Dynamic Constraint Method of Slip Ratio Based on Probability Distribution of Vehicle Handling Stability

Abstract

The present invention belongs to the field of vehicle handling stability control, and specifically is a slip rate dynamic constraint method based on vehicle handling stability probability distribution. The #imgabs0# phase space is established to analyze the vehicle stability under complex working conditions, and further proposes a vehicle handling stability probability distribution P stable ; Analysis P stable The slip rate constraint is defined according to the slip rate change trend; the slip rate constraint under each working condition is extracted by traversal method, and the slip rate dynamic constraint estimation model is trained based on neural network, and the slip rate dynamic constraint method is established by combining model predictive controller. Finally, a double lane change test is carried out on a winter test site using a four-wheel drive electric vehicle. This method gives the probability distribution index of vehicle handling stability under composite working conditions, and accurately estimates the slip rate constraint under any conditions. It is supplemented by model predictive control strategy to realize dynamic constraint of tire slip rate and prevent vehicle instability caused by excessive tire slip.

Description

Technical Field

[0001] The present invention relates to a slip rate constraint method, specifically a dynamic slip rate constraint method based on the probability distribution of vehicle handling stability, and belongs to the field of vehicle handling stability control. Background Technique

[0002] A vehicle is a complex non-linear system. Due to the side slip - longitudinal slip coupling characteristics, the vehicle handling stability control under complex working conditions faces great challenges. As one of the vehicle control systems, the anti-skid control is closely related to the vehicle handling stability. Especially on ice and snow roads, wet and slippery roads with low friction coefficients, excessive tire slip will cause the vehicle to lose its maneuverability and may lead to serious safety accidents. Most of the existing anti-skid control systems are based on classical logic thresholds: when the tire slip rate reaches certain constraint conditions, the control state changes. However, the slip rate constraint is uncertain and is easily affected by factors such as vehicle longitudinal speed, friction coefficient, and front wheel angle. Therefore, the accurate estimation of the slip rate constraint value under different working conditions is one of the research hotspots and difficulties in the current vehicle field.

[0003] On the other hand, the vehicle motion state is complex under complex working conditions. The traditional phase plane analysis method is for a two-degree-of-freedom vehicle model, ignoring the influence of longitudinal motion on vehicle stability and unable to accurately describe the vehicle motion state under complex working conditions. The quasi-steady state assumption method based on a three-degree-of-freedom vehicle model considers the load transfer caused by the tire longitudinal force, but the system error brought by the transient assumption makes the stability of its boundary still to be analyzed. Establishing a vehicle state analysis method for complex working conditions that reflects the vehicle stability at the boundary is also crucial. Summary of the Invention

[0004] Aiming at the problems in the background technique, the present invention provides a dynamic slip rate constraint method based on the probability distribution of vehicle handling stability. The proposed probability distribution of handling stability based on phase space analysis can effectively characterize the vehicle state under complex working conditions, further analyze the probability distribution of vehicle handling stability with different slip rates under complex working conditions, find the slip rate constraint values under different working conditions, so as to realize the dynamic constraint of the tire slip rate and prevent the vehicle from losing stability due to excessive tire slip.

[0005] The technical solution to realize the present invention is as follows:

[0006] A dynamic slip rate constraint method based on the probability distribution of vehicle handling stability, the method includes the following steps:

[0007] Step 1: Establish a vehicle dynamics model;

[0008] Step 2: Establish a model predictive controller;

[0009] Step 3: Establishment of the vehicle handling stability probability distribution model;

[0010] Step 4: Definition of the dynamic constraint value of the slip ratio;

[0011] Step 5: Establishment of the slip ratio dynamic constraint controller.

[0012] The specific method of the said Step 1 is as follows:

[0013] 11) The three-degree-of-freedom vehicle model includes three motion degrees of freedom: longitudinal, lateral, and yaw of the vehicle;

[0014]

[0015] In the formula, m is the vehicle mass, V x , V y are the longitudinal and lateral speeds of the vehicle, r is the yaw angular velocity, F xf is the longitudinal force of the front wheels, F xr is the longitudinal force of the rear wheels, δ f is the front wheel steering angle, F yf is the lateral force of the front wheels, F yr is the lateral force of the rear wheels, I z is the moment of inertia of the vehicle body about the z-axis, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle. The sideslip angle β of the center of mass is:

[0016]

[0017] In the formula, V x and V y are the longitudinal and lateral speeds of the vehicle.

[0018] 12) Conduct a force analysis on the wheels to obtain the following motion equations:

[0019]

[0020] In the formula, J is the tire moment of inertia, ω i (i = fl, fr, rl, rr) is the angular velocity of each wheel tire, T i is the driving torque of each wheel tire, F xi is the longitudinal force of each wheel tire, and R is the effective rolling radius of the tire.

[0021] 13) Among them, the tire force is represented by the UniTire tire model. Under the combined longitudinal slip - side slip condition, the tire force can be expressed as:

[0022]

[0023] In the formula, is a dimensionless tire force, φ is the relative comprehensive slip ratio, φ x is the relative longitudinal slip ratio, φ y is the relative lateral slip ratio, E is the curvature factor, F x is the tire longitudinal force, F y is the tire longitudinal force, μ x is the longitudinal friction coefficient, μ y is the lateral friction coefficient, F z is the tire load.

