TITLE OF INVENTION
[0001] Stability-Enhanced Traction and Yaw Control Using Electronically
Controlled Limited-Slip Differential
CROSS-REFERENCE TO RELATED APPLICATIONS
[0002] This application claims the benefit of Provisional Patent Application
U.S. Serial No. 60/765,046, filed February 3, 2006, in the name of Damrongrit
Piyabongkarn, Jae Young Lew, John Allen Grogg and Robert Joseph Kyle for a
"STABILITY-ENHANCED TRACTION AND YAW CONTROL USING
ELECTRONIC LIMITED SLIP DIFFERENTIAL".
BACKGROUND OF THE DISCLOSURE
[0003] The present invention relates to an active vehicle stability control
system and method using electronically controlled limited-slip differentials to
enhance vehicle lateral dynamics while preserving longitudinal motion.
[0004] Anti-lock braking systems (ABS) have become an integral part of
modern passenger vehicles and may be used to improve vehicle traction and
stability. Typical traction control systems based on brake intervention have the
disadvantage of dissipating an amount of energy roughly equal to that spent in
biasing the high-friction wheel. For example, when a vehicle attempts to
accelerate or climb on a split-friction (split-μ), low-high friction surface, it often
loses its energy to the braking system by dissipating the same amount of energy
it biases to the high-friction wheel. Hence, the braking torque limits the driving
torque on the high-friction wheel and is often insufficient to move the vehicle,
such as in an uphill-driving situation.
[0005] To overcome this limitation, traction control using electronically
controlled limited-slip differentials (ELSDs) may be applied at the driven wheels
so that the vehicle can maintain longitudinal motion by sending more traction
torque to the higher friction wheel. Fully locked differentials achieve the best
possible longitudinal traction but, on slippery or split-μ. surfaces, the lateral
dynamics of the vehicle may be degraded and deviate from the driver's intended
direction. Indeed, the bias traction torque must be properly controlled to prevent

undesired yaw motion and eventual degradation of the lateral dynamics of the
vehicle.
[0006] At relatively high speeds, yaw stability control systems may be
applied to prevent the vehicle from losing control. Most vehicle stability control
systems in the market are brake-based. Brake-based stability control systems
use ABS hardware to apply individual wheel braking forces in order to correct
vehicle yaw dynamics. However, brake-based systems suffer from the limitation
that the speed performance of vehicle is deteriorated and conflicts with the
driver's actions. To overcome the brake-based stability control limitation, the use
of active torque distribution stability control would be more beneficial under
acceleration close to the vehicle's stability limit.
[0007] The last two decades have witnessed significant growth in the
application of four-wheel-drive (4WD) systems to passenger vehicles. Limited-
slip differential (LSD) technology is already being used in many production
models. ELSDs are widely used and available in the automotive market, and are
known to have the capability of adding yaw damping to the vehicle in addition to
their superior traction performance.
BRIEF SUMMARY OF THE INVENTION
[0008] A control system for a vehicle having first and second wheels is
provided that includes a differential apparatus adapted to distribute torque
between the first and second wheels and a traction controller for controlling
operation of the differential apparatus from vehicle launch up to a predetermined
vehicle speed. The traction controller is configured to engage the differential
apparatus in a first vehicle operating state according to at least one vehicle
operating parameter indicative of a low traction operating condition and to further
control engagement of the differential apparatus in a second vehicle operating
state during the low traction operating condition according to a difference
between an actual vehicle yaw rate and a predetermined target vehicle yaw rate.
The control system also includes a stability controller for controlling engagement
of the differential apparatus at or above the predetermined vehicle speed.
[0009] An embodiment of the present invention includes an active stability
control method using ELSDs to enhance the vehicle lateral dynamics while

