The Laplace transfer function for the tank height, $H,$ when the outlet flow, $Q,$ is varied is given by:

$\frac{H^{\text{'}}(s)}{Q^{\text{'}}(s)}=-\frac{100}{20s+1}$

The height is measured in inches, and the outlet flow, $Q$ is measured in liters per minute, and the inlet flow is $q_i,$ a constant value. The variables $Q^{\text{'}}$ and $H^{\text{'}}$ are deviation variables.

The system was initially at a steady state at a height $=10$ feet. For a unit step increase lade in the outlet flow:

A$-$ What will be the new steady state height?

$B-$ How long it will take the system to reach the new steady state?

$C-$ Explain why the system will settle again to a steady state although the remains constant.

What do you name this system from a control point of view?