Electronic Stability Program

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More commonly known by the generic term Electronic stability control (ESC). It is comprised of five components:

ABS (Antilock Brake System), EBD (Electronic Brake-force Distribution), ASR/ASC (Acceleration Slip Regulation/Anti-Slip Control), EDL (Electronic Differential Locking), and MSR (Motor Slip Regulation).

ESP/ESC is a computerized technology that improves the safety of a vehicle's handling by detecting and preventing skids. When ESP/ESC detects loss of steering control (by comparing the output of the steering angle sensor with the yaw sensor), it automatically applies individual brakes to help "steer" the vehicle where the driver wants to go. Braking is automatically applied to individual wheels, such as the inner rear wheel to counter oversteer, or the outer front wheel to counter understeer. Some ESP/ESC systems also reduce engine power (ASR) until control is regained.[1]

EPC (Electronic Power Control) equipped cars (FWD A4?) only came with EBD, EDL and ASR/ASC, but not ESP.

Starting with MY2001, all S4s come standard with ESP. A button inside the cabin disables ESP's throttle intervention (ASR), and numbs ESP per wheel braking, but not EDL or MSR(?)

Fuse #42 can be pulled from the main fuse panel between the driver side door and the side of the console. This disables power to the traction control specific ABS solenoids, which, in turn, disables ESP (but not ABS, EBD, EDL or ASR/MSR?).

Pulling fuse #41 disables ESP, EBD, EDL and ABS (and ASR/MSR?)

Disconnecting the yaw sensor or wiring the hand brake signal input to GND will disable ESP per wheel braking, and ASR/MSR(?). EBD F:R biasing, EDL and ABS unaffected(?).

The engine ECU can be remapped[2] to numb or ignore CAN torque intervention signals from the ESP controller to mitigate (or disable) ASR/MSR.

ESP

Selectively applies braking to wheels (via traction control specific per wheel ABS solenoid) if the ESP controller detects unintended yaw

Numbed but not disabled by ESP button?

Disabled by removing fuse 41 or 42, removing the yaw sensor, or hardwiring the emergency brake signal input to the ESP/ABS controller to GND?

ABS

Antilock Brake System

Selectively pulses braking (via per wheel ABS solenoid) on wheels that are showing signs of locking up.

Is not disabled via ESP button.

Exists in non-ESP equipped cars.

Removing fuse 41 disables ABS and brake biasing (EBD)!

Removing fuse 42 does not affect ABS or EBD?

EBD

Electronic Brake-force Distribution

Controls the ABS F:R proportioning valve control (brake bias) (exists in non-ESP equipped cars?)

Is not disabled via ESP button.

Disabled by removing fuse 41?

Removing fuse 42 does not affect EBD?

EDL

Electronic Differential Locking

Applies braking (via per wheel ABS solenoid) to a wheel that the ABS controller detects is losing traction under acceleration, thus redirecting torque to the opposite wheel (which presumably has more traction) through the open differential. Only active below a certain vehicle speed. The stock S4 threshold is 26mph (40kph)?. There is anecdotal evidence (and Audi documentation) that suggests the 40kph limit is for FWD vehicles only, and that the AWD threshold is 80kph.

Is not disabled via ESP button.

Exists in non-ESP equipped cars.

Can be disabled by removing fuse 41 or hardwiring the emergency brake signal input to the ESP/ABS controller to GND

Removing fuse 42 does not disable EDL?

ASR

Acceleration Slip Regulation (a.k.a. anti slip control or traction control)

Reduces requested torque (slow intervention) and/or cuts timing (fast intervention) if the ESP controller detects wheel spin during acceleration, especially while turning

ESP equipped cars only?

Can be disabled via ESP button.

Can be overridden via map modifications in the ECU.

MSR

Motor Slip Regulation (a.k.a. Engine Drag Torque Control)

Increases requested torque if the ESP controller detects wheel slip due to a sudden decrease in engine speed (torque braking), such as in sudden off-throttle conditions. Anti-stall also uses this mechanism.

Possibly not disabled via ESP button?

Exists in non-ESP equipped cars?

Can be overridden via map modifications in the ECU

Summary

ESP ABS EDL EBD ASR MSR
Per wheel braking F:R brake bias Torque intervention
non-ESP cars no yes yes yes no no?
ESP button numb - - - disable disable?
ECU map modification - - - - variable variable
GND e-brake input signal disable - disable(?) - - (?) - (?)
Fuse 42 removal disable - - (?) - - -
Fuse 41 removal disable disable disable(?) disable disable(?) disable(?)

References