A rear wheel differential cooperative control method for preventing vehicle instability and automobile thereof

Abstract

The application discloses a rear wheel differential cooperative control method for preventing vehicle instability and an automobile thereof, and relates to the technical field of vehicle torque distribution. The method comprises the following steps: under the condition that the steering efficiency of the front axle of the vehicle is degraded, the maximum value of the front wheel steering saturation degree and the lateral tracking deviation degree is taken as a cooperative factor, and linear mapping is taken as an original cooperative weight; a first-order exponential weighted moving average filter is used to perform time domain smoothing on the original weight, so as to generate a final cooperative intervention weight; and the product formula modulation of the additional yaw moment is used. According to the application, the cooperative activation factor is constructed by quantifying the front wheel steering saturation degree and the lateral tracking deviation degree, the cooperative weight is generated through dead zone mapping and low-pass filtering, and the rear axle differential driving can intervene according to the degradation degree of the front axle efficiency as needed, so that the dynamic impact caused by the sudden change of the control authority is eliminated from the mechanism.

Description

Technical Field

[0001] This invention relates to the technical field of vehicle torque distribution, and more particularly to a rear-wheel differential coordinated control method for preventing vehicle instability. Background Technology

[0002] When a vehicle is traveling on a low-traction surface or when the front wheel steering efficiency is reduced, the lateral force of the front wheels approaches the saturation boundary. Continuing to increase the front wheel steering angle not only fails to effectively improve the lateral force but may also exacerbate tire nonlinear slippage, leading to a continuous increase in path tracking error. At this point, the rear axle differential drive is needed to generate additional yaw moment to assist lateral control. However, existing front-rear axle coordination strategies mostly employ threshold-based binary switching logic. When the front axle steering efficiency assessment exceeds a preset threshold, the lateral control responsibility is instantaneously transferred to the rear axle torque vectoring system. This abrupt transfer of control authority causes a sudden surge in the additional yaw moment of the rear axle, which, combined with the large inertia and sluggish response of the wheel hub motors, easily triggers vehicle yaw oscillations. Simultaneously, according to the tire adhesion ellipse theory, the saturation of longitudinal force will drastically compress the available margin of lateral force. Once the rear axle loses its lateral support capacity, the vehicle will enter an uncontrollable fishtailing state. Summary of the Invention

[0003] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0004] In view of the problems existing in the prior art, the present invention is proposed.

[0005] To address the issues of yaw moment step caused by uneven front-to-rear axle coordination in existing technologies and lateral instability resulting from actuator attachment mismatch, this invention provides a rear-wheel differential coordinated control method to prevent vehicle instability. The invention offers the following technical solution: Under conditions of declining front axle steering performance, the front wheel steering saturation will be adjusted. Lateral tracking deviation The maximum value is used as a co-factor : ; Will Linear mapping to original collaborative weights : ; A first-order exponentially weighted moving average filter is used to filter the original weights. Perform temporal smoothing to generate the final collaborative intervention weights. : ; according to Additional yaw moment Product modulation: ; In the above formula, The fundamental robust gain for determining the sliding mode arrival condition; The adjustment parameters are used to define the span of the continuous feedback interval near the sliding surface; For coordinated intervention weights; For sliding surface functions; add yaw moment The torque commands are converted into those of the left and right wheel hub motors on the rear axle to achieve coordinated control of the vehicle.

[0006] As a preferred embodiment of the rear-wheel differential cooperative control method for preventing vehicle instability described in this invention, wherein: the additional yaw moment is... The specific method for converting torque commands into those of the left and right rear axle hub motors is as follows: Differential torque component of the rear axle wheel on one side Calculate the ideal torque command for the left rear wheel Ideal torque command for the right rear wheel Differential drive distribution and coordinated control of the rear axle: ; In the above formula, This refers to the basic longitudinal torque of a single wheel. Additional yaw moment output by the sliding mode controller; The effective rolling radius of the wheel; This refers to the rear axle track of the vehicle. definition and They are respectively and The initial torque command must satisfy the attachment ellipse constraint limit to obtain the torque command within the safety domain. , : ; ; In the above formula, This is the maximum longitudinal force that the rear wheels are allowed to withstand.

[0007] As a preferred embodiment of the rear-wheel differential cooperative control method for preventing vehicle instability described in this invention, wherein: s is designed as follows: ; In the above formula, γ and γ ref These are the actual yaw rate and the reference yaw rate, respectively; β and β refThese are the actual centroid sideslip angle and the target centroid sideslip angle, respectively; c γ With c β These are the weighting coefficients for the corresponding deviation terms.

[0008] As a preferred embodiment of the rear-wheel differential cooperative control method for preventing vehicle instability described in this invention, wherein: the lateral tracking deviation... Designed as follows: ; In the formula, This represents the lateral error magnitude. To allow for the maximum safe lateral error.

[0009] As a preferred embodiment of the rear-wheel differential cooperative control method for preventing vehicle instability described in this invention, the method further includes: the wheels on both sides of the front axle do not participate in yaw differential distribution, maintaining basic torque output, and the relationship is designed as follows: ; in, Torque command to be distributed to the left front wheel; Torque command to be distributed to the right front wheel As a preferred embodiment of the rear-wheel differential cooperative control method for preventing vehicle instability described in this invention, wherein: and Only the peak torque of the motor needs to be accepted. Limit: ; Torque command for both wheels on the front axle after amplitude limiting and When issuing commands directly, a second-order low-pass filter is introduced to smooth the command time domain.

[0010] As a preferred embodiment of the rear-wheel differential cooperative control method for preventing vehicle instability described in this invention, wherein: the reference yaw rate The design method is as follows: Based on the kinematic mapping relationship between steady-state yaw rate and lateral acceleration, the theoretical boundary of the maximum steady-state yaw rate is defined as follows: ; In the formula, The maximum steady-state yaw rate constraint value is calculated based on the current dynamic road surface adhesion limit; g is the gravitational acceleration. The longitudinal speed of the vehicle; The minimum safe speed is used to eliminate numerical singularities caused by the denominator approaching zero when the vehicle is stationary or at extremely low speeds. definition As the initial reference yaw rate, it is limited to the range specified by the above. Within the defined boundary, the final reference yaw rate is obtained. : ; In the formula, It is a continuous saturation limiting function; The Designed as follows: ; In the formula, The initial reference yaw rate is unconstrained by physical boundaries; The reference curvature for the target path; The longitudinal speed of the vehicle; and These are the lateral position deviation and the heading angle deviation, respectively. Gain for lateral deviation feedback compensation; This is the gain for heading deviation feedback compensation.