[0024] 14) Since the longitudinal acceleration will cause tire load transfer, so F in equation (1.4) z can be expressed as:

[0025]

[0026] In the formula, F zf is the front wheel load, F zr is the rear wheel load, m is the vehicle mass, g is the acceleration due to gravity, a x is the longitudinal acceleration, h g is the height of the vehicle center of mass, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle.

[0027] 15) The relative comprehensive slip ratio φ can be expressed as:

[0028]

[0029] In the formula, the relative longitudinal slip ratio φ x and the relative lateral slip ratio φ y can be expressed as:

[0030]

[0031] In the formula, S x 、S y are the longitudinal and lateral slip ratios of the tire respectively, K x 、K y are the longitudinal slip stiffness and cornering stiffness of the tire respectively, μ x 、μ y are the longitudinal and lateral friction coefficients respectively, F z is the tire load.

[0032] 16) The longitudinal and lateral slip ratios of the tire S x 、S y can be expressed as:

[0033]

[0034] In the formula, ω iis the angular velocity of each wheel, R is the effective rolling radius of the tire, V ti is the velocity of the wheel center of each wheel, and the four wheel sideslip angles α fl 、α fr 、α rl 、α rr can be expressed as:

[0035]

[0036] In the formula, δ f is the front wheel steering angle, V x and V y are the longitudinal and lateral vehicle speeds, r is the yaw angular velocity, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle.

[0037] The specific method of the second step is as follows:

[0038] 21) Based on the vehicle model and the wheel angular velocity dynamics model described in the first step, establish the vehicle state space equation:

[0039]

[0040] where A, B, C, and E are the input state coefficient matrix, the control coefficient matrix, the disturbance coefficient matrix, and the output state coefficient matrix respectively. The state variable X, the control input variable U, the disturbance input W, and the control output Y are respectively:

[0041]

[0042] U = [δ f T fl T fr T rl T rr T

[0043] W = [a x a y F xfl F xfr F xrl F xrr T

[0044] Y = [r β ω fl ω fr ω rl ω rr T

[0045] In the formula, r is the yaw angular velocity, β is the center of mass sideslip angle, is the yaw moment of the longitudinal force,​​​ The yaw moment for the lateral force is ω i The angular velocity of each wheel tire is ω i The driving torque of each wheel tire is T xi The longitudinal force of each wheel tire, where i = fl, fr, rl, rr, and δ f The front wheel steering angle is δ x , a y are the longitudinal and lateral accelerations respectively.

[0046] 22) Based on the model predictive control principle, the following performance index is established:

[0047]

[0048] In the formula, N p is the prediction step length, Y ref is the expected reference output of the system, Y k is the output of the prediction model, U k is the output of the predictive control, U d is the steering and torque distribution expected by the driver, U k-1 is the output of the predictive control at the previous moment. The positive definite matrices Q, R, and T are weight matrix functions used to reflect the weights of each performance index in the total performance index. Q, R, and T can be fixed constants or time-varying matrices.

[0049] 23) The reference value r of the vehicle yaw rate d is:

[0050]

[0051] In the formula, δ f is the front wheel steering angle, V x is the longitudinal speed, r is the yaw rate, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, μ is the friction coefficient, g is the acceleration due to gravity, K s is the understeer gradient, r d is the reference value of the vehicle yaw rate.

[0052]

[0053] In the formula, K s is the understeer gradient, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, m is the vehicle mass, K f is the front wheel cornering stiffness, K r is the rear wheel cornering stiffness.

[0054] 24) When the tire slip rate exceeds the slip rate constraint λco,i When it is, the tire angular velocity error can be expressed as:

[0055]

[0056] In the formula, e ωi,d is the tire angular velocity error, ω i is the tire angular velocity of each wheel, ω i,k-1 is the tire angular velocity at the k - 1 moment of the wheel, V x is the longitudinal velocity, r d is the reference value of the vehicle yaw angular velocity, R is the effective rolling radius of the tire, t wf is the front wheel wheelbase, λ co,i is the slip rate constraint.

[0057] The specific method of the said step three is as follows:

[0058] 31) Under the fixed working conditions (the same friction coefficient μ, front wheel steering angle δ f and longitudinal velocity V x ), The phase space consists of multiple trajectories generated by different initial values of the centroid side slip angle and yaw angular velocity within a fixed simulation time. For the convenience of understanding, the trajectories in the phase space are classified. Except for the unstable trajectories, the other trajectories in the phase space can be divided into three categories:

[0059] Type 1: Within the fixed simulation duration, the trajectory can converge to the same axis without deceleration ( Figure 3 (a));

[0060] Type 2: Within the fixed simulation duration, the trajectory can converge to the same axis through deceleration ( Figure 3 (b));

[0061] Type 3: After the fixed simulation duration, the trajectory still oscillates around the same axis ( Figure 3 (c)).

[0062] 32) Through the analysis of the phase space, it can be seen that as the slip rate increases, the number of curve 1 shows a trend of first increasing and then decreasing. As the longitudinal velocity and front wheel steering angle increase, the number of curve 1 gradually decreases.

[0063] 33) With the constant friction coefficient μ, front wheel steering angle δ f and longitudinal velocity V x as the fixed conditions, each slip rate corresponds to a phase space, and the number of trajectories of type 1, type 2, and type 3 in the phase space is extracted, so as to construct the probability distribution of the vehicle handling stability under different working conditions. The specific expression is as follows:

[0064]

[0065] In the formula, P n is the stability of the two types of trajectories. NO1, NO2, and NO3 respectively represent the number of trajectories of types 1, 2, and 3 in the phase space. P stable is the probability distribution of vehicle handling stability.

