A vehicle stability integrated control method based on dual stability envelope

Abstract

The present invention provides a vehicle stability integrated control method based on a dual stability envelope. This method constructs a dual stability envelope control framework using vehicle state soft constraints and actuator stability hard constraints. Vehicle instability conditions are mapped to actuator stability limits as actuator hard constraints. The dual stability envelope range is determined by combining vehicle state soft constraints with dynamic wheel posture updates and a stability boundary correction function, thereby balancing vehicle stability performance and controller computational complexity. The present invention proposes a wheel posture dynamic update method and a stability boundary correction function. The vehicle stability boundary is adjusted in real time based on driving conditions, driver input, and active safety system control input, improving the accuracy of the vehicle stability boundary description. A formula for actuator stability limits is derived based on the vehicle stability boundary. Vehicle instability conditions are mapped to actuator stability limits to determine the actuator stability envelope range. This prevents vehicle instability from a control input perspective and maximizes the vehicle stability boundary.

Description

Technical Field

[0001] The present invention relates to the field of vehicle handling stability control, and in particular to a vehicle stability integrated control method based on a dual stability envelope. Background Art

[0002] Envelope control ensures stability by keeping the vehicle within a safe region in state space. Because the boundaries of the stable state are unclear, traditional envelope control employs simple geometric structures for ease of solution. However, this sacrifices some of the stable region, making envelope control conservative and failing to fully utilize chassis performance. Given certain road conditions and driver inputs, vehicle stability depends on the control inputs to the active safety system. Previous research has often used actuator hardware capabilities as a constraint, but excessive actuator control inputs can lead to vehicle instability during actual driving.

[0003] How to balance vehicle stability performance and controller computational complexity and further expand the vehicle stability boundary is an urgent problem to be solved. Summary of the Invention

[0004] To address the aforementioned technical issues, the present invention provides a dual-stability envelope-based integrated vehicle stability control method. By combining vehicle state soft constraints with actuator stability hard constraints, a state-actuator dual-stability envelope control framework is constructed. Vehicle instability conditions are mapped to actuator stability limits as actuator hard constraints. The dual-stability envelope range is determined by combining vehicle state soft constraints that consider dynamic wheel posture updates and stability boundary correction functions, thereby balancing vehicle stability performance and controller computational complexity. The method comprises the following steps:

[0005] Step 1: Based on the driver and active safety system control inputs, the relationship between wheel camber angle, wheel hop, and tire longitudinal force is established using suspension (Kinematic & Compliance, K&C) characteristic test data. Combined with the body roll angle caused by active steering control and the tire longitudinal force generated by active drive / braking control, the influence of active steering control and active drive / braking control on wheel camber angle is obtained; based on the test data of tire peak lateral force and wheel camber angle under the combined rolling and side slip conditions, the correlation function between tire lateral effective adhesion coefficient and wheel camber angle under different road adhesion coefficients is obtained, and the correction coefficient of wheel posture change on vehicle stability domain boundary is designed; combined with the phase plane and control diagram, the dynamic relationship between the saddle point of the vehicle state trajectory and the peak sideslip angle and peak lateral force of the front and rear axle tires is analyzed, and a semi-empirical vehicle stability boundary correction function is established for the tire sideslip characteristics to accurately describe the front and rear axle tire sideslip angle and lateral force corresponding to the vehicle stability boundary; a preliminary range of the vehicle state stability envelope is formed considering the dynamic update of wheel posture and the stability boundary correction function;

[0006] Step 2: Based on the dynamic action mechanism and phase plane control effect of the active safety system, the phase plane is used to analyze the influence of the active safety system integrated control input type and numerical value on the vehicle state stable equilibrium point and saddle point position, and each active safety system control input is converted into a tire equivalent longitudinal force and a wheel equivalent steering angle to obtain a further improved stability boundary correction function. Combined with the preliminary range of the vehicle state stability envelope in step 1, the final range of the vehicle state stability envelope is formed; it is proposed that when the intersection points of different vehicle state stability boundaries coincide (that is, the phase plane state trajectory stable equilibrium point coincides with the saddle point), the vehicle becomes unstable, and the actuator stability limit value formula is established according to the vehicle stability boundary formula. The vehicle instability condition is mapped to the actuator stability limit value to determine the actuator stability envelope range;

[0007] Step 3: The vehicle state stability envelope is used as a soft constraint for stability control, and the actuator stability envelope is used as a hard constraint for stability control. These soft constraints are combined with the actuator stability constraints to form a state + actuator dual stability envelope control framework. The dual stability envelopes are updated in real time based on driving conditions, driver input, and active safety system control inputs, dynamically adjusting the vehicle stability control constraints.

[0008] Step 4: Based on the dual stability envelope control framework, the control strategy and control object are combined to form a vehicle stability integrated control method based on the dual stability envelope. The soft constraint of vehicle state stability control allows the vehicle to temporarily exceed the vehicle state stability envelope range to improve trajectory tracking capability. The hard constraint of actuator stability control strictly avoids the control input from exceeding the actuator stability envelope range to avoid vehicle instability.

[0009] Furthermore, the design method of step one is as follows:

[0010] First, for distributed drive electric vehicles, the lateral speed V y The vehicle uses the front wheel steering angle δ and the additional yaw moment M generated by the four-wheel hub motor as the control model. z , based on the small angle assumption, the vehicle lateral dynamics expression is:

[0011]

[0012] Where m is the vehicle mass, I z is the moment of inertia; a and b are the distances from the center of mass to the front and rear axles respectively; F yf and F yr are the lateral forces on the front and rear axles respectively; V x is the longitudinal velocity;

[0013] F yf and F yrObtained using a modified brush tire model that takes into account the applied longitudinal force and the variation in lateral force due to dynamic wheel camber:

[0014]

[0015] Where F y is the tire lateral force, C α is the tire's cornering stiffness, F x is the tire longitudinal force, μ is the road adhesion coefficient, F z is the vertical load on the tire, α is the tire slip angle, is the derating factor that represents the effect of the longitudinal force on the residual lateral force capacity based on the friction limit circle:

[0016]

[0017] ξ γ It is a correction factor that represents the effect of wheel camber angle on tire lateral effective adhesion coefficient;

[0018] Front and rear wheel slip angle α f and α r The calculation formula is as follows:

[0019]

[0020] By rotating around the current slip angle at each time step Iteratively linearize the tire force model to model the lateral force F y , we get the affine function of the sideslip angle:

[0021]

[0022] In the formula and Current slip angles Tire lateral force and cornering stiffness at ;

[0023] A proportional-integral-derivative controller and an optimal curvature-estimating driver model are used to track the desired longitudinal velocity and lateral position, respectively.

