Boost Control

Here we talk generally about how the B58 controls the turbo and more specifically about the maps you might need to recalibrate when changing from the stock turbo.

Boost control has several steps:

1. Figure out the boost target
2. Convert the boost target and error into power at the turbine wheel (i.e. how hard and fast the turbo should be spinning).
3. Work out the power inherent in the exhaust flow, how much of that needs to go through the turbine and how much should be ejected through the wastegate.
4. Work out the wastegate position to achieve that.

We note that we are controlling a single variable, the boost, but we have two parameters: the turbine power and the wastegate position with which to affect it. In effect, the turbine power is arbitrary. This makes the problem underconstrained. We will gain an understanding of the turbo control then look at ways to pin this down.

A note on naming and on units

MHD's XDF files use one set of map names and use g/s as the unit for MAF. BMW's A2L files uses a different set of names and kg/h for MAF. In the context of custom turbos, several important maps are missing from the MHD XDF files (presumably because they exist to support development of their stock turbo maps). For that reason, this article generally uses the BMW names and units but there is a bit switching between the two conventions.

Boost setpoint

Here, the DME runs through conversions of temperature and pressure quantities to arrive at the target MAF and target boost pressure for the turbo. It also figures out the deviation of the current boost pressure from the target and the target exhaust massflow by summing the air mass flow and the fuel mass flow. The only intervention from a calibration point of view is to increase some limits to allow the calculations to proceed naturally.

For the pressure calculation, there are two pressure ratio limiting tables. Both are functions of MAF, one of which also includes temperature. The DME takes the min value from each. There is then a third constant which applies to the boost pressure. Probably the best calibration approach is to lift these out of the way:

Name: BMWtchsp_rat_p_CmprPmp_T

Description: Upper limit for compressor pressure ratio setpoint.

Unit info: kg/h --> -

Base:

  500   535   600   650   725   800   850  1051
2.576 2.605 2.665 2.710 2.807 2.911 2.958 3.000

Modified:

  500   535   600   650   725   800   850  1051
4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000

The same change can be applied across the temperature dependent limit table (BMWtchsp_rat_p_CmprMax_M).

The absolute boost limit, the stock value is 2500 hPa (36psi) which is fine for most situations.

Name: BMWtchsp_p_ReqMax_C

Description: Maximum target boost pressure

Units: hPa

Base:

2500.000

The target massflow and pressure are both lowpass filtered using filter constants in tables BMWtchsp_fac_FilPRatCmpr_T and BMWtchsp_fac_mf_FilCmprNorm_T. These are configured for stock-like flows of upto 1100 kg/h (about 305 g/s). Consider adjusting for larger turbos. For example:

Name: BMWtchsp_fac_FilPRatCmpr_T

Description: Filter constant for target pressure ratio

Unit info: kg/h --> -

Axis: BMWtchsp_fac_FilPRatCmpr_Ax

Base:

 200.000  300.000  900.000 1100.000
   0.120    0.120    0.070    0.030

Modified:

 200.000  300.000  900.000 1800.000
   0.120    0.120    0.070    0.030

Name: BMWtchsp_fac_mf_FilCmprNorm_T

Description: Filter constant for corr. Target mass flow

Unit info: kg/h --> -

Base:

 200.000  300.000 1100.000 1120.000
   0.120    0.100    0.100    0.020

Modified:

 200.000  300.000 1100.000 1800.000
   0.120    0.100    0.100    0.020

For an overview of maps and values feeding into the volume flow calculation see below:

For maps and values feeding into the pressure calculation see below:

Power calculation (TchCtr_Pwr)

The first job of the boost controller is to work out how fast and hard is should be spinning the turbo to meet the required boost pressure. As such, (required) boost pressure quantities are converted into (required) power at the turbine wheel (in kW). Likewise boost errors are converted into power errors.

We can understand turbine power in terms of torque x rpm just as we can for engine power. As the boost pressure goes up, the air resistance on the compressor wheel also goes up so it needs more torque to keep turning at the same speed. As the engine speed rises and the airflow picks up, we can picture the compressor chasing the air and so it will have to rotate faster to create the same boost.

Feed-forward compressor map

This intuition is quantified in the compressor characteristic map (BMWtchctr_pwr_Pctl_M). This provides the power output from the compressor as a function of pressure ratio and MAF:

Pressure ratio refers to the boost pressure in the chargepipe divided by the pressure before the turbo.

Initially, the DME uses this map to create a good guess at the required turbine power:

This is fairly straightforward to understand: the map represents the turbo's power at various airflow and pressure-ratio values. The DME reads these off, corrects for temperature and we're done.

Note that with different and possibly bigger turbos than stock

1. They will flow more air so the MAF axis might require scaling up. A Pure800 would flow about 500g/s for example.
2. The power values might be lower not higher. In other words, if the turbo is operating more efficiently, it will generate the same MAF at lower power.

