For the control system whose major transfer functions are given as:

a$.$ Find the closed$-$loop transfer function equation

b$.$ Calculate the offset for a unit step change in the disturbance and using a $K_c=10.$

Indicate this value as a $\%$ of the final value of the response when there is no control.

c$.$ Neglecting the time constant of the valve, what is the recommended controller gain,

$K_c$ that would give a decay ratio of $0\mathrm{.}25?$