[0011] As a preferred embodiment of the rear-wheel differential cooperative control method for preventing vehicle instability described in this invention, the method further includes: applying a physical limit to the steering actuator to obtain the current vehicle steering control command value sent to the steer-by-wire system. : ; In the formula, , These represent the negative and positive physical limit angles of the steering actuator, respectively. For Ackermann feedforward angle: ,in, This refers to the vehicle's wheelbase. The path curvature of the reference path at the current projection point; Original steering command value: The virtual control variables of the u0 system ;in, and These are the proportional and differential gains, respectively. For heading deviation feedback gain, Here, b is the heading angle deviation, and b0 is the nominal estimate of the control channel gain. This is the real-time estimate of the total disturbance; Amplitude is used as an indicator of the saturation degree of the steering actuator to calculate the steering saturation degree of the front wheels. : ; Design a third-order linear extended state observer to estimate the system state and total disturbance in real time; The third-order linear extended state observer is designed as follows: ; in, , , All of these are the gain coefficients of the observer. This represents the actual lateral tracking error. and The estimated lateral tracking error and its derivative are respectively. This is the real-time estimate of the total disturbance. The rate of change of the lateral tracking error. The rate of change of the speed tracking error. The rate of change of the real-time estimate of the total disturbance. This is the input for front wheel steering angle control; The nominal estimate of the control channel gain; Using the forward Euler method with sampling period The observer is discretized to obtain the discrete domain recursive equation, and the real-time estimate of the total disturbance of the system at the current moment is calculated by the discrete domain recursive equation. The discrete-domain recursive equation is designed as follows: ; Among them, the observation error is recorded. The current sampling time The observation error is defined as the current lateral tracking error measurement. Compared with the observer's estimate The difference, The lateral tracking error at the center of the vehicle's front axle at the current moment is the distance from the vehicle's actual position to the reference path normal, which is obtained in real time by the path perception module. This is the estimated value of the first state variable of the observer at the current moment, enabling the assessment of the lateral tracking error. Tracking This is the estimated value of the second state variable of the observer at the current moment, realizing the rate of change of error. Tracking This is the estimated value of the third state variable of the observer at the current moment, thus realizing the total disturbance of the system. Real-time estimation, For the next sampling time The recursive value, For the next sampling time The recursive value, For the next sampling time The recursive value.

[0012] As a preferred embodiment of the rear-wheel differential cooperative control method for preventing vehicle instability described in this invention, the method further includes: Determine the difference between the current time k and the time k triggered by the last steering control command. last interval Is it greater than the minimum trigger interval? ; Determine the current steering control command at time k. Compared to the last trigger time k last Steering control commands issued Is the absolute value of the difference greater than the current adaptive threshold? ; when > and Update trigger time and the current steering control command The signal is sent to the steer-by-wire actuator; otherwise, the vehicle's steer-by-wire actuator maintains the state of the last trigger time k. last Steering control commands issued ; in, In the formula, Based on the steady-state threshold, This is the sensitivity adjustment coefficient. Let be the magnitude of the total rate of change of the disturbance at time k; The amplitude of the total disturbance rate of change The calculation method, based on the first-order difference approximation, is designed as follows: ; in, This represents the total perturbation estimate output by the extended state observer at the current sampling time k. The previous sampling time The total disturbance estimate, i.e., the value corresponding to the previous control cycle at the current moment. value, The system sampling period is the time interval between two adjacent control periods.

[0013] The present invention also provides an automobile, wherein the automobile implements the steps of the above-described rear wheel differential cooperative control method for preventing vehicle instability by controlling the vehicle through a controller to achieve torque distribution of the vehicle.

[0014] The beneficial effects of this invention are: 1. This invention constructs a collaborative activation factor by quantifying the front wheel steering saturation and lateral tracking deviation. Through dead-zone mapping and low-pass filtering, a collaborative weight with a smooth transition within [0,1] is generated, enabling the rear axle differential drive to intervene as needed based on the degree of front axle performance degradation, thus eliminating the dynamic shock caused by sudden changes in control authority. Secondly, the rear axle sliding mode control eliminates the integral term to avoid in-wheel motor integral saturation and replaces the discontinuous sign function with a continuous saturation function, adjusting the smoothing parameters... The high-frequency switching in the neighborhood of the sliding surface is transformed into quasi-linear smooth feedback, which suppresses torque chattering at its source. 2. In the process of torque distribution, the present invention introduces the attachment ellipse constraint, which forces the reserve of the safety margin of the rear wheel lateral force and strictly restricts the wheel working point within the safety subset of the attachment ellipse. This ensures that the lateral stability of the rear axle is always under control during differential cooperation, thereby improving the driving safety boundary and stability of the vehicle under extreme conditions. Attached Figure Description

[0015] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein: Figure 1 This is a schematic diagram of the overall process of a rear-wheel differential cooperative control method for preventing vehicle instability proposed in this invention; Figure 2 This is a schematic diagram of the simulation results for comparing the lateral tracking error in the method of the present invention; Figure 3 This is a schematic diagram of the simulation results of the continuous change of dynamic collaborative weights in the method of the present invention; Figure 4 This is a schematic diagram of the simulation results of the torque distribution between the left and right rear axles in the method of the present invention; Figure 5 This is a schematic diagram of the simulation results of the yaw rate response in the method of the present invention; Figure 6 This is a schematic diagram of the simulation results of the centroid sideslip angle comparison in the method of the present invention; Figure 7 This invention provides a vehicle steering control command control method based on an adaptive event triggering mechanism, as proposed in Embodiment 2 of the present invention. Detailed Implementation

[0016] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0017] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0018] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0019] Example 1 Reference Figure 1 As an embodiment of the present invention, a rear-wheel differential cooperative control method for preventing vehicle instability is provided. This method is based on the following vehicle dynamics models: the vehicle lateral dynamics model and the steer-by-wire actuator model.

[0020] The vehicle dynamics model is used to demonstrate the physical basis of rear axle differential cooperation. The core output of this model is the yaw moment. With yaw rate The transmission relationship between them. From the vehicle's lateral dynamics model, it can be seen that the additional yaw moment... We directly enter the yaw motion equation, which, together with the lateral forces on the front and rear axles, determines the vehicle's yaw response. Current axle lateral force When it decreases due to performance degradation, if If the yaw moment is kept at zero, the yaw moment balance is disrupted, and the vehicle will deviate from the desired yaw trajectory. Therefore, the essence of rear axle differential cooperation is to actively adjust... To compensate The absence of.

