Efficient robust method for traction control system

Abstract

A vehicle includes a system and method of modeling and controlling tractive effort of a wheel of the vehicle. The system includes an observer, a predictive controller, and an online solver. The observer receives dynamic model parameters of the wheel and determines an estimate of a wheel speed and an uncertainty of the wheel speed using a nonlinear model of the wheel. The predictive controller determines an average gain and a differential gain from the estimate of the wheel speed and the uncertainty of the wheel speed. The online solver calculates a motor torque and a wheel brake torque for increasing tractive effort of the wheel on a road based on the average gain and the differential gain. The motor torque and the wheel brake torque are applied on the vehicle.

Description

TECHNICAL FIELD

[0001] The present invention relates to a nonlinear dynamic model for a traction control system, and more particularly, to a method of using a nonlinear dynamic model to capture the nonlinear dynamic forces on the wheels and the nonlinear behavior of the wheels to control wheel slip. BACKGROUND

[0002] Longitudinal or forward motion of a vehicle is generated by turning the wheels of the vehicle in contact with the ground and depends on the friction between the wheels and the ground. In certain situations, the forces or torques applied on the wheels can cause slippage between the wheels and the ground, known as wheel slip. This slippage allows the wheels to spin rapidly while the vehicle has little or no corresponding longitudinal motion. Therefore, traction control systems are commonly used to control the forces and torques or traction control forces on the wheels to increase the traction of the wheels and reduce wheel slip. However, current traction control systems use an analysis of the wheels as linear systems to calculate the traction control forces. Considering only the linear forces on the wheels does not provide a complete picture of the dynamics of the wheels, and thus the resulting traction force control forces can only partially effectively reduce wheel slip. Therefore, it is desirable to provide a traction control system for the wheels that calculates the traction control forces based on nonlinear forces and / or wheel parameters. SUMMARY

[0003] In one example embodiment, a method of modeling and controlling traction of a wheel of a vehicle is disclosed. Dynamic model parameters of the wheel are received at an observer. A nonlinear model of the wheel is used at the observer to determine an estimate of a wheel speed and an uncertainty of the wheel speed. An average gain and a differential gain are determined at a predictive controller from the estimate of the wheel speed and the uncertainty of the wheel speed. A motor torque and a wheel brake torque for increasing traction of the wheel on a road are calculated based on the average gain and the differential gain. The motor torque and the wheel brake torque are applied on the vehicle.

[0004] In addition to one or more features described herein, the wheel brake torque includes a right front brake torque and a left front brake torque. The estimate of the wheel speed and the uncertainty of the wheel speed include an estimate of an average wheel speed, an estimate of a differential wheel velocity, an uncertainty of the average wheel speed, and an uncertainty of the differential wheel velocity. The method further includes solving a first set of equations to determine a longitudinal motion of the vehicle and solving a second set of equations to determine a yaw motion of the vehicle. The solution of the second set of equations is used as a constraint for the first set of equations. The method further includes optimizing a first cost function to determine the average gain and optimizing a second cost function to determine the differential gain. The method further includes using a moment of inertia of the wheel to determine the estimate of the wheel speed and the uncertainty of the wheel speed.

[0005] In another example embodiment, a system for modeling and controlling traction of a wheel of a vehicle is disclosed. The system includes an observer, a predictive controller, and an online solver. The observer receives dynamic model parameters of the wheel and determines an estimate of a wheel speed and an uncertainty of the wheel speed using a nonlinear model of the wheel. The predictive controller determines an average gain and a differential gain based on the estimate of the wheel speed and the uncertainty of the wheel speed. The online solver computes motor torque and wheel brake torque for increasing traction of the wheel on a road based on the average gain and the differential gain.

