# How do EBD algorithms work?

18 replies to this topic

### #1 giskard

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Posted 11 March 2013 - 15:27

Hi,

Can someone tell me how Electronic Brake Distribution works vs a mechanical prop valve? (In a street car)

I understand that the mathematically ideal rear vs. front proportion is a sort of lay-down parabola, and that a mech. prop valve approximates that with 2 linear segments. I also know that with EBD, the prop valve is gone, and the ABS valves are used to do the proportioning.

My specific Q's:

- Does the EBD algorithm then target a specific proportioning curve?
--- or does it do something silly like wait for the fronts to start to slip then add rear line pressure?

- (I understand that EBD may have a means of changing the proportioning depending on inputs such as rear suspension deflection, yaw rate, steering wheel angle, or other inputs from the stability control system)

- Are ABS valves capable of reducing (or adding) line pressure smoothly to yield a given target curve without pulsation?
--- or does it necessarily pulsate?

P.S. I forgot to select "email when replied to". How do I change it after posting?

Edited by giskard, 11 March 2013 - 15:28.

### #2 TC3000

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Posted 11 March 2013 - 16:51

for a given vehicle the load shift between the rear and the front will depend on the value of longitudinal acceleration, CoG height and wheelbase.
the other variable, which would define your starting brake pressure distribution is weight distribution. As higher the load on one axle, as more braking force it can transmit (in simple terms)

wheelbase is fixed, the offset from the base weight distribution can be measured via axle deflection, longitudinal acceleration (deceleration in this case) can be measured
that would leave CoG height as a critical variable, not sure how they will account for this, but my guess would be, that a algorithm would track long. accel. to allocate the pressures, set the distribution,
then offsetting this by static the weight distribution.

There are mechanical/hydraulic systems, mainly in vehicles with large cargo weight (trucks, utes, vans, station wagons, etc.) which use a variable set point proportion valve, to account for the static offset in weight distribution from empty to loaded.

such as this one:

if you can follow the "ideal" brake force distribution curve more closely, you gain braking performance. The shaded area (a), would be what you gain in comparison to a single set point proportion valve.
a proportion valve using two set points can track the "ideal" parable pretty closely ( tri linear approximation)

### #3 giskard

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Posted 11 March 2013 - 20:09

Thanks for the curves. That curve suggests that EBD is able to follow the "ideal" curve. So in addition to my original questions:

- Is that curve baked in?

Edited by giskard, 11 March 2013 - 20:19.

### #4 Greg Locock

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Posted 11 March 2013 - 22:03

I know a bit more about ESC than EBD, but given they are programmed by the same people, I think it'll work like this:

The important thing about EBD is that is it working in the linear range so sensing lockup of a wheel is far too late.

So, they start with a simple model of the car, cgz, wb, track, cgx. They might even build a weight model of the car based on fuel level, seat belts fastened, and any height or pitch sensors that the car has. Then they build a table of 'ideal' proportioning based on that. Then they use feedback from the ABS tone wheels to check that all four wheels are decelerating at the same rate. As the longitudinal g increases then the ABS can take over , btu again the first guess is derived from the simple vehicle model.

### #5 giskard

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Posted 12 March 2013 - 03:33

Thanks. So my only unanswered question is:

- Are ABS valves capable of reducing (or adding) line pressure smoothly to yield a given target curve without pulsation?
--- or does it necessarily pulsate?

### #6 Greg Locock

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Posted 12 March 2013 - 03:52

Thanks. So my only unanswered question is:

- Are ABS valves capable of reducing (or adding) line pressure smoothly to yield a given target curve without pulsation?
--- or does it necessarily pulsate?

I'm guessing no pulsation is necessary. When my ESC kicks in it is so gentle as to be unnoticable, for example. That mey be because of 2 reasons (a) I don't have my foot on the brake pedal at the time, and (b) the interventions with ESC are probably fairly gentle, say 0.2g equivalent on one wheel, ie 0.05 g in a total vehicle sense.

### #7 murpia

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Posted 12 March 2013 - 22:02

- Are ABS valves capable of reducing (or adding) line pressure smoothly to yield a given target curve without pulsation?
--- or does it necessarily pulsate?

I looked into this briefly recently, using some of the VW group 'self study' training that can be found online. My understanding is that some pressure can be reduced without pulsation, but beyond a certain point the displaced fluid must be returned to the pressure side of the ABS valves, which is done via a pump (causing the pulsation).

So the answer to your query is 'it depends'. Having driven a car with EBD for many years I never felt any strange pedal feel unless during an ABS event, so I suspect the EBD authority is below that which requires the return of fluid. Whether this means a different hydraulic circuit in the ABS module to the self-study guides, I don't know.

