Sliding mode correction control method based on vehicle yaw stability domain

Abstract

The invention discloses a sliding mode correction control method based on a vehicle yaw stability domain, and the method comprises the following steps: 1, building a vehicle dynamics model considering the nonlinear characteristics of a tire through a piecewise linear fitting technology, and preliminarily obtaining a vehicle stability boundary through a Helvzz matrix; 2, considering the influence of the cornering stiffness disturbance on the stable boundary, estimating the tire cornering stiffness deviation by observing the vehicle state deviation in real time, and correcting the stable domain boundary; step 3, considering roll constraints, and solving a vehicle yaw state expected value; 4, considering the nonlinear influence of the tire, constructing a stability domain sliding mode correction control strategy in combination with a dynamic correction method, and compensating the system disturbance caused by the nonlinearity of the tire; and step 5, considering single-wheel slippage constraint, and combining a quadratic programming algorithm to optimize four-wheel torque distribution. The stability domain can be accurately judged, and driving saturation can be avoided through hierarchical robust control and efficient torque distribution.

Description

Technical Field

[0001] The present invention belongs to the field of vehicle dynamics control, specifically a method that can correct the stability region boundary, combine the sliding mode algorithm to correct the output and optimize the control distribution to improve the control speed, accuracy and robustness under extreme working conditions. Background Art

[0002] Vehicle yaw stability refers to the ability of a vehicle to maintain stability during cornering and is an important indicator of vehicle safety and driving stability. With the increasing use of cars and the increasing complexity of driving conditions, people's requirements for vehicle yaw stability are also becoming increasingly higher.

[0003] The existing vehicle yaw stability control method has the following problems under extreme working conditions:

[0004] 1. Inaccurate division of the stability domain: Traditional stability judgment is usually based on a fixed parameter model, which does not fully consider the impact of tire nonlinear characteristics on the stability domain boundary, resulting in delayed intervention.

[0005] 2. Insufficient control robustness: In the instability domain, model disturbances and road adhesion changes can easily cause tracking errors. Existing control strategies are difficult to quickly compensate for nonlinear disturbances and lack robustness.

[0006] Therefore, there is an urgent need for a method that can correct the boundary of the stability region, correct the output in combination with the sliding mode algorithm, and optimize the control distribution to improve the control speed, accuracy, and robustness under extreme working conditions. Summary of the Invention

[0007] The present invention proposes a sliding mode correction control method for a vehicle yaw stability region, which aims to:

[0008] 1. Real-time feedback corrects tire cornering stiffness, improving the accuracy of yaw stability region boundary demarcation and enhancing the timeliness of control intervention;

[0009] 2. Optimize control strategies in both stable and unstable domains to improve system robustness and control accuracy;

[0010] 3. Combined with the quadratic programming algorithm, it optimizes the four-wheel torque distribution, balances tire adhesion utilization and control efficiency, and avoids excessive slip of a single wheel.

[0011] The embodiment of the present invention is implemented as follows: a sliding mode correction control method based on a vehicle yaw stability region includes the following steps:

[0012] Step 1: Use piecewise linear fitting technology to establish a vehicle dynamics model that takes into account the nonlinear characteristics of the tire, and preliminarily obtain the vehicle stability boundary through the Hurwitz matrix;

[0013] Step 2: Considering the impact of cornering stiffness disturbance on the stability boundary, the tire cornering stiffness deviation is estimated by observing the vehicle state deviation in real time, and the stability region boundary is corrected.

[0014] Step 3: Consider the roll constraint and solve the expected value of the vehicle yaw state;

[0015] Step 4: Considering the influence of tire nonlinearity, a stable domain sliding mode correction control strategy is constructed in combination with the dynamic correction method to compensate for the system disturbance caused by tire nonlinearity;

[0016] Step 5: Considering the single wheel slip constraint, the four-wheel torque distribution is optimized by combining the quadratic programming algorithm.

[0017] In a more detailed scheme, the specific steps of step 1 are as follows:

[0018] 11) The tire lateral force is piecewise affine modeled (PWA) using the least squares fitting technique, namely:

[0019]

[0020] Where i = {f, r} is the front and rear equivalent wheels of the vehicle, F yi is the tire lateral force; α i is the tire slip angle; α i1 , α i2 is the segmentation point, α max is the maximum value of the sideslip angle constraint, k i0 is α i In [-α i1 ,α i1 ]Equivalent cornering stiffness in the interval, k i1 、k i2 、b i1 、b i2 are the slope and intercept of the corresponding interval line segment respectively.