[0006] In addition to one or more of the features described herein, the wheel brake torque includes a right front brake torque and a left front brake torque. The estimate of the wheel speed and the uncertainty of the wheel speed include an estimate of an average wheel speed, an estimate of a differential wheel speed, an uncertainty of the average wheel speed, and an uncertainty of the differential wheel speed. The predictive controller generates a first cost function based on the estimate of the average wheel speed and the uncertainty of the average wheel speed and a second cost function based on the estimate of the differential wheel speed and the uncertainty of the differential wheel speed, and the online solver optimizes the first cost function to determine the average gain and optimizes the second cost function to determine the differential gain. The online solver solves a first set of equations to determine a longitudinal motion of the vehicle and a second set of equations to determine a yaw motion of the vehicle. The solution of the second set of equations is used as a constraint for the first set of equations. The observer utilizes a moment of inertia of the wheel to determine the estimate of the wheel speed and the uncertainty of the wheel speed.

[0007] In yet another example embodiment, a vehicle is disclosed. The vehicle includes an observer, a predictive controller, and an online solver. The observer receives dynamic model parameters of a wheel of the vehicle and determines an estimate of a wheel speed and an uncertainty of the wheel speed using a nonlinear model of the wheel. The predictive controller determines an average gain and a differential gain based on the estimate of the wheel speed and the uncertainty of the wheel speed. The online solver computes motor torque and wheel brake torque for increasing traction of the wheel on a road based on the average gain and the differential gain.

[0008] In addition to one or more of the features described herein, the wheel brake torques include a right front brake torque and a left front brake torque. The estimates of wheel speeds and the uncertainties of wheel speeds include an estimate of average wheel speed, an estimate of differential wheel speed, an uncertainty of average wheel speed, and an uncertainty of differential wheel speed. The predictive controller generates a first cost function based on the estimate of average wheel speed and the uncertainty of average wheel speed, and generates a second cost function based on the estimate of differential wheel speed and the uncertainty of differential wheel speed, and the online solver optimizes the first cost function to determine an average gain and optimizes the second cost function to determine a differential gain. The online solver solves a first set of equations to determine longitudinal motion of the vehicle and solves a second set of equations to determine yaw motion of the vehicle. The solution of the second set of equations is used as a constraint for the first set of equations.

[0009] The above features and advantages of the present disclosure, and other features and advantages, will become apparent to those skilled in the art from the following detailed description, which, when taken in conjunction with the drawings, discloses various embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0010] Other features, aspects, and details of the application are described in only examples, and with reference to the drawings, in which:

[0011] Figure 1 is a block diagram of a vehicle having a traction control system in an example embodiment;

[0012] Figure 2 shows Figure 1 a plan view of the chassis of the vehicle showing various components for motion of the vehicle;

[0013] Figure 3 shows Figure 2 the chassis with relevant dynamic model parameters labeled thereon;

[0014] Figure 4 shows a process flow of an electronic brake control module of the vehicle in an embodiment;

[0015] Figure 5 is a schematic diagram showing operation of the traction control system;

[0016] Figure 6 shows an actuator for distributing torque to the vehicle;

[0017] Figure 7 shows a flowchart of a method for traction control using the methods disclosed herein;

[0018] Figure 8 shows a plot of the left wheel speed over time; and

[0019] Figure 9 shows a plot of the right wheel speed over time. Detailed Implementation

[0020] The following description is merely exemplary in nature and is not intended to limit this disclosure, its application, or use. It should be understood that in all the figures, corresponding reference numerals denote similar or corresponding components and features. As used herein, the term module refers to processing circuitry, which may include application-specific integrated circuits, electronic circuitry, processors (shared, dedicated, or grouped), and memory executing one or more software or firmware programs, combinational logic circuitry, and / or other suitable components providing the described functionality.

[0021] According to an exemplary embodiment, Figure 1 This is a block diagram of a vehicle 100 having a traction control system 110. Figure 1 The exemplary vehicle 100 shown is a car 101. According to... Figure 1 In the view shown, two of the four wheels 120 of vehicle 100 are visible. Traction control system 110 uses a nonlinear dynamic model of the wheels 120 to determine the torque applied to the wheels, thereby increasing the traction force between the wheels and the ground. Traction control system 110 is shown as part of a controller 105 (e.g., an electronic control unit) of vehicle 100. According to an alternative embodiment, the functionality of traction control system 110 may be separate from controller 105, or it may be performed by a set of controllers 105. Controller 105 operates various modules to implement traction control system 110.