[0066] The specific method of the fourth step is as follows:

[0067] 41) Under any working conditions: with the same friction coefficient, front wheel steering angle, and longitudinal speed, due to different slip ratios, a large number of phase spaces can be drawn. However, under the same working conditions, there is only one slip ratio constraint. Integrate the main data in multiple phase spaces to more simply and intuitively describe the stable nonlinear characteristics of P.

[0068] 42) Divide the change trend of P stable with the slip ratio into 3 characteristic points and 2 change stages: initial value point, growth stage, peak point, decline stage, upper boundary point. Among them, the peak point is defined as the slip ratio constraint of this working condition due to its maximum handling stability probability distribution. Further analyze the influence of vehicle speed, road surface friction coefficient, and front wheel steering angle on the slip ratio constraint under various working conditions.

[0069] The specific method of the fifth step is as follows:

[0070] 51) Use the traversal method to extract the tire slip ratio constraints under each working condition. The value range of the decisive parameters of the phase space working condition is the front wheel steering angle (δ f =-5 to 5 deg), longitudinal speed (V x =10 to 35 m / s), and friction coefficient (μ = 0.3 to 1.0). The working conditions not included in the value range are obtained through the training of the neural network. Use the Levenberg Marquardt algorithm to train the tire slip ratio constraint data set, and thus establish a dynamic constraint estimation model for the tire slip ratio.

[0071] 52) Based on the tire slip ratio model predictive controller involved in the second step, a dynamic constraint controller for the slip ratio is established, realizing the dynamic constraint of the tire slip ratio and preventing the vehicle from losing stability due to excessive tire slip.

[0072] The beneficial effects of the present invention are:

[0073] 1) Established phase space to analyze the vehicle stability under compound working conditions, and further proposed the probability distribution P of vehicle handling stability stable, compared with the traditional vehicle state analysis method, it takes into account the load transfer caused by longitudinal acceleration, reflects the vehicle state at the stability boundary, and accurately gives the vehicle handling stability probability distribution index under composite working conditions;

[0074] 2) Analyzed the probability distribution P of vehicle handling stability under various (high-friction and low-friction) composite slip conditions stable , which is divided into 3 characteristic points and 2 change stages, providing a theoretical basis for determining the slip rate constraint;

[0075] 3) Established a dynamic constraint controller for tire slip rate based on MPC, and verified it with a 4WIMD electric vehicle under the double lane change condition. The results show that this control strategy can calculate the slip rate constraint accurately in real time and prevent vehicle instability caused by excessive tire slip. Description of the Drawings

[0076] Figure 1 is a schematic diagram of a three-degree-of-freedom vehicle model;

[0077] Figure 2 is a schematic diagram of a tire dynamics model;

[0078] Figure 3 a— Figure 3 c is the curve of tire force and slip rate under composite working conditions;

[0079] Figure 4 a— Figure 4 c is the phase space without front wheel steering angle;

[0080] Figure 5 is the phase space with front wheel steering angle;

[0081] Figure 6 is the probability distribution of vehicle handling stability;

[0082] Figure 7 is the slip rate constraint data;

[0083] Figure 8 is the framework of the slip rate dynamic constraint controller;

[0084] Figure 9 a— Figure 9 d is the verification curve of the double lane change condition during dynamic constraint control;

[0085] Figure 10 a— Figure 10 d is the four-wheel slip rate curve during dynamic constraint control;

[0086] Figure 11 a— Figure 11d is the verification curve of the double lane change condition without control;

[0087] Figure 12 a— Figure 12 d is the four-wheel slip ratio curve without control;

[0088] Figure 13 a— Figure 13 b is the bar chart of the average value of the slip ratio (constraint) under the double lane change condition. Detailed implementation mode

[0089] The present invention will be described in detail below with reference to the accompanying drawings.

[0090] The present invention provides a dynamic constraint method for slip ratio based on the probability distribution of vehicle handling stability, as Figure 8 shown. First, based on the three-degree-of-freedom vehicle model and the UniTire tire model, the phase space was used to analyze the vehicle stability under composite conditions; furthermore, the vehicle handling stability probability distribution P stable was proposed, and the slip ratio constraints under different conditions were defined; the tire slip ratio constraints under each condition were extracted by using the traversal method, and a dynamic constraint estimation model for tire slip ratio was trained based on a neural network. Combining with a model predictive controller, a dynamic constraint method for slip ratio was established.

[0091] The detailed implementation process of the method of the present invention is as follows:

[0092] Step 1: Establish a vehicle dynamics model, mainly including a vehicle model, a wheel model, and a UniTire tire model.

[0093] First, establish a three-degree-of-freedom vehicle model as Figure 1 shown. The state space equation of the vehicle model including the longitudinal, lateral, and yaw motion degrees of freedom of the vehicle can be expressed as:

[0094]

[0095] In the formula, m is the vehicle mass, V x , V y are the longitudinal and lateral speeds of the vehicle, r is the yaw angular velocity, F xf is the longitudinal force of the front wheel, F xr is the longitudinal force of the rear wheel, δ f is the front wheel steering angle, F yf is the lateral force of the front wheel, F yr is the lateral force of the rear wheel, I z is the moment of inertia of the vehicle body about the z-axis, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle. The sideslip angle β of the center of mass is:

[0096]

[0097] wherein, V x and V y are the longitudinal and lateral velocities.

