Foreword: I'm going to post some knowledge that very few are privileged to know. This is the result of years of me reverse engineering, meeting the right people, and plain stumbling through it with my own vehicle. I requested a lot of these tables and helped get them defined through Eric, and he's been an excellent help through it all, so props to him. Its a true gift to have someone that helps that much in this industry, especially when he's not getting any extra money by doing so :)
I will warn you all: No part of this is easy. OEMs have access to a lot of data and very talented calibrators, well versed in math and science, and this isn't your typical spark/fuel map that is by comparison cake walk to dial in. That said, lets dive in.
Ford Turbo Model Crash Course
The turbo model for Ford boils down to turbocharger power equations. The turbo model encompasses 5 main parts: Estimation of turbine inlet pressure (ExMAP), Turbine Maximum Efficiency estimation, Compressor Speed Estimation, and Compressor Efficiency Estimation, Actual Turbo Control. Each of these is important, so we'll go over each part. I will be using example values from a Focus ST for reference, but this applies to all Ecoboosts, the main difference is you will see two different strategies to convert the output of the model (desired mass fraction) into wastegate control. If you have two turbos, all of your compressor airflow inputs will be halved (i.e. itll be airflow/2 wherever I list compressor airflow).
Exhaust Manifold Pressure
ExMAP is an important part of calibration for two reasons, 1: It directly scales inputs to the VE equations (so affects all of SD), 2: It plays a roll in the turbine models.
We can find this here:
https://i.imgur.com/0VuCGg9.png
So, you'll notice we have one of two models available: Wastegate Restriction, or Wastegate Duty Cycle, and then 4 or so tables for each. They make up a scaled quadratic equation:
ExMAP = (Quad(x) * Airflow^2 + Linear(x) * Airflow + Offset) * ExBP Multiplier + ExBP
ExBP is created by a separate model that we don't have access to yet, and it doesn't change quite as much due to airflow (its a function of exhaust), so its not quite as vital to have. It represents the turbine outlet pressure, which would be your exhausts "backpressure" seen at the turbine.
The two models merely differ in how they pass their x value in: Wastegate restriction uses a calculation based on the estimated position of the wastegate, wastegate duty cycle uses wg_dc directly.
The restriction model is more common (and more accurate when done right, or they wouldn't waste their time with it), and estimates the position of the wastegate. It does this use ExMAP, ExBP, Estimated Wastegate Canister Pressure and the Spring Preload (which we have) and assumptions about how much canister pressure moves the wastegate and how much it resists the natural pressure on the wastegate valve (which we dont).
Now you may think this is circular: ExMAP depending on WG Pct which depends on ExMAP. You're right! However, your desired airflow will have certain requirements, and so it comes up with desired and estimated/current at all of the steps, and it does things in the right order so that it isn't dependent on itself circularly. I.e., the last estimation of ExMAP is used to predict the next wastegate restriction, then new ExMAP is estimated based on this, then the next restriction is calculated, and so on.
Suffice to say, restriction is complicated, and not all values are exposed to calibrate it, but for the most part, stock values for everything except spring preload will keep you accurate here so thats all you see.
Once you have a restriction, its simply doing the lookup of your coefficients in the tables and working from there.
Now, the main reason we need ExMAP is to calculate turbine expansion ratio (ER), this is the ratio of ExMAP over ExBP. If you've ever looked at a turbine map, you know this affects the efficiency the turbocharger is operating at, which we'll need later.
Also, I should add this is all corrected for estimated exhaust temperatures and so on, so the math can get dicey, but if you do it all, you can end up with outputs like this from the values:
https://i.imgur.com/jtzlGhD.png
In this case I also plotted the Turbine Outlet Pressure (ExBP) as I had access to it to correct these models.
In order to calibrate this in reverse, you need a turbine map with an airflow curve. Its not necessarily easy to do, but you can invert their model to get an airflow to ER at 100% restriction (which they're usually plotted as) and work from there. Else, you're working from scratch, and have to manipulate the equation to get you sensible values, or take measurements of ExMAP yourself and monitor airflow and plot it that way while holding the wastegate at various restrictions. Its not easy, but you can get something "close" using good ol' fashion guess and check. STFTs may even help you dial this in (remember ExMAP is part of VE!)
Turbine Maximum Efficiency estimation
Next, we need an estimation of the maximum efficiency of the turbine. This is black magic, and is rarely available even on plots. True turbine efficiency is a function of speed, expansion ratio, airflow, and so on. Ford boils it down to maximum possible efficiency at a given ER, regardless of speed.
The function takes the form of:
Max Efficiency = (Offset + Slope * ER + Quad * ER^2) * (1 - e^(Gain*(1-ER))).
So its quadratic times an exponential. Fun.
The curve shape ends up being like the red in the following:
https://i.imgur.com/URX0KcV.png
The blue actually comes from correcting the ExMAP model we had before for pressure (like a normal turbine map).
Now, we have these values available here:
https://i.imgur.com/PP3EPn0.png
Now these are the hardest to calibrate. Seldom is this information available, so typically, you just have to get it somewhat close. Some manufacturers give you a maximum efficiency percent, so you just have to trend your curve to do so. The Exp. Gain controls primarily how fast it rises to the max, and the quadratic controls the actual max value for the most part. Typically, find a turbine of similar size, and try to make the shape of the curve look like the above as they all typically are of that shape.
