$1.$Write a mini project report on the below given case studv.

Your boss has discussed implementing a level controller on a troublesome process

tank that contains a boiling liquid. Someone told him that a level transmitter used with

such a system has a very noisy output and that a P $($or$)$ PI $($or$)$ PD $($or$)$ PID will

require a noise filter on the measurement.

$($a$).$ Show how a measurement noises filter can be implemented with a PD $($or$)$ PID

controller by drawing a block diagram of the controller, modified with a $1^{st}$ order

transfer function.

$($b$)$ How the response of a PD $($or$)$ PID controller with step change in the filtered

measurement? If necessary, calculate the time response.

C$.$ Your company purchased a digital control system several years ago that provides a

first order digital filter as one of its many features. Can you suggest why this noise

filter ought to be implemented using an analog instrument, instead of using the

available digital implementation? Assume that the digital controller utilizes a

sampling interval of $1sec.$