[0022] Figure 2 It shows Figure 1 A plan view of the chassis 200 of vehicle 100, showing various components for vehicle motion. Chassis 200 includes a front axle 220, a rear axle 230, and a drive shaft 240 connecting the rear axle 230 to the front axle 220. Drive shaft 240 provides a mechanism by which force or torque can be transmitted between the rear axle 230 and the front axle 220. Drive shaft 240 is aligned along the longitudinal axis 250 of vehicle 100. Front axle 220 supports the left front wheel 120a and the right front wheel 120b. Rear axle 230 supports the left rear wheel 120c and the right rear wheel 120d. Wheel base l represents the distance between the front axle 220 and the rear axle 230. Axle track b represents the distance between the left and right wheels.

[0023] Motor 210 provides motor torque to drive shaft 240, which is then transmitted to rear wheel axle 230 and front wheel axle 220 to rotate wheels 120a-120d. The left front wheel 120a and right front wheel 120b are able to change their rolling direction from side to side to form a steering angle δ relative to the longitudinal axis 250. During longitudinal movement with a non-zero steering angle, vehicle 100 experiences yaw rotation.Figure 2 ψ represents the yaw rate.

[0024] Figure 3 The chassis 200 is shown Figure 2 annotated with relevant dynamic model parameters. At the front axle 220, the longitudinal velocity of the left front wheel 120a is V xLF , and the longitudinal velocity of the right front wheel 120b is V xRF . At the rear axle 230, the longitudinal velocity of the left rear wheel 120c is V xLR , and the longitudinal velocity of the right rear wheel 120d is V xRR . The motor 210 provides a motor torque This torque is transmitted to the four wheels 120a-120d through the front axle 220, the rear axle 230, and the drive shaft 240. A left front brake (not shown) can be activated to apply a left brake torque to the left front wheel 120a, and a right front brake (not shown) can be activated to apply a right brake torque to the right front wheel 120b. In various embodiments, sensors (not shown) on the vehicle 100 obtain measurements of the various torques (i.e., motor torque left brake torque and right brake torque ) as well as various dynamic model parameters (e.g., V xLF , V xRF , V xLR , V xRR , etc.) of one or more wheels 120a-120d in order to calculate traction control torque values to be applied to reduce wheel slip.

[0025] Figure 4 A processing flow of the electronic brake control module 400 of the vehicle 100 in an embodiment is shown. Sensors on the wheels 120 provide kinematic parameters, including wheel speeds, to the electronic brake control module 400. At decision block 402, calculations are performed using the kinematic parameters to determine whether the wheels 120 are experiencing wheel slip. If the wheels are not slipping, the electronic brake control module 400 allows driver commands 404 to control operation of the wheels 120. On the other hand, if there is wheel slip, the electronic brake control module 400 employs the traction control system 110 to reduce or eliminate the wheel slip.

[0026] Figure 5 is a schematic diagram showing operation of the traction control system 110. The traction control system 110 includes a high-gain observer 502 and a feedback controller 504. The feedback controller 504 includes a nonlinear model predictive controller, also referred to herein as a predictive controller 506, and an online solver 508.

[0027] The sensors on the wheels provide kinematic parameters 510 to a high-gain observer 502. The high-gain observer 502 computes various estimates 512 of the dynamic model parameters and uncertainties based on a nonlinear model of the kinematic parameters 510. These estimates 512 of the dynamic model parameters and uncertainties are provided to a predictive controller 506 of a feedback controller 504. The predictive controller 506 generates one or more cost functions from the estimates 512 and uncertainties and optimizes the one or more cost functions to determine various gains for controlling the torques to be applied subsequently. The gains are provided from the predictive controller 506 to an online solver 508. The online solver 508 determines various torques 514 to be provided to the vehicle 100 in order to reduce wheel slip at the wheels 120. 514.

