For the signal flow graph in the figure- the value of CsRs is

Transfer function C(s)R(s) = ∑ P_k Δ _kΔ = G_1G_2G_3G_41 ( G_1G_2H_1 G_2G_4H_2 G_2G_3H_3)+G_1G_2H_1.G_3G_4H_2 C(s)R(s) = G_1G_2G_3G_41+G_1G_2H_1+G_2G_4H_2+G_2G ...

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Control Systems

Basics of Signal Flow Graph

For the signa...

Question

For the signal flow graph in the figure, the value of $\frac{C (s)}{R (s)}$ is

\frac{G_{1} G_{2} G_{3} G_{4}}{1 - G_{1} G_{2} H_{1} - G_{3} G_{4} H_{2} - G_{2} G_{3} H_{3} + G_{1} G_{2} G_{3} G_{4} H_{1} H_{2}}

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\frac{G_{1} G_{2} G_{3} G_{4}}{1 + G_{1} G_{2} H_{1} + G_{3} G_{4} H_{2} + G_{2} G_{3} H_{3} + G_{1} G_{2} G_{3} G_{4} H_{1} H_{2}}

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\frac{1}{1 + G_{1} G_{2} H_{1} + G_{3} G_{4} H_{2} + G_{2} G_{3} H_{3} + G_{1} G_{2} G_{3} G_{4} H_{1} H_{2}}

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\frac{1}{1 - G_{1} G_{2} H_{1} - G_{3} G_{4} H_{2} - G_{2} G_{3} H_{3} + G_{1} G_{2} G_{3} G_{4} H_{1} H_{2}}

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Solution

The correct option is B $\frac{G_{1} G_{2} G_{3} G_{4}}{1 + G_{1} G_{2} H_{1} + G_{3} G_{4} H_{2} + G_{2} G_{3} H_{3} + G_{1} G_{2} G_{3} G_{4} H_{1} H_{2}}$
Transfer function
$\frac{C (s)}{R (s)} = \frac{\sum P_{k} Δ_{k}}{Δ}$
$= \frac{G_{1} G_{2} G_{3} G_{4}}{1 - (- G_{1} G_{2} H_{1} - G_{2} G_{4} H_{2} - G_{2} G_{3} H_{3}) + G_{1} G_{2} H_{1} . G_{3} G_{4} H_{2}}$

$\frac{C (s)}{R (s)} = \frac{G_{1} G_{2} G_{3} G_{4}}{1 + G_{1} G_{2} H_{1} + G_{2} G_{4} H_{2} + G_{2} G_{3} H_{3} + G_{1} G_{2} H_{1} . G_{3} G_{4} H_{2}}$

Suggest Corrections

For the signal flow graph in the figure, the value of C(s)R(s) is

The correct option is B G1G2G3G41+G1G2H1+G3G4H2+G2G3H3+G1G2G3G4H1H2Transfer function C(s)R(s)=∑PkΔkΔ =G1G2G3G41−(−G1G2H1−G2G4H2−G2G3H3)+G1G2H1.G3G4H2 C(s)R(s)=G1G2G3G41+G1G2H1+G2G4H2+G2G3H3+G1G2H1.G3G4H2

For the signal flow graph in the figure, the value of $\frac{C (s)}{R (s)}$ is