WB Exhaust back pressure compensation- pre-turbo

Excuse me if this has been asked or if i have missed something, but a general question regarding exhaust back pressure compensation to correct lambda readings on wideband sensors that are mounted pre-turbo-

Can anybody help me understand the math behind this? are we talking about a multiplier to a lambda value based on pressure or a complex algorithm with many variables?

If it can help.

The back pressure compensation will vary depending on which sensor you are using. I found this useful resource from RB Racing which has a calculator for the NTK sensor - https://www.rbracing-rsr.com/l2h2_backpressure_04.html

The graph Ludo86 posted sums up the situation though. When the actual lambda is richer than 1.00 the displayed reading will be richer, and when the actual lambda is leaner than 1.00 the displayed lambda will be leaner. I don't have a calculator for this though. The AEM 4 channel UEGO unit we have fitted to our 86 compensates for back pressure within the unit.

Andre, I see your Facebook post on this topic. This got me thinking some more about this

I use and distribute a WB controller that utilizes the bosch LSU 4.9. On a test mule I have a pressure sensor fitted to the exhaust near the turbo flange. My thought was to use a calculated field with the WB reading and pressure reading to give me actual O2. I have been thinking of a way to do some testing with this....

I think the key to the answer is in the reply Ashley from Electronz made to my facebook post. What you really need to do is compensate Ip (pump current) based on back pressure, not lambda. What this means is that back pressure needs to be compensated in the core of the controller before it outputs lambda. Backwards compensating for back pressure seems a little more difficult.

On the controller I'm using I can't get a raw Ip output to manipulate so I'm looking at doing some math in the ECU to calculate Ip back from the lambda value (based on the published Ip - Lambda characteristic) and then accounting for back pressure before outputting compensated lambda.

There is some good info in that FB thread, How are you coming along with doing some math in the ECU?

You make a good point- regardless of error it helps you to trim individual cylinder trim-setting up 7 sensors, 1 per hole and 1 post turbo-

For others reference here is what Ashley posted-

Take note that the pressure error correction is applied to the pump current measurement "Ip", not to Lambda. The relationship between pump current and Lambda is not linear so an error of 5% in pump current may not be an error of 5% for Lambda. Refer to section 4.4 "Nominal Characteristic Line" for Ip/Lambda relationship. Quite tricky to back calculate pressure correction, it is best directly applied to the pump current reading before converting it to Lambda. The same applies for temperature compensation. Some controllers with CAN output give you the pump current so you can do the correction and conversion to Lambda in real time with a display that allows configuring maths channels.

It's on hold at the moment as I'm too busy to do justice to it. I've got a 100 PSIA sensor coming next week which is the first part I need to get the job done. Once that's fitted in place of the 100 PSIG sensor I'll have a look at writing some code in build to deal with it.