WO2008095067A1

WO2008095067A1 - Optimized control for all wheel drive system

Info

Publication number: WO2008095067A1
Application number: PCT/US2008/052588
Authority: WO
Inventors: Sohel Anwar; Yifeng Lin
Original assignee: Indiana University Research and Technology Corp
Current assignee: Indiana University Research and Technology Corp
Priority date: 2007-01-31
Filing date: 2008-01-31
Publication date: 2008-08-07
Anticipated expiration: 2009-07-31

Abstract

A traction enhancement system for a vehicle. The system includes a hybrid powertrain having an engine and transmission associated with a pair of front wheels of the vehicle and an electric motor associated with a pair of rear wheels of the vehicle, and a controller adapted to minimize wheel slip error of the vehicle on a surface by activating and dynamically controlling drive torque of the electric motor.

Description

OPTIMIZED CONTROL FOR ALL WHEEL DRIVE SYSTEM

RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Patent Application

Serial No. 60/887,396, filed January 31, 2007, the disclosure of which is expressly incorporated herein in its entirety by this reference.

TECHNICAL FIELD

[0002] The present invention generally relates to a vehicle traction enhancement system, and more particularly to an optimized control for an on-demand all wheel drive system.

BACKGROUND OF THE INVENTION

[0003] Traction control systems (TCS) for all wheel drive (AWD) vehicles have been widely investigated over the past twenty years. To regulate wheel drive torque, most of these systems utilize a wheel slip estimate or rotational speed differences between front and rear wheels. For instance, one traction control system introduced by Hallowell and Ray [1] includes a torque control algorithm that takes advantage of the direct torque control of four electric motors. This system optimizes torque distribution among the wheels by monitoring wheel speeds, driver steering input and vehicle yaw rate. Rather than trying to restrict torque based on predicted tire behavior, the system attempts to apply torque such that the odds of excessive slip in any given tire is minimized by sending torque to the tires with the greatest torque management capacity. A variable torque decrease factor, which in an empirical formula is a function of wheel slip ratio, is used in this system to increase the vehicle's performance.

[0004] Another traction control system, which was presented by Nakamura,

Kosaka, Kadota, and Shimizu [2], includes a motor-assisted 4WD system with a rear- wheel-drive motor. Rather than implementing a propeller shaft and transfer case, this system actually distributes torque to the rear wheels.

[0005] In addition to ΔV-sensitive controls, there are also controls that are activated by rotational speed differences between the front and rear wheels, as well as accelerator-sensitive controls and estimated necessary drive torque controls. For instance, Anon [3] introduced a Super Handling - All Wheel Drive (SH-AWD) system, which freely distributes an optimum amount of torque to all four wheels in accordance with driving conditions. This system has a distribution range from 30:70 to 70:30 for longitudinal torque and from 100:0 to 0:100 for lateral torque. Moreover, the electromagnetic clutches inside the rear differential of this system employ electromagnets to achieve precise, continuously variable transmission (CVT) torque regulation.

[0006] Yet another traction system was presented by Asgari and Hrovat [4] and involves a model for an electronically controlled on-demand 4WD (four-wheel drive) transfer case. When the on-demand 4WD of this system is engaged, torque from the transmission goes to the rear propeller shaft and through the clutch assembly to a secondary front propeller shaft. To determine how much secondary torque should be present, the difference between the rotational speed of the front propeller shaft and the rear propeller shaft is considered.

[0007] Traction systems for hybrid powertrains have also been discussed in the literature. For instance, Liao et al [5] published four different configurations of a hybrid powertrain. Saeks et al [6] also discussed an adaptive control system for a four- wheel drive hybrid electric vehicle. This system uses four separate adaptive controllers to control the vehicle's speed, steering, side-slip, and energy management system. Moreover, Anwar [7] introduced a brake-based traction controller that applies a brake torque command, which is generated by a supervisory controller and based on the acceleration slip of the driven wheels. A closed loop actuator control algorithm generated the brake torque command to control an Eddy current brake system. A generalized predictive control method is used in this system to derive the control law for the brake torque command.

