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$]$