preserving longitudinal motion. Another embodiment of the present invention
includes a control system that provides stability enhancement of the traction
control. The stability-enhanced traction control was evaluated under the condition
of straight-line full-throttle launching on a split-μ ice/asphalt surface. The
experimental data shows a significant stability improvement in the traction control
operating mode.
BRIEF DESCRIPTION OF THE DRAWINGS
[0010] FIG. 1 is an exemplary vehicle driveline configuration including an
electronically controlled limited-slip differentials;
[0011] FIG. 2 is a cross-sectional view of an exemplary electronically
controlled limited-slip differential;
[0012] FIG. 3 is a plot of clutch response time for the exemplary electronically
controlled limited-slip differential shown \n FIG. 2;
[0013] FIG. 4 is a dynamic model of a vehicle axle including an electronically
controlled limited-slip differential;
[0014] FIG. 5 is a dynamic model of an electronically controlled limited-slip
differential clutch;
[0015] FIG. 6 is schematic diagram of a control system according to an
embodiment of the present invention;
[0016] FIG. 7 is a plot showing the effect of locking an electronically controlled
limited-slip differential on the rear wheels of a vehicle axle;
[0017] FIG. 8 is a plot of vehicle yaw rate for a double lane change maneuver
in a vehicle including a control system according to an embodiment of the
present invention;
[0018] FIG. 9 is a plot of clutch torque for an electronically controlled limited-
slip differential corresponding to the plot of FIG. 8;
[0019] FIG. 10 is a composite snap-shot of a vehicle animation run
corresponding to the plot of FIG. 8;
[0020] FIGS. 11-13 illustrate test results, in graphical format, of vehicle
performance during launch using a control system according to an embodiment
of the present invention;
[0021] FIGS. 14-22 illustrate test results, in graphical format, of vehicle

performance during a relatively high-speed slalom maneuver using a control
system according to an embodiment of the present invention; and
[0022] FIGS. 23 and 24 illustrate test results, in graphical format, of vehicle
performance during an open-loop, sine-steer maneuver on a packed-snow road
surface using a control system according to an embodiment of the present
invention.
DETAILED DESCRIPTION
[0023] The present invention will be described as follows. First, an exemplary
vehicle driveline configuration using an electronically controlled limited-slip
differential will be introduced. Second, modeling of a limited-slip differential is
analyzed. Third, a stability control system is described for both traction control
and yaw control. Finally, simulation and experimental results will illustrate the
effectiveness of the control system to control vehicle stability during launch and
relatively high-speed operation.
[0024] Referring to FIG. 1, a proposed driveline configuration 20 is shown,
which is not intended to be limiting. Driveline 20 includes an electronically
controlled limited-slip differential (ELSD) 22a, 22b installed in at least one of a
front axle 24 and a rear axle 26. The ELSD 22 may be used to bias torque
between left and right wheels 28, 30. In an embodiment, the amount of torque
distributed between the left and right wheels 28, 30 by the ELSD 22 is
determined by engagement of a clutch (not shown), as is understood in the art,
which may be implemented by either a hydraulic or an electromagnetic system,
for example. Exemplary ELSDs for use in driveline 20 are described in pending
U.S. patent application 11/167,474 and issued U.S. Patent No. 7,051,857, which
are assigned to the Assignee of the present invention and incorporated by
reference herein in their entirety.
[0025] As shown in FIG. 2, and by way of reference to the aforementioned
references, an ELSD utilized in the front and rear axles 24, 26 achieves its
limited slip functionality by virtue of an actively controlled wet, multi-plate friction
clutch 30 disposed between a first bevel-style side gear 32 and a differential
housing 34. Engagement of clutch 30 limits the slip between the side gear 32
and differential housing 34, and in doing so, limits the slip between a pair of