[0024] Then, by fitting a polynomial to the suspension K&C characteristic test data, the relationship between wheel camber angle, body roll angle, and tire longitudinal force was analyzed. Body roll causes the inner and outer wheels to hop in opposite directions. Within a certain range, the numerical relationship between the unilateral wheel hop z and the body roll angle is φ:

[0025]

[0026] Where d is the wheelbase;

[0027] Changing the wheel camber angle consists of two parts:

[0028]

[0029] Where y γ is the change in wheel camber angle; f γ-φ is the change in wheel camber angle caused by the body roll angle; is the change in wheel camber angle caused by the longitudinal force of the tire;

[0030] The polynomial fitting result of the relationship between wheel camber angle, body roll angle and tire longitudinal force is:

[0031]

[0032] The wheel camber angle will generate additional tire lateral force and affect the tire's lateral adhesion characteristics. The change in wheel camber angle changes the peak value of the tire lateral force and causes differences in the ability of the front and rear axle tires to provide lateral force, thereby affecting the vehicle's stability area and showing understeer or oversteer characteristics. Polynomial fitting is performed on tire test data to obtain the tire's effective lateral adhesion coefficient under different road adhesion coefficients. Functional relationship between ξ and wheel camber angle: γ =f(μ,γ)=0.0048μγ-0.0081γ+0.3012μ+0.5835, using this function to correct the vehicle stability region boundary at different wheel camber angles, where γ is the wheel camber angle, γ=-15°~15°;

[0033] The vehicle stability under cornering and combined driving / braking conditions is analyzed using a quasi-steady-state assumption, assuming that the vehicle speed remains constant over a short period of time. As the absolute value of the vehicle's longitudinal acceleration increases, the maximum steady-state lateral acceleration decreases, and the ω-β stability region narrows. The increasing oversteering characteristic of the vehicle leads to a decrease in lateral stability. The vehicle stability boundary formula, which considers the dynamic update of the wheel posture, is as follows:

[0034]

[0035] in, C ar is the cornering stiffness of the rear axle, L is the wheelbase, g is the acceleration of gravity, and since the boundary of the vehicle's stable region mainly depends on the characteristics of the rear axle tire, ξ r,γ and ξ r ,F x They are the rear axle γ Value and ξ Fx value;

[0036] Furthermore, the specific steps of step 2 are as follows:

[0037] Considering the vehicle's current operating conditions, including road adhesion, steering angle, and yaw rate, the longitudinal acceleration that causes the rear axle slip angle to reach its peak slip angle is defined as the limiting stable longitudinal acceleration. The impact of longitudinal acceleration on lateral stability is mainly reflected in the longitudinal vehicle speed, axle load transfer, and tire slip rate. Incorporating these factors into the limiting stable longitudinal acceleration equation, the implicit expression for the longitudinal acceleration stability limit is obtained as follows:

[0038]

[0039] Where a x,max is the longitudinal acceleration stability limit, Δt is the control step length, h g is the height of the center of mass;

[0040] Similarly, for the steering system, when the steering tire reaches saturation, further increasing the steering angle will not generate additional tire lateral force, but will instead cause the vehicle to lose control and deviate from its original direction of travel. Therefore, analyzing the vehicle's steering angle stability limit as a steering constraint helps prevent vehicle instability. Two boundaries of β are added to the above state stability envelope, determined by the front wheel sideslip angle and steering angle at peak tire force. The boundary inequalities are as follows:

[0041]

[0042] Where α f,sat and α above r,sat are the front and rear axle peak slip angles, respectively;

[0043] When the maximum yaw rate, rear axle slip angle, and front axle slip angle intersect the boundary line, the vehicle state transitions from stable to unstable. Any lateral disturbance to the vehicle will cause the system dynamics to change from stable to unstable. The corresponding steering angle at this time is the steering angle stability limit:

[0044]

[0045] Where δ max is the steering angle stability limit value, p1, p2, p3, p4, and p5 are the parameters of the stability boundary correction function, which are obtained by fitting the experimental data;

[0046] Analysis of the handling diagram shows that in the vehicle state corresponding to the saddle point, the front and rear axle tires do not reach their peak slip angles simultaneously, and the vehicle's stable lateral force limit is not equal to μmg. At the saddle point, the front axle slip angle is in an increasing region, while the rear axle slip angle is in a decreasing region, neither reaching its peak slip angle. A series of boundary correction functions are used to adjust the boundary position of the vehicle's stable region in response to changes in driving conditions and control inputs. The vehicle stability boundary is as follows:

[0047]

[0048] Where ω s is the yaw rate stability boundary, β fs is the front axle slip angle stability boundary, β rs is the rear axle slip angle stability boundary, ω s , β fs and β rs is the preliminary range of the vehicle state stability envelope considering the dynamic update of wheel posture and the stability boundary correction function in step 1; f1 is the yaw rate boundary correction function, f2 is the front axle slip angle boundary correction function, and f3 is the rear axle slip angle boundary correction function;

[0049] The above functions represent the maximum yaw rate and the minimum vehicle center of mass slip angle determined by the front and rear axle slip angles, respectively. The same principle applies to the correction of the other three extreme values ​​(minimum yaw rate and maximum vehicle center of mass slip angle determined by the front and rear axle slip angles). The boundary correction function is defined as:

[0050]

[0051] In terms of control objectives, the additional yaw moment causes the vehicle to yaw, shifting the stable equilibrium point toward a position in the phase plane with a larger center of mass slip angle and yaw velocity, similar in effect to the steering angle. In terms of controlled variables, the additional yaw moment is converted into four-wheel longitudinal force, reducing the tire's ability to provide lateral force and shrinking the vehicle's stable region in the phase plane, similar to the dynamic mechanism of longitudinal acceleration. Based on the similarities in the effects and mechanisms of the additional yaw moment, steering angle, and longitudinal acceleration, a method for deriving the stability limit of the additional yaw moment was determined. Based on the experimental data, a polynomial fitting was performed on the correction boundaries of yaw velocity, front axle slip angle, and rear axle slip angle, and the formula is expressed as follows:

[0052]

[0053] In the above formula, f4 and f5 are boundary correction functions that adjust the boundaries of the stable region as the additional yaw moment changes. They are defined as follows:

[0054]

[0055] Where d is the wheelbase, p6, p7, p8, p9, p 10 To stabilize the boundary correction function parameters, the values ​​are obtained by fitting the experimental data;

[0056] Finally, the additional yaw moment corresponding to the state trajectory bifurcation is the additional yaw moment stability limit value:

[0057]

[0058] Furthermore, the control strategy described in step 4 includes a hierarchical control strategy integrating steer-by-wire (SBW) and torque vector control (TVC) for distributed drive electric vehicles, utilizing a designed dual stability envelope to constrain the desired vehicle state and actuator inputs. The hierarchical control strategy includes:

[0059] Upper level control:

[0060] In order to effectively judge the degree of vehicle instability, the normalized vehicle stability evaluation index is defined as:

[0061]

[0062] Where λ is the normalized vehicle stability evaluation index, ω max and β max Obtained by modifying the boundary value of the ω-β stable region; q is the weight coefficient;

[0063] Based on the vehicle state stability envelope obtained in steps 1 and 2, combined with the normalized vehicle stability evaluation index, the phase plane is divided into three regions. Based on the relationship between the vehicle's current state and the boundaries of each region, it is determined whether the vehicle is in a stable, critically stable, or unstable region. Accordingly, the dynamic demand and control architecture are adaptively adjusted according to the current region: when λ<λ s , the vehicle state position is in the stable area, the dynamic requirements are economy and maneuverability, and the control architecture adopts SBW; when λ s ≤λ<λ cs , the vehicle state position is in the critical stability area, the dynamic requirements are maneuverability and stability, and the control architecture adopts SBW+TVC; when λ cs ≤λ, the vehicle state position is in the unstable area, the dynamic demand is stability, and the control architecture adopts SBW+TVC, where λ s is the boundary of the stable region, λ cs is the boundary of the critical stability region;