[0021] Considering the coupling characteristics of lateral and yaw motion in a distributed drive electric vehicle, a two-degree-of-freedom single-track vehicle dynamics model is established. Assume a longitudinal vehicle speed... If the change is gradual within the control cycle or maintained by an independent longitudinal controller, the lateral motion equation of the system can be described as follows: ; In the formula, m is the total vehicle mass. Let be the yaw moment of inertia about the z-axis. and These are the distances from the center of mass to the front and rear axles, respectively. The sideslip angle is the angle of the center of mass. The yaw rate is angular velocity. The additional yaw moment generated by the rear axle differential drive and These represent the lateral forces of the front and rear axle tires, respectively. Within the tire's linear operating range, the lateral forces can be approximated as... , ,in , For the equivalent lateral stiffness of the front and rear axles, , These are the front and rear tire slip angles. The front and rear tire slip angles are determined by kinematic relationships. , Provided.

[0022] In this model, the front axle lateral force Depends on front wheel steering angle This is the primary source of control for path tracing. When When the actual output is limited due to changes in actuator performance, The shortcomings will be directly reflected in the lateral tracking error. The increase in [something]. This causal relationship provides the physical basis for the subsequent estimation of the total perturbation by the extended state observer.

[0023] The steer-by-wire actuator model is used to demonstrate that ADRC (Active Disturbance Rejection Control) has passive fault tolerance capability. The core feature of this model is the first-order inertial element. .in, The target front wheel steering angle calculated by the controller, The actual steering angle acting on the vehicle's front wheels. The steering system time constant is defined as follows: during the event triggering process (referring to the triggering control process of the front axle event-triggered active disturbance rejection controller), the steer-by-wire system has an inherent dynamic response delay, the time constant of which is... This determines the actual steering angle and the speed at which the command is followed. When the steering efficiency coefficient... When a gradual change occurs, its impact on lateral error is not instantaneous, but rather gradually permeates the vehicle response dynamically through the actuators. The total disturbance estimation channel of the extended state observer continuously senses error changes during this process and cancels them out in the feedforward channel. Therefore, ADRC has a natural passive fault tolerance capability for gradually changing steering performance. That is, as long as the rate of performance change is within the observer bandwidth, the controller can maintain tracking accuracy without adjusting parameters.

[0024] Having understood the principles of the above dynamic model, the method of this invention will now be discussed in detail: This invention constructs a collaborative activation factor by quantifying the front wheel steering saturation and lateral tracking deviation. Through dead-zone mapping and low-pass filtering, a collaborative weight with a smooth transition within [0,1] is generated, enabling the rear axle differential drive to intervene as needed based on the degree of front axle performance degradation, thus eliminating the dynamic shock caused by sudden changes in control authority. Secondly, the rear axle sliding mode control eliminates the integral term to avoid in-wheel motor integral saturation and replaces the discontinuous sign function with a continuous saturation function by adjusting the smoothing parameters. The high-frequency switching within the sliding surface neighborhood is transformed into quasi-linear smooth feedback, suppressing torque chattering at its source. Finally, an attachment ellipse constraint is introduced at the torque distribution layer to enforce a safety margin for rear wheel lateral forces, strictly limiting the wheel operating point to a safe subset of the attachment ellipse, ensuring that the rear axle lateral stability remains under control throughout the differential coordination process. This strategy forms a complete protection chain from three levels: coordinated scheduling, execution smoothing, and physical constraints, comprehensively improving the vehicle's driving safety boundaries and stability under extreme conditions. To further facilitate understanding of this solution, a detailed explanation follows: I. The intervention intensity of the rear axle differential drive should be positively correlated with the degree of degradation of the front axle control capability. This invention constructs dimensionless saturation indices from two orthogonal dimensions: "actuator capability" and "tracking effect," and generates dynamic collaborative weights through smooth mapping. Specifically: 1.1 Applying physical limits to the steering actuators to obtain the current vehicle steering control command value sent to the steer-by-wire system. : ; In the formula, , These represent the negative and positive physical limit angles of the steering actuator, respectively. For Ackermann feedforward angle: ,in, This refers to the vehicle's wheelbase. The path curvature of the reference path at the current projection point; Original steering command value: ; For the virtual control quantity of the system, ;in, and These are the proportional and differential gains, respectively. For heading deviation feedback gain, For heading angle deviation, To control the nominal estimate of channel gain, This is the real-time estimate of the total disturbance; Will Amplitude is used as an indicator of the saturation degree of the steering actuator to calculate the steering saturation degree of the front wheels. In terms of "actuator capability," the main consideration is to calculate the front wheel steering saturation and define the front wheel steering saturation. The current steering command amplitude Equivalent maximum steering angle based on road adhesion limit The ratio: ; Among them, the equivalent maximum steering angle Derivation of steering dynamics: Maximum steady-state yaw rate of the vehicle under the tire lateral force saturation boundary. Subject to lateral acceleration limit constraints, i.e. steady-state yaw rate With steering angle satisfy Combine the two equations and introduce a minimum safe speed. Low-speed singularity yields: ; In the formula, The longitudinal speed of the vehicle; For the minimum safe speed, This refers to the vehicle's wheelbase. is the dynamic adhesion coefficient of the road surface; is the acceleration due to gravity. The value represents the degree to which the front axle steering performance approaches the physical limit: the closer the value is to 1, the closer the lateral force of the front wheels is to saturation, and increasing the steering angle can no longer effectively improve lateral control.

[0025] 1.2. In the "tracking effect" dimension, the main consideration is the normalization of the lateral tracking deviation, defining the lateral tracking deviation. The current lateral error magnitude With the maximum permissible lateral error The ratio: ; The value is determined by taking into account both lane width and vehicle half-width. It reflects the urgency of the vehicle deviating from the reference path.

[0026] The larger of the two indicators mentioned above is taken as the system's co-activation factor. : ; The physical meaning of this maximum operation is that either the front axle's saturation or the trajectory deviation exceeding the limit, when either condition worsens, constitutes an effective demand signal for rear axle assistance.