[0098] Secondly, a wheel dynamics model is established as Figure 2 shown. The wheel angular velocity dynamics model is:

[0099]

[0100] wherein, J is the tire moment of inertia, ω i (i = fl, fr, rl, rr) are the tire angular velocities of each wheel, T i is the driving torque of each wheel tire, F xi is the tire longitudinal force, and R is the effective rolling radius of the tire.

[0101] Finally, the UniTire tire model is introduced into the vehicle and wheel models, and the tire force under its combined working conditions can be expressed as:

[0102]

[0103] wherein, is the dimensionless tire force, φ is the relative comprehensive slip ratio, φ x is the relative longitudinal slip ratio, φ y is the relative lateral slip ratio, E is the curvature factor, F x is the tire longitudinal force, F y is the tire longitudinal force, μ x is the longitudinal friction coefficient, μ y is the lateral friction coefficient, F z is the tire load. Since the longitudinal acceleration will cause tire load transfer, thus F z can be expressed as:

[0104]

[0105] wherein, F zf is the front wheel load, F zr is the rear wheel load, m is the vehicle mass, g is the acceleration due to gravity, a x is the longitudinal acceleration, h g is the vehicle center of mass height, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle.

[0106] The relative comprehensive slip ratio φ can be expressed as:

[0107]

[0108] In the formula, the relative longitudinal slip ratio φ x and the relative lateral slip ratio φ y can be expressed as:

[0109]

[0110] In the formula, K x and K y are the longitudinal slip stiffness and the cornering stiffness of the tire respectively, μ x and μ y are the longitudinal and lateral friction coefficients respectively, and F z is the tire load. The longitudinal and lateral slip ratios S x and S y of the tire can be expressed as:

[0111]

[0112] In the formula, ω i is the angular velocity of each wheel tire, R is the effective rolling radius of the tire, and V ti is the speed of the wheel center of each wheel. The sideslip angle can be expressed as:

[0113]

[0114] In the formula, δ f is the front wheel steering angle, V x and V y are the longitudinal and lateral speeds of the vehicle, r is the yaw angular velocity, l f is the distance from the center of mass to the front axle, and l r is the distance from the center of mass to the rear axle. The relevant conditions based on the model are summarized as follows:

[0115] Condition 1: Excessive lateral force of the tire will hinder the vehicle acceleration.

[0116] According to Newton's second law, the longitudinal acceleration of the vehicle can be expressed as:

[0117]

[0118] In the formula, a x is the longitudinal acceleration, F xf , F xr are the longitudinal forces of the front and rear wheels respectively, δ f is the front wheel steering angle, F yf is the lateral force of the front wheel, and m is the mass of the whole vehicle. Under the acceleration condition, the longitudinal forces F xf , F xr > 0. If the excessive lateral force of the tire satisfies the inequality:

[0119]

[0120] where a x is the longitudinal acceleration, F xf , F xr are the longitudinal forces of the front and rear wheels respectively, δ f is the front wheel steering angle, F yf is the lateral force of the front wheel. At this time, the longitudinal acceleration a x ≤0, that is, excessive lateral tire force will prevent the vehicle from accelerating.

[0121] Condition 2: The lower the longitudinal speed, after the peak point of the tire longitudinal force, the less obvious the trend of the tire longitudinal force decreasing with the increase of the tire slip ratio, as Figure 3 shown.

[0122] The friction coefficient is a function of the tire slip speed. The dynamic friction coefficient of the tire can be expressed as:

[0123]

[0124] where μ d is the dynamic friction coefficient, μ s is the friction coefficient when the tire is completely slipping, μ m is the peak friction coefficient, μ h is the characteristic factor controlling the change process of the friction coefficient, V sm is the tire slip speed corresponding to the peak slip ratio, V s is the tire slip speed and can be expressed as:

[0125]

[0126] where V sx is the longitudinal slip speed of the tire, V sy is the longitudinal slip speed of the tire, S x is the longitudinal slip ratio, S y is the lateral slip ratio, V x is the longitudinal speed, α i is the tire sideslip angle. It can be seen that the lower the longitudinal speed, the lower the tire slip speed, and the dynamic friction coefficient μ d changes insignificantly, and the longitudinal force basically maintains the peak after the peak point.

[0127] Step 2: Establish a model predictive controller.

[0128] First, based on the vehicle model and the wheel angular velocity dynamics model, establish the vehicle state space equation:

[0129]

[0130] where A, B, C, and E are the input state coefficient matrix, control coefficient matrix, disturbance coefficient matrix, and output state coefficient matrix respectively. The state variable X, control input variable U, disturbance input W, and control output Y are respectively:

[0131]

[0132] U = [δ f T fl T fr T rl T rr T

[0133] W = [a x a y F xfl F xfr F xrl F xrr T

[0134] Y = [r β ω fl ω fr ω rl ω rr T

[0135] In the formula, r is the yaw rate, β is the sideslip angle of the center of mass, is the yaw moment of the longitudinal force, is the yaw moment of the lateral force, ω i is the angular velocity of each wheel tire, T i is the driving torque of each wheel tire, F xi is the longitudinal force of each wheel tire, where i = fl, fr, rl, rr, δ f is the front wheel steering angle, a x , a y are the longitudinal and lateral accelerations respectively.