Compressor Speed Estimation
Those of you familiar with compressor maps will probably have an idea of how this works. Its a function of compressor pressure ratio(PR), and compressor airmass. The ECU calculates two speeds in this case: One for our desired airflow (and the resulting boost and thus TIP that will need), and one for our current airflow and TIP. I say this roughly, it does estimate the airflow effects from transients based on intercooler and manifold volume, as well as loss from TIP which is after the intercooler to compressor outlet which is pre-intercooler, as well as loss from barometric to compressor inlet pressure, but we have no access currently to any of those models.
So, Ford could use a 3D table airflow(AM) vs PR (compressor outlet over compressor inlet) vs Speed to do this. GM takes this route for example. However, Ford is crafty, and instead use a 3D equation instead. Why? I don't know, possibly processing constraints, better accuracy, etc.
The equation is:
Speed = Offset + A*AM + B*PR + C*AM*PR + D*AM^2 + E*PR^2 + F*AM^2*PR^2.
These are the seven values in the "Inferred Speed" category, labelled for which they correspond to.
If you plot out the stock ST (best done in contour maps like a true compressor map) you get this:
https://i.imgur.com/bVG06zD.png
Now remember a true compressor map doesn't necessarily cover all these areas because a compressor wouldn't operate there, so its safe to assume they do a curve fit to create these, with weight placed on operational areas they'll actually see (I.e. 20lbs, 2.0 PR vs 99lbs, 4.0PR). Once you get outside their intended range, it might not be accurate at all. In OPs case, his model clearly blows up with speeds of nearly 400k! I don't know of any turbochargers that actually operate at those speeds in automobiles, so we can safely assume its blown up :)
To get this, you need a compressor map, and some curve fitting software that can give you an accurate fit. Not easy, but can be done to give you these values. That, or you can scale the above equation to scale your current map. If you know you have 30% more airflow at the same PR for a given speed, you could roughly scale the airflow axis , i.e. substitute 1/1.3 * AM everywhere AM is, and work out the equation. Typically that means A*1/1.3, C*1/1.3, D*1/1.3^2, F*1/1.3^2. Guessing here will probably hurt you as you'll end up with a shape that doesn't make sense, so either scale, or fit your actual compressor data.
Compressor Efficiency Estimation
Compressor Efficiency uses the same equation as above:
Efficiency = Offset + A*AM + B*PR + C*AM*PR + D*AM^2 + E*PR^2 + F*AM^2*PR^2.
Again, a contour plot like a compressor map:
https://i.imgur.com/TfPXM6Q.png
I have limited the minimum efficiency in this case, but this as you can see looks less like true lines than an actual efficiency plot would be, but its the closest Ford could get for the compessor in operating regions they care about most likely. Now, this fit is important. If it goes to 0 at a point you're operating on, your Mass Fraction will blow up (we'll get to why shortly) and you won't have any control of the system any longer (like OP, in his case you can see it in the Turbo Mass Flow Desired). The ECU clips the value between 0 and 1 for sanity, but 0 will cause a definite blow up.
Actual Turbo Control
So I've shown you the "guts" so lets get to how its used.
The answer? Physics.
The ECU calculates your current speed, current efficiency, desired speed (based on desired airflow/TIP), desired efficiency (based on desired airflow/TIP as well), and maximum turbine efficiency (based on calculated ExMAP at closed wastegate).
Using this, we know we will thus have a Speed Error. So we have a control problem, control the turbocharger to minimize speed error.
To do so, we have the wastegate as output, and the above as inputs.
Ford boils this down to a physics equation: Knowing the efficiencies, airflows and pressures involved (PR,ER, Comp Eff, Turb Eff) we can calculate a power requirement for the compressor to operate at this zone, as well as how much power we have currently. This is why zero efficiency blows up. Zero efficiency = infinite power requirements! So, we need to control the turbine power produced to equal our desired compressor power. Doing so will accelerate the turbocharger (spool it) so that we can operate at our desired condition. It calculates a natural turbocharger acceleration produced by this power, and you can also "shape" this power with a Shaping Profile which is provided.
So, once we have this desired power, this can be converted into a desired exhaust flow using physics and the info we know. This is our "Turbo Mass Flow Desired" as logged. This is how much flow we need to get to our desired acceleration. However, we have only so much exhaust currently available. This is where "MFRACT" or mass fraction comes from. MFRACT is our Desired TURBINE mass Flow over our Current EXHAUST mass flow. This is an important distinction. Exhaust flow = Turbine flow + Wastegate flow. So, a value <1 implies we want some wastegating. A value >=1 implies we want all our exhaust flow into the turbine.
Thus, we get a desired MFRACT. The remaining parts of turbo control all involve converting this desired MFRACT into a commanded wastegate DC.
A value >1 means we want more exhaust flow than the system can produce currently. I.e. we're in a spooling stage OR the model believes the turbocharger can not operate at that condition. A value <1 means we're capable of hitting this demanded compressor power with our current exhaust flow.
The final part of the equation is converting this mfract into an actual WG DC. Depending on year and vehicle, this can be a single step (airflow and MFRACT to DC) or multistep (airflow and mfract to canister pressure, canister pressure and compressor outlet to DC), surrounded by a PI (on the single step) based on accel error, or an adaptive PID (in multistep) based on boost error. I may cover each of those more in-depth later, but they're the far easier part.
Hopefully this helps, or at least convinces you its not an easy task and you may have to experiment to try to get something stable.
I'm sure someone "in the know" has figured out a way to hack around this system and get control they desire. I know Cobb on the vehicles they support created an entire custom WG system just to work around this system for larger turbos.