[0021] 12) Ignoring the load transfer between the left and right wheels, a two-degree-of-freedom vehicle yaw dynamics model is constructed:

[0022]

[0023] Among them, β and r represent the vehicle's center of mass sideslip angle and yaw rate respectively; They represent the sideslip angular velocity and yaw angular acceleration of the center of mass, m represents the mass of the vehicle; V x Indicates the longitudinal speed of the vehicle; I z represents the vehicle's yaw moment of inertia; l f Indicates the distance from the center of mass to the front axle; l r Indicates the distance from the center of mass to the rear axle; M DYC represents the additional yaw moment; k f , kr is the equivalent cornering stiffness, δ is the front wheel turning angle, b f 、b r are the intercepts corresponding to the lateral force of the segmented tire model.

[0024] 13) According to the Routh-Hurwitz stability criterion, the necessary and sufficient condition for the stability of the equilibrium point is that all the main diagonal minors of the Hurwitz matrix of the state space equation are positive, that is, they satisfy the following equation:

[0025]

[0026] Filter the linear cornering stiffness k that meets the conditions f , k r , according to the piecewise linear model, the tire side slip angle α is obtained f , α r , combined to form the envelope boundary r, β:

[0027]

[0028] Because k f 、k r In order to change with the sideslip angle range, the Routh-Hurwitz segmented envelope boundary can be obtained according to the above formula, and the area inside the envelope boundary is defined as the stable region, and the area outside the envelope boundary is defined as the unstable region.

[0029] In a more detailed scheme, the specific steps of step 2 are as follows:

[0030] 21) The segmented stability region is clearly affected by tire nonlinearity, primarily due to modeling errors and road adhesion disturbances. The cornering stiffness disturbance is characterized by the deviation of vehicle state parameters, and the observed deviation is compared using the following formula:

[0031]

[0032] Among them, F yfo , F yro Defined as the actual lateral force of the front and rear wheels, F yfn , F yrn Defined as the nominal lateral force on the front and rear wheels; is the observed value of the center of mass sideslip angular velocity and nominal value The deviation, is the observed value of yaw angular acceleration and nominal value The deviation, and Obtained from the vehicle yaw dynamics model, and Obtained directly or indirectly by on-board sensors.

[0033] The nominal and actual lateral forces are expressed by combining the segmented tire model:

[0034]

[0035] Where: i = {f, r}, k in and k io is the nominal slope and actual slope of the tire force segment interval, b i is the intercept of the corresponding interval.

[0036] In summary, we can obtain the corrected cornering stiffness Δk f and Δk r :

[0037]

[0038] 22) In the cornering stiffness correction formula, the mass and inertia parameters involved are considered constant during motion, while the longitudinal position of the center of mass varies depending on load distribution and dynamic characteristics. Therefore, the accuracy of the cornering stiffness correction value can be ensured by estimating the longitudinal position of the center of mass in real time.

[0039] The observation equation is established according to the yaw dynamics model:

[0040]

[0041] Where: T is the sampling period, the distance from the center of mass to the front axle is l f (t) is the state variable, the yaw angular velocity r(t) is the measurement variable, L = l f +l r The distance between the front and rear axles

[0042] Since the center of mass position changes slowly, it can be modeled as a random walk process:

[0043] l f (t+1)=1 f (t)+w(t) (10)

[0044] Where: w(t) is the process noise.

[0045] Identifying centroid position parameters l based on extended Kalman filter f :

[0046]

[0047]

[0048] Where: P is the estimation error covariance matrix, Q is the process noise covariance matrix, K is the Kalman gain matrix, and R is the measurement noise covariance matrix.

[0049] In a more detailed solution, the specific method of step 3 is as follows:

[0050] 31) The vehicle's center of mass slip angle β and yaw rate r, which characterize the vehicle's yaw stability, are used as stability control targets; the desired center of mass slip angle β is set ref is 0; the desired yaw rate r ref Identification through information such as the front wheel angle δ:

[0051]

[0052] Among them, r s is the expected yaw rate before correction.