[0136] Based on the model predictive control principle, the following performance index is established:

[0137]

[0138] In the formula, N p is the prediction horizon, Y ref is the desired reference output of the system, Y k is the output of the prediction model, U k is the prediction control output, U d is the steering and torque distribution desired by the driver, U k-1 ​​​is the output of the predictive control at the previous moment. The positive definite matrices Q, R, and T are distribution weight matrix functions used to reflect the weights of various performance indicators in the total performance indicator. Q, R, and T can be fixed constants or time-varying matrices.

[0139] Reference value r of vehicle yaw rate d is:

[0140]

[0141] In the formula, δ f is the front wheel steering angle, V x is the longitudinal speed, r is the yaw rate, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, μ is the friction coefficient, g is the acceleration due to gravity, K s is the understeer gradient, r d is the reference value of the vehicle yaw rate.

[0142]

[0143] In the formula, K s is the understeer gradient, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, m is the vehicle mass, K f is the front wheel cornering stiffness, K r is the rear wheel cornering stiffness. When the tire slip ratio exceeds the slip ratio constraint λ co,i , the tire angular velocity error is used. For example, the left front wheel can be expressed as:

[0144]

[0145] In the formula, e ωi,d is the tire angular velocity error, ω i is the tire angular velocity of each wheel, ω i,k-1 is the tire angular velocity at the k-1 moment of the wheel, V x is the longitudinal speed, r d is the reference value of the vehicle yaw rate, R is the effective rolling radius of the tire, t wf is the front wheel wheelbase, λ co,i is the slip ratio constraint. The slip ratio constraints of each wheel are distributed according to the vertical load of the wheel and can be expressed as.

[0146]

[0147] In the formula, F zfl , F zfr , F zrl , F zrr are the tire loads of the left front, right front, left rear, and right rear wheels respectively, λco,fl , λ co,fr , λ co,rl , λ co,rr are the tire slip ratio constraints for the left front, right front, left rear, and right rear wheels respectively. is the average tire slip ratio constraint, m is the vehicle mass, and g is the acceleration due to gravity.

[0148] Step 3: Establish the vehicle handling stability probability distribution model.

[0149] Firstly, it is necessary to clarify the prerequisite conditions: compared with the pure sideslip condition, the introduction of the longitudinal force in the combined working condition will lead to the transfer of tire load and the change of slip ratio; on the other hand, according to the traditional phase plane analysis method, the vehicle has stronger stability at low speeds, and whether the vehicle can achieve acceleration or constant-speed steering operation is a more important performance index for evaluating the performance of the vehicle electronic control unit (ECU). Therefore, based on the three-degree-of-freedom vehicle model considering tire load transfer, a phase space is established with a fixed slip ratio, and the vehicle stability is discussed under the accelerating combined slip condition.

[0150] Under the fixed working condition, that is, the same friction coefficient μ, front wheel angle δ f and longitudinal speed V x , the phase space consists of multiple trajectories generated by different initial values of the centroid sideslip angle and yaw rate (β0, r0) within a fixed simulation time.

[0151] Secondly, analyze the vehicle state in the phase space. For the convenience of understanding, the trajectories in the phase space are classified in this patent. Except for the unstable trajectories, the other trajectories in the phase space can be divided into three categories:

[0152] Type 1: Within the fixed simulation duration, the trajectory can converge to the same axis without deceleration ( Figure 4 (a));

[0153] Type 2: Within the fixed simulation duration, the trajectory can converge to the same axis through deceleration ( Figure 4 (b));

[0154] Type 3: After the fixed simulation duration, the trajectory still oscillates around the same axis ( Figure 4 (c)).

[0155] Figure 4 is the phase space without the front wheel angle. As the slip ratio increases, the trajectory type of the stability boundary gradually changes from type 2 to type 1, and then to type 3. This is because the longitudinal force first increases and then decreases with the change of the slip ratio. Therefore, the number of curve 1 also shows a trend of first increasing and then decreasing with the increase of the slip ratio.

[0156] Figure 5 For the phase space with the front wheel angle. Except for the front wheel angle, its working conditions are completely the same as (b). Due to the input of the front wheel angle, due to the tire coupling effect, the types of some trajectories have changed. Figure 4 (b) is exactly the same. Due to the input of the front wheel angle, due to the tire coupling effect, the types of some trajectories have changed.

[0157] Type 1 → Type 2: Due to the input of the front wheel angle, when the lateral force increases, that is, when the longitudinal force decreases, the trajectory changes from Type 1 to Type 2 (Condition 1), as shown by the thickened curve on the positive semi-axis in Figure 5 the figure.

[0158] Type 1 → Type 3: Due to the input of the front wheel angle, when the lateral force decreases, that is, when the longitudinal force increases, the convergence speed of the trajectory slows down and changes from Type 1 to Type 3, as shown by the thickened curve on the negative semi-axis in Figure 5 the figure.

[0159] Due to the increase in the front wheel angle, the total number of Type 1 trajectories changes from 64 to 47, and the vehicle stability region becomes narrower, which is consistent with the conclusion of the traditional phase plane analysis method.

