Testing Gain and Phase margin of multiple embedded loops

[mercurous]

We are testing the margins of stability on a rather complicated feedback control system. In this system, the feedback block contains IIR filters implemented within an FPGA. We had issues with these IIR filters themselves becoming unstable intermittently (while running the main control open or closed loop) as they are feedback systems by themselves. Now that we think we are stable, we want to make sure that our testing uncovers the margins of stability for these IIR filters as well.

The question is: Will testing the overall gain and phase margin of the main control loop show us what our margins of stability are for the IIR filters as well?
OR
Do we need to break each little IIR loop, and test their individual gain and phase margins (via simulation), in addition to the overall loop GM and PM (via test)?

In testing the overall gain and phase margin, we think that these IIRs are stable for our specific situation, but I don't know how to tell our margins of stability from this information.

FYI: I am not referring to multiple feedback paths of the main loop. There are many articles that cover that. I am referring to little feedback loops entirely contained within the main feedback block and how to test the little feedback loops.

If you have any reference material related to this issue, I would greatly appreciate it if you would pass it along, as I have been looking for something all day...

 

[IRstuff]

But, if those loops are closed-loop systems, in of themselves, then you should be able to measure gain/phase margins, shouldn't you?

TTFN

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[mercurous]

Yes, I can measure the gain and phase margin of each little loop. The question is, do I have to? Or does measuring the GM and PM of the main loop suffice?

Please link to reading material if you have some on this. Thanks!

 

[lacajun]

I've not worked with this before or read anything on it so I could be entirely wrong but I'll throw my thoughts out for you to ponder. I've done just enough controls work to be dangerous.

I would think the GM and PM for each loop would be different because the transfer functions are different, i.e., each will have different poles and zeroes. Your equations defining the processes may be accurate and they may not. Then there are unknown disturbances that may "throw one for a loop." Depending on the application's level of danger to human life and/or property, I would investigate each one to ensure stability of each loop will be maintained.

When tuning loops of this nature, you always tune the inner loops first then the outer loop. If you can't tune an inner loop you won't be able to tune the outer loop. I guess that's driving my thinking more than anything I can remember from the "S" domain, without dragging out books. On root loci plots, you sure don't want to end up in the right plane.

I hope someone else has a lot more experience and knowledge to help you out. Control theory is an interesting topic.

 

[mercurous]

lacajun:

That is my train of thought as well, but I have some more experienced collegues who are disagreeing with me. I have done about 6 hours of reading this week on the subject (books and online) and have yet to find a definative answer.

However, I was able to come up with an example that I think proves that its possible to have a main control loop that appears to have good GM and PM even while one of its feedback blocks contains a smaller loop with a PM that will cause instability.

 

[lacajun]

I love control theory and the math behind it. You apply all the theory, crunch through the math, and still have to think about the answer and its suitability for the task at hand. It doesn't get any better.

I took controls at the graduate level but don't remember covering this topic. If I get time, I'll look through some of my books and let you know if I find anything. It's been 10+ years so I may not find anything quickly.

 

[sreid]

It appears that what you are asking is, "The IIR Fliters appear to be stable but what is the margin of stability?" You most certainly need to check this.

For IIR Filters especially, make certain to check saturation conditions. The filter code needs to specifically take care of under-over flow conditions.

If the IIR Filters are used as part of an inner loop, you also need to check how stable the inner loops are.

 

[FeX32]

Sounds to me you are experiencing a common problem when filters are set in the feedback loop.
These filters cause a nonlinear delay in the signal back to the controller. This causes significant performance degradation and "easier instability".

The question is: Will testing the overall gain and phase margin of the main control loop show us what our margins of stability are for the IIR filters as well?

In short. Yes. As you are testing the combine actual which is your system and the filters and controller as one package.
You can certainly test and obtain the gain margin for stable controller doing this. If you want to increase this margin you can change the controller or the filters or both. Simulations may show what type fo filter is best.


Fe

 

[mercurous]

FeX32: How much experience do you have in control systems analysis and theory? Please let me know if my explanation below is incorrect. Otherwise, I am still inclined to agree with sreid.

I have been doing more reading and am now more inclined than before to think that you need break each little loop to determine the margins of stability for each loop. Gain and phase margins are open loop characteristics. Since the phase margins of the little loops are different than the phase margins for the big loop, I have come up with example situations where an inner loop is close (1 degree) to instability, but the main loop has plenty of gain and phase margin. The closed loop gain and phase of the small loops is what contributes to the open loop gain and phase margin of the big loop. But the open loop gain and phase of the small loop is what determines its gain and phase margin.

So, I don't think you can use the closed loop characteristics of the small loops to determine their margins of stability.

 

[FeX32]

I am the author of a few international publications on control theory. (including applications)
Although, I don't have any direct experience with IIR filters themselves I understand the problems associated with feedback signals to plants when filters are used. Robust control theory is the best option in these cases but it is not easy to implement.

I presume you could determine the stability of each filter independently. However, why would you use a filter that has a region of attraction lesser then that of the entire system.

About your reasoning. I have not seen it done like that before. But, it is partially logical. What kind of system are you controlling? I would suggest also doing a closed loop analysis. This will ensure your controller functions properly and you can also tune its performance.
There are many references you can read. I just pulled these off google. But I remember there were a few better ones. I will try to find them when I have a chance.

http://techteach.no/publications/books/models_estim_control/stab_analysis_feedback_syst.pdf

http://www.sciencedirect.com/science/article/pii/0005109894901007

Fe