The liquid level control system, where the liquid level is measured and the level transmitter output is sent to a feedback controller $($LC$)($level controller$),$ is shown below. In the steady state, $=2m,V=1000L$ and $F^{-}1=50\frac{L}{m}in,$ as well as $Gv=1$ and $Gm=1.$

a$)$ Draw the flow diagram of the system $($process $+$ control$).$

In case the reference value is increased to $2\mathrm{.}5m$;

b$)$ Find the offset for $P$ control with Kc value of $2.$

c$)$ Find the offset for PI control with Kc value of $2$ and $$ value of $1.$

d$)$ Due to the malfunction in the controller, the P function does not work and therefore the controller only works as I. In this case, find the offset.