[0027] To avoid frequent back-axis interventions caused by minor demand fluctuations, an activation dead zone threshold is introduced. ,Will Linear mapping to the original collaborative weights: ; when hour, Lateral control is handled independently by the front axle; when hour, Follow Linear growth. The co-activation factor maximization operation ensures that deterioration in any dimension can trigger subsequent axis intervention; the subsequent low-pass filtering constrains the rate of weight change to avoid transient shocks during the intervention process.

[0028] To suppress high-frequency jitter in the weights caused by sensor noise and state fluctuations, a first-order exponentially weighted moving average filter is used to adjust the original collaborative weights. Perform temporal smoothing to generate the final collaborative intervention weights. : ; In the formula, These are the filter coefficients, which control the smoothness of the weight response. It is in The continuously varying scalars within the axis constitute the allocation coefficients for front and rear axle control authority: When the lateral control torque approaches 0, it is mainly provided by the lateral force of the front wheels; when it approaches 1, it is mainly provided by the additional yaw torque generated by the rear axle differential drive.

[0029] Second, traditional open-loop reference models cannot provide a corrective response to existing tracking deviations. This invention addresses this by using a reference model (here, the traditional model is considered as...) The code introduces a feedback compensation term consisting of lateral deviation and heading deviation, and applies attachment limit constraints, specifically: 2.1 Constructing a composite reference yaw rate that includes curvature feedforward and bias feedback: ; In the formula, The initial reference yaw rate; The reference curvature for the target path; The longitudinal speed of the vehicle; and These are the lateral position deviation and the heading angle deviation, respectively. Gain for lateral deviation feedback compensation; This is the gain for heading deviation feedback compensation.

[0030] Compensation , This generates additional expected yaw motion to guide the vehicle back to the target trajectory, enabling the reference signal itself to have closed-loop correction capability and reducing the adjustment burden on the lower-level feedback controller.

[0031] 2.2 Based on the quasi-steady-state vehicle lateral dynamics assumption, the vehicle's lateral acceleration is constrained by the peak road adhesion coefficient. Its maximum absolute value cannot exceed Based on the kinematic mapping relationship between steady-state yaw rate and lateral acceleration, the theoretical boundary of the maximum steady-state yaw rate can be defined as follows: ; In the formula, This is the maximum steady-state yaw rate constraint value calculated based on the current dynamic road surface adhesion limit; It is the acceleration due to gravity; This is a preset minimum constant (the minimum safe speed mentioned above) used to eliminate numerical singularities caused by the denominator approaching zero when the vehicle is stationary or operating at extremely low speeds.

[0032] By strictly limiting the initial composite reference value within this constraint range, the final reference yaw rate is obtained: ; In the formula, This is a continuous saturation limiting function. This constraint ensures that upper-level decision commands always remain within the vehicle's physical reachability domain.

[0033] Third, to suppress the torque impact on the hub motor drive system caused by the switching of the symbol function in traditional sliding mode control, this invention constructs a sliding surface without an integral term and adopts a continuous approach law for smooth adjustment parameters, combined with cooperative weight output of additional yaw torque, specifically as follows: 3.1 The control objective is to track the yaw rate to the reference value while suppressing the sideslip angle. The integral term is eliminated to avoid the integral saturation effect of the large inertia actuator, and a sliding surface is constructed: ; In the formula, For sliding surface functions; and These are the actual yaw rate and the reference yaw rate, respectively. and These are the actual centroid sideslip angle and the target centroid sideslip angle, respectively. and are the weighting coefficients of the corresponding deviation terms, respectively.

[0034] 3.2 Replace the discontinuous sign function with a continuous saturated function, and introduce the aforementioned collaborative weights. The amplitude of the control quantity is modulated using a product method: ; In the formula, Additional yaw moment output by the rear axle system; The fundamental robust gain for determining the sliding mode arrival condition; The adjustment parameters are used to define the span of the continuous feedback interval near the sliding surface.

[0035] Specifically, traditional sliding mode reaching laws often employ discontinuous sign functions. Its definition ( ), ( ), ( This function generates constant amplitude control variable jumps on both sides of the sliding surface, which is the root cause of high-frequency chattering. This invention uses a continuous saturation function... To substitute, which is defined as: when hour The output is linearly proportional to the sliding mode variable; when hour The output reaches the saturation limit value. In the formula... To smoothly adjust the parameters, the width of the linear feedback interval within the sliding surface neighborhood was determined. This substitution ensures that the control quantity changes continuously rather than abruptly when the system state is near the sliding surface, thus eliminating torque chattering mechanistically. The calculation formula can be directly introduced Replace traditional This results in a smooth additional yaw moment command.

[0036] This step has two core physical implications: firstly, it smoothly adjusts parameters. The introduction of [a certain mechanism] maps the high-frequency discrete switching behavior of the system state in the neighborhood of the sliding surface into a quasi-linear smooth feedback, thereby significantly reducing the torque chattering effect on the hub motor in terms of mechanism; secondly, cooperative weighting The product-based modulation mechanism ensures that the output amplitude of the additional yaw moment is strictly controlled by the coupling degree between the front axle performance degradation and the lateral trajectory deviation, thereby realizing the on-demand distribution and compliant intervention of the lateral intervention moment under the multi-actuator architecture.

[0037] Under conditions of declining steering performance on the front axle, the differential torque component passing through one wheel on the rear axle. Calculate the ideal torque command for the left rear wheel and the ideal torque command for the right rear wheel. Differential drive distribution and coordinated control of the rear axle: ， ， ; In the above formula, This refers to the basic longitudinal torque of a single wheel. Additional yaw moment output by the sliding mode controller; The effective rolling radius of the wheel; This refers to the rear axle track width. To ensure lateral force reserve for the front wheel steering system, the wheels on both sides of the front axle do not participate in yaw differential distribution, maintaining their basic torque output. This relationship is expressed as: ; In the formula, Torque command to be distributed to the left front wheel; Torque command to be distributed to the right front wheel.

[0038] IV. The underlying torque distribution module transforms longitudinal drive requirements and lateral coordination requirements into four-wheel motor commands. In designing the torque distribution logic, this invention first establishes a physical constraint boundary based on the tire attachment ellipse, and then performs analytical distribution and command smoothing within this boundary to ensure that all torque commands are within a safe subset of the vehicle's physical capabilities. Specifically: 4.1 The frictional force between the tire and the road surface has a physical upper limit, and the coupling relationship between its longitudinal and lateral forces can be described by an adhesion ellipse. When the longitudinal force of the tire approaches the adhesion limit, the lateral load-bearing capacity decreases sharply, which can easily lead to vehicle sideslip and instability. To ensure lateral stability when the rear axle performs differential cooperation, this invention first establishes constraint boundaries before the rear wheel torque distribution, forcibly reserving a lateral force safety margin.

