A system A has a variable gain G which can be set to any value.The only problem

Question

A system A has a variable gain G which can be set to any value.The only problem with system A is that its gain G is not stable and can fluctuate with+ or minus 10%.for example if u set the gain to 100 then it can be as high as 110 or as low as 90. so if the input is 2 then the output could be as high as 220 or as low as 180. One way to minimize the gain fluctuation is to connect a feedback subsystem with gain H to the system A . Your task is to choose values for G and H such that the total gain of the system with its feedback is 100 with fluctuation that does not exceed + or minus 1%. for example if the input is 2 then the output should be between 198 and 202(99*2 and 101*2)

Explanation / Answer

Output = A

Input = B

A/B = G/(1+G*H)

G= +Or - 0.1

We want A/B= 0.01

So

0.01= 0.1/(1+0.1H)

0.01((1+0.1H)) = 0.1

0.01 +0.001H =0.1

So H= 90

So G=10

H =90 (Answer)

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