[0008] Most of the systems described above use experimental data or empirical formulas (e.g., [1], [6]) to determine the torque split ratio between the default driven wheels and the secondary driven wheels in order to enhance vehicle traction. Moreover, these systems have been largely built around the dynamic characteristics of actuators. However, as newer generations of actuators (e.g. electrohydraulic and electromechanical) become available, there is an increased need to design supervisory vehicle control systems which have issue control input-based torque command vehicle dynamics. The present invention is intended to address, overcome and/or improve upon these and other shortcomings of the prior art. SUMMARY OF THE INVENTION

[0009] Generally, the present invention is directed to an on-demand all wheel drive (ODAWD) vehicle system, which has a hybrid powertrain and uses slip regulation to enhance traction while driving. The system is based on a closed-loop actuator control law and is derived from a modified vehicle model, which has an optimized performance index based on wheel slip. To enhance vehicle longitudinal traction, the optimal controller minimizes wheel slip error by activating and dynamically controlling the electric motor drive torque to a non-driven pair of wheels, for example, the rear wheels. Moreover, when an over-threshold slip is sensed, the system automatically energizes the rear wheel motor drive system. According to this exemplary embodiment, the front wheels are the default driven wheels and the overall traction of the vehicle is enhanced by switching the driving mode of the vehicle from two-wheel drive (2WD) to four-wheel drive (4WD).

[0010] The sensors for detecting wheel slip constantly deliver the relevant sensory information to the computing unit of the controller, which estimates the slip and, by comparing with the slip threshold value, calculates a desired motor torque, T_n, . T_m is used to generate a current command to the electric motor so that it transmits the optimal drive torque to the rear wheels. If for a 2WD vehicle, the front wheels are driven, then by applying drive torque to the rear wheels as well, the vehicle becomes a 4WD vehicle.

[0011] Furthermore, by controlling the rear wheel motor torque dynamically, the exemplary system is able to reduce acceleration slip, thereby giving enhanced traction to vehicles on low friction coefficient surfaces.

[0012] According to one specific exemplary embodiment of the present invention, a traction enhancement system for a vehicle is provided. The system comprises a hybrid powertrain having an engine and transmission associated with a pair of front wheels of the vehicle and an electric motor associated with a pair of rear wheels of the vehicle. The system also has a controller that is adapted to minimize wheel slip error when the vehicle is on a surface by activating and dynamically controlling drive torque of the electric motor.

[0013] According to yet another exemplary embodiment of the present invention, a process for minimizing the wheel slip error of a vehicle is provided. According to this exemplary embodiment, the process comprises deriving a closed-loop actuator control law from an optimized performance index that is based on the wheel slip of a vehicle having a hybrid powertrain, the hybrid powertrain having an engine and transmission associated with a pair of front wheels and an electric motor associated with a pair of rear wheels; and minimizing the wheel slip of the vehicle by using the control law to activate and dynamically control drive torque of the electric motor. [0014] According to still another exemplary embodiment of the present invention, a method for optimizing the performance of a vehicle having a hybrid powertrain including an engine and transmission associated with a pair of front wheels and an electric motor associated with a pair of rear wheels is provided. According to this exemplary embodiment, the method comprises providing a modified vehicle model and an optimized performance index to derive a closed-loop actuator control law, the optimized performance index being based on the wheel slip of the vehicle; and using the control law to minimize the wheel slip of the vehicle by activating and dynamically controlling drive torque of the electric motor.

BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The above-mentioned aspects of the present invention and the manner of obtaining them will become more apparent and the invention itself will be better understood by reference to the following description of the embodiments of the invention taken in conjunction with the accompanying drawings, wherein:

[0016] FIG. 1 depicts vehicle dynamics of a modified exemplary on-demand all wheel drive vehicle system in accordance with the present invention and shown in a straight-line driving scenario;

[0017] FIG. 2 depicts wheel rotational dynamics of an exemplary wheel model during a driving event in accordance with the present invention;

[0018] FIG. 3 depicts an exemplary hybrid ODAWD control system in accordance with the present invention;

[0019] FIG. 4 depicts a graph showing friction coefficient vs. slip ratio for different surfaces in accordance with the present invention;

[0020] FIG. 5 depicts a flowchart which can control the operation of a motor used in the vehicle.

