# Traction control: an overview

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This article is predominantly a summary of SAE paper 942475 that was presented at MSEC 1994 by engineers from Bosch and Chrysler (Lamborghini F1 engine builders for the Larrouse team).

With well over 1000hp/tonne and grooved dry-weather tyres, the modern Formula One car can easily become overpowered for the available tractive force. Thus the main aim of a traction control system is to optimise the power delivery with respect to the available traction.

## Conceptual definition

The torque that can be transmitted by the tyre contact patch is limited by the friction coefficient and the normal force pressing down on the tyre.

The friction coefficient (‘mu’) is predominantly a function of slip ratio, but is also affected by tyre wear, track surface conditions and the tyre compound and construction.

The equations that govern tractive force are given below:

$F_{normal} = F_{weight} + F_{downforce}$

$T_{wheel} = 0.5 * T_{engine} * i_{gear} * i_{diff}$

$F_{tractive} = \mu*F_{normal} = T_{wheel} / r_{wheel}$

Where:

$F_{normal}$ = Normal force (N) acting downward on the tyre contact patch.
$F_{weight}$ = Normal force due to the car’s mass.
$F_{downforce}$ = Normal force due to aerodynamic downforce.
$F_{wheel}$ = Torque (Nm) at the wheel centre.
$F_{engine}$ = Torque at the engine flywheel.
$i_{gear}$ and $i_{diff}$ = ratios of the gearbox and final drive.
$r_{wheel}$ = radius (m) of driven wheel.
$\mu$ = friction coefficient of the tyre (NONLINEAR FUNCTION OF SLIP RATIO).

The reality is that during normal running it is very hard to achieve the limits implied by these equations. More specifically it is impossible to achieve in a standing race start.

A traction control system must control the power delivery of the engine to ensure the torque available matches the tyre’s ability to transmit it to the road.

## Torque reduction concepts

Engine torque can be reduced by the throttle position, ignition retard, or a switching off of ignition or injection for a defined number of cylinders.

The acceleration of a driven wheel can be more than 50g, this means that to counteract the inertial time constant of the drivetrain masses the system must react very fast. Hydraulic and electric throttles react at around 30ms or more which is too slow to be accurate.

Ignition retard was initially favoured, but during prolonged retardation events it caused an elevation in exhaust temperature, which gave reliability problems.

This process of elimination produced fuel injection cut-off as the technique for the final system.

A ‘rotating injection cut-off’ scheme was devised that operated over a 1440 crank angle window (720*2). This allowed a number of criteria to be met:

1. A cylinder could be shut of for a single cycle.
2. Deactivating a cylinder every 720 degrees could shut off a ‘half’ cylinder.
3. A specific pattern of injection shutoff could be programmed to ensure smooth operation across the rev range.
4. The shutoff program can be designed to minimise crankshaft torsional stresses.
5. Finally a rotating pattern ensured that no single cylinder was shutoff long enough to allow fuel evaporation from the inlet port walls. This allowed the cylinder to re-fire consistently on demand.

## Controlled variable: slip

The controlled variable of the traction control system is the slip ratio of the rear wheels. This parameter is defined as follows:

slip ratio = $0.5 * (V_{rr}+V_{lr}) / (V_{ref}-1)$

Where:

$V_{rr}$ = Right rear wheel angular velocity (rad/s)
$V_{lr}$ = Left rear wheel angular velocity (rad/s)
$V_{ref}$ = Car reference speed – filtered maximum front wheel angular velocity (rad/s)

The basic slip value is further manipulated by the control algorithms to allow for conditions where only one rear wheel spins.

## Control system

The control system is of the PID variety. I will allow those of you out there who are better versed in control engineering to explain the internal workings of such a system. I will simply describe the overall control process for traction control.

The output of the PID is the percentage reduction in engine torque (multiplicatively compensated by the current overall transmission ratio) required to reach the desired slip ratio goal.

The controller also compensates for any driver response to a perceived wheelspin event, i.e. throttle lifting.

## Engine torque reduction

The torque reduction required was converted to an injection cut-off pattern by dyno testing a race engine and collating the data into a 24-point curve. A key finding was that the decrease in torque for a given cut-off strategy was nearly independent of engine speed and load.

## GP start procedure

The solution to the particular problem of the standing race start was addressed with a two-stage process.

Stage One consisted of an rpm hold feature which allowed the driver to keep the throttle wide open while the ECU’s P component kept the rpm at the desired value for the start.