[0053] 32) Considering the influence of road surface and roll stability, the expected yaw rate is corrected to:

[0054]

[0055] Among them, r ref is the corrected desired yaw rate, μ is the road adhesion coefficient, g is the acceleration of gravity, d is the wheelbase of the left and right wheels, h is the height of the center of mass, and sgn(δ) is the sign function.

[0056] In a more detailed solution, the specific method of step 4 is as follows:

[0057] 41) Construct the integral sliding surface function:

[0058]

[0059] Where c is the design parameter, e is the error of yaw rate and sideslip angle, and dt is the time differential;

[0060] e=rr ref +τ(β-β ref ) (16)

[0061] Where, τ is the design parameter;

[0062] To further reduce system chattering, this paper adopts the exponential function approach rate and replaces sgn(s) with the saturation function sat(s), which yields:

[0063]

[0064] Among them, K1, K2 are the approach rate parameters 1;

[0065] 42) The final additional yaw moment is:

[0066]

[0067] Among them, Mz is the sliding mode control torque in the stable region, ΔM z is the sliding mode correction torque in the unstable region, is the weight parameter. In the corrected stable domain, the model disturbance is small. When the vehicle is outside the correction stability domain, it is in an unstable state and the model disturbance increases. In order to ensure the control accuracy,

[0068]

[0069] In a more detailed solution, the specific method of step five is as follows:

[0070] 51) The yaw moment M DYC Distribute the torque to each wheel, ignore the effect of transient slip, and make the sum of the longitudinal forces of each wheel zero, then:

[0071]

[0072] Where, ij = {fl, fr, rl, rr}, T ij is the additional driving torque for the wheel, and Re is the rolling radius of the tire.

[0073] 52) Taking tire adhesion utilization as the optimal control target, the quadratic programming objective function is used to distribute the four-wheel torque:

[0074]

[0075] Among them, F zij is the tire load, T max is the maximum torque of the motor.

[0076] Compared with the prior art, the present invention has the following beneficial effects:

[0077] 1. This invention accurately determines the stability region and dynamically corrects the tire's cornering stiffness using a nonlinear tire dynamics model. Using methods such as the Hurwitz criterion, the system accurately determines the vehicle's current stability or instability region and dynamically adjusts the stability region boundary based on actual operating conditions, improving the real-time and adaptability of the stability region boundary.

[0078] 2. This invention implements layered robust control. When the vehicle is in the stable region, the system uses conventional control algorithms to ensure high efficiency. However, once the vehicle enters the unstable region, the control system automatically switches to the sliding mode robust control layer. At this point, combined with dynamic correction of tire cornering stiffness and center of mass position identification, the system can increase correction torque in real time to effectively compensate for model errors and external disturbances. This layered and sliding mode correction mechanism significantly enhances the system's ability to suppress complex disturbances such as road adhesion variations and tire nonlinearities, ensuring excellent vehicle stability and safety even under extreme operating conditions.

[0079] 3. This invention enables efficient torque distribution. By incorporating a highly effective quadratic programming optimization algorithm, it optimizes the global, real-time distribution of all-wheel drive torque. This algorithm fully considers tire adhesion utilization and drive saturation constraints, ensuring that each tire operates within its optimal adhesion range and avoiding drive saturation issues caused by overloading or slipping a single tire. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 This is the architecture diagram of the sliding mode correction control strategy in the stable domain;

[0081] Figure 2 Comparison diagram of cornering force fitting for piecewise affine tire model;

[0082] Figure 3 Schematic diagram of the vehicle yaw-roll dynamics model;

[0083] Figure 4 This is a diagram showing the influence of tire cornering stiffness disturbance on the stability boundary;

[0084] Figure 5 Steering wheel angle input for J-Turn condition

[0085] Figure 6 Comparison of the control effects of yaw rate and sideslip angle under high adhesion disturbance conditions;

[0086] Figure 7 To correct the cornering stiffness diagram;

[0087] Figure 8 is the dynamic response diagram of the additional yaw moment;