[0021] FIG. 6 depicts a graph showing front wheel slip ratios of an exemplary straight-line acceleration maneuver with and without a controller turned on in accordance with the present invention; [0022] FIG. 7 depicts a graph showing rear wheel slip ratios of an exemplary straight-line acceleration maneuver with and without a controller turned on in accordance with the present invention;

[0023] FIG. 8 depicts a graph showing motor torque to the rear wheels at differential output in accordance with the present invention;

[0024] FIG. 9 depicts a graph showing vehicle velocity with and without a controller turned on in accordance with the present invention; and

[0025] FIG. 10 depicts a graphical comparison of cost function for a vehicle without and with an exemplary controller in accordance with the present invention.

DETAILED DESCRIPTION

[0026] The embodiments of the present invention described below are not intended to be exhaustive or to limit the invention to the precise forms disclosed in the following detailed description. Rather, the embodiments are chosen and described so that others skilled in the art may appreciate and understand the principles and practices of the present invention.

[0027] Before moving to a detailed description of the exemplary embodiments of the present invention, a listing of various abbreviations used throughout the present disclosure is now provided. More particularly, as used herein, F_wmd refers to "air drag resistance"; F_R refers to "rolling resistance of the vehicle"; Fτ_eiTam refers to "forces arising out of road slopes/grades"; F_m refers to "rolling resistance force of i-th wheel"; F₂₁ refers to "normal force to i-th wheel"; g refers to "gravitational constant"; J_w refers to "general wheel inertia"; J_wf refers to "front wheel inertia"; J_W1 refers to "rear wheel inertia"; M_cog refers to "total mass of vehicle"; R refers to "effective radius of wheel"; T_m refers to "motor torque command"; S_f refers to "slip ratio of the front wheel"; S, refers to "slip ratio of the rear wheel"; S₁ refers to "slip ratio of i-th wheel"; S_deSπe,f refers to "desired slip ratio of front wheel"; S_desπe,i refers to "desired slip ratio of rear wheel"; T_totai refers to "total driving torque from the engine"; T_f refers to "torque to front wheel"; T₁ refers to "torque to rear wheel"; V_x refers to "longitudinal velocity"; O_f refers to "angular speed of front wheel"; ω, refers to "angular speed of rear wheel"; CO₁ refers to "angular speed of i-th wheel"; and μ refers to "road/tire Friction coefficient." [0028] As confirmed by survey [2], many 4WD users desire to have their vehicles exhibit improved performance in two different driving conditions. First, they desire to have enhanced traction so as not to become stuck when driving through deep snow and sand. Second, they desire to have start-off traction and the ability to drive on icy and/or snowy roads more easily. To address these concerns, the present invention is primarily directed to straight-line driving scenarios, particularly as straight-line driving scenarios uniformly involve low friction coefficient (μ) surfaces and do not deal with situations having rapidly varying friction coefficients, road surfaces and/or winding driving trajectories.

[0029] In a straight-line driving scenario, the vehicle model can be simplified to match that of a standard bicycle model, i.e. a structure with one front wheel and one rear wheel connected by an actuator (motor). Such an exemplary straight-line bicycle model is shown in FIG. 1 , which more specifically depicts a modified exemplary ODAWD vehicle system in accordance with the present invention. In this exemplary embodiment, the optimal controller focuses on the drive torque of the motor and is not concerned with the further torque split of the non-driven axle to the left and/or right. Further simplification of this straight-line scenario is made by assuming that the steer wheel angle is zero, thereby resulting in zero lateral motion. As such, the vehicle motion in the longitudinal direction on the road plane can be described by the following equation:

M - V_x = ZF = F_x - F_wmd - F_R -F_{tenam (1 )}

wherein the effect of F_wind is small at normal driving speeds and rolling resistance F_R is insignificant when compared to the driving force of a driving event. In addition, for the sake of simplicity, terrain force F_teπain can be neglected (i.e. no road slope or grade). As such, equation (1) becomes:

M - V_x = ZF = F_{x (2)}

[0030] In accordance with this exemplary embodiment, it is assumed that the load distribution, (i.e. the ratio of front wheel load to rear wheel load) is 60:40. Thus, equation (2) becomes: y F_x M(S₁ ) - F₂, ₊ μ{S, ) - F_zι

[0031] Next, wheel rotational dynamics are considered. For instance, in FIG. 2, wheel rotational dynamics of an exemplary simplified wheel model are depicted during a driving event in accordance with the present invention. Here, the wheel rotational dynamics are given by the following equation: J_^ - ώ^ ΣT^ ^ - F_^ - R - F_^ - R ₍₄₎

wherein the force relationships are defined as F_x, = μ(S,) ^• F_zι ; F_1n = η ^■ F_n and μ(SJ is the friction coefficient and η is the rolling resistance coefficient.

[0032] In equation (4), F_m is much smaller than T_d, and F_X1. Hence, it is neglected and equation (4) becomes:

J_m - ώ, = ^T_y, = T_dι - F_xι - R ₍₅₎

[0033] FIG. 3 depicts an exemplary hybrid ODAWD control system 300 in accordance with the present invention. According to this exemplary embodiment, the front wheels 302 each include a wheel speed sensor 303. The wheel speed sensors are typically mounted individually between an axle housing and a wheel as is understood by those skilled in the art. The wheel speed sensors provide the wheel speed of the respective wheels. The front wheels 302 are driven by the engine and transmission 304. The rear wheels 306 each include a wheel speed sensor 307 which provide a wheel speed of a respective rear wheel. The rear wheels 306 are driven by an electric motor 308 in an on-demand fashion. The electric motor 308 is coupled to the wheels 306 through a differential 310. The electric motor is also coupled to a controller 312. The controller 312 can include an optimal controller based on instantaneous optimization as would be understood by those skilled in the art. The controller can include a processing unit or computing unit and a memory as is understood by those skilled in the art.

[0034] The controller 312 receives a wheel speed from each of the wheel speed sensors 303 and 307 through an input 314. The wheel speed or sensor feedback provided to the controller 312 can be used to generate a control signal applied to the motor 308 through a saturation block 316 to ensure that the current value of the control signal does not exceed the maximum rating of the input current for the motor 308. The motor 308, in response to the control signal generates, a torque according to the control law of equation 14 to be described later herein. The motor can be adequately sized given the vehicle weight and engine power.

[0035] The controller processes wheel speed data using the described torque command, T_m, to actuate the electric motor as would be understood by one skilled in the art. The memory can store the torque command for use by the processor as well as the various constants used in the torque command and the data received from the wheel sensor. The processing unit will then calculate the value of T_m using the stored values of wheel sensor data and the other constants used in the calculation. [0036] From a control standpoint, there are two distinct control scenarios that can be used for this exemplary system 300. In a first embodiment, the electric motor 308 can be controlled to minimize wheel acceleration slip without any engine 304 intervention. In a second embodiment, the electric motor 308 can be controlled along with an engine output torque reduction scheme to thereby minimize wheel acceleration slip. In the second embodiment, the controller can be coupled to the engine/transmission 304 to provide a control signal through the control lines 318. [0037] In the first embodiment, the controller does not interact with the engine or with the transmission. It generates the rear wheel drive torque command, T_mj based on the driven wheel slip conditions and then subsequently estimates the motor current command which it applies to the motor. The differential distributes the motor torque to the rear wheels evenly. The engine/transmission drives the front wheels without any control or modification to the front wheel drive torque in this embodiment. [0038] In the second embodiment, when the front wheel slip does not track the desired slip level even after the rear wheel drive torque generation by the electric motor, the controller can also command the engine controller to reduce the front wheel drive torque in order to reduce the front wheel slip to the desired level. In the second embodiment, in addition to the rear wheel drive torque control via the electric motor, the proposed controller can communicate with the engine/transmission system through the control lines 318 to provide a signal to reduce front wheel drive torque in order to ensure optimal slip performance both at the front and the rear wheels. In this embodiment, the controller checks on the front wheel slip condition after actuating the electric motor for the rear wheels based on the proposed control law. If the front wheel slip condition is still higher than the desired level, the controller will instruct the engine controller to reduce the drive torque to the front wheels.