[0160] Further observation Figure 4 and Figure 5 show that obviously, the greater the sideslip angular velocity of the center of mass, that is, the closer the trajectory is to the boundary of the stable region, the more the number of Type 2 and Type 3 trajectories. This also means that the closer to the stability boundary, although the vehicle state is stable, it often needs to maintain stability by sacrificing speed (Type 2), or it needs long-term oscillation and cannot converge quickly (Type 3). Therefore, it is crucial to establish a vehicle state analysis method for composite working conditions that reflects the stability of the boundary vehicle.

[0161] First, with a constant friction coefficient μ, front wheel angle δ f and longitudinal velocity V x as fixed conditions, each slip ratio corresponds to a phase space, and the number of Type 1, Type 2, and Type 3 trajectories in the phase space is extracted, so as to construct the probability distribution of vehicle handling stability under different working conditions. The specific expression is as follows:

[0162]

[0163] In the formula, P n is the stability degree of Type 2 trajectories, NO1, NO2, and NO3 respectively represent the number of Type 1, Type 2, and Type 3 trajectories in the phase space, and P stable is the probability distribution of vehicle handling stability.

[0164] Step 4. Definition of the dynamic constraint value of the slip ratio constraint.

[0165] As the slip ratio increases, the variation law of the probability distribution of vehicle handling stability can be roughly divided into three characteristic points and two change stages: the initial point, the extreme point, the upper boundary point, the growth stage, and the decline stage, as Figure 6 shown.

[0166] Initial point: When the slip ratio is 0.01, the corresponding P stable is defined as the initial point, as Figure 6 shown by the "·" point in. At this time, the lateral force is relatively large, and most trajectories can converge to the stable axis within a fixed time; the longitudinal force is relatively small, and some trajectories need to converge to the stable axis by losing speed (Condition 1);

[0167] Growth stage: After the initial value point, P stable has a growth stage, as Figure 6 shown by the solid line in. As the slip ratio increases, the lateral force gradually decreases, the trajectory convergence speed gradually decreases, and a few trajectories are "Type 1 → Type 2"; the longitudinal force increases sharply, and a large number of trajectories are "Type 2 → Type 1". Therefore, P stable shows a growth trend;

[0168] Extreme point: As Figure 6 shown by the "*" point in, the point with the maximum P stable is defined as the extreme point. At this time, the tire longitudinal force reaches the peak, and the tire forces of most trajectories do not satisfy the inequality (1.11), the lateral force is relatively large, and the total amount of Type 2 and Type 3 trajectories is the least. It should be noted that the extreme point is not necessarily the peak point of the tire longitudinal force, but the extreme point of the tire adhesion area used under the current conditions, which will be further analyzed later;

[0169] Decline stage: When P stable passes through the extreme point, it will enter the decline stage, as Figure 6 shown by the dashed line in. As the slip ratio further increases, the tire lateral force decreases, and the convergence speed gradually slows down; the longitudinal force decreases due to the large tire slip speed (Condition 2), and some trajectories are "Type 1 → Type 2, 3". Therefore, P stable shows a decline trend;

[0170] Upper boundary point: As Figure 6 shown by the "△" point in, draw a parallel line to the X-axis through the initial value point and intersect with the decline stage, and its intersection point is defined as the upper boundary point. This means that before the upper boundary point, the P stable at any slip ratio is greater than the value of the upper boundary point.

[0171] On the one hand, the tire slip energy generated by excessive tire slip will reduce the motor output efficiency; on the other hand, the probability distribution of vehicle handling stability at the extreme point is the largest. Considering both safety and energy conservation, the extreme point is regarded as the slip ratio constraint for this working condition. That isFigure 6 (μ = 0.8, δ f = 5, V x = 30 m / s) The slip ratio constraint under this condition is approximately 0.045.

[0172] Step six: Use phase space to extract the slip ratio constraint. The decisive parameters of the phase space include: front wheel steering angle (-5° to 5°), longitudinal speed (10 m / s to 35 m / s), and friction coefficient (0.3 to 1.0). Conditions not included in the dataset are obtained by training a neural network. The vehicle parameters involved are shown in Table 1.

[0173] The slip ratio constraint data is as Figure 7 shown, showing the variation trend of the slip ratio constraint with the longitudinal speed at different front wheel steering angles, with a friction coefficient of 0.8. Obviously, the data curve with the slip ratio constraint has two inflection points, which makes it decrease slowly first, then drop sharply, and finally seems to converge to a certain value.

[0174] According to the data characteristics of the slip ratio constraint, it has only three parameters: friction coefficient, longitudinal speed, and front wheel steering angle, and the number of samples is relatively small. The Levenberg - Marquardt algorithm is used to train the data. Among them, the longitudinal speed, front wheel steering angle, and friction coefficient are inputs, and the slip ratio constraint is the output, thereby establishing a dynamic constraint model of the slip ratio.

[0175] Furthermore, based on the slip ratio constraint model predictor established in step two, a dynamic constraint controller for tire slip ratio is built, as Figure 8 shown, to improve the vehicle handling stability. The controller includes: "wheel dynamics model" and "vehicle model" for obtaining the reference centroidal side - slip angle β d , yaw rate r d and wheel speed ω id ; the "MPC controller" distributes torques for each wheel according to the performance index J and the slip ratio constraint λ co,i .

[0176] Step seven: Use the method of the present invention to conduct on - vehicle verification on a low - adhesion road surface, and the condition is the double - lane change condition.