[0028] The kinematic parameters 510 provided from the wheel sensors to the high-gain observer 502 are now discussed. The longitudinal velocity of the rear axle 230 (V x rear ) is related to the wheel dynamics at each wheel 120a-120d by the kinematic equations shown in equations (1)-(4):

[0029]

[0030] where the index LF represents the left front wheel 120a, the index RF represents the right front wheel 120b, the index LR represents the left rear wheel 120c, and the index RR represents the right rear wheel 120d. The parameter r is the radius of the wheels, l is the wheelbase, b is the track of the axles, and ψ is the yaw rate of the vehicle. Thus, the average front wheel speed is given by equation (5):

[0031]

[0032] The difference in front wheel speeds is given by equation (6):

[0033]

[0034] Similar equations to equations (5) and (6) can be generated to determine the average rear wheel speed and the difference in rear wheel speeds

[0035] In operation, the observer 502 receives various kinematic parameters 510 from sensors at the wheels 120, including but not limited to, the average front wheel speed the front wheel speed difference and the current torques on the vehicle, such as the front motor torque T Mf , the left front brake torque T BLf , and the right front brake torque TBRf The observer 502 also receives or has access to state parameters, such as the steering angle δ, the steering rate δ, the wheelbase l, the axle track b, and the like. The observer 502 performs calculations on the dynamic model parameters to generate estimates of the dynamic model parameters of the front wheels, such as the estimate of the average front wheel speed the estimate of the difference between the front wheel speeds and the associated uncertainty (i.e., respectively and ). The calculations performed at the observer 502 are detailed in equations (7)-(14).

[0036] Equation (7) shows a dynamic model equation for the time derivative of the average front wheel speed:

[0037]

[0038] where J f is the wheel inertia, and and are the longitudinal forces of the left and right front wheels, respectively. Equation (7) further includes an uncertainty term σ avgf , which is an unknown wheel tire interaction term that accounts for the uncertainty in the values of the state parameters and the dynamic model parameters. Equation (7) does not provide a complete description of the vehicle longitudinal motion. In addition, several parameters of equation (7) cannot be measured. Therefore, the observer 502 instead implements equations (8) and (9) to include the effects due to missing or unmeasurable parameters.

[0039] The observer 502 determines estimates of the average front wheel speed and the uncertainty in the wheel dynamic model shown in equations (8) and (9):

[0040]

[0041]

[0042] Equation (9) is the time evolution equation for the uncertainty in the average speed. Equation (8) describes the time evolution of the estimate of the average speed. While equation (9) describes the time evolution of the missing and / or unmeasured parameters. In equations (8) and (9), hi and h2 are observer gains, and ε is a small positive number (0 < ε « 1). The observer gains hi and h2 are chosen such that the polynomial:

[0043] s 2 + hi s + h2 = 0 equation (10)

[0044] is a Hurwitz polynomial. The constant difference equations shown in equations (8) and (9) can be solved to produce outputs and

[0045] Similarly, the equation of motion for the front wheel speed difference is shown in equation (11):

[0046]

[0047] where J f is the wheel inertia, and and are the longitudinal forces acting on the left and right front wheels, respectively. The uncertainty term is an unknown wheel tire interaction term that accounts for uncertainty in the state parameters and dynamic model parameter values.

[0048] The observer 502 solves the equations for the estimate of the front wheel speed difference shown in equations (12) and (13):

[0049]

[0050] Equation (13) is the time evolution equation for the uncertainty in the differential velocity. Equation (12) describes the time evolution of the estimate of the differential velocity, while equation (13) describes the time evolution of the lost and / or unmeasured parameters. In equations (12) and (13), h3and h4are observer gains, and ε is a small positive number (0 < ε « 1). The observer gains h3and h4are chosen such that the polynomial:

[0051] s 2 + h3s + h4 = 0 equation (14)

[0052] is a Hurwitz polynomial. The constant difference equations shown in equations (12) and (13) can be solved to produce outputs and

[0053] A discussion of the operation of the predictive controller 506 is now presented. The predictive controller 506 uses two separate models to calculate gain values. The first model is an average dynamic model that describes the longitudinal motion of the vehicle and generates average gain values. The second model is a differential dynamic model that describes the yaw rotation of the vehicle and generates differential gain values.

