The stocking speed F on a paper machine is controlled by both the pressure P and the height of the slurry h in a feed drum with cross-sectional area A. F is proportional to the square root of the pressure in the exit slot. The air ventilation rate G is proportional to the square root of the air pressure in the box P. The Feedback controllers set the airflow rates G0 and the suspension F0 to maintain P and h. The system is isothermal. Derive a dynamic mathematical model that describes the manufacture of paper.

Please show all the work done, add the matlab script.