[0177] Figure 9 For the verification of the double - lane change condition using the method of the present invention, the friction coefficient is close to 0.3. The longitudinal speed is approximately 65 km / h, and the maximum front wheel angle is approximately 3°, as Figure 9 (a) shown. Figure 9 (b) shows the tracking curve of the yaw rate. Under dynamic constraint control, the yaw rate can better track the target and complete the double - lane change condition. Figure 9(c) and (d) respectively show the lateral / longitudinal acceleration and driving torque of the vehicle, and the peak acceleration is less than 0.1g.

[0178] The tire slip ratio is as Figure 10 shown. The dynamic constraint of the tire slip ratio designed in this patent is as Figure 10 shown by the dashed line in. When there is no front wheel steering angle, the tire slip ratio constraint remains at about 0.06. Input the front wheel steering angle, the tire slip ratio constraint becomes smaller, and the larger the front wheel steering angle, the smaller the tire slip ratio constraint. Obviously, this controller effectively controls the slip ratio below the constraint value.

[0179] The results without control are as Figure 11 and Figure 12 shown. The longitudinal speed is also 65 km / h, as Figure 11 (a) shown. At about 42 s, the yaw rate of the vehicle gradually fails to track the target value, see Figure 11 (b). According to Figure 12 , without control, at about 42 s, the tire slip ratio exceeds the constraint value. At this time, the tire force shows obvious non-linearity, the longitudinal force decreases, the slip ratio further increases, the tire locks, and the vehicle drifts.

[0180] The average value of the tire slip ratio (constraint) under the double lane change condition is as Figure 13 shown. The average value of the tire slip ratio constraint for each wheel is close to 0.06. When the MPC strategy is adopted, the tire slip ratio is lower than the constraint value, only 0.03; without control, the tire slip ratio is much higher than the constraint value, and the average value even exceeds 0.2.

[0181] Table 1 Vehicle related parameters

[0182]

Claims

1. A dynamic constraint method for slip ratio based on the probability distribution of vehicle handling stability, characterized in that The dynamic constraint method includes the following steps: Step 1: Establish a vehicle dynamics model; Step 2: Establish a model predictive controller; Step 3: Establish a probability distribution model of vehicle handling stability; 31) Under fixed conditions, i.e., the same friction coefficient μ, front wheel steering angle δ f and longitudinal speed V x , phase space, where β is the sideslip angle of the vehicle's center of mass, is the sideslip angular velocity of the vehicle's center of mass, V x is the longitudinal vehicle speed, which consists of multiple trajectories generated by different initial values of the sideslip angle and yaw angular velocity within a fixed simulation time. Classify the trajectories in the phase space. Except for the unstable trajectories, the other trajectories in the phase space are divided into three categories: Type 1: Within a fixed simulation duration, the trajectory does not converge to the same axis by deceleration; Type 2: Within a fixed simulation duration, the trajectory converges to the same axis by deceleration; Type 3: After a fixed simulation duration, the trajectory still oscillates around the same axis; 32) For phase space analysis, as the slip rate increases, the number of type 1 shows a trend of first increasing and then decreasing, and as the longitudinal speed and the front wheel steering angle increase, the number of type 1 gradually decreases; 33) With a constant coefficient of friction μ, front wheel steering angle δ f and longitudinal speed V x as fixed conditions, each slip ratio corresponds to a phase space. The number of trajectories of type 1, type 2, and type 3 in the phase space is extracted to construct the probability distribution of vehicle handling stability under different working conditions. The specific expression is as follows: where, P n is the stability of the type 2 trajectory, and NO1, NO2, and NO3 respectively represent the numbers of type 1, type 2, and type 3 trajectories in the phase space, and P stable is the probability distribution of vehicle handling stability; Step 4: Define the dynamic constraint value of the slip ratio; 41) Under any working conditions: with the same friction coefficient, front wheel steering angle and longitudinal speed, due to different slip ratios, a large number of phase spaces are plotted. However, under the same working conditions, there is only one slip ratio constraint, and the main data in multiple phase spaces are integrated to more simply and intuitively describe the stable nonlinear characteristics of P; 42) Divide the variation trend of P stable with the slip ratio into 3 characteristic points and 2 variation stages: the initial value point, the growth stage, the peak point, the decline stage, and the upper boundary point. Among them, due to its maximum handling stability probability distribution, the peak point is defined as the slip ratio constraint under this working condition. Further, the influences of vehicle speed, road surface friction coefficient, and front wheel steering angle on the slip ratio constraint under various working conditions are analyzed; Step 5: Establish a dynamic constraint controller for the slip ratio; 51) The tire slip ratio constraints under each working condition are extracted by using the traversal method. The value range of the decisive parameters of the phase space working condition is as follows: front wheel steering angle: δ f = -5 to 5 deg, longitudinal speed: V x = 10 to 35 m / s, and friction coefficient: μ = 0.3 to 1.

0. The working conditions not included in the value range are obtained through the training of the neural network. The Levenberg Marquardt algorithm is used to train the tire slip ratio constraint data set, and thus a dynamic constraint estimation model of the tire slip ratio is established; 52) Based on the tire slip ratio model predictive controller involved in Step 2, a dynamic constraint controller for the slip ratio is established, realizing the dynamic constraint of the tire slip ratio and preventing the vehicle from losing stability due to excessive tire slip.