P error term

The DME then calculates a proportional error term:

This is a more subtle scenario.

Firstly we have the P-Factor (MHD's name) which is based on airflow and pressure-ratio (same as the compressor characteristic). Note that this does not depend on the boost error. It is more a property of the turbo as a system in the sense of how aggressively it responds. Note in particular

• When there is airflow through the turbo (i.e. it is spooled up), the turbo is responsive and P-Factor will be higher.
• When boost rises, the turbo has to work harder (to cut through the air, so to speak), it becomes less responsive and P-Factor will be lower.

The degree to which these effects occur depend on the turbo.

Then we have the P correction. Note that the inputs here are turbine massflow and boost error.

We note the following:

• This is where the error is factored in. When the error is zero, the value will be zero so as to cancel the P term in the PID control.
• boost error = (target - actual) so underboost is a +ve error (which is confusing because we intuively think of under as meaning less, but it is the other way around here).
• the correction provides a weighting to the boost error according to how far out of step it is with what's required in the exhaust.
• If we need a lot of exhaust flow and we are underboosting, the correction table will increase the p factor to hurry the turbo into meeting the demand.
• If we need not so much exhaust flow and are underboosting, the correction table will slow down the p factor.
• There is an additional spool mode table, however, this is often unused. The DME has a notion of spooling and an associated spooling factor which it determines from the boost error in the sense that, if we require a lot of boost but the actual boost is low, then the turbo must be spooling and so the spool factor that will be close to 1. Then, the DME can interpolate between the normal p-correction table and the spool table according to a second blending factor which it gets from a table (BMWtchctr_fac_FadeDyn_M). In practice this blending factor is zero, meaning only the normal table is used. To our mind, this is too much complexity but we mention it for anyone wanting to introduce a few more variables.

We can see this process in action in the following log:

Note that the names in the log are confusing. The 'p-factor' here is the final p term (and not the turbo gain property from the P-factor table).

D error term

Here, MHD's naming is to use D-Factor as the table which accounts for the error and D-Correction is now the power-based property-of-the-system factor.

Note that the gradient of the error is itself a pressure quantity (in hPa). As such, we think about it as the difference between successive boost error samples. (In other words, if gradient is rise/run then the rise the difference in the boost error samples but we do not bother with the run because it is always the same value.

Generally, the D-Factor values are small. This means we can worry less about them. For example, on the stock tune, with large underboost of 400 hPa (6psi) and maxed out gradient, the maximum possible D term would only adds 1.5kW to the compressor target.

Max possible D

Error (hPa)	Error Gradient (hPa)	Compr Power (kW)	D term (kW)
400	30	21	1.62
400	30	31	1.62
400	30	41	1.62
400	30	51	1.62
360	30	21	1.566
...	...	...	...

Generally, on logs, we want to see the feed-forward compressor map get as close to target as possible (in other words, the feed-forward compressor power and the compressor power after PD correction are the same to within a few percent). The caveat, at this point, is that we do not yet know whether the boost errors being fed back are caused by errors in our compressor map or errors in our wastegate position calculation. Let's move on to look at that problem.

Required turbine power

Once the feed forward and error terms have been calculated, the DME adds them up to arrive at a final value for the turbine power. This will be fed into the wastegate position control (see next section).

Limiting PID control (TchCtr_PwrFade)

Disabling PID control

In some cases, the DME will discard the PID output in favour of the value from the compressor map. This happens when:

1. the boost target drops below the actual boost by a value controlled by BMWtchco_p_HysAcv_C. Stock, this is 15MPa (0.2 psi). This can be interpreted as a hysteresis value. If the car is asking for more boost than it has currently, the PID will stay enabled to meet it. If the target drops, the PID will not be disabled unless the target drops sufficiently. This prevents jittery switching off of boost control.
2. changing gear, when stationary, when heating the cat, in limp mode, in launch mode, in eco mode, when the car wants to open the wastegate for sounds like braps.

Capping PID control

Optionally, the DME can be setup to cap the level to which the PID controller can increase the power from the compressor map. This is primarily to protect the turbo from overspeed conditions due to (experimental) PID output.

The cap is itself controlled by a map called BMWtchctr_fac_pwr_CompLimPctl_T or (Max factor for the increase of WGDC due to P and D in MHD's XDF files).

The capping calculation applied is $P_{required}=\min(P_{pid},P_{map}*factor)$. If, for example, the factor is 1.08 (i.e 8%), and the output of the PID is then 10% more than the compressor map output then the DME will take the value from the compressor map.

Notice that the factor is MAF dependent and

1. values at low to medium MAF allow the PID controller to raise the power target substantially (50-20%).
2. becomes restrictive at higher MAF (down to 6%).
3. the breakpoints on this curve are scaled for the mass flow range of the stock turbo. Rescaling the breakpoints might be needed for different turbos.