[0039] In accordance with the first embodiment, motor torque control is the only control variable and is based solely on wheel slip information. Because the design of this control system is less complex, the control scheme may produce sub-optimal wheel slip reduction for all four wheels. With respect to the second embodiment, the motor control is required to perform in conjunction with engine control, thereby making the control problem more complex. [0040] Still focusing on the first embodiment, motor torque is denoted by T₁₁, and equals zero in normal driving conditions because no wheel acceleration slip is present. In case of front wheel slippage due to acceleration on a low friction coefficient μ surface, the controller activates the motor to drive the rear wheels via the differential by applying the commanded torque T_m. The wheel dynamic equation can thereby be written using equations (5), (6) and (7).

T₁₀₁₀₁ - μ{S, ) - F_zr R ω_f = (6)

ώ_{ι =} τ. -MS. )-F. -R ₍₇₎

[0041] The wheel slip ratio in an acceleration event is defined as [I]: s _ ω_ι - R - V_{x = l} V ω, - R ω, - R ₍₈₎

[0042] In order to keep the wheel acceleration slip ratio at an optimal level, which leads to a maximum friction coefficient, the objective function is set as follows, and is based on the bicycle type model:

J

^~ ^i )

(9) [0043] Substituting (8) in (9), J is expressed as follows:

wherein, Ci = S_desiie;f - 1, and C₂ = S_desne,i - 1 -

[0044] FIG. 4 depicts a graph showing friction coefficient versus wheel slip ratio for three different surfaces [8]. The relationship between slip and friction coefficients can illustrates the available traction. As can be seen in FIG. 4, the friction coefficient reaches its maximum at slip ratio value 0.15 on asphalt and snow surfaces. Therefore, the proposed design provides a method and apparatus to keep the vehicle at a wheel slip ratio of about 0.15 during acceleration slip. This embodiment focuses on tracking the slip ratio at 0.15 for acceleration slip, which can yield the optimal friction coefficient. However, a friction coefficient range of 0.1-0.2 can be acceptable, but may not yield the optimal friction coefficient. Both the friction coefficient and the slip ratio are non-dimensional and have ranges between 0-1.2 and 0-1, respectively. [0045] From FIG.4, it is determined that the slip ratio, providing maximum friction coefficient, is about 0.15. Hence, S_deSne,i is set about 0.15, for both the front and rear wheels. Therefore, a more general constant C can be defined as: C = Cl = C2 = Sdesiie,i - 1 = -0.85, whereby:

[0046] Taking the time derivative of J, the following is obtained:

J = → 2-Kr-F^÷ ₁( ,÷ 1 + ÷ 1 , 2- F² ,ώ^, ώ. . 2 —-C-F ^₁ , 1 ^1 ,.± 2^-C-^F, j ώ_f ώ,

-²T) co.)- R² ω_r co. R ω. co, R co.

Moreover, rearranging the equation to make the longitudinal acceleration, front wheel angular acceleration and rear wheel angular acceleration explicit, the following is obtained:

R^' ωf ω; R ω_f ω, ωf-R ω_f-R ω, -R ω,-R

[0047] Substituting (3), (6) and (7) in (12), j=_{^ R^~ ₍± ωf₊± a>-₎₊^ R ₍± ω_f+± Co₁»«v- M u-^F.