[0088] Figure 9 is the phase plane. DETAILED DESCRIPTION

[0089] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0090] Example 1

[0091] like Figure 1 As shown in FIG, the present invention discloses a schematic diagram of a sliding mode correction control method based on a vehicle yaw stability domain, comprising the following steps: (1) Trucksim model outputs the vehicle longitudinal velocity V x , steering angle δ, center of mass sideslip angle β, yaw rate r, nominal value of center of mass sideslip rate Nominal value of yaw rate Road adhesion coefficient μ. (2) Estimation of the center of mass position based on EKF and dynamic parameter deviation and Get the cornering stiffness correction value Δk f and Δk r (3) The segmented stability domain is further corrected in real time through the lateral stiffness correction value, and the range of the stability domain is clarified. (4) On this basis, a sliding mode correction control strategy for the stability domain is constructed, and the sliding mode correction torque ΔM is added in the instability domain. z To compensate for the control deviation caused by the model disturbance. (5) Based on the optimal slip ratio, the four-wheel torque is distributed and transmitted to the target vehicle to achieve yaw stability control. The above steps are explained in detail below.

[0092] A vehicle yaw sliding mode robust control method based on a stable region comprises the following steps:

[0093] Step 1: Use piecewise linear fitting technology to establish a vehicle dynamics model that takes into account the nonlinear characteristics of the tire. The vehicle stability boundary is initially obtained through the Hurwitz matrix, as follows:

[0094] 11) Under extreme working conditions, the tire cornering force shows strong nonlinearity. The “magic formula” (MF) can improve the calculation accuracy, but also brings real-time calculation complexity to the control model. Figure 2 As shown in the figure, in order to balance the model accuracy and operation speed, the least squares fitting technique is used to perform piecewise affine modeling (PWA) on the tire lateral force, namely:

[0095]

[0096] Where i = {f, r} is the front and rear equivalent wheels of the vehicle, F yi is the tire lateral force; α i is the tire slip angle; α i1 , α i2 is the segmentation point, α max is the maximum value of the sideslip angle constraint, k i0 is α i In [-α i1 ,α i1 ]Equivalent cornering stiffness in the interval, k i1 、k i2、b i1 、b i2 are the slope and intercept of the corresponding interval line segment respectively.

[0097] 12) If Figure 3 As shown, the present invention focuses on the vehicle yaw stability control under extreme working conditions, ignores the load transfer between the left and right wheels, and constructs a two-degree-of-freedom vehicle yaw dynamics model:

[0098]

[0099] Among them, β and r represent the vehicle's center of mass sideslip angle and yaw rate respectively; They represent the sideslip angular velocity and yaw angular acceleration of the center of mass, m represents the mass of the vehicle; V x Indicates the longitudinal speed of the vehicle; I z represents the vehicle's yaw moment of inertia; l f Indicates the distance from the center of mass to the front axle; l r Indicates the distance from the center of mass to the rear axle; M DYC represents the additional yaw moment; k f , k r is the equivalent cornering stiffness; δ is the front wheel turning angle, b f 、b r are the intercepts corresponding to the lateral force of the segmented tire model.

[0100] 13) According to the Routh-Hurwitz stability criterion, the necessary and sufficient condition for the stability of the equilibrium point is that all the main diagonal minors of the Hurwitz matrix of the state space equation are positive, that is, they satisfy the following equation:

[0101]

[0102] Filter the linear cornering stiffness k that meets the conditions f , k r , according to the piecewise linear model, the tire side slip angle α is obtained f , α r , combined to form the envelope boundaries r, β:

[0103]

[0104] Because k f 、k r In order to change with the sideslip angle range, the Routh-Hurwitz segmented envelope boundary can be obtained according to the above formula and defined as the stability limit of the vehicle yaw process.

[0105] Step 2: Consider the impact of cornering stiffness disturbance on the stability boundary, identify the tire cornering stiffness deviation by observing the vehicle state deviation in real time, and correct the stability domain envelope boundary. The details are as follows:

[0106] 21) If Figure 4 As shown in Figure 2, the segmented stability region is clearly affected by tire nonlinearity, mainly due to modeling errors and road adhesion disturbances. The cornering stiffness disturbance is characterized by the deviation of vehicle state parameters, and the observed deviation is compared with the following formula:

[0107]

[0108] Among them, F yfo , F yro Defined as the actual lateral force of the front and rear wheels, F yfn , F yrn Defined as the nominal lateral force on the front and rear wheels; is the observed value of the center of mass sideslip angular velocity and nominal value The deviation, is the observed value of yaw angular acceleration and nominal value deviation. and Obtained from the vehicle yaw dynamics model, and Obtained directly or indirectly by on-board sensors.

