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 stability for ckts having two feedback loops (Read 2570 times)
 justdoit New Member Offline Posts: 6 IIT-Kharagpur,India stability for ckts having two feedback loops Dec 19th, 2007, 10:18pm   Hi all ,Can any one give me the references for doing the stability analysis if there are multiple feedback loops (i have two feedback loops in my circuit ) in circuit ...  Thanks in advance Back to top Haribabu,M.tech.IIT-Kharagpur,India.   IP Logged
 buddypoor Community Fellow Offline Posts: 529 Bremen, Germany Re: stability for ckts having two feedback loops Reply #1 - Dec 20th, 2007, 9:24am   Hi Haribabu !You have picked up a very interesting point in control theory since this question is not answered in most text books. I face this problem since several years and I came to the conclusion that there is no other way than to do  an open loop analysis for each of the possible loops.In your case, if you have two feedback loops, there are three possible options:1.)Loop 1 open, loop 2 closed2.)Loop 2 open, loop 1 closed3.) Both loops open. Than, the most critical stability margin determines the system margin. With other words, the loop with the least margin is dominant.Interestingly, to reduce the system to a single loop system prior to the open-loop-analysis gives exactly the same results. The reason is that - in your example - there are exactly three different ways to do this (with three different loop gains and, hence, three different margins). I hope this could help a little.Good luck and greetings from Germany.Lutz Back to top LvW (buddypoor: In memory of the great late Buddy Rich)   IP Logged
 HdrChopper Community Fellow Offline Posts: 493 Re: stability for ckts having two feedback loops Reply #2 - Dec 22nd, 2007, 8:31pm   Hi Haribabu,This topic is a very tough one. However the analysis of multi-loop feedback systems can be simplified to a single loop case if any of this two conditions is met:1) All the feedback loops have a break point in common. In this case, by breaking the loops at that point the stability analysis is performed as if it were a single loop case.2) A multi-loop feedback which comprises one general feedback network and several inner (local) feedback loops can be analyzed by just breaking the general feedback network (single loop) if each of its inner feedback networks is stable by itself (which must be left intact during the analisys).The paper "Determination of stability using return ratios in balanced fully differential feedback circuits" by Paul Hurst, IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS-11: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 42, NO. 12, DECEMBER 1995 , has examples of the cases mentioned aboveHope this helpstosei Back to top Keep it simple   IP Logged
 buddypoor Community Fellow Offline Posts: 529 Bremen, Germany Re: stability for ckts having two feedback loops Reply #3 - Dec 26th, 2007, 12:32am   The above reply from TOSEI is, of course, completely correct as it takes two special cases into consideration.The first example refers to the common case that an amplifier has one negative and one positive feedback circuit. The second example can be found in control circuits with one or more "local" loops and one overall feedback loop, which than is the most "slowest" of all.But, what is the procedure if none of these cases applies ? There are a lot of cases where, for example, two loops exist which cannot discriminated by "inner loop" resp. "outer loop". In this case, I think, the procedure has to be as described in my first reply to HARIBABU on Dec. 20th.Best wishes and a happy new year to all community membersLutz (Germany) Back to top LvW (buddypoor: In memory of the great late Buddy Rich)   IP Logged
 HdrChopper Community Fellow Offline Posts: 493 Re: stability for ckts having two feedback loops Reply #4 - Jan 14th, 2008, 10:56am   Hi Lutz,From your previous reply, you suggested thatbuddypoor wrote on Dec 20th, 2007, 9:24am:Hi Haribabu !In your case, if you have two feedback loops, there are three possible options:1.)Loop 1 open, loop 2 closed2.)Loop 2 open, loop 1 closed3.) Both loops open. Than, the most critical stability margin determines the system margin. With other words, the loop with the least margin is dominant. My question is, how do you account for the influence of the two loops closed at the same time in your analysis?. I understand that by analyzing them in a separate way, the one with the least margin will dominate. However, things might be even worse when considering all the cases you enumerated at the same time, because of the relative margin between the different options. Could you please clarify?ThanksTosei Back to top Keep it simple   IP Logged
 Eugene Senior Member Offline Posts: 262 Re: stability for ckts having two feedback loops Reply #5 - Jan 14th, 2008, 10:41pm   I thought there was already a discussion of this somewhere in the Forum but I could not find it. Oh well, perhaps it's just a case of deja vu. Anyway, the most direct method of assessing stability of multiloop systems is to compute the Eigen values of the closed loop system matrix. This is not that practical in electric circuits because the poles are often widely separated and the order of the system can also be quite high. Spectre and SPICE have tools for computing closed loop poles but they sometimes list RHP (i.e. unstable) poles when none exist. Such poles are usually in close proxmity to closed loop zeros such that they nearly cancel. If you insist on using more classical frequency domain methods, there is a little known procedure called sequential loop closures, or sequential return differences. The procedure is as follows:1. Open all loops such that the resulting system is stable.2. Assess the loop gain of one loop with all other loops open. Keep track of the number of clockwise encirclements of the Nyquist point. 3. Close that loop and assess the loop gain of the next loop. Keep track of the net number of encirlcements of the Nyquist point. 4. Close that loop and do the same for the next loop. And so on.5. If the net number of encirclements (clockwise - counter clockwise) equals zero, the system is stable. If the net is greater than zero, the system is unstable.The only problem with this method is that it is hard to identify a single phase margin or gain margin. You could select the minimum phase margin and minimum gain margin as you assessed each loop but you may get different numbers if you select a different sequence. Despite this shortcoming, the procedure is mathematically rigorous.This method is often mis-applied, most commonly when common mode feedback loops are involved. Suppose we have two interacting loops called loop one and loop two. The mistake is to start with loop one closed while you assess loop two. You then look at loop one with loop two closed.  The problem is that the logic is circular because you do not know how many RHP poles you are starting with. If loop one has one RHP pole, loop two MUST encircle the Nyquist point exactly once counter clockwise to make the closed loop system stable. In short, the mis-applied method is the same as saying loop one is stable because loop two is stable and loop two is stable because loop one is stable, therefore the system is stable. Imagine two brothers going to court saying "I'm telling the truth because my brother never lies and he says I'm telling the truth". The other brother says the same thing. Does that prove they are both truthful? To get the net encirclements at the end of the procedure, you must start with all loops open; you must start knowing for sure that one brother never lies. Back to top IP Logged
 Frank Wiedmann Community Fellow Offline Posts: 673 Munich, Germany Re: stability for ckts having two feedback loops Reply #6 - Jan 14th, 2008, 11:31pm   Eugene wrote on Jan 14th, 2008, 10:41pm:I thought there was already a discussion of this somewhere in the Forum but I could not find it. You may have been thinking of http://www.designers-guide.org/Forum/YaBB.pl?num=1163532257/1#1 (see the last paragraph of reply #1). By the way, for Bode's method, you must open the loops not by cutting a wire but by setting the controlled sources to zero (so that the impedances you are seeing are not changed). This is very difficult with traditional circuit simulators because the controlled sources are usually inside transistor models and you do not have direct access to them. Back to top IP Logged