In a surge tank shown helow

$F_i$

The flow rate out of the

$F(t)=C_{v}x(t)\sqrt[\phantom{2}]{l(t)}$

where $C_k$ is the valve's constant, $l(t)$ is the liquid level in the tank, and $x(t)$ is the valve's

opening $($the manipulated variable$).$

Draw the open$-$loop $($only a box signifying the manipulated variable, the disturbance and the

controlled variable$)$ and closed$-$loop block diagrams for this system and specify the input

$($manipulated variable and disturbance$)$ and the output variable $($controlled variable$)$ for this

system.

Write down the dynamic and steady$-$state mass balance for this process.

Linearize the non$-$linear dynamic equation.

Express the linearized equation in terms of deviation variables.

Derive the following transfer functions.

$G_p(s)=\frac{L(s)}{x(s)}$ and $G_d(s)=\frac{L(s)}{F_i(s)}$

Use the following steady$-$state data to obtain the numerical values for the time constant

and steady$-$state gains of the process and disturbance transfer functions.

$-\frac{?}{\text{b}\text{a}\text{r}}(A)=2m^2\frac{,}{b}ar(l)=4m\frac{,}{b}ar(F_i)=0\mathrm{.}01\frac{m^3}{s},\stackrel{}{x}=0\mathrm{.}5$

Using the above process and disturbance transfer functions and Matlab, obtain the

responses in the liquid level in the tank to a step increase in $F_1$ of $0\mathrm{.}1\frac{m^3}{s}$ and a step

decrease in $x$ of $0\mathrm{.}2.$ Obtain the two step responses separately, one at a time, and

attach your results to your assignment.