[0039] Let the vertical load on a single rear wheel be approximately... The dynamic adhesion coefficient of the road surface is Then the nominal limit longitudinal force of the tire is Considering that the rear wheels still need to provide lateral force to maintain vehicle stability during differential drive, a lateral force reserve ratio is defined. The maximum longitudinal force that the rear wheel can withstand is defined as follows: ; In the formula, This is the maximum longitudinal force that the rear wheels are allowed to withstand. The proportion of lateral force safety margin reserved; This represents the current dynamic road surface adhesion coefficient. For a single wheel, the vertical static load is 1.

[0040] Mapping this to the drive execution domain, the absolute torque limiting threshold for the rear wheels is calculated as follows: ; In the formula, The absolute limiting threshold for rear-wheel drive torque Let be the effective rolling radius of the wheel. This constraint equation essentially restricts the wheel's operating point strictly to the inscribed safe subset of the attached ellipse, ensuring that the rear wheel always retains the mechanical reserve necessary to maintain the vehicle's lateral stability during differential intervention.

[0041] 4.2 Definition The above are respectively and The calculated initial torque command must satisfy the attachment ellipse constraint limit to obtain the torque command within the safety domain. , .

[0042] ; ; In the above formula, This is the maximum longitudinal force that the rear wheels are allowed to withstand.

[0043] Meanwhile, the front wheel torque only needs to be limited by the peak torque of the motor: If the torque command after amplitude limiting is issued directly, the step change may trigger dynamic overshoot in the hub motor servo system. The method of this invention introduces a second-order low-pass filter for time-domain smoothing of the command; its continuous-domain transfer function is: ; In the formula The undamped natural frequency of the filter. Given the damping ratio, the filter is configured to the critical damping state. To ensure response speed while eliminating overshoot, the transfer function is discretized using the Tustin bilinear transform method, establishing a differential recursive equation. The filtered and smoothed torque command balances the transient response speed of coordinated intervention with the compliance protection of the large-inertia hub motor, and is finally sent to the four-wheel motor controller for execution via the vehicle communication bus.

[0044] In summary, when the steering performance of the vehicle's front axle deteriorates due to malfunction or extreme operating conditions, the lateral force of the front wheels alone is insufficient to maintain path tracking accuracy and vehicle stability. This invention proposes a rear-wheel differential cooperative control method to prevent vehicle instability. This method generates continuous cooperative weights by quantifying the degree of front axle performance degradation, driving the sliding mode controller to output additional yaw torque. Furthermore, it introduces attached elliptical constraints and a command smoothing mechanism at the torque distribution layer to achieve front-to-rear axle control transition and actuator protection.

[0045] To further verify the technical effects of the present invention, the specific dynamic cooperative stability control performance is first verified through the following simulation examples.

[0046] 1. Simulation Condition Settings: The simulation vehicle parameters are shown in Table 1 below: Table 1 Main Physical Parameters of the Vehicle The reference path uses a combination of straight sections and circular curves with a radius of 100m. The initial straight section is 40m long, the circular curve has an arc length of 160m, and the straight section connects after the curve, with a total path length of approximately 400m. The target cruising speed for the vehicle is set to 20m / s. To simulate front axle steering system failure and low-adhesion limit conditions, a composite fault is injected into the simulation: the steering actuator gain is reduced to 40% (i.e., the actual steering angle is only 40% of the commanded value), and the peak road adhesion coefficient decreases to 0.70. Set it to 30.

[0047] 2. Comparison Scheme: A comparison is made between the pure front axle active disturbance rejection steering control (with the rear axle only maintaining longitudinal speed tracking and not applying additional yaw moment) and the dynamic cooperative fault-tolerant control proposed in this invention. The method of this invention enables event-triggered active disturbance rejection steering, dynamic cooperative weight scheduling, and smooth sliding mode direct yaw moment control. The cooperative weight dead zone threshold is set to 0.2, the sliding mode smoothing adjustment parameter is 0.6, and a 15% rear wheel lateral force margin is reserved.

[0048] 3.Reference Figure 2-6 The simulation results are analyzed in detail below: like Figure 2 The comparison of lateral tracking errors shows that the red curve (pure ADRC) diverges sharply about 2 seconds after entering the curve, exceeding the preset 0.5m safety boundary and exhibiting large-amplitude divergent oscillations. In contrast, the blue curve (dynamic cooperative DYC) remains strictly contained within the safety boundary with minimal fluctuations. Under conditions of 60% gain attenuation in the online steering motor and low-traction road surfaces, the lateral force of the front tires is severely saturated. If relying solely on front axle steering, the system would continuously increase the front wheel steering angle command to eliminate errors, leading to integral saturation and nonlinear tire slippage, resulting in vehicle instability. Introducing cooperative DYC reduces the error by 66.5%, demonstrating that active intervention from the rear axle can effectively compensate for the lack of lateral force from the front axle, achieving active fault tolerance and trajectory convergence.

[0049] like Figure 3 The dynamic collaborative weights shown change continuously, as indicated by the green curve. The weight remains at 0 for 0-2 seconds (below the activation dead zone). After 2 seconds, as the vehicle enters the curve and the front axle saturates, the weight rapidly and continuously climbs to a near-full-throttle state of 1.0, maintaining a high level throughout the curve, and then smoothly declining around 12 seconds as operating conditions change. This figure demonstrates the design advantages of smooth permission scheduling. It proves that the current strategy can accurately capture the co-activation factors of the front axle. More importantly, the rise and fall of the weight is continuous and smooth (stepless adjustment), completely avoiding the control signal abrupt changes caused by traditional logic threshold switching. This smooth intervention maximizes the protection of the actuators and eliminates longitudinal jerking caused by sudden changes in chassis torque.

[0050] like Figure 4 The torque distribution between the left and right rear axles is shown, with the orange (left rear wheel) and blue (right rear wheel) curves exhibiting perfect mirror symmetry, representing the application of differential torque. Crucially, the peak torque is strictly limited within the pink dashed line (the upper limit of the attachment constraint) and does not reach the black dashed line (the motor's physical peak value).

