework question, so perhaps we shouldn't be too helpful just yet.

author: danadak
author_rank: Super Contributor
timestamp: February 11, 2017, 11:46:34 pm
content: You can do either closed or open loop stability analysis for a closed loop system.http://www.chemengr.ucsb.edu/~ceweb/faculty/seborg/teaching/SEM_2_slides/Chapter_14.pdfhttp://www.cds.caltech.edu/~murray/books/AM08/pdf/am06-analysis_16Sep06.pdfYou can, in time domain, inject an impulse into a closed loop system and look at time domain response.By examining with a scope for ringing, oscillation behavior, you can get a "feel" for phase margin in thesystem. You can analytically, using Laplace, predict phase margin, ringing behavior, without too mucheffort for 1'st and 2'ond order systems.Simple experiment, take a fast OpAmp, one with two pole open loop response, and feed a squarewave into it, and use different Cload to watch effects of load C on phase margin. Also vary closed loopG. Fun stuff.Regards, Dana.

author: LvW
author_rank: Frequent Contributor
timestamp: February 12, 2017, 09:25:55 am
content: Quote from: danadak on February 11, 2017, 11:46:34 pmYes - however, we must disinguish between the two cases:* With aclosed - loop analysesin the time domain you can only verify IF a circuit with feedback wil be stable or not. In contrast, in the frequency domain, plotting the transfer function provides no reliable information about stability properties. However, when a simulation program allows us to find the poles of the closed-loop system, the location of these poles will indicate if the system is stable or not (stable: poles in the left half of the s-plane, otherwise unstable.).* Withloop gain analysesin the frequency domain (Bode diagram or Nyquist plot) we are able to determine the DEGREE of stability resp. instability using the phase and/or gain margin criterion.

author: hans
author_rank: Super Contributor
timestamp: February 12, 2017, 09:28:52 am
content: Find the transfer function for a closed loop system. That's much different than for an open loop system due to feedback. You'll likely end up with the open loop transfer function in nominator and denominator. Now that will certainly mess things up in the denominator, and thus closed loop system poles.If then there are tunings available in any process, those tunings will likely appear in the system poles and thus affect stability directly

author: danadak
author_rank: Super Contributor
timestamp: February 12, 2017, 11:23:06 am
content: QuoteLook at the second link, Nyquist analysis, margins can be determined closed loop.Regards, Dana.

author: LvW
author_rank: Frequent Contributor
timestamp: February 12, 2017, 02:46:54 pm
content: Quote from: danadak on February 12, 2017, 11:23:06 amSorry - but this is definitely wrong.The whole text (your second link) deals with the loop transfer function only (loop gain, open loop).Without any doubt - stability margins are defined for the loop gain only!

author: danadak
author_rank: Super Contributor
timestamp: February 12, 2017, 03:00:57 pm
content: I am looking at page 10, seems to cover the closed loop case ?In addition this, attached.Regards, Dana.

author: LvW
author_rank: Frequent Contributor
timestamp: February 12, 2017, 05:36:24 pm
content: Quote from: danadak on February 12, 2017, 03:00:57 pmIt may be interesting for you - but I am the author of the linked document.Nevertheless, stability margins are DEFINED for loop gain functions (frequency domain) only.

author: danadak
author_rank: Super Contributor
timestamp: February 12, 2017, 10:15:06 pm
content: I stand corrected. I should have read the paper end to end.Thanks, Dana.

author: LvW
author_rank: Frequent Contributor
timestamp: February 13, 2017, 10:31:13 am
content: Quote from: danadak on February 12, 2017, 10:15:06 pmThank you.(I must admit, that the title of my article - intentionally - is a bit "misleading". In fact, the loop does not remain closed in its "normal" sense, because inserting of an extra phase-shifting block can be seen as an "opening "of the loop)