Clutch engagement causes a slight rise in speed that engages Stage Two. Stage Two control allowed continued full throttle application with modulation with fuel cut-off. When a second critical speed is reached the system reverts from this two-stage start procedure to conventional PID control.

## Development lessons

Crankshaft Stresses:

Dyno testing revealed the optimum cut-off strategies to minimise crankshaft stresses.

Engine Smoothness:

It was felt by some that fuel cut-off might be more violent than ignition cut-off and that this might upset the chassis. Tests were done and one driver perceived a misfire at 1.5 cylinders per cycle cut-out, while another driver felt nothing until 2 cylinders per cycle. This gave the confidence to proceed with fuel cut-off as the control output.

Cockpit Switch:

An off/wet/dry switch was added in the cockpit. It allowed the driver to disable the system if he felt it was malfunctioning and to switch between wet and dry specific versions of the control algorithm.

Slip Goal Level:

From testing at the smooth Paul Ricard circuit a goal of 4-6% maximum slip was arrived at.

Good vs. Bad Slip:

Bad slip is defined as a difference in rear wheel speeds caused by cornering. Good slip occurs in straight-line conditions and is the predominant area under which the system has control.

When exiting a corner the point at which the TC system ‘kicked in’ had to be determined. It was found that this threshold correlated well with the driver’s natural throttle input, and this was used to determine how the system was tailored to a particular driver.

## Driver feedback

Driver feedback is vital in TC system development. The driver is still part of the control loop and his response to new responses such as power-on UNDERSTEER can crucially affect how the system must be developed.

A key point discovered by the Larrouse engineers was that total elimination of slip was NOT a desirable system goal. It appears that a degree of residual slip was required for the driver to feel what the car was doing. A total elimination of slip could be seen as analogous to a total elimination of steering feel with basic power steering systems.

## Calibration methodology

The need for a calibration methodology can be summarised by stating that there are surprisingly (for some) downsides to TC.

These downsides are things like; The inability to place the car with power oversteer, and the corollary of this, which is power understeer. Also it was found that improved TC response came at a cost in vehicle stability.

"The driver’s belief in an electronic system programmed by engineers under extreme time pressure required human trust and courage of the highest order."

This quote from SAE 942475 confirms for me why TC is NOT a bad thing for the competitiveness of Formula One. The driver’s courage is still required to trust the system at the limit and thus the more sensitive and courageous driver will still extract the most from the system. Michael Schumacher made comments to this effect recently and I don’t believe for a second that anyone will get closer to him because of traction control.

The methodology itself was initially based on a realisation that the optimum 4-6% slip goal was too simplistic. A range of 12-15% at low speeds, and less than 2% at high speeds was more accurate. Further it was found that percentage slip was not the best way to characterise slip. The 4% ‘optimum’ was only optimum at a nominal corner velocity of 90-100kph.

A slip percentage of 4% at 90kph was best understood as describing the actual delta speed (4-5kph) between the front and rear wheels. The relative difference in rotational speeds gave the car it’s characteristic feel in yaw and what the driver was actually experiencing.

This allowed a calibration chart of delta speed (the new variable) and percentage slip to be created. Once this had been done the following procedure was instigated at race meetings.

Practice Session #1:

A lap would be driven with the TC disengaged to highlight specific problem areas at the particular circuit. A number of preset TC calibrations would be tested and the driver feedback compared between them.

Qualifying Session#1:

The driver’s preferred calibration from practice was loaded in the dry position of the ECU with a standard calibration in the wet position. The standard calibration was kept throughout the season and used as a reference to any changes made.

Debrief #1:

This was used to summarise the different directions often taken by the two drivers and to decide which was best for the weekend. Invariably calibration was satisfactory and further calibration wasn’t necessary during the remainder of the race meeting.

Saturday:

Any additional changes were made in the light of set-up issues often related to car stability. The final calibration had to be fixed for qualifying to allow accurate fuel consumption figures to be gathered. These being essential for race strategy.

Debrief #2:

This was usually used to inform the drivers of final telemetry readings and fuel consumption figures. Only in exceptional circumstances were any further changes proposed for evaluation in Sunday warm-up.

This information does obviously relate to a specific team and it is almost certain that more sophisticated systems exist, particularly in terms of integrating yaw rate data into the control system.

What the paper does show is the fundamental processes behind TC and gives some fascinating insights into the interactions between the driver and TC system that go beyond the facile media pronouncements that fail to consider the complexity of the issue.

Ben Michell