Regards, Ian

### #8 giskard

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Posted 15 March 2013 - 15:07

OK so could someone corroborate:

- EBD only reduces rear brake line pressure and leaves front pressure unmodified (up to the point where ABS kicks in of course)
- Rear brake line pressure reduction curve is baked into the EBD algorithm (and possibly changing according to inputs such as rear static ride height)
- Said pressure reduction up to near max braking (i.e. no tire slippage) can be performed by the ABS valves, without pulsation

### #9 TC3000

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Posted 15 March 2013 - 18:34

- EBD only reduces rear brake line pressure and leaves front pressure unmodified (up to the point where ABS kicks in of course)

o.k. maybe it's just me being picky, but if you want to make it a "general statement", I would say EBD only adjusts rear brake pressure......, is more accurate.
Now, this may very well apply only/mainly in the context of racing, where you don't brake with a constant deceleration value into a corner, but nonetheless, I feel it would be a more correct.
If you "read" the brake force distribution diagram backwards, that would be the case when coming from maximum braking force and easing off the brakes, you will see, that you would actually
need to increase rear brake pressure to stay close to the ideal distribution.

Ignore the lower graphic, you will see that the "ideal" brake force distribution parable will change with load.
Any form of "fixed" distribution, which would mean a straight line, will intersect the parable only at one given point. This given point would correspondent with a certain deceleration value (G).
Only for this one value, would the brake force distribution be "ideal", meaning both front and rear would lock up at the same time (assuming no ABS).
Until you reach this point, you will lock up one axle before the other (usually the front), after this point the other axle would lock up first.
This should be seen in the context of overall grip (road condition). As you will see, when you look at the second diagram.
Let's assume we estimate overall grip with 0.85 (longitudinal braking force/vertical force) and optimize a fixed distribution so that the both axle would lock up at the same time, when deceleration is 0.85G.
This means both axle use all the available grip and nothing is left "on the table" (max. braking efficiency).
Now, if it rains and the overall grip reduces, so that we can only get a max. deceleration of 0.5G, we would lock the front wheels first (no ABS) which means under this conditions we underutilized the rear axles possible contribution to overall braking.
On the other hand, if we encounter a higher then anticipated grip condition, where we could brake harder, decelerate with more then 0.85G, the rear axle would lock up first (because, due to the higher deceleration, more weight/load will get transfered to the front tyres). This can cause stability issues, if we have a side force (cornering, banked road, side wind etc.) at the same time.

Now, with ABS, in theory, we could say, that we would not need to worry about this, because the ABS will just take care, of the axle which is going to lock up.
That's true to an extent, and would be the rear if we opt for equal brake moment distribution front and rear (as a side note, brake moment is not only dependent on brake pressure, brake disc/drum and tyre diameter/radius have a effect as well).
But for most people it would be very "unpleasant" and "confusing" if they sense ABS activity under "normal" braking. This would lead to the impression, that they have reached the limit of grip, and that more braking effort is not possible. This in turn would lead to greatly increased stopping distances, as most people, would not "dare" to brake harder.

To avoid this, brake moment (pressure) distribution is used, to take into account the effects of load/weight transfer. But with any fixed distribution, you will get only one intersection with the ideal parable.
If you use a proportioning valve, you can get two (bi linear) intersections/or near intersections and in general minimize the area between the two curves. With a two set point proportioning valve, you would
get three intersections (tri linear) and can minimize the area even more.
If you can track the parable perfectly, you have optimized your overall braking efficiency for all deceleration values, and both axle would (without ABS) lock up at the same time, now ABS intervention would start at both axles, and really signal that the overall limit of available grip is reached.
If the brake force distribution is not "ideal" the axle which has the larger brake force proportion will trigger the ABS action, but that still leaves the other axle underutilized, reducing overall braking efficiency.
The advice given to "brake as hard as you can" and let the ABS sort out the rest, is good, but some (most?) people will not follow it, and stop increasing or even reducing pedal pressure when they sense ABS intervention. While a "normal" ABS can prevent the lock up of the over utilized axle, it can do nothing to use the other, underutilized axle more.
Therefore, as long as people don't brake harder when ABS kicks in, this axle will not contribute it's full potential and overall braking performance/efficiency will be less, then it could be.
EBD tries to account for this, by getting both axle "to the limit together", ABS then controls the overall deceleration value, in accordance to the available grip, but both axles will contribute there max potential to the overall braking effort.

This diagram shows the optimum brake force distribution for a given vehicle configuration.
The thin black diagonal lines, represent the longitudinal acceleration/deceleration values and are labeled at the intersection with the ideal parable (0.1-0.8 G)
The thin dotted lines which meet at the intersection of the diagonal lines and the parable are the "grip" values for the individual axles.
The red/black line (ß) would represent a fixed brake force distribution front/rear. (this schematic is from a hybrid, therefore it shows the combined effect of generator and brakes, but you can ignore this for now)
As you can see, the shown distribution intersects the ideal parable at 0.5G - only at this one value, would the front and rear axle reach the limit of grip together.
At all value below <0.5G, the red line crosses the "grip lines" coming from the front axle first.
In practice this means that for example at 0.3G deceleration the front axle would lock up in the moment the red line crosses the 0.3 Mü (grip) line coming from the front axle. The overall deceleration at front lockup would be ~ 0.28G (the front wheels would lock up or ABS would intervene at the front axle only).
If the driver keeps increasing brake pressure, the overall deceleration would continue on the dotted line, until when intersecting the parable and also the "grip line" coming from the rear, the rear would lock up too the overall deceleration peaks at 0.3G which would be the maximum at this grip level.
If the driver would not increase the brake pressure (until rear wheel lockup) just keeping at the lockup threshold of the front axle only (or let ABS do that for him) the total deceleration he can achieve is ~0.27-0.28G, which is less then the overall grip would permit in this situation.
As further away, the brake force distribution line is from the ideal parable at any one point, as larger this difference (utilized deceleration vs. possible deceleration) will become.
This is where EBD can help to increase the overall braking efficiency and augment ABS.

