QUESTION $1$

$1\mathrm{.}1$ Your company has contracted an electrician to install an air$-$conditioner in one of the offices. The aircon has a temperature controller with an $85\%PB$ that has an input range of $0$ to $100C$ and an output range of $10$ to $58$ mA $.$ Calculate the controller gain.

$1\mathrm{.}2$ Consider a control system for the level of process liquid in a storage tank. An integral only controller is utilised. The algorithm has an integral time value of $32$ seconds. What will be the bias value after $2$ seconds if there is a sudden change to constant error of $8\%,$ when the controller output value is $-2\mathrm{.}5\%.$

$[21$ Marks$]$