[0064] Based on model predictive control and the control-oriented linear time-varying vehicle dynamics model established above, an upper-level controller integrating SBW and TVC is designed; the vehicle dynamics equations are as follows:

[0065]

[0066] Convert the above vehicle model into state space form:

[0067]

[0068] Among them, the system state variable is X = [β ω] T , the control variable is U=[δ M z ] T ;

[0069] Using the forward Euler method, at sampling time t s Discretize the above formula to obtain the discrete state space form:

[0070]

[0071] Among them, A s (k) = I + AT, B s (k) = BT, C s (k) = C, d s (k) = dT;

[0072] Select the steady-state response as the reference yaw rate and center-of-mass slip angle; use the vehicle state stability region established by the results of steps 1 and 2 to limit the reference yaw rate and center-of-mass slip angle; when the reference value exceeds the stability region, it should be limited to the stability boundary:

[0073]

[0074] Among them, Y ref is the reference value, β ref is the reference value of the center of mass sideslip angle, ω ref is the yaw rate reference value, δ d The driver inputs the front wheel steering angle, ω s , β s are the yaw rate stability reference value and the center of mass sideslip angle stability reference value of the vehicle state stability region limit established using the results of step 1 and step 2, respectively.

[0075] Step 2 Result The actuator stability envelope is designed as the control variable constraint of the upper controller:

[0076]

[0077] The objective function of the controller is defined as follows:

[0078]

[0079] Based on the vehicle stability evaluation index λ, an adaptive adjustment scheme for the weight matrices Q and R is designed to meet the dynamic safety requirements and control architecture of different control areas. To avoid chattering, a hyperbolic tangent function is used to design the weight coefficient adaptive adjustment function. Taking R as an example:

[0080]

[0081] Where R is the weight matrix, η, ρ, R0, s, and λ0 are the parameters of the adaptive adjustment function of the weight coefficient, which are tuned by trial and error;

[0082] Then, the control problem is transformed into a quadratic programming problem; the first element Δu of the optimal control increment sequence is * (k) Applied to the vehicle as the actual control increment; the vehicle status is continuously updated, and rolling optimization is used to adjust the control variables to enhance the effectiveness of the integrated control;

[0083] Lower level control:

[0084] Tracking the required vehicle longitudinal force F based on the longitudinal velocity x , the additional yaw moment M generated by the upper controller z And the tire longitudinal force F generated by the hub motor xi The relationship between , a torque allocation method based on quadratic programming is introduced for real-time constraint optimization:

[0085]

[0086] Among them C i and Q i is the weight coefficient, F xi and F yi are the longitudinal and lateral forces of the four wheels, i = 1,…,4, representing the left front wheel, right front wheel, left rear wheel and right rear wheel respectively; df is the front axle track, dr is the rear axle track, T imax is the maximum torque of the hub motor, R w is the effective rolling radius of the wheel;

[0087] The first term of the objective function represents the deformed tire workload rate The first prevents one tire from saturating before the others, thereby avoiding vehicle instability; the second ensures that the wheel slip ratio remains within the appropriate range to prevent wheel locking.

[0088] Beneficial technical effects of the present invention:

[0089] (1) The state + actuator dual stable envelope control framework proposed in this invention avoids vehicle instability from the perspective of control input and maximizes the vehicle stability boundary;

[0090] (2) The wheel attitude change correction coefficient, stability boundary correction function, and actuator stability limit value formula derived by combining vehicle dynamics and test data are semi-empirical formulas and are all low-order formulas, thereby reducing the complexity of data processing while ensuring high accuracy;

[0091] (3) The wheel attitude dynamic update method and stability boundary correction function proposed in the present invention can adjust the vehicle stability boundary in real time according to the driving conditions, driver and active safety system control input, thereby improving the accuracy of the vehicle stability boundary description. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 Schematic diagram of the overall block diagram of the control method of the present invention;

[0093] Figure 2 Schematic diagram of vehicle dynamics model;

[0094] Figure 3 Comparison of suspension K&C characteristic test data and fitting curve results: Relationship between rear axle wheel camber angle and (a) wheel hop and (b) tire longitudinal force;

[0095] Figure 4 Comparison of tire adhesion ellipses under combined rolling, side-slip and side-slip conditions: (a) μ = 0.5, (b) μ = 1.0;

[0096] Figure 5 The tire lateral force and roll lateral force curve: F z =4kN,μ=1.0,F y =F yα +F yγ Among them F yα is the lateral force due to lateral deviation;

[0097] Figure 6 V is the vehicle ω-β phase plane diagram: x =10m / s,δ f =10°(a)μ r =0.9μ f ,μ f =0.55,(b)μ f =0.9μ r ,μ r =0.55;

[0098] Figure 7 The tire cornering characteristic curve for combined cornering and longitudinal slip conditions: μ = 0.85 (a) a x =0,(b)a x =-0.4g;

[0099] Figure 8 The ω-β phase plane diagram of a vehicle in a combined lateral and longitudinal slip condition: μ = 0.85(a)a x =0,(b)a x =-0.4g;

[0100] Figure 9 Schematic diagram of the vehicle's ω-β stability region boundary;

[0101] Figure 10 The tire cornering characteristic curve and handling diagram are as follows: (a) and (b) x = -0.2g, (c) and (d) a x =-0.4g;

[0102] Figure 11 for Iso-cline plot: V x =10m / s, μ=0.8 (a) δ = 0, (b) δ = 5°, (c) δ = 10°, (d) δ = 11°;

[0103] Figure 12 is the vehicle ω-β phase plane diagram and Iso-cline plot: V x =10m / s,μ=0.8(a) and (b)Mz=2kNm, (c) and (d)Mz=4kNm;

[0104] Figure 13 V is the vehicle ω-β phase plane diagram: x =20m / s, μ=0.4 (a) δ = -1.8°, (b) δ = 1.8°, (c) Mz = -650Nm, (d) Mz = 650Nm;

[0105] Figure 14 Schematic diagram of the vehicle stability integrated control system architecture based on dual stability envelope;

[0106] Figure 15 Results of simulation tests on high-speed double lane-changing conditions on low-adhesion roads: (a) vehicle trajectory, (b) longitudinal velocity, (c) sideslip angle of center of mass, (d) yaw rate, (e) steering angle, (f) additional yaw moment, and (g) trajectory tracking, stability, and additional yaw moment evaluation indicators. DETAILED DESCRIPTION

[0107] The present invention provides a vehicle stability integrated control method based on a dual stability envelope, comprising the following steps:

[0108] Step 1: Based on the driver and active safety system control inputs and the suspension K&C characteristic test data, the relationship between wheel camber angle, wheel hop, and tire longitudinal force is established. Combined with the body roll angle caused by active steering control and the tire longitudinal force generated by active drive / braking control, the influence of active steering control and active drive / braking control on wheel camber angle is obtained. Based on the test data of tire peak lateral force and wheel camber angle under the combined rolling and side-slip conditions, the correlation function between the tire lateral effective adhesion coefficient and wheel camber angle under different road adhesion coefficients is obtained, and the correction coefficient of the vehicle stability domain boundary due to wheel posture change is designed. Combined with the phase plane and control diagram, the dynamic relationship between the saddle point of the vehicle state trajectory and the peak sideslip angle and peak lateral force of the front and rear axle tires is analyzed. A semi-empirical vehicle stability boundary correction function is established based on the tire sideslip characteristics to accurately describe the front and rear axle tire sideslip angle and lateral force corresponding to the vehicle stability boundary. In summary, a preliminary range of the vehicle state stability envelope is formed considering the dynamic update of wheel posture and the stability boundary correction function. The specific method is as follows:

[0109] First, for distributed drive electric vehicles, the lateral speed V y , a plane bicycle model with yaw angular velocity ω is used as the control model, such as Figure 2 As shown; the vehicle uses the front wheel steering angle δ and the additional yaw moment M generated by the four-wheel hub motor z , based on the small angle assumption, the vehicle lateral dynamics expression is:

[0110]

[0111] Where m is the vehicle mass, I z is the moment of inertia; a and b are the distances from the center of mass to the front and rear axles respectively; F yf and F yr are the lateral forces on the front and rear axles respectively; V x is the longitudinal speed.

[0112] F yf and F yr Obtained using a modified brush tire model that takes into account the applied longitudinal force and the variation in lateral force due to dynamic wheel camber:

[0113]

[0114] Where F y is the tire lateral force, C α is the tire's cornering stiffness, F x is the tire longitudinal force, μ is the road adhesion coefficient, F z is the vertical load on the tire, α is the tire slip angle, is the derating factor that represents the effect of the longitudinal force on the residual lateral force capacity based on the friction limit circle:

[0115]

[0116] ξ γ It is a correction factor that represents the effect of wheel camber angle on tire lateral effective adhesion coefficient;

[0117] Front and rear wheel slip angle α f and α r The calculation formula is as follows:

[0118]

[0119] To reduce the computational complexity of the optimization problem, the nonlinear tire forces are linearized. To do this, the tire forces are linearized by taking the current slip angle Iteratively linearize the tire force model to model the lateral force F y , this linearized tire force model is an affine function of the sideslip angle:

[0120]

[0121] In the formula and Current slip angles Tire lateral force and cornering stiffness at ;

[0122] A proportional-integral-derivative controller and an optimal curvature prediction driver model are used to track the desired longitudinal velocity and lateral position, respectively.

[0123] The impact of various active safety systems on the vehicle's stability zone, as altered by tire adhesion, is crucial for accurate vehicle stability assessment and coordinated design of integrated controls. In an embodiment of the present invention, a study of the vehicle's stability envelope considering steer-by-wire (SBW) and torque vector control (TVC) is discussed.

[0124] When the body roll generated by front wheel steering, the tire driving / braking forces generated by driving / braking operations, and the K&C characteristics of the suspension are combined, the wheel camber angle changes. By fitting a polynomial to the suspension K&C characteristics test data, the relationship between the wheel camber angle, body roll angle, and tire longitudinal force was analyzed. Since the boundary of the vehicle's stable region is mainly determined by the rear axle tire characteristics, the results are as follows: Figure 2 shown.

[0125] The roll of the vehicle body will cause the inner and outer wheels to jump in opposite directions. Within a certain range, the numerical relationship between the unilateral wheel jump z and the vehicle body roll angle is φ:

[0126]

[0127] Where d is the wheelbase;

[0128] Changing the wheel camber angle consists of two parts:

[0129]

[0130] Where y γ is the change in wheel camber angle; f γ-φ is the change in wheel camber angle caused by the body roll angle; is the change in wheel camber angle caused by the longitudinal force of the tire;

[0131] The polynomial fitting result of the relationship between wheel camber angle, body roll angle and tire longitudinal force is:

[0132]

[0133] The wheel camber angle will generate additional tire lateral force and affect the tire lateral adhesion characteristics, such as Figure 3 As shown in Figure 2. The change of wheel camber angle changes the peak value of tire lateral force, as shown in Figure 2. Figure 4 As shown, it causes the difference in the ability of the front and rear axle tires to provide lateral force, thereby affecting the vehicle's stability area and showing understeering or oversteering characteristics, such as Figure 5 As shown. Polynomial fitting is performed on the tire test data to obtain the tire lateral effective adhesion coefficient under different road adhesion coefficients. The functional relationship between camber and wheel camber is shown in Table I. This function is used to modify the boundaries of the vehicle's stability region at different wheel camber angles. Through research on variable-geometry suspensions with active camber control, a camber angle range was selected, allowing the optimized vehicle state envelope to be applied to a wider range of research areas.

[0134] Table I

[0135]

[0136] Where γ is the wheel camber angle;

[0137] Compared to pure cornering, the primary factors affecting vehicle stability in combined cornering and driving / braking conditions are front-to-rear axle load transfer and wheel slip. Vehicle stability in these combined conditions is analyzed using a quasi-steady-state assumption, assuming that the vehicle speed remains constant over a short period of time. Figure 6 and 7The ω-β phase plane diagram and tire slip characteristic curves for different longitudinal accelerations are presented, where ω is the yaw rate and β is the axle slip angle. It can be seen that as the absolute value of the vehicle's longitudinal acceleration increases, the maximum steady-state lateral acceleration decreases, and the ω-β stability region narrows. The vehicle's increasing oversteer behavior leads to a decrease in lateral stability. The vehicle stability boundary formula, which takes into account the dynamic updating of wheel attitude, is as follows:

[0138]

[0139] in, C ar is the cornering stiffness of the rear axle, L is the wheelbase, g is the acceleration of gravity, and since the boundary of the vehicle's stable region mainly depends on the characteristics of the rear axle tire, ξ r,γ and ξ r,Fx They are the rear axle γ Value and ξ Fx value.

[0140] Step 2: Based on the dynamic action mechanism of the active safety system and the phase plane control effect, the phase plane is used to analyze the influence of the active safety system integrated control input type and numerical value on the vehicle state stable equilibrium point and saddle point position. Each active safety system control input is converted into an equivalent tire longitudinal force and an equivalent wheel steering angle to obtain a further improved stability boundary correction function. Combined with the preliminary range of the vehicle state stability envelope obtained in step 1, the final range of the vehicle state stability envelope is formed. It is proposed that when the intersection points of different vehicle state stability boundaries coincide (that is, the phase plane state trajectory stable equilibrium point coincides with the saddle point), the vehicle becomes unstable. Based on the vehicle stability boundary formula, the actuator stability limit value formula is established, and the vehicle instability condition is mapped to the actuator stability limit value to determine the actuator stability envelope range. The specific steps are as follows:

[0141] For the drive / brake system, due to the vehicle's lateral-longitudinal coupled dynamics, excessive control requirements for longitudinal acceleration will indirectly reduce the vehicle's ability to maintain lateral stability. The control diagram is used to analyze the inherent mechanism of vehicle instability caused by longitudinal acceleration. Figure 10 As shown in , it indicates that as the absolute value of the longitudinal acceleration increases, the distance between the two saddle points representing the vehicle's stable region decreases, and the rear wheel slip angle corresponding to the saddle point always exceeds the peak slip angle. Therefore, considering the vehicle's current operating conditions, including road adhesion, steering angle, and yaw rate, the longitudinal acceleration that causes the rear axle slip angle to reach the peak slip angle is defined as the limiting stable longitudinal acceleration. The impact of longitudinal acceleration on lateral stability is primarily reflected in longitudinal vehicle speed, axle load transfer, and tire slip rate. Incorporating these factors into the limiting stable longitudinal acceleration equation, the implicit expression for the longitudinal acceleration stability limit is obtained as:

[0142]

[0143] Where a x,max is the longitudinal acceleration stability limit, Δt is the control step length, h g is the height of the center of mass;

[0144] Similarly, for the steering system, when the steering tire reaches saturation, further increasing the steering angle will not generate additional tire lateral force, but will cause the vehicle to lose control and deviate from the original driving direction. Therefore, analyzing the vehicle steering angle stability limit as a steering constraint is helpful to prevent vehicle instability, such as Figure 11 As shown, two boundaries of β are added to the above state stability envelope, which are determined by the front wheel sideslip angle and steering angle at the peak tire force. The inequalities of the boundaries are as follows:

[0145]

[0146] Where α f,sat and α above r,sat are the front and rear axle peak slip angles, respectively;

[0147] Figure 11 The figure shows the variation of the iso-slope geometry of the yaw acceleration with the steering angle, and the dashed lines represent the iso-slopes with constant yaw acceleration. There is an equilibrium point at the isocline, and its trajectory is given by The geometry of the zero slope is determined. At the same time, the vehicle equilibrium point lies on the straight line between point A and point B (the intersection of the front and rear axle slip angle boundaries), which is a linear approximation of the zero slope. For a given speed and friction coefficient, only the boundary associated with the extreme value of the front axle slip angle moves, while the overall shape of the isocline remains unchanged. However, the position of the isocline on the phase plane shifts toward higher center of mass slip angles and yaw rates. When point A or point B coincides with the saddle point, that is, when the maximum yaw rate, rear axle slip angle and front axle slip angle boundary intersect, the vehicle state transitions from stable to unstable, and any lateral disturbance to the vehicle will cause the system dynamics to change from stable to unstable. The corresponding steering angle at this time is the steering angle stability limit:

[0148]

[0149] Where δ maxis the steering angle stability limit, and p1, p2, p3, p4, and p5 are the parameters of the stability boundary correction function. Experimental data fitting and control diagram analysis indicate that, in the vehicle state corresponding to the saddle point, the front and rear axle tires do not reach their peak slip angles simultaneously. Therefore, the vehicle's stable lateral force limit is not equal to μmg. At the saddle point, the front axle slip angle is in the increasing region, while the rear axle slip angle is in the decreasing region, neither reaching its peak slip angle. Therefore, the present invention designs a series of boundary correction functions to adjust the boundaries of the vehicle's stability region in response to changes in driving conditions and control inputs. The vehicle stability boundaries are as follows:

[0150]

[0151] Where ω s is the yaw rate stability boundary, β fs is the front axle slip angle stability boundary, β rs is the rear axle slip angle stability boundary, ω s , β fs and β rs is the preliminary range of the vehicle state stability envelope considering the dynamic update of wheel posture and the stability boundary correction function in step 1; f1 is the yaw rate boundary correction function, f2 is the front axle slip angle boundary correction function, and f3 is the rear axle slip angle boundary correction function;

[0152] The above functions represent the maximum yaw rate and the minimum vehicle center of mass slip angle determined by the front and rear axle slip angles, respectively. The same principles apply to the correction of the other three extreme values ​​(minimum yaw rate and maximum vehicle center of mass slip angle determined by the front and rear axle slip angles), so they will not be repeated here. The boundary correction function is defined as:

[0153]

[0154] Since the control objective and the control variable involve direct control of the longitudinal and lateral degrees of freedom of the vehicle, it is more complicated to determine the stability limit of the additional yaw moment. In terms of the control objective, the additional yaw moment causes the yaw motion of the vehicle, and the stable equilibrium point shifts to the position with larger sideslip angle and yaw rate in the phase plane, such as Figure 12 As shown in (a) and (c), its effect is similar to that of the steering angle. In terms of control variables, the additional yaw moment is converted into four-wheel longitudinal force, which reduces the ability of the tire to provide lateral force and reduces the range of the vehicle stability area in the phase plane, as shown in Figure 12 As shown in (a) and (c), the dynamic mechanism is similar to that of longitudinal acceleration.

[0155] Based on the similarity between the additional yaw moment and the steering angle and longitudinal acceleration in terms of effect and mechanism, the derivation method of the additional yaw moment stability limit value is determined. Figure 12(b) and (d) show that as the additional yaw moment increases, the stable equilibrium point moves along the yaw angular acceleration zero slope until it coincides with the saddle point, causing the vehicle to become unstable. Figure 12 In the figure, the black dotted line represents M z = 0, and the red dotted line indicates the boundary of the yaw rate and the sideslip angle of the front and rear axles. z The main reasons for the boundary position changes are as follows: 1. The longitudinal tire force that generates the additional yaw moment reduces the maximum achievable yaw rate; 2. The additional yaw moment has a similar effect on vehicle motion as the steering angle and tire slip angle, resulting in an equivalent turning radius. Therefore, based on the test data, a polynomial fit is performed to correct the boundaries of yaw rate, front axle slip angle, and rear axle slip angle. The formula is expressed as follows:

[0156] In the above formula, f4 and f5 are boundary correction functions that adjust the boundaries of the stable region as the additional yaw moment changes. They are defined as follows:

[0157]

[0158] Where d is the wheelbase, p6, p7, p8, p9, p 10 To stabilize the boundary correction function parameters, the values ​​are obtained by fitting the experimental data;

[0159] Finally, the additional yaw moment corresponding to the state trajectory bifurcation is the additional yaw moment stability limit value:

[0160]

[0161] The present invention verifies the accuracy of the front wheel steering angle stability limit and the additional yaw moment stability limit. Based on the test data, the least squares algorithm is used to fit the parameters in the boundary correction function, and to prevent vehicle instability, the actuator limit is multiplied by the stability factor ξ s =0.95.

[0162] like Figure 13 As shown in the figure, for a given road adhesion coefficient and vehicle speed, the actuator input calculated using the proposed actuator stability limit formula results in a stable equilibrium point very close to the saddle point, causing the vehicle to approach instability. These operating conditions verify the high accuracy of the proposed actuator stability limit formula. Furthermore, the actuator stability limit is solved using linear and quadratic functions, which reduces the computational burden.

[0163] Step three, such as Figure 14As shown in the figure, the vehicle state stability envelope range is used as a soft constraint for stability control, and the actuator stability envelope range is used as a hard constraint for stability control. The vehicle state stability control soft constraint and the actuator stability control hard constraint are combined to form a state + actuator dual stability envelope control framework. The dual stability envelope range is updated in real time according to driving conditions, driver and active safety system control inputs, and the vehicle stability control constraints are dynamically adjusted.

