Controlling the automatic starting of a motor vehicle uphill in a μ split situation

1. A method for controlling a vehicle comprising:

while the vehicle is stationary, setting an initial locking torque of an electronic limited slip differential based on a road gradient; and

after vehicle movement is detected, setting the locking torque based on a slip ratio of a slowest driven wheel, wherein the slip ratio SR xx for the slowest driven wheel is calculated according to

SR xx =(V xx −V Ref )/V Crit in response to a reference velocity V Ref being between 0 and a critical velocity V Crit , and according to

SR xx =(V xx −V Ref )/V Ref in response to the reference velocity being greater than the critical velocity.

2. The method of claim 1 wherein the initial locking torque is greater than a lower limiting value of torque capacity required for the vehicle to travel uphill at the road gradient with only one driven wheel being powered.

3. The method of claim 1 wherein the initial locking torque is less than an upper limiting value of torque capacity such that powertrain torque does not cause the slowest driven wheel to spin.

4. The method of claim 1 wherein:

the locking torque is maintained in response to the slip ratio being within a range of permissible slip ratios;

the locking torque is reduced in response to the slip ratio increasing above a maximum permissible slip ratio; and

the locking torque is increased in response to the slip ratio decreasing below a minimum permissible slip ratio.

5. A vehicle control system comprising:

sensors for determining a road gradient and a driven wheel speed; and

a controller programmed to

while the vehicle is stationary, set an initial locking torque of an electronic limited slip differential based on the road gradient; and

in response to detecting vehicle movement, set the locking torque based on a slip ratio of a slowest driven wheel, wherein the slip ratio SR xx for the slowest driven wheel is calculated according to

SR xx =(V xx −V Ref )/V Crit in response to a reference velocity V Ref being between 0 and a critical velocity V Crit , and according to

SR xx =(V xx −V Ref )/V Ref in response to the reference velocity being greater than the critical velocity.

6. The control system of claim 5 wherein the initial locking torque is greater than a lower limiting value of torque capacity required for the vehicle to travel uphill at the road gradient with only one driven wheel being powered.

7. The control system of claim 5 wherein the initial locking torque is less than an upper limiting value of torque capacity such that powertrain torque does not cause the slowest driven wheel to spin.

8. The control system of claim 5 wherein the controller is programmed to:

maintain the locking torque in response to the slip ratio being within a range of permissible slip ratios;

reduce the locking torque in response to the slip ratio increasing above a maximum permissible slip ratio; and

increase the locking torque in response to the slip ratio decreasing below a minimum permissible slip ratio.

9. A vehicle comprising:

a first axle having first and second driven wheels;

a second axle having third and fourth wheels;

an electronic limited slip differential connected between the first and second driven wheels, wherein the differential is configured to control rotation of the first and second driven wheels based on a locking torque of the differential; and

a controller programmed to

while the vehicle is stationary, set an initial valve for the locking torque based on a road gradient, wherein the initial locking torque is greater than a lower limiting value of torque capacity required for the vehicle to travel uphill at the road gradient with only one of the driven wheels being powered, and the initial locking torque is less than an upper limiting value of torque capacity such that powertrain torque does not cause the slowest of the driven wheels to spin; and

in response to detecting vehicle movement and detecting a mu split condition in which the first wheel has a higher coefficient of friction with the road than the second wheel, adjust the locking torque based on a slip ratio of the first wheel, wherein the slip ratio of the first wheel is based on a ratio of a speed of the first wheel and a critical velocity if a speed of a slower of the third and fourth wheels is between 0 and the critical velocity, and is based on a ratio of the speed of the first wheel and the speed of the slower of the third and fourth wheels if the speed of the slower of the third and fourth wheels is greater than the critical velocity.

10. The vehicle of claim 9 wherein the controller is programmed to calculate the slip ratio according to

Slip ratio=the speed of the first wheel minus the speed of the slower of the third and fourth wheels divided by the critical velocity if the speed of the slower of the third and fourth wheels is between 0 and the critical velocity and according to

Slip ratio=the speed of the first wheel minus the speed of the slower of the third and fourth wheels divided by the speed of the slower of the third and fourth wheels if the speed of the slower of the third and fourth wheels is greater than the critical velocity.

11. The vehicle of claim 9 wherein the controller is programmed to:

maintain the locking torque in response to the slip ratio being within a range of permissible slip ratios;

reduce the locking torque in response to the slip ratio increasing above a maximum permissible slip ratio; and

increase the locking torque in response to the slip ratio decreasing below a minimum permissible slip ratio.