Distributed driving electric vehicle multi-actuator coordination control method based on phase plane

Abstract

The invention discloses a phase plane-based distributed driving electric vehicle multi-actuator coordination control method, which belongs to the technical field of electric vehicle control, and comprises the following steps of: establishing a vehicle model and a trajectory tracking model; a phase plane stability domain boundary of vehicle driving is dynamically divided by adopting a double-line method and a vehicle speed and road adhesion coefficient, a vehicle instability factor is calculated, a transition area proportion is adjusted by utilizing fuzzy logic, and trajectory tracking and stability target judgment are carried out; dividing a linear region, a transition region and a saturation region according to the tire lateral deviation characteristics, and distributing AFS and DYC weights by adopting a Sigmoid function; and coordination of a control target and control of multiple actuators are carried out based on the weight parameters in the step S2 and the step S3. By the adoption of the method, smooth switching and weight optimization of the AFS and the DYC are achieved through dynamic stability domain division, fuzzy logic boundary adjustment and tire side deviation characteristic analysis, and finally coordinated control over the multiple controllers is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of electric vehicle control, and particularly to a multi-actuator coordinated control method for distributed drive electric vehicles based on the phase plane. Background Art

[0002] With the development of new energy vehicles and autonomous driving technologies, DDEV has become an ideal platform for improving vehicle handling stability due to its advantages such as high transmission efficiency and independently controllable tire driving torque. However, currently in terms of vehicle stability judgment and division, the phase plane is mainly used to judge whether the vehicle is in a stable region, without considering the change of the stable transition boundary under different driving conditions and lacking accurate quantitative indicators. In terms of actuator control quantities, AFS (Active Front-wheel Steering) and DYC (Direct Yaw-moment Control) are common strategies for electric vehicle trajectory tracking and stability control. AFS is used for trajectory tracking and DYC is used for stability control. However, both AFS and DYC can achieve vehicle steering for trajectory tracking and can also change the vehicle driving state for stability control. Currently, in the actuator control of AFS and DYC, single-input control is mostly carried out according to the control target, with less consideration of adjusting according to the characteristics of the actuator itself and lacking a research method for multi-input control of the control target. Summary of the Invention

[0003] The purpose of the present invention is to provide a multi-actuator coordinated control method for distributed drive electric vehicles based on the phase plane to solve the problems mentioned in the background art.

[0004] To achieve the above purpose, the present invention provides a multi-actuator coordinated control method for distributed drive electric vehicles based on the phase plane, and the steps include:

[0005] S1. Establish a vehicle model and a trajectory tracking model;

[0006] S2. Use the double-line method and the dynamic relationship between vehicle speed and road surface adhesion coefficient to divide the boundary of the stable region of the phase plane in which the vehicle travels, calculate the vehicle instability factor, and use fuzzy logic to adjust the proportion of the transition region to judge the trajectory tracking and stability targets;

[0007] S3. Divide the linear region, transition region and saturation region according to the tire side slip characteristics, and use the Sigmoid function to allocate the weights of AFS and DYC;

[0008] S4. Based on the weight parameters in steps S2 and S3, coordinate the control targets and control multiple actuators, optimize the front wheel steering angle and yaw moment through a hierarchical controller, and minimize the tire load rate to distribute the four-wheel driving torque.

[0009] Preferably, in step S1, the vehicle model is a seven-degree-of-freedom dual-rail vehicle dynamics model. The seven degrees of freedom include vehicle longitudinal, lateral, yaw about the z-axis of the vehicle body coordinate system, and four rotations of the wheels. The trajectory tracking model includes the X and Y coordinate positions of the vehicle center of mass and the heading angle.

[0010] Preferably, the process of establishing the vehicle model and the trajectory tracking model includes:

[0011] Establishing the vehicle model:

[0012] Based on the vehicle coordinate system, the dynamic equations for the three dimensions of vehicle longitudinal, lateral, and yaw are expressed as:

[0013] Longitudinal along the x-axis:

[0014]

[0015] Lateral along the y-axis:

[0016]

[0017] Yaw about the z-axis:

[0018]

[0019] In the formula, m represents the vehicle mass, u represents the longitudinal speed at the vehicle center of mass, v represents the lateral speed at the vehicle center of mass, ω r represents the yaw angular velocity, respectively represent the first-order derivatives of the variables u, v, ω r F xfl , F xfr , F xrl , F xrr represent the longitudinal forces of the front left, front right, rear left, and rear right tires of the vehicle, F yfl , F yfr , F yrl , F yrr similarly represent the lateral forces of the four tires of the vehicle, δ is the front wheel steering angle of the vehicle, I z represents the moment of inertia of the vehicle about the z-axis, a represents the distance from the vehicle center of mass position to the front axle, b represents the distance from the vehicle center of mass position to the rear axle, and d represents the wheelbase;

[0020] The rotational motion equation is expressed as:

[0021]

[0022] In the formula, J w is the wheel moment of inertia, ω w is the wheel rotational speed, T di is the driving torque applied to the wheel, F fi is the wheel rolling resistance, Fxi is the longitudinal force of the wheel, R w is the tire radius;

[0023] A trajectory tracking model is established. The trajectory tracking model represents the relationship between the vehicle motion state and the position and attitude of the vehicle in the earth coordinate system. The vehicle centroid displacement and yaw angle change are expressed as:

[0024]

[0025] where X and Y represent the position of the vehicle centroid in the earth coordinate system, are the first derivatives of X and Y respectively, is the vehicle's yaw angle, represents the vehicle's yaw angular velocity, ψ is the vehicle's heading angle, is the vehicle's heading angular velocity, β is the vehicle's centroid side slip angle, is the vehicle's centroid side slip angular velocity.