[0164] Step 4: Based on the dual stability envelope control framework, the control strategy and the control object are combined to form a vehicle stability integrated control method based on the dual stability envelope. The vehicle state stability control soft constraint allows the vehicle to temporarily exceed the vehicle state stability envelope range to improve the trajectory tracking capability. The actuator stability control hard constraint strictly prevents the control input from exceeding the actuator stability envelope range to avoid vehicle instability. The control strategy includes: a hierarchical control strategy integrating the SBW and the torque vector control TVC of a distributed drive electric vehicle, such as Figure 14 As shown in Figure 2, the designed dual stable envelope is used to constrain the desired vehicle state and actuator input. The hierarchical control strategy includes:

[0165] Upper level control:

[0166] In order to effectively judge the degree of vehicle instability, the normalized vehicle stability evaluation index is defined as:

[0167]

[0168] Where λ is a parameter, ω max and β max It is obtained by modifying the boundary value of the ω-β stable region. q is the weight coefficient. Considering the vehicle safety requirements, q = 0.55 is selected.

[0169] According to the vehicle state stability envelope obtained in step 1 and step 2, combined with the normalized vehicle stability evaluation index, the phase plane is divided into three regions, such as Figure 9 As shown in Table II, based on the relationship between the vehicle's current state and the boundaries of each region, it is possible to determine whether the vehicle is in a stable, critically stable, or unstable region. Accordingly, the dynamic requirements and control architecture are adaptively adjusted based on the current region, as shown in Table II.

[0170] Table II

[0171]

[0172] where λ s is the boundary of the stable region, λ cs is the boundary of the critical stability region;

[0173] Based on model predictive control and the control-oriented linear time-varying vehicle dynamics model established above, an upper-level controller integrating SBW and TVC is designed; the vehicle dynamics equations are as follows:

[0174]

[0175] Convert the above vehicle model into state space form:

[0176]

[0177] Among them, the system state variable is X = [β ω] T , the control variable is U=[δ M z ] T .

[0178] Using the forward Euler method, at sampling time t s Discretize the above formula to obtain the discrete state space form:

[0179]

[0180] Among them, A s (k) = I + AT, B s (k) = BT, C s (k) = C, d s (k) = dT.

[0181] The steady-state response is selected as the reference yaw rate and slip angle. However, defining these reference values ​​solely based on the linear cornering stiffness may result in excessively large values, leading to vehicle instability. Therefore, the reference yaw rate and slip angle are constrained using the vehicle stability region established by the results of steps 1 and 2. When the reference values ​​exceed the stability region, they are constrained to the stability boundary.

[0182]

[0183] Among them, Y ref is the reference value, β ref is the reference value of the center of mass sideslip angle, ω ref is the yaw rate reference, δ d The driver inputs the front wheel steering angle, ω s , β s are the yaw rate and center of mass sideslip angle stability reference values ​​of the vehicle state stability region limit established using the results of step 1 and step 2, respectively.

[0184] The results of step 2 are as follows: The actuator stability envelope is designed as the control variable constraint of the upper controller to provide additional safety guarantee for stable control.

[0185]

[0186] The objective function of the controller is defined as follows:

[0187]

[0188] Based on the vehicle stability evaluation index λ, an adaptive adjustment scheme for the weight matrices Q and R is designed to meet the dynamic safety requirements and control architecture of different control areas. To avoid chattering, a hyperbolic tangent function is used to design the weight coefficient adaptive adjustment function. Taking R as an example:

[0189]

[0190] Where R is the weight matrix, η, ρ, R0, s, and λ0 are the parameters of the adaptive adjustment function of the weight coefficient, which are tuned by trial and error;

[0191] Then, the control problem is transformed into a quadratic programming problem; the first element Δu of the optimal control increment sequence is * (k) Applied to the vehicle as the actual control increment; the vehicle status is continuously updated, and rolling optimization is used to adjust the control variables to enhance the effectiveness of the integrated control.

[0192] Lower level control:

[0193] The present invention designs an optimal torque distribution controller that considers both lateral and longitudinal control requirements. x , the additional yaw moment M generated by the upper controller z And the tire longitudinal force F generated by the hub motor xi The relationship between , a torque allocation method based on quadratic programming is introduced for real-time constraint optimization:

[0194]

[0195] Among them C i and Q i is the weight coefficient, F xi and F yi are the longitudinal and lateral forces of the four wheels, i = 1,…,4, representing the left front wheel, right front wheel, left rear wheel and right rear wheel respectively; df is the front axle track, dr is the rear axle track, T ima x is the maximum torque of the hub motor, R w is the effective rolling radius of the wheel;

[0196] The first term of the objective function represents the deformed tire workload rate It prevents one tire from saturating before the others, thus avoiding vehicle instability; the second ensures that the wheel slip ratio remains within the appropriate range, preventing the wheels from locking.

[0197] The following specific experiments verify the authenticity and effectiveness of the present invention:

[0198] To verify the effectiveness of the vehicle stability integrated control method based on dual stability envelopes in this paper, a simulation test of a high-speed double lane change on a low-adhesion road was conducted on the MATLAB / Simulink simulation platform. The high-speed double lane change on a low-adhesion road is a typical collision avoidance scenario. The tire-road friction coefficient is μ = 0.4, and the longitudinal speed reference value is V x =90km / h, refer to ISO-3888-1; the vehicle model is an eight-degree-of-freedom vehicle dynamics model, which includes four degrees of freedom: longitudinal, lateral, roll, and yaw, as well as the rotational freedom of the four wheels.

[0199] In order to verify the superiority of the controller proposed in this invention (controller A), it is compared with the commonly used stability controller based on model predictive control (controller B). Controller B uses the limit adhesion μF z The vehicle state constraints and the actuator constraints of the fixed hardware structure execution capability are considered. In addition, to verify the robustness of the controller to the controller parameters, three sets of controller parameters were selected. Finally, to evaluate the trajectory tracking and stability control capabilities of different controllers, the trajectory tracking, stability, and actuator mean error evaluation indicators were defined as follows:

[0200]

[0201] Among them, J path , J stad , is the trajectory tracking, stability and average error evaluation index of the actuator, y real 、y ref is the true value and reference of the lateral position, V x,real 、V x,ref are the true value and reference value of longitudinal velocity, ω real 、ω ref is the true value and reference value of yaw angular velocity, β real , β ref is the true value and reference value of the vehicle center of mass side slip angle, M z,upper is the output value of the upper controller, t f is the duration of the simulation test.

[0202] The results are as follows Figure 15 The simulation results show that controller A always maintains satisfactory stability and trajectory tracking performance. Controller B is highly sensitive to controller parameters. Figure 15In (a)-(d), the vehicle may even become unstable. This is because controller B does not consider the dynamic impact of the active safety system on the tire adhesion characteristics under the state constraint, and lacks the correction of the vehicle stability boundary. Ideally, the use of extreme adhesion results in a vehicle state constraint range that is too large and cannot be used as an effective constraint. In order to accurately track the desired trajectory during sharp turns, controller B continuously increases the control variables, such as Figure 15 As shown in (e) and (f), when the actuator exceeds the stability constraint but has not yet reached the hardware capability constraint, the vehicle stability deteriorates and the trajectory tracking accuracy decreases. Controller A prioritizes stability control to ensure that the steering angle and additional yaw moment always remain within the actuator stability envelope to ensure vehicle stability. At the same time, the vehicle state soft constraint allows controller A to temporarily exceed the vehicle state stability envelope to optimize trajectory tracking. In addition, for different controller parameters, the stability and trajectory tracking performance indicators of controller A are better than those of controller B, as shown in Figure 2. Figure 15 (g) The method proposed in this invention enhances the robustness of the controller and reduces the workload of parameter calibration. In addition, considering the coupling characteristics between active safety systems under actuator constraints, controller A effectively achieves the expected additional yaw torque output, while controller B Figure 15 There is a large error in (g).

