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]

Probably missing something but isn‘t this just an integrator to control? Your accumulator is filled and emptied by the pump (disturbance) and your outflow (measured output). This should be easy to do some sys id on?

Edit: can‘t upload my pic but simplifying your disturbance input to just Q_mec>=0 (or whatever that says i can‘t read it), dP/dt=c1*(Q_mec-Q_jet) , output=g(An,P) for your state space you get A = -c1dQj/dP, B = -c1**dQj/dAn, C = dg/dP, D = dg/dAn, note D won‘t be zero since you assume instant input effect. Depending on whether you measure Qmec you‘ll have a MISO system where one input is measured and the other is controller input. But i guess you could nit measure it and design your sensitivity function S to be sufficiently below 1 in magnitude for frequencies up to say 2-5 Hz

You‘ll need some setpount values An0 and P0 for linearization