ASSIGNMENT $8$

Liquid level control system is shown below where liquid level is measured and the level transmitter $($LT$)$ output is sent to a feedback controller $($LC$).$ The tank is $1\mathrm{.}597$ m in diameter and the valve on the exit line acts as a linear resistance with $R=5mi\frac{n}{m^2}.$

The block diagram for this level control system is given below.

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a$)$ Please define the load variable $($disturbance$),$ manipulated variable and controlled variable according to the first figure $($tank$).$

b$)$ Given that $G_{p1}$ and $G_{p2}$ are the transfer functions of the process, $K_m=12\frac{}{m},K_v=0\mathrm{.}01\frac{m^3}{m}in*$ and controller is P $-$only control with $K_c.$ Please calculate the offset to a step change in the load variable with a magnitude of $0\mathrm{.}1\frac{m^3}{m}in$ for the values of $K_c=1,2$ and $5.$

c$)$ Calculate the offset to unit step change in the set value, again for the values of $K_c=1,2$ and $5.$

d$)$ Please plot $h^{\text{'}}(t)$ versus time for $($b$)$ and $($c$)$ for the different values of and $5)$ in Excel.