engineering recuitment GATE ECE 2023-24 Test Series Control Systems Signal Flow Graph and Block Diagram Mason's Gain Formula

t/f function \(\frac{C}{R}\) for above signal flow graph ?

1

\(\frac{{{G_1}{G_2}{G_3}{G_4}{G_5}{G_6} + {G_1}{G_2}{G_3}{G_6} + {G_1}{G_2}{G_3}{G_4}{G_7}}}{{1 - \left( {{G_3}{G_4}{H_2} + {G_7}{H_3}{H_4} + {G_2}{G_3}{H_5}} \right) + {G_2}{G_3}{G_7}{H_3}{H_4}{H_5}}}\)

2

\(\frac{{{G_1}{G_2}{G_3}{G_4}{G_5}{G_6} + {G_1}{G_2}{G_3}{G_6}{H_1} + {G_1}{G_2}{G_3}{G_4}{G_7}}}{{1 - \left( {{G_3}{G_4}{H_2} + {G_7}{H_3}{H_4} + {G_2}{G_3}{H_5}+G_3H_1G_6H_4H_2} + G_5G_6H_4H_3\right) + {G_2}{G_3}{G_7}{H_3}{H_4}{H_5}}}\)

3

\(\frac{{{G_1}{G_2}{G_3}{G_4}{G_5}{G_6} + {G_1}{G_2}{G_3}{G_6}{H_1}\left( {1 - {H_3}{H_4}{G_7}} \right) + {G_1}{G_2}{G_3}{G_4}{G_7}}}{{1 - \left( {{G_3}{G_4}{H_2} + {G_7}{H_3}{H_4} + {G_2}{G_3}{H_5}} \right) + {G_3}{G_4}{G_7}{H_2}{H_3}{H_4}}}\)

4

\(\frac{{{G_1}{G_2}{G_3}{G_4}{G_5}{G_6} + {G_1}{G_2}{G_3}{G_6}{H_1} + {G_1}{G_2}{G_3}{G_7}\left( {1 - {H_3}{H_4}{G_7}} \right)}}{{1 - \left( {{G_1}{G_4}{H_2} + {G_7}{H_3}{H_4} + {G_2}{G_3}{H_5} + {G_2}{G_3}{G_7}{H_3}{H_4}{H_5}} \right)}}\)

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