Edited by TC3000, 18 March 2013 - 03:37.

### #10 mariner

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Posted 17 March 2013 - 11:21

As an historical reference the DS Citroen had fully dynamic F/R proportional braking in 1955.

It used a roller and balance bar assembly under the foot pedal which adjusted the F/R ratio continously according to the vehicle weight distribution. The distribution was known from the ride height sensors in the hydraulic suspension sytem.

You could also remove the rear wings/fenders by using the jack handle but it was an odd car!

### #11 Tony Matthews

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Posted 17 March 2013 - 13:25

You could also remove the rear wings/fenders by using the jack handle but it was an odd car!

A very interesting car, and as a side note, I saw one in King's road, Chelsea, body and all brightwork painted matt black. It looked sensational, and that was in 1973/4, and matt/satin finishes are regarded as daringly new now...

### #12 desmo

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Posted 17 March 2013 - 15:59

My grandparents had a DS in the late sixties they'd bought in France and brought back, it really was a fabulous car in many ways, certainly advanced for its day. I can however remember the police not being happy about the typically French yellow headlights. The ride was pluuuuush and I imagine the aero drag was competitive with anything today. This was back when Citroën built cars that were actually substantively different than the norm.

### #13 TC3000

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Posted 17 March 2013 - 18:27

sorry for going semi-off topic
but in regards to the DS, maybe some like a bit background info, about the guy behind most of it's innovations.

and a photo of the brake pedal assembly as mentioned by Mariner:

the DS proportioning system:

not from the DS, but the XM used a proportioning system too, here a complete hydraulic systems schematic:

Edited by TC3000, 17 March 2013 - 18:51.

### #14 Tony Matthews

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Posted 17 March 2013 - 19:50

and a photo of the brake pedal assembly as mentioned by Mariner:

At first glance I thought it was a hydraulic clay-pigeon thrower...

### #15 desmo

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Posted 18 March 2013 - 01:54

Excellent. I noticed Magrès, the man behind the electrohydraulic wizardry, was hired as an unskilled worker and trained within the company. Can you even imagine a company investing in worker training to that degree today? Modern corporations want the workers themselves and the government to pay the bill for their training so those workers become disposable commodities as the companies have nothing substantive invested in them.

### #16 rory57

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Posted 18 March 2013 - 10:17

Magrès, the man behind the electrohydraulic wizardry,

Nothing electro about Citroen Hydraulics until Activa etc much later.
I have never driven a DS but the brakes of Citroens GS,CX and BX have no peers in my experience.
Such a shame that once great company is reduced to flair-free, progress-free junk like Saxo, C2 etc.

### #17 Magoo

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Posted 18 March 2013 - 13:45

Excellent. I noticed Magrès, the man behind the electrohydraulic wizardry, was hired as an unskilled worker and trained within the company. Can you even imagine a company investing in worker training to that degree today? Modern corporations want the workers themselves and the government to pay the bill for their training so those workers become disposable commodities as the companies have nothing substantive invested in them.

Paul Mages is one of my heroes.

Another: John Wandersee. Not far into his campaign to build a mass volume, high-quality, low-price car, Henry Ford perceived that advanced steel alloys were crucial. Ford, Wills, and a few others were standing on the shop floor pondering how they could obtain one of the world's leading metallurgists for their own use when Ford pointed to a guy sweeping the floor nearby, one of Ford's first employees, and said, "Let's make Wandersee a metallurgist." And they did. Wandersee became Ford's chief metallurgist, one of the sharpest in the world, and was one of the company's key technical people for decades.

The story is often misunderstood or mistold to indicate that Ford had a disdain of formal knowledge. More accurately, he had a disdain of experts. Of the multiple innovations that made the Model T possible, Ford once said, "At some point we found it necessary to dispense with the services of experts."

### #18 desmo

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Posted 18 March 2013 - 13:52

Nothing electro about Citroen Hydraulics until Activa etc much later.

Of course. I knew that.

### #19 giskard

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Posted 07 November 2013 - 20:20

Why are dual-master setups with balance bars used in club racer type cars?

AFAICT they don't have a breakpoint in their rear pressure characteristic like prop valves do (left diagram below).

Wouldn't that make them inferior to a properly set up proportioning valve?