[0054] The first model involves creating a first cost function based on the sum of torques, which is represented by in equation (15):

[0055]

[0056] The cost function describing the dynamics of the average force on the wheels is given in equation (16):

[0057]

[0058] The cost function is optimized by taking the derivative of equation (16) with respect to and setting the derivative to zero, as shown in equation (17):

[0059]

[0060] Equation (17) can be simplified to obtain equation (18):

[0061]

[0062] By defining the average gain k avg as shown in equation (19):

[0063]

[0064] The average gain k avg can be determined by solving equation (18).

[0065] The second model involves creating a second cost function based on the difference between the left front wheel torque and the right front wheel torque, denoted by u in equation (15):

[0066]

[0067] The calculations are similar to those in equations (16)-(19) and result in a difference gain k diff as shown in equation (21):

[0068]

[0069] where is referred to as the time horizon. The gains k avg and k diff are then provided from the predictive controller 506 to the online solver 508.

[0070] A discussion of the operation of the online solver 508 is now presented. The online solver 508 uses parameters from the observer 502 and from the predictive controller 506 to perform calculations. The online solver 508 solves a first set of equations to determine the average force to be applied to determine the value of the torque sum, as shown in equation (15).

[0071] The first set of equations is discussed in equations (22)-(25). The average front wheel force function is generated from the difference between the average of the front wheel forces and the average of the rear wheel forces, as shown in equation (22):

[0072]

[0073] where the average front wheel force is given in equation (23):

[0074]

[0075] where the average rear wheel force is given in equation (24):

[0076]

[0077] The time derivative of the torque sum is defined by the average wheel force function using equation (25):

[0078]

[0079] where a1 and b1 are lower and upper limit values of the actuator capacity, respectively, and the control parameter δ a is chosen to have the condition: 0 < δ a <<1. The online solver solves equation (25) to determine

[0080] The second set of equations is discussed in equations (26)-(29). The difference wheel force function is generated from the difference between the differential front wheel forces and the differential rear wheel forces, as shown in equation (26):

[0081]

[0082] where the differential front wheel force is given in equation (27):

[0083]

[0084] where the differential rear wheel force is given in equation (28):

[0085]

[0086] The time derivative of the torque difference is defined by the difference wheel force function using equation (29):

[0087]

[0088] where a2 and b2 are lower and upper limit values of the actuator capacity, respectively, and the control parameter δ dThe conditions shown in the following equations are selected: 0 < δ d The online solver solves equation (29) to determine u.

[0089] In various embodiments, the second set of equations in equations (26)-(29) can be solved first, and the results used to form the construction of the solution of the first set of equations (equations (22)-(25)). When or then and and When then and and The parameter s f is a control parameter that can be selected or set by the designer based on the capabilities of the motor. In various embodiments, s f may be set to -10.

[0090] Figure 6 An actuator 600 for distributing torque to a vehicle 100 is shown. The actuator 600 receives the computed results (i.e., the and u) from the online solver 508 and computes the front motor torque T Mf , the left front brake torque T BLf and the right front brake torque T BRf and applies these torques to the vehicle.

[0091] Figure 7 A flowchart 700 of a method of traction control using the methods disclosed herein is shown. In block 702, measurements of the wheel dynamics are obtained using sensors at the vehicle. In block 704, rear axle speed estimates (average and difference) and associated uncertainties are determined at the observer. In block 706, a cost function is formed at the predictive controller from the rear axle speed estimates and uncertainties. In block 708, the cost function is solved at the online solver to determine average and difference gains. In block 710, the average and difference gains are used to determine the torques to be applied to the vehicle to increase the wheel traction. In block 712, the torques are applied to the vehicle.

[0092] Figure 8A plot 800 of left wheel speed versus time is shown. Time is shown in seconds on the horizontal axis, and left wheel speed is shown in kilometers per hour (km / h) on the vertical axis. Line 802 represents the target speed of the left wheel. Curve 804 represents the left wheel speed of a wheel experiencing wheel slip and controlled using a conventional linear traction control system. Curve 806 represents the left wheel speed of a wheel experiencing wheel slip and controlled using the traction control system disclosed herein. Curve 804 exhibits large changes in left wheel speed (e.g., between approximately 0 km / h and approximately 27 km / h) and a long decay time (e.g., approximately 0.8 seconds) to obtain a wheel speed consistent with the target wheel speed. Meanwhile, curve 806 exhibits relatively smaller changes in left wheel speed (e.g., between approximately 0 km / h and approximately 12 km / h) and a shorter decay time (e.g., approximately 0.5 seconds) to obtain a wheel speed consistent with the target wheel speed.