output axle shafts (not shown) connected to each wheel 28, 30. This slip limiting
function results in the ability to produce a torque bias between the output axle
shafts, the magnitude of which will be less than or equal to the clutch torque.
Exemplary features, such as a relatively high locking torque level, thermal
capacity, durability, and noise free operation epitomize this clutch design.
Rotational motion between the differential housing 34 and a secondary housing
38 operates a gerotor pump 40 that displaces oil from an axle sump to a
discharge passage in direct communication with both a clutch actuation piston 42
and a solenoid operated pressure regulation valve 44. When the valve 44 is de-
energized, oil flows freely through the valve 44 resulting in little or no hydraulic
pressure against the clutch actuation piston 42. When the valve 44 is energized,
oil flow is restricted by the valve 44 creating hydraulic pressure against the
actuation piston 42 to engage the clutch 30 according to a level proportional to
that of the hydraulic pressure.
[0026] Hydraulic system optimization is an essential design component of an
ELSD and at the core of this optimization is proper pump design and porting
control. The gerotor pump 40 in the exemplary ELSD design shown in FIG. 2 is
operated with a high degree of hydraulic efficiency required for excellent low
speed (e.g., less than 32 kilometers per hour (kph)) traction control, while not
unduly penalizing the mechanical efficiency at higher vehicle speeds (e.g.,
greater than around 113 kph). Highway speed fuel economy measurements
obtained from a test vehicle incorporating an ELSD design described above
revealed no measurable reduction in fuel economy. Similarly, laboratory bench
testing of the exemplary differential shown in FIG. 2 exhibited a power loss of
approximately 0.11 kW at about 113 kph due to the mechanical losses of the
pump 40.
[0027] Regardless of the mechanical construction of either ELSD 22, the
clutch response time needs to be sufficient to guarantee the effectiveness of the
stability control system. The ELSD design shown in FIG. 2 requires minimal
electrical current draw for rapid peak torque development, for example 2000 Nm
of torque using 2.67 Amps (32W) of electrical current, particularly when
compared to that of other systems that use electromagnetic or electric-motor
based actuators. Relatively fast differential torque bias application and removal
is required for both driveline torque control based vehicle dynamic operation (as

described herein), and also for compatibility with many of the current brake-
based vehicle dynamic intervention systems. FIG. 3 illustrates a plot of step
torque bias application and removal performed with the exemplary ELSD
described herein. As illustrated, both the clutch engagement and disengagement
times are less than 50ms for a vehicle traveling at about 64 kph.
[0028] Referring to FIGS. 4 and 5, a dynamic model of an ELSD will be
described for vehicle control system evaluation. The model is based on the
dynamic properties of the clutch and focuses on locking and unlocking (or
slipping) clutch conditions, including the conditions for transitioning clutch
engagement between an unlocked/slipping state and a locked state.
[0029] An ELSD generally has the same components as an open differential,
except for a clutch that provides an additional path for torque transfer. Referring
to FIG. 4, Tin is the torque transferred to the rear prop-shaft, Tdiff is the torque
transferred through the differential gears, and TCT is the torque transferred
through the clutch. rCT is not necessary the same as the applied clutch torque
level controlled by the vehicle electronic control unit (ECU) or other controller,
depending on locked, unlock, or slipping states. Assuming that the efficiency of
the torque transmission is 100%, the differential gear ratio from the prop-shaft to
the differential is 1, and the differential has little or no mass inertia, then:

Since torque transferred through the differential gears Tdiff is equally distributed
[0030] Referring to FIG. 5, the clutch may be modeled as a spring-damper
torsional element according to the following equation:
to the left and right axle, the net torque to the rear-left inertia and the rear-right
inertia may be expressed as:



wherein c is the clutch damping coefficient, k is the clutch spring coefficient, and
Ω =ωdiff -ωL which represents the difference in speed between the differential
and the left axle.
[0031] The clutch may be further modeled in the locking state. TCT-max
represents the clutch torque applied to the clutch plates and controlled by the
vehicle controller. However, depending on the locking state, the actual
transferred clutch torque is not necessary the same as the applied clutch torque
level. In fact, the transferred clutch torque may be limited by TCT-max as follows:


The modeling for this condition may be derived from equations (2) and (3) as:

[0032] The locking conditions for the iimited-slip differential are modeled as
follows. Transition from the locked state to the unlocked/slipping state occurs
when:
[0033] Transition from the unlocked/slipping state to the locked state occurs
when:

[0034] This model represents the situation where the applied clutch torque is
larger than the torque difference between the clutch plates and, accordingly,
describes the locking dynamics of the clutch.

[0038] Utilizing the above transition conditions, the dynamics of the torque-
biasing devices may be implemented in simulation software, such as
Matlab/Simulink. The discrete-time modeling of both devices is summarized
below.
When changing from the locked state to the unlocked/slipping state, then:

[0039] While torque distribution though the ELSD may be used to change
vehicle tractive forces at the wheels, consequently the dynamic yaw response of
the vehicles changes. Application or engagement of the clutch 30 may be
adjusted to tune the desired vehicle yaw dynamics behavior for specific driving
conditions.
[0040] Referring to FIG. 6, a vehicle control system 50, including a method of
improving vehicle stability using torque biasing according to an embodiment of
the present invention, will be described. In an embodiment, the control system
50 includes two primary controllers: a stability-enhanced traction controller 52
and a yaw damping controller 54. A supervisory controller 56 may be used to
select the control actions in accordance with one or more vehicle operating
parameters, such as vehicle speed, as determined by vehicle sensor information

received from one or more vehicle sensors 58. At relatively low vehicle speeds,
a stability-enhanced traction control algorithm is applied to improve the vehicle
stability while the traction control is active. At relatively high vehicle speeds, the
stability-enhanced traction control is switched off and only the yaw damping
control is active. Traction controller 52 and yaw damping controller 54 may be
provided in communication with or be contained within a separate control unit,
such as a vehicle electronic control unit (ECU), made integral within the vehicle
ECU or with each other, or form a non-hardware component (e.g., software) of
the vehicle ECU or other vehicle controller.
[0041] Traction control systems utilizing actively controlled, fully lockable
differentials generally achieve the best possible longitudinal vehicle acceleration,
but degrade a vehicle's lateral dynamics under a split-μ condition. More
particularly, while a conventional differential-controlled traction control system
may be capable of controlling the differential clutch in real-time based on the
feedback of wheel slip information, the system may create yaw instability due to
over-application of the clutch.
[0042] The vehicle stability control system according to an embodiment of the
present invention overcomes this limitation by providing an enhanced-stability
traction control controller in addition to the normal active traction controller. In
stability-enhanced traction controller 52, it is determined whether the actual
vehicle yaw rate exceeds a predetermined desired yaw rate, as follows:

wherein Vx is the vehicle longitudinal speed, δ is the steered angle, L is the
vehicle wheel base, and Kux is the understeer gradient.
[0043] Whenever the actual vehicle yaw rate exceeds a predetermined
desired yaw rate, the differential dutch is disengaged proportional to the
difference between the actual and desired yaw rates, allowing the vehicle driver
to turn the vehicle back on track. The stability-enhanced traction control is


implemented by modifying the original or normal differential applied torque
according to the following equation:
wherein u is the differential applied torque; utraction is the original traction control
signal; deadband is a threshold function for the yaw rate difference which can be
adjusted based on the driver skill of controlling a vehicle; sat is a saturation
function set at [-a,+a]; and a is an error range value which is a design parameter.
[0044] In addition to improving stability in a low-traction straight-line vehicle
operation, the vehicle stability control system may also contribute to increased
stability while the vehicle is cornering. When the stability enhanced traction
control function is complete, the ELSD may still be used to bias the prop-shaft
torque between the left and right vehicle wheels. If the differential clutch torque is
applied while the vehicle is turning, the device only transfers driving torque from
the outside wheel to the inside wheel, thus generating a yaw moment in opposite
direction of the turn and increasing the understeer tendency of the vehicle. This
phenomenon may be explained by considering equations (19) and (20). The
speed of the outside wheel is normally larger than the speed of the inside wheel
while turning. Application of the differential clutch will attempt to bring the speeds
of both outside wheel and inside wheel to the same value. The outside wheel
speed and acceleration will be reduced, along with the driving torque, and vice
versa, while the driving torque at the inner wheel will be increased. Hence, the
control strategy is based on the principle that locking the ELSD induces more
understeering behavior.
[0045] The yaw damping controller 54 locks the differentials to increase yaw
damping when the actual yaw rate is larger than a predetermined desired yaw
rate. As described above, the desired yaw rate may be determined based on
vehicle speed and steering wheel angle. The actual yaw rate may then be
compared to the desired yaw rate in real time. If the actual yaw rate is less than
the desired yaw rate, the differentials are not further engaged since increasing
the locking torque on the front and rear differentials increases yaw damping,
thereby reducing the yaw rate. The yaw rate comparison may not be active
when the lateral acceleration is below 0.03g and yaw rate variation between the

actual and desired yaw rates is less than 3%. Differential applied torque to be
applied by yaw damping controller 54 may be determined according to the
following equation:

wherein u is the differential applied torque, deadband is a threshold function for
the yaw rate difference which can be adjusted based on sensitivity of the control
system, Kp and Ki are a proportional gain and an integral gain, respectively, and
pos is a positive value function. Yaw damping controller 54 engages the ELSD
whenever there is too much yaw rate overshoot under a constant-μ condition.
Operation of yaw damping controller 54 is described in more detail in Applicant's
co-pending U.S. Patent Application entitled "Minimizing Dynamic Rollover
Propensity with Electronic Limited Slip Differentials," which is incorporated by
reference herein in its entirety.
[0046] A dynamic model of control system 50 was generated in a
Matlab/Simulink environment. A full vehicle model developed by CarSim was
used and modified to include the exemplary ELSDs described above so that a
co-simulation could be performed. FIG. 7 shows the validation of the developed
model. When a high clutch torque was applied for a turning maneuver, the
speeds of the left wheel and the right wheel became substantially similar within
the engagement time.
[0047] To evaluate the performance of the proposed control system 50
operating under the control of yaw damping controller 54, a standardized double
lane-change maneuver was simulated to validate the effects of the proposed yaw
control on vehicle dynamics. This maneuver was performed to evaluate yaw-
damping performance in rear-wheel-drive mode. All conditions were set to the
same speed of 100 km/h on a relatively slippery road (μ = 0.6).
[0048] FIG. 8 illustrates the comparison of a vehicle with and without yaw
damping control. The vehicle with yaw damping control has superior
performance and stability compared to the vehicle without yaw damping control,
which eventually became unstable. FIG. 9 indicates the corresponding clutch
torque levels that were used to control the torque-biasing devices. The ELSD
clutch was activated only when the vehicle was oversteering. Finally, FIG. 10

shows a snap shot of an animation run in CarSim.
[0049] Vehicle testing was conducted on a modified Ford F-150 equipped with
Eaton Corporation's EGerodisc™ differential in both the front axle and rear axle,
and a modified Chevrolet Silverado equipped with Eaton Corporation's
EGerodisc II™ differential in the rear axle. To obtain objective test results, the
vehicles were instrumented to record the relevant operating parameters. A
MicroAutoBox from dSPACE was used to develop a real-time controller for the
vehicles, providing a rapid prototyping environment in Matlab/Simulink. The
controller was designed as an in-vehicle unit, similar to a vehicle ECU, and the
sampling time was set at 10 ms. ControlDesk experiment software from dSPACE
was used to manage, monitor and record the experimental data through a
graphic user interface mode (GUI).
[0050] A real-time vehicle navigation system, RT3000, from Oxford Technical
Solutions was also used for the test. The RT3000 is a full, six-axis inertial
navigation system with combined GPS. The GPS outputs were connected to the
MicroAutoBox via the vehicle's CAN communication at the baud rate of 0.5
Mbits/sec. The sensor information used in the stability test included wheel speed
sensors, a steering angle sensor, and RT3000 signals (e.g., vehicle speed,
global X, global Y, lateral acceleration, longitudinal acceleration, body slip angle
and yaw rate).
[0051] The stability-enhanced traction control test was conducted using a
straight-line full-throttle vehicle launch on a split-μ dry and icy surface. The
steering wheel angle was set to zero during the duration of the test (e.g., open-
loop) for objective validation. The yaw error in the deadband function in equation
(23) was set to ± 0.5 deg/sec. The error range value, a, was set to 0.5 deg/sec for
this test. As shown in FIGS. 11-13, the experimental data demonstrated a
significant improvement in vehicle stability during vehicle launch in the stability-
enhanced traction control mode. The vehicle spun-out quickly toward the icy
portion of the road surface when operated solely using the normal traction control
mode. With the stability-enhanced traction control, the vehicle yaw dynamics
were stable and the vehicle maintained a substantially straight heading.
Minimum undesired yaw was achieved with low deadband threshold, but the
vehicle was launched slower. The deadband, however, can be adjusted based