2. According to the slip ratio dynamic constraint method based on the probability distribution of vehicle handling stability described in Claim 1, the specific method of Step 1 is as follows: 11) The three-degree-of-freedom vehicle model includes three motion degrees of freedom: longitudinal, lateral, and yaw of the vehicle; where m is the vehicle mass, V x , V y are the longitudinal and lateral vehicle speeds, r is the yaw rate, F xf is the longitudinal force of the front wheels, F xr is the longitudinal force of the rear wheels, δ f is the front wheel steering angle, F yf is the lateral force of the front wheels, F yr is the lateral force of the rear wheels, I z is the moment of inertia of the vehicle body about the z-axis, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, and the sideslip angle β of the center of mass is: where V x and V y are the longitudinal and lateral vehicle speeds; 12) Analyze the forces on the wheels to obtain the following motion equations: where J is the tire moment of inertia, ω i (i = fl, fr, rl, rr) is the angular velocity of each wheel tire, T i is the driving torque of each wheel tire, F xi is the longitudinal force of each wheel tire, and R is the effective rolling radius of the tire; 13) Among them, the tire force is represented by the UniTire tire model, and the tire force under the combined longitudinal slip - lateral slip condition is expressed as: In the formula, is the dimensionless tire force, φ is the relative comprehensive slip ratio, φ x is the relative longitudinal slip ratio, φ y is the relative lateral slip ratio, E is the curvature factor, F x is the tire longitudinal force, F y is the tire longitudinal force, μ x is the longitudinal friction coefficient, μ y is the lateral friction coefficient, F z is the tire load; 14) Since longitudinal acceleration causes tire load transfer, F in equation (1.4) is expressed as: z which is: Wherein, F zf is the front wheel load, F zr is the rear wheel load, m is the vehicle mass, g is the acceleration due to gravity, a x is the longitudinal acceleration, h g is the vehicle center of mass height, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle; 15) The relative comprehensive slip ratio φ is expressed as: wherein, the relative longitudinal slip ratio φ x and the relative lateral slip ratio φ y are expressed as: where S x and S y are the longitudinal and lateral slip ratios of the tire, K x and K y are the longitudinal slip stiffness and cornering stiffness of the tire, μ x and μ y are the longitudinal and lateral friction coefficients respectively, and F z is the tire load; 16) Longitudinal and lateral slip ratios S of the tire x , S y are expressed as: S y = -tan(α i )(1 - S x ), where ω i is the angular velocity of each wheel tire, R is the effective rolling radius of the tire, V ti is the velocity of the center of each wheel, and the four-wheel sideslip angles α fl , α fr , α rl , α rr are expressed as: where δ f is the front wheel steering angle, V x and V y are the longitudinal and lateral vehicle speeds, r is the yaw rate, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle.

3. According to the slip ratio dynamic constraint method based on the probability distribution of vehicle handling stability described in Claim 1, the specific method of Step 2 is as follows: 21) Based on the vehicle model and the wheel angular velocity dynamics model described in Step 1, establish the vehicle state space equation: Among them, A, B, C, and E are the input state coefficient matrix, control coefficient matrix, disturbance coefficient matrix, and output state coefficient matrix respectively. The state variable X, control input variable U, disturbance input W, and control output Y are respectively: U = [δ f T fl T fr T rl T rr T ​ W = [a x a y F xfl F xfr F xrl F xrr T ​ Y = [r β ω fl ω fr ω rl ω rr T ​ where r is the yaw rate, β is the sideslip angle at the center of mass, is the yaw moment of the longitudinal force, is the yaw moment of the lateral force, ω i is the angular velocity of each wheel tire, T i is the driving torque of each wheel tire, F xi is the longitudinal force of each wheel tire, where i = fl, fr, rl, rr, δ f is the front wheel steering angle, a x , a y are the longitudinal and lateral accelerations respectively; 22) Based on the model predictive control principle, establish the following performance index: where, N p is the prediction step length, Y ref is the reference output expected by the system, Y k is the prediction model output, U k is the predictive control output, U d is the steering and torque distribution expected by the driver, U k-1 is the output of the predictive control at the previous moment. The positive definite matrices Q, R, and T are weight matrix functions assigned to reflect the weights of various performance indicators in the total performance indicator. Q, R, and T are fixed constants or time-varying matrices; 23) Vehicle yaw rate reference value r d is as follows: where δ f is the front wheel steering angle, V x is the longitudinal speed, r is the yaw rate, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, μ is the friction coefficient, g is the acceleration due to gravity, K s is the understeer gradient, r d is the reference value of the vehicle yaw rate where K s is the understeer gradient, l f is the distance from the center of mass to the front axle, l r is the distance from the center of mass to the rear axle, m is the vehicle mass, K f is the cornering stiffness of the front wheels, K r is the cornering stiffness of the rear wheels; 24) When the tire slip ratio exceeds the slip ratio constraint λ co,i it is expressed using the tire angular velocity error as: where, e ωi,d is the angular velocity error of the tire, ω i is the angular velocity of each wheel tire, ω i,k-1 is the angular velocity of the tire at the (k-1)th moment of the wheel, V x is the longitudinal velocity, r d is the reference value of the vehicle yaw angular velocity, R is the effective rolling radius of the tire, t wf is the front wheelbase, λ co,i is the slip rate constraint.

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