[0109] Combining the segmented tire model to express the nominal lateral force F yin and the actual lateral force F yio :

[0110]

[0111] Where: i = {f, r}, k in and k io is the nominal slope and actual slope of the tire force segment interval, b i is the intercept of the corresponding interval.

[0112] In summary, we can obtain the corrected cornering stiffness Δk f and Δk r :

[0113]

[0114] 22) In the cornering stiffness correction formula, the load parameters involved are considered constant during motion, while the longitudinal center of mass position parameters vary depending on the load distribution and dynamic characteristics. Therefore, the accuracy of the cornering stiffness correction value can be ensured by estimating the longitudinal center of mass position parameters in real time.

[0115] The observation equation is established according to the yaw dynamics model:

[0116]

[0117] Where: T is the sampling period, the distance from the center of mass to the front axle is l f (t) is the state variable, the yaw angular velocity r(t) is the measurement variable, L = l f +l r The distance between the front and rear axles

[0118] Since the center of mass position changes slowly, it can be modeled as a random walk process:

[0119] l f (t+1)=1 f (t)+w(t) (10)

[0120] Where: w(t) is the process noise.

[0121] Identifying centroid position parameters l based on extended Kalman filter f :

[0122]

[0123]

[0124] Where: P is the estimation error covariance matrix, Q is the process noise covariance matrix, K is the Kalman gain matrix, and R is the measurement noise covariance matrix.

[0125] Step 3: Consider the roll constraint and solve the expected value of the vehicle's yaw state. The details are as follows:

[0126] 31) The vehicle's center of mass slip angle β and yaw rate r, which characterize the vehicle's yaw stability, are used as stability control targets; the desired center of mass slip angle β is set ref is 0; the desired yaw rate r ref Identify through information such as the front wheel angle δ,

[0127]

[0128] Among them, r s is the expected yaw rate before correction.

[0129] 32) Considering the tire force saturation caused by the road adhesion limit, the maximum yaw rate is:

[0130]

[0131] During extreme steering, excessive speed may cause severe body roll, so the rollover stability index constraint is introduced. Constrained steady-state yaw rate:

[0132]

[0133] Combining equations (9), (11), and (12), the expected yaw rate r ref express:

[0134]

[0135] Among them, r ref is the corrected desired yaw rate, μ is the road adhesion coefficient, g is the acceleration of gravity, d is the wheelbase of the left and right wheels, h is the height of the center of mass, and sgn(δ) is the sign function.

[0136] Step 4: Considering the influence of tire nonlinearity, a stable domain sliding mode correction control strategy is constructed in combination with the dynamic correction method to compensate for the system disturbance caused by tire nonlinearity. The details are as follows:

[0137] 41) Construct the integral sliding surface function.

[0138]

[0139] Where c is the design parameter, e is the error of yaw rate and sideslip angle, and dt is the time differential.

[0140] e=rr ref +τ(β-β ref ) (20)

[0141] Where τ is the design parameter.

[0142] To further reduce system chattering, this paper adopts the exponential function approach rate and replaces sgn(s) with the saturation function sat(s), which yields:

[0143]

[0144] Among them, K1 and K2 are the approach rate parameters 1.

[0145] 42) The final additional yaw moment is:

[0146]

[0147] Among them, M z is the sliding mode control torque in the stable region, ΔM z is the sliding mode correction torque in the unstable region, is the weight parameter. In the corrected stable domain, the model disturbance is small. When the vehicle is outside the correction stability domain, it is in an unstable state and the model disturbance increases. In order to ensure the control accuracy,

[0148]

[0149] Step 5: Considering the single wheel slip constraint, optimize the four-wheel torque distribution by combining the quadratic programming algorithm. The details are as follows:

[0150] 51) The yaw moment M DYC Distribute the torque to each wheel, ignore the effect of transient slip, and make the sum of the longitudinal forces of each wheel zero, then:

[0151]

[0152] Where, ij = {fl, fr, rl, rr}, T ij is the additional driving torque for the wheel, and Re is the rolling radius of the tire.

[0153] 52) Taking tire adhesion utilization as the optimal control target, the quadratic programming objective function is used to distribute the four-wheel torque:

[0154]

[0155] Among them, F zij is the tire load, T max is the maximum torque of the motor.

