Basics of Sig...

Basics of Signal Flow Graph

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Q. In the signal flow graph of figure the gain C/R will be

Q. The signal flow graph of figure shown below, has forward paths and feedback loops.

Q. The signal flow graph of a system is given below:

The transfer function (C/R) of the system is

$(G_{1} G_{2} + G_{1} G_{3}) / (1 + G_{1} G_{2} H_{2})$
$(G_{1} G_{2} + G_{1} G_{3}) / (1 - G_{1} G_{2} + G_{1} H_{2} H_{2})$
$(G_{1} G_{2} + G_{1} G_{3}) / (1 - G_{1} H_{1} + G_{1} G_{2} H_{2} + G_{1} G_{3} G_{2})$
$(G_{1} G_{2} + G_{1} G_{3}) / (1 - G_{1} H_{1} + G_{1} G_{2} H_{2} + G_{1} G_{2} G_{3} H_{1})$

Q. The input-output transfer function of a plant

H (s) = \frac{100}{s (s + 10)^{2}}

, The plant is placed in a unity negative feedback configuration as shown in the figure below.

The signal flow graph that DOES NOT model the plant transfer function

H (s)

Q. For the signal flow graph in the figure, the value of

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

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

Q. The transfer function between

y_{2}

and

y_{1}

in figure

Q. Which of the options is an equivalent representation of the signal flow graph shown here?

Q. An electrical system and its signal-flow graph representations are shown in the figure (a) and (b) respectively. The values of

G_{2}

and

H_{1}

respectively, are

$\frac{Z_{3} (s)}{Z_{2} (s) + Z_{3} (s) + Z_{4} (s)}, \frac{- Z_{3} (s)}{Z_{1} (s) + Z_{3} (s)}$
$\frac{- Z_{3} (s)}{Z_{2} (s) - Z_{3} (s) + Z_{4} (s)}, \frac{- Z_{3} (s)}{Z_{1} (s) + Z_{3} (s)}$
$\frac{Z_{3} (s)}{Z_{2} (s) + Z_{3} (s) + Z_{4} (s)}, \frac{Z_{3} (s)}{Z_{1} (s) + Z_{3} (s)}$
$\frac{- Z_{3} (s)}{Z_{2} (s) - Z_{3} (s) + Z_{4} (s)}, \frac{Z_{3} (s)}{Z_{1} (s) + Z_{3} (s)}$

Q. In the system whose signal flow graph is shown in figure.

U_{1} (s)

and

U_{2} (s)

are inputs. the transfer function

Y (s) / U_{1} (s)

$\frac{k_{1}}{J L s^{2} + J R s + k_{1} k_{2}}$
$\frac{k_{1}}{J L s^{2} - J R s - k_{1} k_{2}}$
$\frac{k_{1} - U_{2} (R + S L)}{J L s^{2} + (J R - U_{2} L) s + k_{1} k_{2} - U_{2} R}$
$\frac{k_{1} - U_{2} (S L + R)}{J L s^{2} - (J R - U_{2} L) s - k_{1} k_{2} + U_{2} R}$