In an experimental study, in order to control the liquid level with feedback control

system, three different cases were investigated to see the effect of the controller

type and additionally a set without a controller was also performed.

The responses of liquid level process for the four cases are plotted in the Figure

below and information on the sets are given in Table.

Figure. Responses of liquid level process under different cases

Table. Information on the controller types

steady$-$state gain

time constant

Investigating the responses of liquid level process under different cases, fill the blanks

in Table.

a$.$ Determine the type of the controller $($if used$)($fill the blanks in table$)$

b$.$ Indicate the corresponding response curve $($i$,$ ii$,$ iii or iv$)($fill the blanks in table$)$

c$.$ Discuss the four cases and specify which of the four cases would be more

appropriate to apply to control the liquid level.

Please write your answer step by step and clearly. I'll remember to evaluate your answer.