[0051] This diagram provides a visual representation of the underlying actuator, showcasing our designed attachment ellipse constraint and lateral force margin reserve mechanism. The system does not blindly meet the yaw torque demand of the sliding mode controller; instead, it calculates the physical extreme value of the longitudinal force on a single wheel in real time. By clamping the torque within the limiting range, it ensures that while the rear wheel provides longitudinal differential force, it still retains sufficient lateral friction margin, thus fundamentally preventing tail-wagging and loss of control of the rear axle due to "powered slippage."

[0052] like Figure 5 The comparison of yaw rate responses shows that the red curve exhibits high-frequency, large-span oscillations, while the blue curve is much smoother and quickly approaches a steady state. Yaw rate is a core dynamic parameter characterizing the lateral stability of a vehicle. The violent alternation under pure front axle control indicates that the vehicle is in a severe yaw instability state due to underdamped yaw. The blue line shows that sliding mode control (SMC) based on a wide boundary layer continuous approaching law, combined with rear axle DYC, is equivalent to injecting strong virtual yaw damping into the chassis, effectively absorbing nonlinear disturbance energy and forcing the vehicle state to closely approximate the reference yaw model.

[0053] like Figure 6 The comparison of sideslip angles shows that the red curve frequently exhibits sharp peaks, with peak values ​​exceeding 3 to 4 degrees. The blue curve's amplitude is significantly compressed, remaining within a very small range of approximately 1 degree. Sideslip angle is a performance indicator for assessing whether a vehicle is drifting / losing control. (Generally speaking, this applies to civilian vehicles.) A deviation exceeding 3 degrees is considered entering the nonlinear instability zone. The sharp peak of the red curve indicates a significant deviation between the vehicle's direction and its actual trajectory. The good convergence of the blue curve demonstrates the crucial role played by our constructed rear axle differential cooperative control system. The additional yaw moment applied by DYC not only corrects the vehicle's heading but also effectively counteracts lateral inertial forces, stabilizing the vehicle within the tire's linear adhesion zone.

[0054] In summary, the simulation results demonstrate that the dynamic cooperative stability control method proposed in this invention can achieve smooth and gradual intervention of the rear axle differential torque through continuous cooperative weighting under the combined conditions of reduced front axle steering efficiency and low adhesion. This significantly reduces lateral tracking error and suppresses vehicle yaw oscillation. The adhesion ellipse constraint mechanism effectively protects the rear axle lateral stability during differential cooperation. The entire control architecture exhibits a certain degree of fault tolerance to adverse factors such as changes in steering efficiency and decreased road adhesion, comprehensively improving the vehicle's driving safety boundaries and stability.

[0055] Example 2 Reference Figure 7 This embodiment discloses a vehicle steering control command based on an adaptive event triggering mechanism. During vehicle operation, the front axle event triggers an active disturbance rejection controller with a fixed sampling period. It operates continuously. Its extended state observer recursively updates the state estimate in each control cycle. , , , where is the real-time estimate of the lumped disturbance of the system.

[0056] System lumped disturbance The design process for real-time estimation is as follows: S1: When the steer-by-wire actuator experiences a gain attenuation fault, the actual steering angle applied to the front wheels is... ,in Let this be the steering efficiency coefficient. By incorporating the fault effects into the lumped disturbance term, the error dynamics can be rewritten as: ; Among them, the total system disturbance Defined as: ; In the above formula, The nominal estimate of the control channel gain; This refers to the steering efficiency coefficient; The input is the front wheel steering angle control input; through the above transformation, the system nonlinearity, parameter uncertainty, external environmental disturbances, and actuator performance degradation (total system disturbance) are uniformly reduced to a one-dimensional scalar time-varying function. The complex vehicle dynamics coupling and actuator failures are equivalently merged into a single lumped disturbance term, simplifying the original nonlinear system into a second-order integral model. This processing allows the extended state observer to directly treat this lumped disturbance as a new state variable for real-time observation and estimation.

[0057] S2: Total disturbance The expanded state variable is the third state variable of the system, denoted as the expanded state vector. Under the assumptions that the total disturbance is differentiable and its derivative is bounded, the system state-space equations are: ; in Unknown but bounded This is the time derivative of the first component of the expanded state vector. Therefore ; The second component of the extended state vector is defined as the first derivative of the lateral error, i.e. ; The time derivative of . From the original system and , can be obtained ; The third component of the extended state vector, i.e., the total system disturbance resulting from the extension. ; The time derivative of is equal to the rate of change of the total disturbance. ; for the total system disturbance The first time derivative of represents the time-varying rate of lumped perturbation; The nominal estimate for controlling channel gain has been defined above.

[0058] Transition from state-space equations to extended state observer: Transforming the total perturbation After expanding to the third state variable of the system, we obtain the third-order extended state-space equation: ; This equation can be written in matrix form: ; in The coefficient matrix is ​​as follows: ; The system output equation is That is, only the lateral error can be directly measured, while the error derivative and the total disturbance need to be estimated by the observer.

[0059] For the above system, a linearly extended state observer of the Romberg form is constructed: ; in For the state estimation vector, For the observer's estimate of the output, Let be the observer gain vector to be tuned. Expanding the matrix yields the observer equation in fractional form: ; Where l1, l2, and l3 are all gain coefficients of the observer. This represents the actual lateral tracking error. and These represent the estimated lateral tracking error and the velocity tracking error, respectively. This is the real-time estimate of the total disturbance. The rate of change of the lateral tracking error. The rate of change of the speed tracking error. The rate of change of the real-time estimate of the total disturbance. This is the input for front wheel steering angle control; The core of designing a nominal estimate observer for controlling channel gain lies in the gain vector. Tuning. Defining observation error. Subtracting the state-space equation from the observer equation yields the error dynamic equation: ; in This is the output matrix. The convergence rate of the error system is determined by the matrix. The eigenvalues ​​determine the eigenvalues. Using a bandwidth parameterization method, the eigenvalues ​​of this matrix are uniformly allocated on the negative real axis of the complex plane. Location: ; By comparing the coefficients, we can obtain the analytical expression for the observer gain: ; in The observer bandwidth (rad / s) is the only tuning parameter for the observer. When bounded, observation error It will asymptotically converge to a neighborhood centered at zero, with the convergence rate increasing. Increase and accelerate.

[0060] To implement this in an onboard digital controller, the forward Euler method is used with a sampling period of... Discretize the continuous-domain observer. Denote the observation error. Replacing the differential with the difference Substituting into the continuous observer equation and rearranging, we obtain the discrete domain recurrence equation as follows: ; In the above formula, For the first Observational error at the sampling time; For the first Lateral tracking error at the sampling time; For the first The estimated value of the first state variable of the time-time observer; For the first The estimated value of the second state variable of the time-time observer; For the first The estimated value of the third state variable (expanded state) of the time-observer; For the next sampling time The recursive value; For the next sampling time The recursive value; For the next sampling time The recursive value.

