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Question

# Find the transfer function Y(s)R(s) for the system with following diagram block diagram:

A
Y(s)R(s)=G1G2G3G41+G1H1G1G2H2+G1G2G3H3+G1G2G3G4
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B
Y(s)R(s)=G1G2G3G41G1H1+G1G2H2+G1G2G3H3
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C
Y(s)R(s)=G1G2G3G41+G1H1+G1G2H2+G1G2G3H3
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D
Y(s)R(s)=G1G2G3G41G1H1G1G2H2+G1G2G3H3+G1G2G3G4
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Solution

## The correct option is A Y(s)R(s)=G1G2G3G41+G1H1−G1G2H2+G1G2G3H3+G1G2G3G4 G1 and H1 from a negative feedback loop and that loop is in cascade with G2. The block diagram can be simplified as : Now G1G21+G1H1 forms a positive feedback loop with H2 and that loop is in cascade with G3. The block diagram can be further simplified as: Now there is another negative feedback loop with H3 and cascade with G4. Block diagram becomes Y(s)R(s)=G1G2G3G41+G1H1−G1G2H2+G1G2G3H3+G1G2G3G4

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