A Two$-$Tank Liquid$-$Level System

The Two$-$Tank Liquid$-$Level System is shown above. This is a fluid $($hydraulic$)$ system

Two tanks have cross$-$sectional areas $A_1$ and $A_2,$ respectively. A pump is connected to the bottom of Tank $1$

through a valve of linear resistance $R_1.$ The liquid flows from Tank $1$ to Tank $2$ through a valve of linear

resistance $R_2$ and leaves Tank $2$ through a valve of linear resistance $R_3.$ The density $$ of the liquid is

constant.

The pump pressure $p$ is the system input, while the liquid heights $h_1$ and $h_2$ are the system outputs.

Question

$1.$ Develop the input$-$output equations and transfer functions of your $($open$-$loop$)$ system.

$2.$ Construct a Simulink program for your system using the input$-$output equations and transfer

functions. That is$,$ two Simulink diagrams that should produce the same output.

$3.$ Carry out simulations and analyse your system. Consider the nature of your system inputs and the

values of your parameters when performing your analysis.