I have successfully developed a mathematical model for my physical system. My objective is to control the mass of gas in and out of the system.
The mass flowrate is given by:
$V_f = C_d.\sqrt{2.\frac{\Delta P}{\rho}}$
$\frac{dM_{gas}}{dt} = A_{valve}.\rho.V_f$
where $V_f$ is the volumetric flow rate of the valve.
Assuming I am using a simple PI controller in the system.
$u(t) = K_p.e(t) + K_i \int_0^t e(t) dt$.
How can I relate the controller output $u(t)$ to the system model?
My objective is to open and close the valve.
When the valve is closed $V_f = 0$
I have not been able to find any reference material that explained how to achieve this task.
Please I will appreciate if someone can please explain how to perform this task or direct me to reference material.
Thank you for your help.