2-V_x K , T^-M(S_j)-FfR 2-V_x V_λ T_1n - μ(S,)- F_n ^■ R _{U) ωf -R ω_f-R J_u ω,² R co, -R J_n

[0048] The above objective function is to be minimized with respect to T_m. By

FONC (First Order Necessary Condition), T_m's optimal value can be obtained by setting dJ/dT_m= 0. However, the derivative of J in (13) is related to time, so the relationship between dJ/dt and dJ/dT_m has to be evaluated. It is known that dJ/dt = (dJ/dT_m) * (dT_m/dt). As such, if dT_m/dt is not equal to 0 at all times, then dJ/dt = 0 implies that δJ/δT_m = 0. T₁₁₁ is the control variable, changing with respect to time. So T₁₁₁' s optimal value can be obtained by setting dJ/dt = 0.

[0049] It is further assumed that J_wf and J_w, are equal and are equal to the general wheel inertia of J_w (since the wheel inertia of the front and rear wheels is very similar). As such, setting J = O yields:

)]^*

[μ(S_f)-F_:f+μ{S_r)-F_:ι]- _ω/ . (V_{x +} C-_CO1 -R) ω_f ■ R ' (14)

(T_ιoιal-μ(S_f)-F_:f-R) Now, the control law is given by equation (14), which is a function of estimated engine torque and driving conditions.

[0050] T₁₁, is the torque command to actuate the electric motor. However, based on motor type, the control input to the motor can be a current command. Since torque is proportional to the current input, the current command can be computed via the motor torque constant for a given torque command, T_m. The current command corresponding to T_n, is passed through the saturation block 316 to ensure that the current value does not exceed the maximum rating of the input current for the selected motor.

[0051] Advantages and improvements of the processes and methods of the on- demand traction controller system of the present invention are now demonstrated in the following exemplary SIMULINK model evaluation example. This example is illustrative only and is not intended to limit or preclude other embodiments of the invention.

[0052] FIG. 5 illustrates a flow diagram illustrating a control sequence of the present invention. As illustrated in FIG. 5 at block 400, the wheel speed is received by the controller 312 as previously described. At block 402, the wheel slip is estimated for all four wheels based on the described algorithms. Once the controller is engaged, the controller determines at step 404 whether the front left (FL) or front right (FR) wheel slip is greater than the desired slip. IfNO, then the controller 312 continues to monitor wheel slip at step 404. If however, the wheel of either the front left of front right wheel is greater than the desired slip, then at step 406, the torque value, T_1n, is calculated as well as the current command signal to be applied to the motor. The current command signal is a current signal based on the computed torque value which is used to control the speed of the electric motor. In the computation of T_m, the wheel slip information (which is estimated via the wheel speed sensor data) is used through the control law. Once the slip value departs from the desired value during an acceleration slip event, the controller actuates the electric motor to provide additional traction to the rear wheels. [0053] The current command signal is applied to the electric motor to drive the rear wheels at step 408. Once the current signal is applied to the rear wheels, the wheel slip estimate for all four wheels is used at step 410 to determine whether the desired front left or front right wheel slip has been achieved. If the front left or front right slip is greater than the desired slip, then the desired slip has not been achieved. Consequently, if the answer is YES at step 410, then at step 412 the controller reduces the front wheel drive torque by computing T_m and actuating the electric motor to drive the rear wheels to achieve the desired slip. If, however, the answer is NO at step 410, then the desired wheel slip has been achieved. EXAMPLE:

[0054] In accordance with this exemplary simulation example, the controller model was placed in a 14 degree-of- freedom vehicle model, thereby closing the loop. The vehicle model was for a Volkswagen Golf. The vehicle and motor parameters are shown in table 1. The drive torque, the vehicle longitudinal velocity, and the wheel angular speeds were directly taken from the vehicle model. The wheel slip ratio was calculated based on the vehicle longitudinal velocity and wheel speeds. It is noted that the drive torque and the vehicle longitudinal velocity were to be estimated in the final implementation of the control algorithm on a vehicle. Based on this information, the commanded motor torque was calculated using equation (14). The closed loop actuator controller ensures that the amount of torque transferred to the rear wheels is in accordance with the commanded torque. Simulation runs were performed for a straight-line acceleration maneuver on a packed snow surface. The following graphs show the comparison between driving situations without the controller and that with the controller, as well as the motor control torque, T₁₁₁. [0055]