[0061] Among them, the third state of the extended state observer The rate of change of the lumped disturbance acting on the transverse dynamics was estimated in real time. This reflects the degree to which the system deviates from its steady state.

[0062] Specifically, the linear error feedback control law is based on , and heading angle deviation Solving virtual control quantities ; Total disturbance feedforward compensation After superimposing the curvature feedforward term, the target front wheel steering angle at the current moment is obtained. The target turning angle is determined by the event triggering mechanism and then sent to the steering actuator by steer-by-wire.

[0063] When the steering efficiency of the front axle decreases due to changes in mechanical characteristics, the actual steering angle acting on the front wheels is only a reduced proportion of the commanded value, i.e. ,in This refers to the steering efficiency coefficient. Because the actual steering angle is lower than the commanded value, the front axle lateral force is insufficient to track the reference path, resulting in a lateral tracking error. It begins to increase. The expanded state observer detects observation errors. Perceive this change, This increases to reflect the increased total disturbance. Although the active disturbance rejection controller attempts to increase its passive disturbance rejection capability... The compensation can be made in this way, but the compensation effect is limited by the physical capabilities of the front axle actuator.

[0064] Under this operating condition (deterioration of front axle steering performance), the target front wheel steering angle While the amplitude cannot be fully executed, its magnitude accurately reflects the degree of saturation achieved by the front axle controller in maintaining path tracking. This information is then fed into the rear axle cooperative evaluation module to calculate the front wheel steering saturation. This initiates the weight generation and torque scheduling process for rear axle differential coordination. Rear axle coordination does not replace front axle control, but rather provides supplementary yaw torque when the front axle is continuously operating but its efficiency is insufficient.

[0065] For example, suppose the vehicle is currently traveling at a longitudinal speed Driving within radius The circular curve, reference path curvature Road surface adhesion coefficient When the front axle steering performance is normal, the front wheel steering angle required to maintain steady driving in this curve is approximately the Ackermann angle. .

[0066] Current axle steering efficiency decays to At that time, the active disturbance rejection controller calculates the target's front wheel steering angle based on real-time feedback of lateral error and heading deviation. Suppose that at a certain moment in the curve, the lateral error... heading deviation Observer output , . Obtain controller bandwidth ,but , Heading feedback gain Control channel gain Virtual control variables .

[0067] At this point, the total disturbance estimate is... Because the persistent error feedback has risen from near the steady-state value to approximately 2.5 (the dimensions of this value are... Consistent). Original steering command Superimposed with curvature feedforward After physical limiting, the target's turning angle .

[0068] However, because The actual angle acting on the tire is only The actual turning angle is far from sufficient to generate the lateral force required to maintain path tracking: under normal circumstances, it would require... (about It can achieve steady-state cornering, but currently, due to error accumulation, the controller expects... However, only the actual output is... There exists approximately The corner gap.

[0069] This notch at the corner causes lateral force on the front axle. Sustained insufficiency, lateral error Unable to converge. Observer in third state. The value climbed from approximately 2.5 to approximately 5.0 over several control cycles, reflecting that the total disturbance intensity had exceeded the front axle compensation capability. At this point, although the front axle ADRC continued to operate and correctly resolved the commands, the actuators were unable to perform the required compensation; this state is the physical criterion for triggering rear axle differential coordination. Simultaneously, the target steering angle... The amplitude is sent to the front axle performance evaluation module: equivalent maximum steering angle. Front wheel steering saturation This indicates that the front axle is fully saturated. Simultaneously, the weight generation and torque scheduling process for rear axle differential coordination, as described in Example 1, is initiated. Rear axle coordination does not replace front axle control, but rather provides supplementary yaw torque when the front axle is continuously operating but its efficiency is insufficient. In addition, when the front wheels perform steering control, an adaptive event triggering mechanism is involved to issue vehicle steering control commands. Specifically, this involves comparing the current time k with the time k of the last steering control command trigger. last interval Is it greater than the minimum trigger interval? ; Determine the current steering control command at time k. Compared to the last trigger time k last Steering control commands issued Is the absolute value of the difference greater than the current adaptive threshold? ; when > and Update trigger time and the current steering control command The signal is sent to the steer-by-wire actuator; otherwise, the vehicle's steer-by-wire actuator maintains the state of the last trigger time k. last Steering control commands issued ; in, In the formula, Based on the steady-state threshold, This is the sensitivity adjustment coefficient. Let be the magnitude of the total rate of change of the disturbance at time k; The amplitude of the total disturbance rate of change The calculation method, based on the first-order difference approximation, is designed as follows: ; in, The current sampling time The total disturbance estimate output by the extended state observer. The previous sampling time The total disturbance estimate, i.e., the value corresponding to the previous control cycle at the current moment. The value represents the system sampling period, which is the time interval between two adjacent control periods.

[0070] In summary, the adaptive event triggering mechanism described above achieves a dynamic match between the triggering frequency and the risk of system instability: the threshold is high and communication is sparse under steady-state conditions; the threshold shrinks and control updates are intensive under transient disturbances, thereby effectively reducing the average communication load while ensuring tracking accuracy.

[0071] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A rear-wheel differential cooperative control method for preventing vehicle instability, characterized in that, Includes the following steps: Under conditions of declining front axle steering performance, the front wheel steering saturation will be adjusted. Lateral tracking deviation The maximum value is used as a co-factor : ; Will Linear mapping to original collaborative weights : ; A first-order exponentially weighted moving average filter is used to filter the original weights. Perform temporal smoothing to generate the final collaborative intervention weights. : ; according to Additional yaw moment Product modulation: ； In the above formula, The fundamental robust gain for determining the sliding mode arrival condition; The adjustment parameters are used to define the span of the continuous feedback interval near the sliding surface; For coordinated intervention weights; For sliding surface functions; add yaw moment The torque commands are converted into those of the left and right wheel hub motors on the rear axle to achieve coordinated control of the vehicle.