on driver skill.
[0052] Above a predetermined vehicle speed, as determined by vehicle
sensors such as the wheel speed sensors, the yaw damping controller becomes
active. Slalom maneuvers, in particular, may create an unstable vehicle
situation. Oversteering behavior can be observed under a low-μ surface slalom
maneuver; hence, a slalom maneuver was selected to evaluate the active yaw
control. The course used seven cones in a straight line with about 100 feet of
separation on a packed-snow surface. A driver then drove the vehicle up to a
speed of about 50 km/h, before getting into the slalom course.
[0053] Referring to FIGS. 14-24, the experimental results show that active
control of the vehicle differential improves vehicle dynamics during the slalom
maneuvers. However, if the vehicle is not driven up to the handling limit, it is
difficult to distinguish the difference between the systems with and without yaw
control, as shown in FIG. 14. It is noted that driver skill has a significant
influence on the performance when the vehicle is not driven at the handling limit.
[0054] FIGS. 14-22 illustrate test results for the slalom maneuver when the
handling limit was reached with and without constant velocity control using yaw
damping controller 54. The vehicle with yaw damping controller 54 maintained its
direction to follow the desired yaw rate while the vehicle without yaw damping
controller 54 lost its stability and spun out off the track. A comparison of the
vehicle longitudinal speed is also shown in FIGS. 16 and 20. The vehicle without
control of yaw damping controller 54 shows an adverse speed performance due
to vehicle spin. Using yaw damping controller 54, the differential was engaged
when oversteering behavior was detected to add yaw damping, which made it
easier for the driver to maintain the desired vehicle track.
[0055] Referring to FIGS. 23 and 24, an open-loop sine-steer maneuver on a
packed-snow road surface was performed to evaluate the handling
characteristics with yaw damping controller 54. A driver drove the vehicle with a
sine-shape steering angle at about 0.5 Hz with a constant speed control. The
experimental results illustrated in FIGS. 23 and 24 show that the vehicle was
under-steered most of the time, except from late mid-corner to the comer exit
where the yaw damping controller 54 corrected the oversteer behavior.
[0056] The invention has been described in great detail in the foregoing

specification, and it is believed that various alterations and modifications of the
invention will become apparent to those skilled in the art from a reading and
understanding of the specification. It is intended that all such alterations and
modifications are included in the invention, insofar as they come within the scope
of the appended claims.

What is claimed is:
1. A control system (50) for a vehicle having first and second wheels (28,
30), comprising:
a differential apparatus (22) adapted to distribute torque between the first
and second wheels (28, 30);
a stability-enhanced traction controller (52) for controlling operation of the
differential apparatus (22) from vehicle launch up to a predetermined vehicle
speed, the traction controller (52) configured to engage the differential apparatus
(22) in a first vehicle operating state according to at least one vehicle operating
parameter indicative of a low traction operating condition and to further control
engagement of the differential apparatus (22) in a second vehicle operating state
during the low traction operating condition according to a difference between an
actual vehicle yaw rate and a predetermined target vehicle yaw rate; and
a stability controller (54) for controlling engagement of the differential
apparatus (22) at or above the predetermined vehicle speed.
2. The control system of claim 1, wherein the traction controller (52) is
configured to modulate engagement of the differential apparatus (22) during the
low traction operating condition according to a difference between the actual
vehicle yaw rate and the predetermined target vehicle yaw rate.
3. The control system of claim 1, wherein the traction controller (52) is
configured to engage the differential apparatus (22) according to a desired
differential applied torque signal that is based on a modified original differential
applied torque signal.
4. The control system of claim 3, wherein the desired differential applied
torque signal is equal to the original differential applied torque signal multiplied by
a modifier, the modifier including in its numerator the difference between an error
range value and the multiplication of a saturation function, a deadband and the
difference between the actual vehicle yaw rate and the predetermined target
vehicle yaw rate, and the modifier including in its denominator the error range
value.

5. The control system of claim 1, wherein in the first vehicle operating state,
the actual vehicle yaw rate is less than or substantially equal to the
predetermined target vehicle yaw rate, and in the second vehicle operating state,
the actual vehicle yaw rate is greater than the predetermined target vehicle yaw rate.

A control system (50) for a vehicle having first and second wheels, (28, 30) is provided that includes a differential apparatus (22) adapted to distribute torque between the first
and second wheels (28,30) a traction controller (52) for controlling operation of the differential apparatus (22) from vehicle launch up to a predetermined vehicle speed. The traction controller (52) is configured to engage the differential apparatus (22) in a first operating state according to at least one vehicle operation parameter indicative of a low traction operating condition and to further control engagement of the differential apparatus (22) in a second vehicle operating state during the low traction operating condition according to a difference between an actual vehicle yaw rate and a predetermined target vehicle yaw rate. The control system (50) also includes a stability controller (54) for controlling engagement of the differential apparatus (22) at or above the predetermined vehicle speed.