Finally, the capping only applies to target boost pressure below a certain maximum and target pressure ratios above a certain minimum:

1. The boost maximum limit is BMWtchctr_p_ReqDynLimPctl_C
2. And pressure ratio minimum limit is BMWtchctr_rat_p_ComprLimPctl_T (MAF dependent pressure ratios)

This provides a windowing mechanism for the PID cap.

On the stock tune, this capping path is disabled (because the upper limit, BMWtchctr_p_ReqDynLimPctl_C, is set to 0hPa and the pressure ratio minium to 6) so the capping condition is never true. Nonetheless, if you are changing the PID settings, this path is available for overspeed protection.

The diagram below show the blackbox view of the entire function. The crucial thing is the output: this is power target that gets handed over to the turbine side, which will then be met with wastegate position.

Turbine pressure ratio to mass flow calculation

An important characteristic of any turbo is how freely it flows air through the exhaust side. The DME quantifies this by asking if I apply a certain pressure across the turbo, how much exhaust will it flow?. It does this for the turbine alone and the turbine plus wastegate, where the wastegate position can change.

This introduces some new tables:

1. KF_AUSY_TURB -- this is the massflow table for the turbine + wastegate combined. This depends on both the pressure ratio across the turbine and the wastegate position (because there will be more flow if the wastegate is open).
2. KL_AUSY_TURB -- this is the massflow curve for the turbine. This only depends on the pressure ratio (because the hole has a fixed size).
3. KL_AUSY_TURB_DIFF -- this is a table of the slope of KL_AUSY_TURB.
4. KL_TABG2TABG_WZINV -- this contains pre-calculated values for $1/{\sqrt {exhausttemp}}$. It is scaled out to temps of 1400K (1125 C). (We will consider exhaust temps and pressures separately).

Stock, the massflow tables above are scaled out to a pressure ratio of 2.8, so you should consider extending the axes for custom turbos. In most tuning scenarios there will be higher maximum pressures in the exhaust manifold due to higher loads and lower pressure after the turbo because less restrictive downpipes.

The DME applies the following calculations:

$KF\_AUSY*p_{ak}*360/{\sqrt {t_{ab}}}=M_{turbo}(kg/h)$ ...1

$KL\_AUSY*P_{ak}*360/{\sqrt {t_{ab}}}=M_{turbine}(kg/h)$ ...2

$(KF\_AUSY-KL\_AUSY)*p_{ak}*360/{\sqrt {t_{ab}}}=M_{wg}(kg/h)$...3

$KF\_{AUSY_{D}IFF}*p_{ak}*0.36/{\sqrt {t_{ab}}}=M_{turbinediff}(kg/h/hPa)$...4

where

1. $KF\_AUSY$ is the output of map KF_AUSY_TURB (turbine plus wastegate flow map)
2. $KL\_AUSY$ is the output of curve KL_AUSY_TURB (the turbine flow curve)
3. $M_{turbo},M_{wg}andM_{turbine}$ are the massflows of turbo, wastegate and turbine respectively (BMW names: Msturb, Mswg, Msturbine).
4. p_{ak} is the exhaust manifold pressure (in hPa)
5. t_{ab} is the exhaust gas temperature (in Kelvin)
6. $KF\_{AUSY\_DIFF}$ is the the output of map KF_AUSY_TURB_DIFF (the slope of the exhaust flow map).

Target turbine pressure ratio

From the above massflow calculation, the DME knows massflow given pressure ratio. It now turns this question around to ask, given massflow (from MAF and fuel mass), what is the pressure ratio? To do this, it inverts KF_AUSY_TURB.

Because the exhaust massflow here is the target massflow, the corresponding turbine pressure ratio is the target pressure ratio.

The wastegate position is also a variable and it is the quantity we are ultimately trying to figure out. As such, the DME proceeds iteratively, using the current wastegate position to complete its calculation, which will provide an updated position and so on.

Exhaust massflow

Now the DME software incorporates the required turbine power and pressure ratio to obtain a turbine massflow. The flow is as follows:

Note there are two tables that have axes which depend on pressure ratio:

1. BMWtchctr_fac_TrbEffIvs_T. This is the so called turbine efficiency. It reflects properties of the turbo (so consider scaling the axis and setting suitable values).
2. BMWtchctr_fac_TrbExp_T. Specific temperature change curve. This is a pre-calculated table. A spreadsheet formula to recalculate it with different axis values is =1/(1-(1/X)^((1.395-1)/1.395)) (where X is a reference to the axis value).

Wastegate Position calculation (TchCtr_Pwr2Pos)

At last, the turbine and exhaust massflow requirements are fed into the feedforward wastegate position table:

Note:

1. The X axis is the massflow fraction to send down the turbine.
2. The stock exhaust flow axis is scaled to 300g/s (1080 kg/h) which is too low for even hybrid turbos.
3. 100% wastegate position here corresponds to the wastegate being closed (i.e. all flow through the turbine and none through the wastegate, see below).