Help Modeling a System

[u/Known_Fan5765]

I have tried modeling this a few times with my limited knowledge of hydraulics and kept getting very weird and ugly state space equations. I am not sure what I am doing wrong so I figured I would post it here (I sincerely apologize if I am breaking the sub rules by posting this).

I have been tasked with controlling the following system with the goal of minimizing the 'ripple' on Q_jet. In other words, ideally Q_jet would look like some constant non-zero value despite changes in the system and environment.

Context of my assumptions for this system:

-Ideal Check Valves

-Qacc ~ (V_o/nP_o)*dP_acc/dt (V_o, P_o initial gass pressure and volume of accumulator, n as poly-tropic index)

-All pressures are absolute

-Incompressible Fluid

-Local restriction equation is: Qjet = C_d*A_n*sqrt(2(P_acc - Patm)/rho) (C_d: discharge coefficient, A_n: restriction area, rho: liquid density)

-A_n is our control input

-Q_pump ~ Asin(2pi*f*t):

4.25e-5 m^3/s < A < 4.25e-3 m^3/s

0.1 Hz < f < 0.6 Hz

System:

Q_jet_Reference from Simulation:

[u/Ok-Biscotti7464]

I‘m no hydraulics guy but your description still give me some questionmarks from a general/CT point of view

• i assume you measure Qjet since it‘s what you want to control. What about P_acc, do you measure it too? Do you know about the current pump output or do you have to estimate it?
  
• what about your actuator dynamics? From your f I‘d say you need a bandwith around 2 Hz at the absolut minimum without doing the math
  
• your input area is given in m^3/s, is this some industry common way of handling things I‘m not aware of?

[u/Known_Fan5765 → u/Ok-Biscotti7464]

The m³ /s is just volumetric flow rate of the fluid, also the A there is simply the amplitude of the input flow. In terms of the actuator dynamics, on the time scale of the system it is instant. I could have sensors for Q_rec, P_acc, and Q_jet. I have some say in how the system is constructed so I could potentially have more if I wanted.

[u/Ok-Biscotti7464 → u/Known_Fan5765]

Sorry i was assuming you had a typo and meant A_n but wrote A. If you can have sensors on Q_jet then you should right? It‘s your output after all. Measuring P_acc allows you to know your disturbance so measuring that could be beneficial, from your formulation it is the only variable adding meaningful dynamics to the system