Claims

1. A vehicle stability integrated control method based on a dual stability envelope, characterized by: The following steps are involved: Step 1: Based on the driver and active safety system control inputs, the relationship between wheel camber angle, wheel hop, and tire longitudinal force is established using suspension K&C characteristic test data. Combined with the body roll angle caused by active steering control and the tire longitudinal force generated by active drive / braking control, the influence of active steering control and active drive / braking control on wheel camber angle is obtained. Based on the test data of tire peak lateral force and wheel camber angle under the combined rolling and side-slip conditions, the correlation function between tire lateral effective adhesion coefficient and wheel camber angle under different road adhesion coefficients is obtained, and the correction coefficient of wheel posture change on vehicle stability domain boundary is designed. Combined with the phase plane and control diagram, the dynamic relationship between the saddle point of the vehicle state trajectory and the peak sideslip angle and peak lateral force of the front and rear axle tires is analyzed. A semi-empirical vehicle stability boundary correction function is established for the tire sideslip characteristics to accurately describe the front and rear axle tire sideslip angle and lateral force corresponding to the vehicle stability boundary. A preliminary range of the vehicle state stability envelope is formed considering the dynamic update of wheel posture and the stability boundary correction function. Step 2: Based on the dynamic action mechanism and phase plane control effect of the active safety system, the phase plane is used to analyze the influence of the active safety system integrated control input type and numerical value on the vehicle state stable equilibrium point and saddle point position, and each active safety system control input is converted into the tire equivalent longitudinal force and wheel equivalent steering angle to obtain a further improved stability boundary correction function. Combined with the preliminary range of the vehicle state stability envelope in step 1, the final range of the vehicle state stability envelope is formed; it is proposed that the vehicle is unstable when the intersection points of different vehicle state stability boundaries coincide, and the actuator stability limit value formula is established based on the vehicle stability boundary formula. The vehicle instability condition is mapped to the actuator stability limit value to determine the actuator stability envelope range; Step 3: The vehicle state stability envelope is used as a soft constraint for stability control, and the actuator stability envelope is used as a hard constraint for stability control. These soft constraints are combined with the actuator stability constraints to form a state + actuator dual stability envelope control framework. The dual stability envelopes are updated in real time based on driving conditions, driver input, and active safety system control inputs, dynamically adjusting the vehicle stability control constraints. Step 4: Based on the dual stability envelope control framework, the control strategy and control object are combined to form a vehicle stability integrated control method based on the dual stability envelope. The soft constraint of vehicle state stability control allows the vehicle to temporarily exceed the vehicle state stability envelope range to improve trajectory tracking capability. The hard constraint of actuator stability control strictly avoids the control input from exceeding the actuator stability envelope range to avoid vehicle instability.

2. The vehicle stability integrated control method based on dual stability envelope according to claim 1, characterized in that: The design method for step one is as follows: First, for distributed drive electric vehicles, the lateral speed V y The vehicle uses the front wheel steering angle δ and the additional yaw moment M generated by the four-wheel hub motor as the control model. z , based on the small angle assumption, the vehicle lateral dynamics expression is: Where m is the vehicle mass, I z is the moment of inertia; a and b are the distances from the center of mass to the front and rear axles respectively; F yf and F yr are the lateral forces on the front and rear axles respectively; V x is the longitudinal velocity; F yf and F yr Obtained using a modified brush tire model that takes into account the applied longitudinal force and the variation in lateral force due to dynamic wheel camber: Where F y is the tire lateral force, C α is the tire's cornering stiffness, F x is the tire longitudinal force, μ is the road adhesion coefficient, F z is the vertical load on the tire, α is the tire slip angle, is the derating factor that represents the effect of the longitudinal force on the residual lateral force capacity based on the friction limit circle: ξ γ It is a correction factor that represents the effect of wheel camber angle on tire lateral effective adhesion coefficient; Front and rear wheel slip angle α f and α r The calculation formula is as follows: By rotating around the current slip angle at each time step Iteratively linearize the tire force model to model the lateral force F y , we get the affine function of the sideslip angle: In the formula and Current slip angles Tire lateral force and cornering stiffness at ; A proportional-integral-derivative controller and an optimal curvature-estimating driver model are used to track the desired longitudinal velocity and lateral position, respectively. Then, by fitting a polynomial to the suspension K&C characteristic test data, the relationship between wheel camber angle, body roll angle, and tire longitudinal force was analyzed. Body roll causes the inner and outer wheels to hop in opposite directions. Within a certain range, the numerical relationship between the unilateral wheel hop z and the body roll angle is φ: Where d is the wheelbase; Changing the wheel camber angle consists of two parts: Where y γ is the change in wheel camber angle; f γ-φ is the change in wheel camber angle caused by the body roll angle; is the change in wheel camber angle caused by the longitudinal force of the tire; The polynomial fitting result of the relationship between wheel camber angle, body roll angle and tire longitudinal force is: Perform polynomial fitting on tire test data to obtain the tire lateral effective adhesion coefficient under different road adhesion coefficients. Functional relationship between ξ and wheel camber angle: γ =f(μ,γ)=0.0048μγ-0.0081γ+0.3012μ+0.5835, using this function to correct the vehicle stability region boundary at different wheel camber angles, where γ is the wheel camber angle, γ=-15°~15°; The vehicle stability under cornering and combined driving / braking conditions is analyzed using a quasi-steady-state assumption, assuming that the vehicle speed remains constant over a short period of time. As the absolute value of the vehicle's longitudinal acceleration increases, the maximum steady-state lateral acceleration decreases, and the ω-β stability region narrows. The increasing oversteering characteristic of the vehicle leads to a decrease in lateral stability. The vehicle stability boundary formula, which considers the dynamic update of the wheel posture, is as follows: in, C αr is the cornering stiffness of the rear axle, L is the wheelbase, g is the acceleration of gravity, and since the boundary of the vehicle's stable region mainly depends on the characteristics of the rear axle tire, ξ r,γ and ξ r,Fx They are the rear axle γ Value and ξ Fx value.