[0093] Figure 9 A plot 900 of right wheel speed versus time is shown. Time is shown in seconds on the horizontal axis, and right wheel speed is shown in kilometers per hour (km / h) on the vertical axis. Line 902 represents the target speed of the right wheel. Curve 904 represents the right wheel speed of a wheel experiencing wheel slip and controlled using a conventional linear traction control system. Curve 906 represents the right wheel speed of a wheel experiencing wheel slip and controlled using the traction control system disclosed herein. Curve 904 exhibits large changes in right wheel speed (e.g., between approximately 0 km / h and approximately 27 km / h) and a long decay time (e.g., greater than 1 second) to obtain a wheel speed consistent with the target wheel speed. Meanwhile, curve 906 exhibits relatively smaller changes in right wheel speed (e.g., between approximately 0 km / h and approximately 12 km / h) and a shorter decay time (e.g., approximately 0.4 seconds) to obtain a wheel speed consistent with the target wheel speed.

[0094] While the foregoing disclosure has been described in reference to illustrative embodiments, those skilled in the art will understand that various changes can be made and equivalents can be substituted without departing from the scope of the disclosure. In addition, many modifications can be made to adapt a particular situation or material to the teachings of the disclosure without departing from the central scope thereof. Therefore, it is intended that the disclosure not be limited to the particular embodiments disclosed, but will include all embodiments falling within the scope of the disclosure.

Claims

1. A method for modeling and controlling the traction force of a vehicle's wheels, comprising: Receive dynamic model parameters of the wheel at the observer; At the observer, a nonlinear model of the wheel is used to determine the estimate of the wheel speed and the uncertainty of the wheel speed, wherein the estimate of the wheel speed and the uncertainty of the wheel speed include the estimate of the average wheel speed, the estimate of the differential wheel speed, the uncertainty of the average wheel speed and the uncertainty of the differential wheel speed. The average gain and differential gain are determined at the predictive controller based on the wheel speed estimate and the wheel speed uncertainty. The motor torque and wheel braking torque used to increase the traction of the wheels on the road are calculated based on average gain and differential gain. as well as The motor torque and wheel braking torque are applied to the vehicle.

2. The method according to claim 1, wherein, The wheel braking torque includes the right front braking torque and the left front braking torque.

3. The method according to claim 1 further includes solving a first set of equations to determine the longitudinal motion of the vehicle, and solving a second set of equations to determine the yaw motion of the vehicle.

4. The method of claim 1, further comprising optimizing a first cost function to determine average gain, and optimizing a second cost function to determine differential gain.

5. A system for modeling and controlling the traction force of a vehicle's wheels, comprising: An observer is used to receive dynamic model parameters of the wheel and use a nonlinear model of the wheel to determine the estimate and uncertainty of the wheel speed, wherein the estimate and uncertainty of the wheel speed include the estimate of the average wheel speed, the estimate of the differential wheel speed, the uncertainty of the average wheel speed, and the uncertainty of the differential wheel speed. A predictive controller is used to determine the average gain and differential gain based on the wheel speed estimate and the wheel speed uncertainty. as well as An online solver for calculating motor torque and wheel braking torque to increase wheel traction on the road, based on average gain and differential gain.

6. The system according to claim 5, wherein, The wheel braking torque includes the right front braking torque and the left front braking torque.

7. The system according to claim 5, wherein, The predictive controller generates a first cost function based on the estimate and uncertainty of the average wheel speed, and generates a second cost function based on the estimate and uncertainty of the differential wheel speed. An online solver optimizes the first cost function to determine the average gain and optimizes the second cost function to determine the differential gain.

8. The system according to claim 5, wherein, The online solver solves the first set of equations to determine the vehicle's longitudinal motion and the second set of equations to determine the vehicle's yaw motion.

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