[0156] Example 2

[0157] Building a joint simulation based on Simulink-Trucksim

[0158] A simulation experiment was built in conjunction with Simulink-Trucksim to test the sliding mode correction control method designed in this invention based on the vehicle yaw stability domain. The control target is in the J-Turn condition, the longitudinal speed is 80km / h, and the road surface coefficient μ is n = 0.8, and the adhesion disturbance is ±15%. The driver input is Figure 5 The test results are shown in Figure 6 As shown. Under strong adhesion disturbance conditions, the single moment M z The output is out of control due to the accumulation of tire cornering force output deviation, which is manifested as yaw rate tracking response lag and the center of mass slip angle deviating from the expected range. The output realizes the real-time intervention of the sliding mode compensation torque in the unstable domain by constructing the sliding mode correction control in the stable domain, significantly improves the yaw rate tracking performance, and effectively suppresses the sideslip angle deviation of the center of mass. Figure 7 , 8 is the cornering stiffness correction value and the additional yaw moment. The dynamic feedback correction method proposed in this paper can still provide a good cornering stiffness correction. The instability domain effectively compensates for the influence of the model disturbance, especially when the cornering stiffness disturbance is severe, so that the vehicle can quickly restore stability during extreme yaw. Figure 9 It is the phase plane diagram. Compared with the invariant domain, the control strategy proposed in this paper has a more convergent phase plane than the single torque control.

[0159] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. The replacement may be a replacement of a portion of a structure, device, or method step, or it may be a complete technical solution. Any equivalent replacement or modification based on the technical solution and inventive concept of the present invention shall be covered by the scope of protection of the present invention.

Claims

1. A sliding mode correction control method based on vehicle yaw stability region, characterized in that: The following steps are involved: Step 1: Use piecewise linear fitting technology to establish a vehicle dynamics model that takes into account the nonlinear characteristics of the tire, and preliminarily obtain the vehicle stability boundary through the Hurwitz matrix; Step 2: Considering the impact of cornering stiffness disturbance on the stability boundary, the tire cornering stiffness deviation is estimated by observing the vehicle state deviation in real time, and the stability region boundary is corrected. Step 3: Consider the roll constraint and solve the expected value of the vehicle yaw state; Step 4: Considering the influence of tire nonlinearity, a stable domain sliding mode correction control strategy is constructed in combination with the dynamic correction method to compensate for the system disturbance caused by tire nonlinearity; Step 5: Considering the single wheel slip constraint, the four-wheel torque distribution is optimized by combining the quadratic programming algorithm.

2. The sliding mode correction control method based on the vehicle yaw stability region according to claim 1, characterized in that: The specific steps of step 1 are as follows: 11) The tire lateral force is piecewise affine modeled (PWA) using the least squares fitting technique, namely: Where i = {f, r} is the front and rear equivalent wheels of the vehicle, F yi is the tire lateral force; α i is the tire slip angle; α i1 , α i2 is the segmentation point, α max is the maximum value of the sideslip angle constraint, k i0 is α i In [-α i1 ,α i1 ]Equivalent cornering stiffness in the interval, k i1 、k i2 、b i1 、b i2 are the slope and intercept of the corresponding interval line segment respectively; 12) Ignoring the load transfer between the left and right wheels, a two-degree-of-freedom vehicle yaw dynamics model is constructed: Among them, β and r represent the vehicle's center of mass sideslip angle and yaw rate respectively; They represent the sideslip angular velocity and yaw angular acceleration of the center of mass, m represents the mass of the vehicle; V x Indicates the longitudinal speed of the vehicle; I z represents the vehicle's yaw moment of inertia; l f Indicates the distance from the center of mass to the front axle; l r Indicates the distance from the center of mass to the rear axle; M DYC represents the additional yaw moment; k f , k r is the equivalent cornering stiffness, δ is the front wheel turning angle, b f 、b r are the intercepts corresponding to the lateral force of the segmented tire model; 13) According to the Routh-Hurwitz stability criterion, the necessary and sufficient condition for the stability of the equilibrium point is that all the main diagonal minors of the Hurwitz matrix of the state space equation are positive, that is, they satisfy the following equation: Filter the linear cornering stiffness k that meets the conditions f , k r , according to the piecewise linear model, the tire side slip angle α is obtained f , α r , combined to form the envelope boundaries r, β: Because k f 、k r In order to change with the sideslip angle range, the Routh-Hurwitz segmented envelope boundary is obtained according to the above formula, and the area inside the envelope boundary is defined as the stable region, and the area outside the envelope boundary is defined as the unstable region.