2. The rear wheel differential cooperative control method for preventing vehicle instability according to claim 1, characterized in that: The additional yaw moment The specific method for converting torque commands into those of the left and right rear axle hub motors is as follows: Differential torque component of the rear axle wheel on one side Calculate the ideal torque command for the left rear wheel Ideal torque command for the right rear wheel Differential drive distribution and coordinated control of the rear axle: ； In the above formula, This refers to the basic longitudinal torque of a single wheel. Additional yaw moment output by the sliding mode controller; The effective rolling radius of the wheel; This refers to the rear axle track of the vehicle. definition and They are respectively and The initial torque command must satisfy the attachment ellipse constraint limit to obtain the torque command within the safety domain. , : ； ； In the above formula, This is the maximum longitudinal force that the rear wheels are allowed to withstand.

3. The rear wheel differential cooperative control method for preventing vehicle instability according to claim 1, characterized in that: The design of s is as follows: ； In the above formula, γ and γ ref These are the actual yaw rate and the reference yaw rate, respectively; β and β ref These are the actual centroid sideslip angle and the target centroid sideslip angle, respectively; c γ With c β These are the weighting coefficients for the corresponding deviation terms.

4. The rear wheel differential cooperative control method for preventing vehicle instability according to claim 3, characterized in that: The lateral tracking deviation Designed as follows: ； In the formula, This represents the lateral error magnitude. To allow for the maximum safe lateral error.

5. The rear wheel differential cooperative control method for preventing vehicle instability according to claim 1, characterized in that: The method also includes: the wheels on both sides of the front axle do not participate in the differential yaw distribution, maintaining the basic torque output, and the relationship is designed as follows: ； in, Torque command to be distributed to the left front wheel; Torque command to be distributed to the right front wheel.

6. The rear wheel differential cooperative control method for preventing vehicle instability according to claim 5, characterized in that: The and Only the peak torque of the motor needs to be accepted. Limit: ; Torque command for both front axle wheels after amplitude limiting and When issuing commands directly, a second-order low-pass filter is introduced to smooth the command time domain.

7. The rear wheel differential cooperative control method for preventing vehicle instability according to claim 3, characterized in that: The reference yaw rate The design method is as follows: Based on the kinematic mapping relationship between steady-state yaw rate and lateral acceleration, the theoretical boundary of the maximum steady-state yaw rate is defined as follows: ； In the formula, The maximum steady-state yaw rate constraint value is calculated based on the current dynamic road surface adhesion limit; g is the gravitational acceleration. The longitudinal speed of the vehicle; The minimum safe speed is used to eliminate numerical singularities caused by the denominator approaching zero when the vehicle is stationary or at extremely low speeds. definition As the initial reference yaw rate, it is limited to the range specified by the above. Within the defined boundary, the final reference yaw rate is obtained. : ； In the formula, It is a continuous saturation limiting function; The Designed as follows: ； In the formula, The initial reference yaw rate is unconstrained by physical boundaries; The reference curvature for the target path; The longitudinal speed of the vehicle; and These are the lateral position deviation and the heading angle deviation, respectively. Gain is used for lateral deviation feedback compensation. This is the gain for heading deviation feedback compensation.

8. The rear wheel differential cooperative control method for preventing vehicle instability according to claim 1, characterized in that: The method further includes: applying a physical limit to the steering actuator to obtain the current vehicle steering control command value sent to the steer-by-wire system. : ； In the formula, , These represent the negative and positive physical limit angles of the steering actuator, respectively. For Ackermann feedforward angle: ,in, This refers to the vehicle's wheelbase. The path curvature of the reference path at the current projection point; Original steering command value: The virtual control variables of the u0 system ;in, and These are the proportional and differential gains, respectively. For heading deviation feedback gain, Here, b is the heading angle deviation, and b0 is the nominal estimate of the control channel gain. This is the real-time estimate of the total disturbance; Amplitude is used as an indicator of the saturation degree of the steering actuator to calculate the steering saturation degree of the front wheels. : ; Design a third-order linear extended state observer to estimate the system state and total disturbance in real time; The third-order linear extended state observer is designed as follows: ； in, , , All of these are the gain coefficients of the observer. This represents the actual lateral tracking error. and The estimated lateral tracking error and its derivative are respectively. This is the real-time estimate of the total disturbance. The rate of change of the lateral tracking error. The rate of change of the speed tracking error. The rate of change of the real-time estimate of the total disturbance. This is the input for front wheel steering angle control; The nominal estimate of the control channel gain; Using the forward Euler method with sampling period The observer is discretized to obtain the discrete domain recursive equation, and the real-time estimate of the total disturbance of the system at the current moment is calculated by the discrete domain recursive equation. The discrete-domain recursive equation is designed as follows: ； Among them, the observation error is recorded. The current sampling time The observation error is defined as the current lateral tracking error measurement. Compared with the observer's estimate The difference, The lateral tracking error at the center of the vehicle's front axle at the current moment is the distance from the vehicle's actual position to the reference path normal, which is obtained in real time by the path perception module. This is the estimated value of the first state variable of the observer at the current moment, enabling the assessment of the lateral tracking error. Tracking This is the estimated value of the second state variable of the observer at the current moment, realizing the rate of change of error. Tracking This is the estimated value of the third state variable of the observer at the current moment, thus realizing the total disturbance of the system. Real-time estimation, For the next sampling time The recursive value, For the next sampling time The recursive value, For the next sampling time The recursive value.

9. The rear wheel differential cooperative control method for preventing vehicle instability according to claim 8, characterized in that: The method also includes: Determine the difference between the current time k and the time k triggered by the last steering control command. last interval Is it greater than the minimum trigger interval? ; Determine the current steering control command at time k. Compared to the last trigger time k last Steering control commands issued Is the absolute value of the difference greater than the current adaptive threshold? ; when > and Update trigger time and the current steering control command The signal is sent to the steer-by-wire actuator; otherwise, the vehicle's steer-by-wire actuator maintains the state of the last trigger time k. last Steering control commands issued ; in, In the formula, Based on the steady-state threshold, This is the sensitivity adjustment coefficient. Let be the magnitude of the total rate of change of the disturbance at time k; The amplitude of the total disturbance rate of change The calculation method, based on the first-order difference approximation, is designed as follows: ； in, This represents the total perturbation estimate output by the extended state observer at the current sampling time k. The previous sampling time The total disturbance estimate, i.e., the value corresponding to the previous control cycle at the current moment. value, The system sampling period is the time interval between two adjacent control periods.

10. An automobile, wherein the automobile achieves torque distribution by controlling the vehicle to perform the steps of the rear wheel differential cooperative control method for preventing vehicle instability as described in any one of claims 1 to 9 via a controller.

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