3. The vehicle stability integrated control method based on dual stability envelope according to claim 1, characterized in that: Step 2 includes the following steps: Considering the vehicle's current operating conditions, including road adhesion, steering angle, and yaw rate, the longitudinal acceleration that causes the rear axle slip angle to reach its peak slip angle is defined as the limiting stable longitudinal acceleration. The impact of longitudinal acceleration on lateral stability is mainly reflected in the longitudinal vehicle speed, axle load transfer, and tire slip rate. Incorporating these factors into the limiting stable longitudinal acceleration equation, the implicit expression for the longitudinal acceleration stability limit is obtained as follows: Where a x,max is the longitudinal acceleration stability limit, Δt is the control step length, h g is the height of the center of mass; The vehicle steering angle stability limit is analyzed as a steering constraint to prevent vehicle instability. Two boundaries of β are added to the above state stability envelope, which are determined by the front wheel sideslip angle and steering angle at peak tire force. The boundary inequalities are as follows: Formula α f,sat and α above r,sat are the front and rear axle peak slip angles, respectively; When the maximum yaw rate, rear axle slip angle, and front axle slip angle intersect the boundary line, the vehicle state transitions from stable to unstable. Any lateral disturbance to the vehicle will cause the system dynamics to change from stable to unstable. The corresponding steering angle at this time is the steering angle stability limit: Where δ max is the steering angle stability limit value, p1, p2, p3, p4, and p5 are the parameters of the stability boundary correction function, which are obtained by fitting the experimental data; Analysis of the handling diagram shows that in the vehicle state corresponding to the saddle point, the front and rear axle tires do not reach their peak slip angles simultaneously, and the vehicle's stable lateral force limit is not equal to μmg. At the saddle point, the front axle slip angle is in an increasing region, while the rear axle slip angle is in a decreasing region, neither reaching its peak slip angle. A series of boundary correction functions are used to adjust the boundary position of the vehicle's stable region in response to changes in driving conditions and control inputs. The vehicle stability boundary is as follows: Where ω s is the yaw rate stability boundary, β fs is the front axle slip angle stability boundary, β rs is the rear axle slip angle stability boundary, ω s , β fs and β rs is the preliminary range of the vehicle state stability envelope considering the dynamic update of wheel posture and the stability boundary correction function in step 1; f1 is the yaw rate boundary correction function, f2 is the front axle slip angle boundary correction function, and f3 is the rear axle slip angle boundary correction function; The boundary correction function is defined as: In terms of control objectives, the additional yaw moment causes the vehicle to yaw, shifting the stable equilibrium point to a position in the phase plane where the center of mass slip angle and yaw rate are larger. This has an effect similar to that of the steering angle. In terms of control variables, the additional yaw moment is converted into four-wheel longitudinal force, reducing the tire's ability to provide lateral force and shrinking the vehicle's stable region in the phase plane, similar to the dynamic mechanism of longitudinal acceleration. Based on the test data, a polynomial fitting is performed on the correction boundaries of the yaw rate, front axle slip angle, and rear axle slip angle. The formula is expressed as follows: In the above formula, f4 and f5 are boundary correction functions that adjust the boundaries of the stable region as the additional yaw moment changes. They are defined as follows: Where d is the wheelbase, p6, p7, p8, p9, p 10 To stabilize the boundary correction function parameters, the values ​​are obtained by fitting the experimental data; Finally, the additional yaw moment corresponding to the state trajectory bifurcation is the additional yaw moment stability limit value:

4. The vehicle stability integrated control method based on dual stability envelope according to claim 1, characterized in that: The control strategy described in step 4 includes a hierarchical control strategy integrating steer-by-wire (SBW) and torque vector control (TVC) for distributed drive electric vehicles, utilizing a dual stability envelope to constrain desired vehicle states and actuator inputs. The hierarchical control strategy includes: Upper level control: In order to effectively judge the degree of vehicle instability, the normalized vehicle stability evaluation index is defined as: Where λ is the normalized vehicle stability evaluation index, ω max and β max Obtained by modifying the boundary value of the ω-β stable region; q is the weight coefficient; Based on the vehicle state stability envelope obtained in steps 1 and 2, combined with the normalized vehicle stability evaluation index, the phase plane is divided into three regions. Based on the relationship between the vehicle's current state and the boundaries of each region, it is determined whether the vehicle is in a stable, critically stable, or unstable region. Accordingly, the dynamic demand and control architecture are adaptively adjusted according to the current region: when λ<λ s , the vehicle state position is in the stable area, the dynamic requirements are economy and maneuverability, and the control architecture adopts SBW; when λ s ≤λ<λ cs , the vehicle state position is in the critical stability area, the dynamic requirements are maneuverability and stability, and the control architecture adopts SBW+TVC; when λ cs ≤λ, the vehicle state position is in the unstable area, the dynamic demand is stability, and the control architecture adopts SBW+TVC, where λ s is the boundary of the stable region, λ cs is the boundary of the critical stability region; Based on model predictive control and the control-oriented linear time-varying vehicle dynamics model established above, an upper-level controller integrating SBW and TVC is designed; the vehicle dynamics equations are as follows: Convert the above vehicle model into state space form: Among them, the system state variable is X = [β ω] T , the control variable is U=[δ M z ] T ; Using the forward Euler method, at sampling time t s Discretize the above formula to obtain the discrete state space form: Among them, A s (k) = I + AT, B s (k) = BT, C s (k) = C, d s (k) = dT; Select the steady-state response as the reference yaw rate and center-of-mass slip angle; use the vehicle state stability region established by the results of steps 1 and 2 to limit the reference yaw rate and center-of-mass slip angle; when the reference value exceeds the stability region, it should be limited to the stability boundary: Among them, Y ref is the reference value, β ref is the reference value of the center of mass sideslip angle, ω ref is the yaw rate reference value, δ d The driver inputs the front wheel steering angle, ω s , β s are the yaw rate stability reference value and the center of mass sideslip angle stability reference value of the vehicle state stability region limit established using the results of step 1 and step 2, respectively. Step 2 Result The actuator stability envelope is designed as the control variable constraint of the upper controller: The objective function of the controller is defined as follows: Based on the vehicle stability evaluation index λ, an adaptive adjustment scheme for the weight matrices Q and R is designed to meet the dynamic safety requirements and control architecture of different control areas. To avoid chattering, a hyperbolic tangent function is used to design the weight coefficient adaptive adjustment function. Taking R as an example: Where R is the weight matrix, η, ρ, R0, s, and λ0 are the parameters of the adaptive adjustment function of the weight coefficient, which are tuned by trial and error; Then, the control problem is transformed into a quadratic programming problem; the first element Δu of the optimal control increment sequence is * (k) Applied to the vehicle as the actual control increment; the vehicle status is continuously updated, and rolling optimization is used to adjust the control variables to enhance the effectiveness of the integrated control; Lower level control: Tracking the required vehicle longitudinal force F based on the longitudinal velocity x , the additional yaw moment M generated by the upper controller z And the tire longitudinal force F generated by the hub motor xi The relationship between , a torque allocation method based on quadratic programming is introduced for real-time constraint optimization: Among them C i and Q i is the weight coefficient, F xi and F yi are the longitudinal and lateral forces of the four wheels, i = 1,…,4, representing the left front wheel, right front wheel, left rear wheel and right rear wheel respectively; df is the front axle track, dr is the rear axle track, T imax is the maximum torque of the hub motor, R w is the effective rolling radius of the wheel; The first term of the objective function represents the deformed tire workload rate The first prevents one tire from saturating before the others, thereby avoiding vehicle instability; the second ensures that the wheel slip ratio remains within the appropriate range to prevent wheel locking.

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