3. The sliding mode correction control method based on the vehicle yaw stability region according to claim 1, characterized in that: The specific steps of step 2 are as follows: 21) The segmented stability region is clearly affected by tire nonlinearity, primarily due to modeling errors and road adhesion disturbances. The cornering stiffness disturbance is characterized by the deviation of vehicle state parameters, and the observed deviation is compared using the following formula: Among them, F yfo , F yro Defined as the actual lateral force of the front and rear wheels, F yfn , F yrn Defined as the nominal lateral force on the front and rear wheels; is the observed value of the center of mass sideslip angular velocity and nominal value The deviation, is the observed value of yaw angular acceleration and nominal value The deviation, and Obtained from the vehicle yaw dynamics model, and Obtained directly or indirectly by on-board sensors; The nominal and actual lateral forces are expressed by combining the segmented tire model: Where: i = {f, r}, k in and k io is the nominal slope and actual slope of the tire force segment interval, b i is the intercept of the corresponding interval; Get the corrected cornering stiffness Δk f and Δk r : 22) In the cornering stiffness correction formula, the mass inertia parameters involved can be considered as constant values ​​during the motion process, while the longitudinal position parameters of the center of mass will change due to load distribution and dynamic characteristics; The observation equation is established according to the yaw dynamics model: Where: T is the sampling period, the distance from the center of mass to the front axle is l f (t) is the state variable, the yaw angular velocity r(t) is the measurement variable, L = l f +l r The distance between the front and rear axles Since the center of mass position changes slowly, it can be modeled as a random walk process: l f (t+1)=l f (t)+w(t) (10) Where: w(t) is the process noise. Identifying centroid position parameters l based on extended Kalman filter f : Where: P is the estimation error covariance matrix, Q is the process noise covariance matrix, K is the Kalman gain matrix, and R is the measurement noise covariance matrix.

4. The sliding mode correction control method based on the vehicle yaw stability region according to claim 3, characterized in that: The specific method of step 3 is as follows: 31) The vehicle's center of mass slip angle β and yaw rate r, which characterize the vehicle's yaw stability, are used as stability control targets; the desired center of mass slip angle β is set ref is 0; the desired yaw rate r ref Identification through information such as the front wheel angle δ: Among them, r s is the expected yaw rate before correction. 32) Considering the influence of road surface and roll stability, the expected yaw rate is corrected to: Among them, r ref is the corrected desired yaw rate, μ is the road adhesion coefficient, g is the acceleration of gravity, d is the wheelbase of the left and right wheels, h is the height of the center of mass, and sgn(δ) is the sign function.

5. The sliding mode correction control method based on the vehicle yaw stability region according to claim 4, characterized in that: The specific steps of step 4 are as follows: 41) Construct the integral sliding surface function: Where c is the design parameter, e is the error of yaw rate and sideslip angle, and dt is the time differential; e=rr ref +τ(β-β ref ) (16) Where, τ is the design parameter; To further reduce system chattering, we use the exponential function approach rate and replace sgn(s) with the saturation function sat(s), and we get: Among them, K1, K2 are the approach rate parameters 1; 42) The final additional yaw moment is: Among them, M z is the sliding mode control torque in the stable region, ΔM z is the sliding mode correction torque in the unstable region, is the weight parameter. In the corrected stable domain, the model disturbance is small. When the vehicle is outside the correction stability domain, it is in an unstable state and the model disturbance increases. In order to ensure the control accuracy, 6. The sliding mode correction control method based on the vehicle yaw stability region according to claim 5, characterized in that: The specific steps of step 5 are as follows: 51) The yaw moment M DYC Distribute the torque to each wheel, ignore the effect of transient slip, and make the sum of the longitudinal forces of each wheel zero, then: Where, ij = {fl, fr, rl, rr}, T ij is the additional driving torque for the wheel, and Re is the rolling radius of the tire. 52) Taking tire adhesion utilization as the optimal control target, the quadratic programming objective function is used to distribute the four-wheel torque: st.|T ij |≤min(μReF zij ,T max ) (22) Among them, F zij is the tire load, T max is the maximum torque of the motor.

Images