Table 1

[0056] FIG. 6 depicts a graph showing front wheel slip ratios of an exemplary straight-line acceleration maneuver with and without a controller turned on in accordance with the present invention. As can be seen from this graph, the controller effectively enhanced the front wheel traction by reducing the slip ratio from a maximum value of 60% to 50%. The desired slip ratio of the front wheels (15-20%) was not achieved due, in part, to the lack of engine torque reduction via engine control. This figure shows the performance comparison of the front wheel slip condition with or without the controller. Because one embodiment of the present invention can provide a sub-optimal solution in the first embodiment, the controlled performance does not reach the optimal slip value of 0.15. But it does reduce the slip level at the front wheels, thus increasing the overall traction. In the second embodiment, however, the front wheel slip performance can be substantially optimal.

[0057] FIG. 7 depicts a graph showing rear wheel slip ratio of an exemplary straight-line acceleration maneuver without and with the controller on, respectively. Due to the motor torque applied to the rear wheels, acceleration slip is introduced with the controller turned on, but the maximum value of acceleration slip was limited to 6.5%. This may be attributed to the underpowered motor (3.3 kW), which was picked as a test case, resulting in less wheel slip than the desired value of 15%. In the first embodiment, the rear wheels can provide a sub-optimal traction to vehicle when it increases the slip ratio from zero.

[0058] FIG. 8 shows a plot of the control variable motor torque (Tm) to the rear wheels at differential output in accordance with the present invention. As can be seen from this plot, the graph is similar in shape to the graph of the rear wheel slip ratio. This figure shows the change of the electrical motor output when the vehicle accelerates from a speed of zero to about twenty meters per second. This torque output can gain the vehicle more traction. The X axis is time by seconds; the Y axis is torque by Newton'meter (N'm).

[0059] FIG. 9 shows the vehicle velocity without and with the controller turned on. According to this graph, the traction enhancement due to the controller resulted in increased vehicle speed by about 8% for the vehicle with controller on. This figure shows an increase in velocity or velocity enhancement by the controller. The X axis is time in seconds and the Y axis is the longitudinal velocity in meters per second. [0060] Finally, FIG. 10 depicts the comparison of the cost function for the vehicle without and with the proposed controller. It is clear that the cost function is significantly reduced with the controller. Equation (9) describes the objective function, 'J', which is minimized in process of the controller design. Without the controller activated, 'J' is much higher than that with the controller activated. Therefore, by applying the motor torque, T_m, 'J' is minimized to its sub-optimal solution. [0061] A novel design of a control law optimizing the performance of an on- demand all wheel drive vehicle for traction enhancement via slip regulation in a driving event is described. Simulation of the proposed controller was performed on a validated 14 degree-of-freedom detailed vehicle model in MATLAB / SIMULINK. The simulation results show that the control algorithm provides acceleration slip regulation in a vehicle traction maneuver on low friction coefficient surfaces when compared with that without the traction-enhanced controller. The limited performance may be attributed to lack of engine intervention to reduce the front wheel drive torque and to the rear motor drive lacking adequate power.

[0062] While an exemplary embodiment incorporating the principles of the present invention has been disclosed hereinabove, the present invention is not limited to the disclosed embodiments. Instead, this application is intended to cover any variations, uses, or adaptations of the invention using its general principles. Further, this application is intended to cover such departures from the present disclosure as come within known or customary practice in the art to which this invention pertains and which fall within the limits of the appended claims.

[0063] REFERENCES

[0064] The following references are incorporated herein by reference in their entirety:

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[0067] [3] Asgari, J. and Hrovat, D. "On-demand four wheel-drive transfer case modeling", SAE Special Publications, v 1241, 970969.

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Claims

CLAIMS:What is claimed is:

1. A traction enhancement system for a vehicle, comprising: a hybrid powertrain having an engine and transmission associated with a pair of front wheels and an electric motor associated with a pair of rear wheels; and a controller adapted to minimize wheel slip error of the vehicle on a surface by activating and dynamically controlling drive torque of the electric motor.

