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What if circuit has multiple feedback loops

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freescale_bharat

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If there are more than one feedback loop in any circuit ( voltage regulator); to check the stability should one break all the loops and check for stability OR the loop having highest loop gain (A*beta) will have potential stability threat, if the circuit is safe there, other feedback loops may not be as significant.

In other words, having more than feedback loop is bad design, because optimising the circuit for all the three loops (say) to be stable is difficult task.

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snafflekid

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That is a good question. Multiple loops do not make a bad design. In a voltage regulator there are at least two nested feedback loops, one being the output voltage feedback and the other being the integrator capacitor.
 

LvW

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Indeed, it is a good and important question and it is not easy to give a final answer. This may be the reason most of the books on control theory do not touch this question. Some people think that the problem can be solved by using known rules to transfer a multi-loop system into a single loop system. But this does not help because if you have - let´s say - three different loops there exist exactly three different ways for reducing the multi-loop system and one does not know which method gives the right answer - because: Each of the mentioned ways gives another loop gain.
This is not surprising since three loops offer three different ways to open the loop and to measure three different loop gains.

But there is one general rule: Normally there are one or some LOCAL loops and only one OVERALL loop. The purpose of the local loops is to increase the speed of reaction of the whole system. Thus, the local loops have smaller time constants if compared with the overall feedback loop. And, therefore, the loop with the largest time constant determines the stability properties of the system - and in most (if not in all) cases this is the outer loop - if it can be identified !
Perhaps this helps a bit.

Question to the community: Does anybody knows about a book which gives a comprehensive answer to this question ?
 
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