Mason’s Gain ...

Mason’s Gain Formula

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Q. For the signal flow graph show in figure, the transfer function is C(s)/R(s)=

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

Q. The signal flow graph of a system is shown in the figure. The transfer function

\frac{C (s)}{R (s)}

of the system is

$\frac{6}{s^{2} + 29 s + 6}$
$\frac{6 s}{s^{2} + 29 s + 6}$
$\frac{s (s + 2)}{s^{2} + 29 s + 6}$
$\frac{s (s + 27)}{s^{2} + 29 s + 6}$

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Q. A control system is represented by the block diagram shown in figure.

ratio is

\frac{C (s)}{R (s)}

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

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Q. The signal flow graph for a system is given below. The transfer function Y(s)/U(s) for this system is

$\frac{s + 1}{5 s^{2} + 6 s + 2}$
$\frac{s + 1}{s^{2} + 6 s + 2}$
$\frac{s + 1}{s^{2} + 4 s + 2}$
$\frac{1}{5 s^{2} + 6 s + 2}$

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Q. The C/R for the signal flow graph in figure is:

$\frac{G_{1} G_{2} G_{3} G_{4}}{(1 + G_{1} G_{2}) (1 + G_{3} G_{4})}$
$\frac{G_{1} G_{2} G_{3} G_{4}}{(1 + G_{1} + G_{2} + G_{1} G_{2}) (1 + G_{3} + G_{4} + G_{3} G_{4})}$
$\frac{G_{1} G_{2} G_{3} G_{4}}{(1 + G_{1} + G_{2}) (1 + G_{3} + G_{4})}$
$\frac{G_{1} G_{2} G_{3} G_{4}}{(1 + G_{1} + G_{2} + G_{3} + G_{4})}$

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Q. The gain

\frac{Y}{R}

for the system with the following signal flow graph using Mason's gain formula is _________.

1.913

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Q. Consider the signal flow graph shown in the figure.
The gain

x_{5} / x_{1}

$\frac{1 - (b e + c f + d g)}{a b c}$
$\frac{b e d g}{1 - (b e + c f + d g)}$
$\frac{a b c d}{1 - (b e + c f + d g) + b e d g}$
$\frac{1 - (b e + c f + d g) + b e d g}{a b c d}$

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Q. In the signal flow graph of figure, y/x equals

$3$
$5 / 2$
$2$
None of the above

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Q. The signal flow graph of a system is shown below. U(s) is the input and C(s) is the output.

Assuming,

h_{1} = b_{1}

and

h_{o} = b_{0} - b_{1} a_{1}

, the input- output transfer function,

G (s) = \frac{C (s)}{U (s)}

of the system is given by

$G (s) = \frac{b_{0} s + b_{1}}{s^{2} + a_{0} s + a_{1}}$
$G (s) = \frac{a_{1} s + a_{0}}{s^{2} + b_{1} s + b_{0}}$
$G (s) = \frac{b_{1} s + b_{0}}{s^{2} + a_{1} s + a_{0}}$
$G (s) = \frac{a_{0} s + a_{1}}{s^{2} + b_{0} s + b_{1}}$

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Q. For the signal-flow graph shown in the figure, which one of the following expressions is equal to the transfer function

\frac{Y (s)}{X_{2} (s)} |_{x_{1} (s) = 0}

$\frac{G_{1}}{1 + G_{2} (1 + G_{1})}$
$\frac{G_{2}}{1 + G_{1} (1 + G_{2})}$
$\frac{G_{1}}{1 + G_{1} G_{2}}$
$\frac{G_{2}}{1 + G_{1} G_{2}}$

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Q. Consider the following block diagram.

Overall gain C(s)/R(s) of the above system is

1.316
-1.316
1.456
-1.456

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Q. The signal flow graph for a system is given below. The transfer function Y(s) / U(s) for this system given as

$\frac{s + 1}{5 s^{2} + 6 s + 2}$
$\frac{s + 1}{s^{2} + 6 s + 2}$
$\frac{s + 1}{s^{2} + 4 s + 2}$
$\frac{1}{s^{2} + 6 s + 2}$

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Q. The signal flow graph representation of a control system is shown below:
The transfer fucntion

\frac{Y (s)}{R (s)}

is computed as

$\frac{1}{s}$
$\frac{s^{2} + 1}{s (s^{2} + 2)}$
$\frac{s (s^{2} + 1)}{s^{2} + 2}$
$1 - \frac{1}{s}$

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Q. The system shown in figure below.

can be reduced to the form with

$X = c_{0} s + + c_{1,} Y = 1 / (S^{2} + a_{0} s + a_{1}), Z = b_{o} s + b_{1}$
$X = 1, Y = (c_{o} s + c_{1}), / (s^{2} + a_{0} s + a_{1}), Z + b_{0} s + b_{1}$
$X = c_{1} s + c_{o}, Y = (b_{1} s + b_{0}) (s^{2} + a_{1} s + a_{0})) Z = 1$
$X = c_{1} s + c_{o, Y = 1 / (s^{2} + a_{1} s - a_{o}), Z = b_{1} s + b_{0}}$

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Q. The transfer function of the open loop system G(s) which is represented by the singal flow graph shown in the figure below is

$\frac{G_{1} G_{2}}{1 + G_{1} H_{1} + G_{2} H_{2}}$
$\frac{G_{1} G_{2}}{1 - G_{1} H_{1} + G_{2} H_{2}}$
$\frac{G_{1} G_{2}}{(1 + G_{1} H_{1}) (1 + G_{2} H_{2})}$
$\frac{G_{1} G_{2}}{1 + (G_{1} + H_{1}) (G_{2} + H_{2})}$

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