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Breaking an algebraic loop

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Mathis Sterling Allen
Mathis Sterling Allen 2020 年 12 月 9 日
編集済み: Jon 2020 年 12 月 9 日
My model has an seemingly unsolvable algebraic loop in it. It is continous-time, so I put in a quick filter in the loop to try to break it. All that did was make it run for less than a microsecond simulation time with many small steps ( < 1 ns). The total simulation time I trying to do is 0.25 s. Below is a picture of my model. The places in red are the places where I have tried to put the filters in and the blue is just to highlight where they are now. The S-function block seems to work as a lookup table. My controllers have worked when the plant I was working on was just a set of EOM's.
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Mathis Sterling Allen
Mathis Sterling Allen 2020 年 12 月 9 日
With the filters removed, the loop is highlighted below.

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Jon
Jon 2020 年 12 月 9 日
I usually put in a delay block with a relatively small value set for the one sample delay to break algebraic loops. If you use a filter, of course you should be sure that the numerator polynomial is lower order than the denominator so that there is no direct feedthrough.
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Jon
Jon 2020 年 12 月 9 日
Your model is too complicated for me to see what the specific problem is just by looking at a screen shot. So I can only give you generic suggestions as follows. Algebraic loops come from a cyclic sequence of blocks that all have direct feedthrough. Direct feedthrough implies that the bandwidth of the element is also infinite. There will be no high frequency rolloff. Any actual system will eventually roll off, so you can look to see if your elements are overly idealized/simplified resulting in direct feeedthrough. Also are the SMC blocks sliding mode controllers? I have never tried simulating them, but from my understanding sliding mode controllers are based upon chattering phenomena, so you have to be very careful that your plant has enough low pass characteristics to not have the chattering frequency get infinititely high.

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