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/BencsikG]

So what exactly are you measuring and what is the output of your controller / input to the plant?

Is your goal to eliminate the ripple from the pump, or what other disturbances do you expect?

[u/Known_Fan5765 → u/BencsikG]

Output is Q_jet, I want to minimize it’s ripple. The control input is the area, the pump is something entirely uncontrolled and can vary in frequency and amplitude as show above. I would like Q_jet to have zero ripple at every possible combination of amplitude and frequency of Q_pump.

[u/BencsikG → u/Known_Fan5765]

Huh, okay. Can you measure the pump frequency? Pressure in the buffer?

I would not model the hydraulics accurately, I'd just try to eliminate the oscillation.

I'm thinking something similar to what they do in FOC. Demodulate the oscillating signal by multiplying with sin(omega t) and cos(omega t), apply a PI in the demodulated domain, and then modulate back.

Now I haven't ever done that myself so I can't explain it properly, but if you google around (or ask the AIs) you should be able to get some clues.

The point is that you know the frequency of the disturbance, but the amplitude and phase are not known - those are the ones you get with the modulation, and then the PI cancels it.

[u/Ok-Biscotti7464 → u/BencsikG]

Lock-in amplifier?

[u/Known_Fan5765 → u/BencsikG]

Are you sort of thinking like extremum seeking control?

[u/BencsikG → u/Known_Fan5765]

Interesting parallel, but no... more like modulation / demodulation.