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Q. Find the transfer function

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

for the system with following diagram block diagram:

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

Q. The equivalent transfer function of the system shown in block diagram is:

G_{1} = \frac{1}{s + 1}; G_{2} = \frac{1}{s + 4} a n d G_{3} = \frac{s + 2}{s + 5}

Q. The equivalent of the block diagram in the figure is given as

Q. Block diagram of a control system is shown in the figure.

The condition that must be satisfied to remove the effect of disturbance on the reponse of the system.

Q. Consider the system shown in the figure below:

The transfer function \frac{C}{R} of this system is

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

Q. The transfer function

Y (s) / R (s)

of the system shown is