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$]$

QUESTION $2$

Various control $($globe$)$ valves are categorised based on the link between the position of the stem of the valve and the flow rate obtained through the control valve. List and briefly describe the mode of operation of the most common types of control valve $($globe$)$ applied in manufacturing processes $($Also include their characteristic equations$)$

$[18$ Marks$]$

QUESTION $3$

In a normal situation, the controller must first be switched to automatic mode and set up for proportional only control. After this, a series of slight set point changes are introduced into the system and the control loop response is examined. The primary objective is to obtain a sustained oscillation as the control loop response by fluctuating the controller gain. If a set point change causes the oscillation of the loop's response to disappear, the controller gain should be increased. As new oscillations start growing $($meaning that the control loop is starting to be unstable$),$ the controller gain should be decreased rapidly. As soon as sustained oscillations are achieved, the controller gain is noted as "ultimate gain" and the period of oscillation can also be measured as "ultimate period".

$2$

To achieve the above goal, which steps should be carefully followed when using the Ziegler$-$Nichols tuning procedure?

$[11$ Marks$]$