The objective of the IPA control loop is to take data from instrumentation on the engine (i.e. pressure data) and use that data as a feedback parameter to control fuel mass flow in real time.
This image, taken from a paper by Airborne Engineering, depicts a fuel throttle control loop. To understand how the loop works, it is useful to first examine the basic fuel throttling process, which is shown in (a). Here, a pulse width (mu_s) is applied to a servo, which turns the throttle valve by a certain angle (to see how exactly the valve and servo are connected, see "Throttle Mechanism"). From the pulse width sent to the servo, the flow coefficient (Cv or Kv) of the valve can be determined; the specific testing methodology in which a flow curve can be obtained from a valve is outlined in the "Testing Campaign" section of this project.
Once the flow coefficient has been obtained, it is passed into another controller, which multiplies it by sqrt(2*rho*dP_v). This should look familiar now, as you have the flow coefficient (Cv or Cd*A) multiplied by sqrt(2*rho*dP_v), which results in the single phase incompressible (SPI) mass flow rate equation (mdot = Cd*A*sqrt(2*rho*dP)).
Once the mass flow through the valve is calculated, it is used to calculate the pressure drop across the injector. This is actually still a point of confusion for us – usually, the injector sets the mass flow, but in this case it looks like the throttle valve does. We're unsure if the valve area needs to be smaller than the injector area for this to happen. Anyhow, assuming that the valve sets the flow rate through the system, we can say that the mass flow through the injector is the same as the mass flow through the valve. Then, using the same SPI equation, we can use a controller to convert from mass flow to injector pressure drop.
One thing I also just realized is that I'm not sure how to calculate the pressure drop across the valve. A dP sensor could be used, but would take up a lot of space. I need to find out if it is safe to assume that the upstream valve pressure is the tank pressure and the downstream is the injector manifold pressure...hmm
Anyways, let's look at the actual IPA throttle control process now. For the IPA, the controller is trying to enforce a demanded mass flow rate through the system. The way it knows if the mass flow rate is being achieved or not is by subtracting the demanded mass flow from an instantaneously-measured massflow. If this error is zero, the controller does not need to change the valve throw; if it is nonzero, then it does need to (the error will always be at least slightly nonzero). The controller computes this difference (mdot_err), and passes it into a controller, which converts mdot_err into psi. Psi = mu_s * sqrt(dP_v). The paper states that psi "is required so that the control loop can be designed using linear control system techniques, because it removes the nonlinear pressure drop relationship from the main loop."
After psi is calculated, it branches off in two directions. The first direction passes psi into a controller that removes the sqrt(dP_v) term from psi, converting it into a pulse width mu_s. An offset in mu_s is added to mu_s to get the final mu_s, likely trying to regulate the difference in required pulse width necessary depending on whether the valve is opening or closing. The second direction is passed into a controller that calculates Cd_val*A_val*sqrt(dP_v) / (Cd_inj*A_inj). This is where I begin to get lost, as I don't really understand the significance of this value. I also don't understand how passing it through a plumbing delay removes the Cd*A ratio and converts the sqrt(dP_valve) into the sqrt(dP_injector), so I will come back to this later.
The injector pressure drop is used to calculate the mass flow through the injector, which is used to calculate mdot_err.