2. The traction enhancement system of claim 1, wherein the electric motor is configured to drive the pair of rear wheels in an on-demand fashion.

3. The traction enhancement system of claim 1, wherein the electric motor is configured to minimize wheel acceleration slip without intervention from the engine and transmission.

4. The traction enhancement system of claim 3, wherein the wheel acceleration slip is minimized by controlling the electric motor by an engine output torque reduction scheme.

5. The traction enhancement system of claim 1, wherein the controller calculates a torque value, T_m, used to generate a current signal applied to the electric motor to minimize wheel slip error.

6. The traction enhancement system of claim 5, wherein the torque value, T_m, is generated using the formula:

M ^■ V_x ^■ ( V_x + C ^■ ω, ^■ R) R- ωf ω ^~ R ω_f ω, ω- - ^R (^ ₊ C) *

[μ{S_f ) - F_:f + μ{S, ) - F_:, ] - co ÷ . _{(V + C} . ω, - R) ω_f - R

(T_lolal - μ(S_f ) - F_:f - R)

7. A process for minimizing the wheel slip error of a vehicle, comprising: deriving a closed-loop actuator control law from an optimized performance index that is based on the wheel slip of a vehicle having a hybrid powertrain, the hybrid powertrain having an engine and transmission associated with a pair of front wheels and an electric motor associated with a pair of rear wheels; and minimizing the wheel slip of the vehicle by using the control law to activate and dynamically control drive torque of the electric motor.

8. The process of claim 7, wherein the electric motor is configured to drive the pair of rear wheels in an on-demand fashion.

9. The process of claim 7, wherein the electric motor is configured to minimize wheel acceleration slip without intervention from the engine and transmission.

10. The process of claim 9, wherein the wheel acceleration slip is minimized by controlling the electric motor by an engine output torque reduction scheme.

11. The process of claim 7, wherein the closed-loop actuator control law is a function of an estimated engine torque value and driving conditions associated with the vehicle.

12. The process of claim 7, wherein the minimizing step comprises using a control law which calculates a torque value, T_m, used to provide a current signal applied to the electric motor to minimize wheel slip.

13. The method of claim 12, wherein the torque value, T_m, is generated using the formula:

ω.' - R K _{| C ) *}

( „ ⁺ W

[M(S_f ) - F_:f + M(S₁ ) - FJ - C₀^ (V_{x +} C - CO₁ - R) ω, ■ R

(T_loml - μ(S_f ) - F_zf - R)

14. A method for optimizing the performance of a vehicle having a hybrid powertrain, the hybrid powertrain including an engine and transmission associated with a pair of front wheels and an electric motor associated with a pair of rear wheels, comprising: providing a modified vehicle model and an optimized performance index to derive a closed-loop actuator control law, the optimized performance index being based on the wheel slip of the vehicle; and using the control law to minimize the wheel slip of the vehicle by activating and dynamically controlling drive torque of the electric motor.

15. The method of claim 14, wherein the electric motor is configured to drive the pair of rear wheels in an on-demand fashion.

16. The method of claim 14, wherein the electric motor is configured to minimize wheel acceleration slip without intervention from the engine and transmission.

17. The method of claim 16, wherein the wheel acceleration slip is minimized by controlling the electric motor by an engine output torque reduction scheme.

18. The method of claim 14, wherein the closed-loop actuator control law is a function of an estimated engine torque value and driving conditions associated with the vehicle.

19. The method of claim 14, wherein the using step comprises using control law which calculates a torque value, T_m, used to provide a current signal applied to the electric motor to minimize wheel slip error.

20. The method of claim 19, wherein the torque value, T_m, is generated using the formula:

M -V_^ -(V_x +C ^■ O)₁ ^■ R) R^' ω_f (O₁ R ω_f ω_t ω- ^'R ( ^K i C)*

[M(S₁)- F_:f+μ(S,)-F_:ι]- _ω/.(V_χ+C-ω, -R) ω_f ■ R

(T_ιoωl-μ(S_f)-F_:f-R)