[0026] Preferably, in step S2, the double-line method and the dynamic relationship between vehicle speed and road surface adhesion coefficient are used to divide the boundary of the phase plane stability region of vehicle driving. The calculation of the vehicle instability factor includes:

[0027] Based on the vehicle model, a phase plane diagram is established. The double-line method is used to divide the boundary of the vehicle phase plane stability region. The double-line method formula is:

[0028]

[0029] In the formula, k β is the slope of the straight line of the stable region boundary, b 0 is the intercept of the straight line on the positive half-axis of the vertical axis;

[0030] Determine the boundary parameters of the stability region according to the vehicle speed and road surface adhesion coefficient;

[0031] Introduce the vehicle instability factor κ to characterize the vehicle stable state, and quantify the vehicle stability state according to the magnitude of κ. The formula is:

[0032]

[0033] In the formula, D c is the distance from the current state point of the vehicle to this straight line, D sat is the distance from the stability region boundary to the straight line passing through the origin and parallel to it.

[0034] Preferably, the utilization of fuzzy logic to adjust the proportion of the transition region includes:

[0035] Set the transition domain according to the phase plane. According to the current vehicle speed and road surface adhesion coefficient, use fuzzy logic to adjust the proportion of the transition area. Use the shrinking method to shrink the boundary of the stable domain to obtain the transition area, with a distance of D t , the proportion q of the transition area relative to the initial stable domain is expressed as:

[0036]

[0037] Based on the trajectory tracking model, allocate the trajectory tracking and stability control objective weight functions according to the instability factor κ and the proportion q of the transition domain. At the same time, use the sigmoid function to achieve weight coordination and realize the dynamic intervention of stability control. After translation and scaling, the coordinated weight function is:

[0038]

[0039] Obtain the trajectory tracking control weight parameter q according to the weight function tt and the stability control weight parameter q sc , respectively:

[0040]

[0041] In the formula, q ttmax and q scmax are the maximum weights of trajectory tracking and stability control, respectively.

[0042] Preferably, step S3 specifically includes:

[0043] Divide the action interval of the tire lateral force into three regions: the linear region, the non-linear region, and the saturation region. Among them, the linear region is the region of the tire's linear cornering stiffness, the non-linear region is the region from when the tire cornering stiffness starts to enter the non-linear stage until before the tire lateral force reaches the maximum saturation, and the saturation region is the region after the tire lateral force reaches the maximum value;

[0044] Define the slip angle at the critical point of the linear region as the cornering stiffness saturation angle α ksat , and the slip angle at the critical point between the non-linear region and the saturation region as the lateral force saturation angle α Fsat , and use AFS for vehicle trajectory tracking and stability control under normal conditions in the linear region of the tire stiffness; perform the transition between AFS and DYC between the cornering stiffness saturation angle α ksat and the lateral force saturation angle α Fsat ; finally, fully use DYC for trajectory tracking and stability control after the front wheel lateral force is completely saturated. Design a tire lateral force saturation factor to characterize whether the tire lateral force is saturated, and the formula is:

[0045]

[0046] In the formula, α is the front wheel slip angle;

[0047] The sigmoid function is used to coordinate the weights, and the formula is:

[0048]

[0049] According to the weight ratio factor calculation formula, the weight r AFS of the active front wheel steering control quantity and the weight r DYC of the direct yaw moment control quantity are respectively:

[0050]

[0051] In the formula, r AFSmax and r DYCmax are the maximum weights of AFS and DYC respectively.

[0052] Preferably, in step S4, the hierarchical controller includes an upper controller and a lower controller. The upper controller is used to optimize the front wheel steering angle and the yaw moment, and the lower controller minimizes the tire load rate to distribute the four-wheel driving torque, realizing coordinated control.

[0053] Preferably, step S4 specifically includes: the upper controller determines the state x(t) = [β, ω r , X, Y, ψ] T of the prediction model according to the state space equation. Using the ideal vehicle trajectory, the ideal vehicle dynamics parameters based on the two-degree-of-freedom model and the road surface constraints, the control target weight parameters obtained based on step S2, and the AFS and DYC weight parameters obtained based on step S3 as the input of the prediction model, and outputting the direct yaw moment M z and the front wheel steering angle δ f ; the lower controller defines the tire load rate, and uses the quadratic programming algorithm to solve the driving torque according to the direct yaw moment and the tire load rate, and obtains the four-wheel driving torque with minimized distribution.

[0054] Therefore, the present invention adopts the above-mentioned multi-actuator coordinated control method for distributed drive electric vehicles based on the phase plane, and has the following beneficial effects:

[0055] (1) Establish a stability control dynamic intervention mechanism based on the phase plane, analyze the vehicle stability according to the phase plane, design an instability factor, enable the stability control to intervene at a reasonable time, and adjust the variable ratio transition region based on fuzzy logic to realize the reasonable transition between the trajectory tracking and the stability control system.

[0056] (2) Design the control weights of AFS and DYC according to the actuator characteristics, divide the working range of the actuator according to the cornering characteristics of the tire, establish a multi-objective and multi-input optimization mapping relationship between the control target domain and the dynamic working domain of the actuator, realize the independence of actuator coordination and control target coordination, better coordinate the end actuator and give full play to the function of the actuator.

[0057] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Description of the Drawings

[0058] Figure 1 It is the flowchart of the control method according to the embodiment of the present invention;

[0059] Figure 2 It is the phase plane and phase trajectory distribution diagram according to the embodiment of the present invention;

[0060] Figure 3 It is the look-up table diagram of the boundary parameters of the dynamic stability domain according to the embodiment of the present invention;

[0061] Figure 4 It is the schematic diagram of the calculation of the instability factor according to the embodiment of the present invention;

[0062] Figure 5 It is the phase plane transition region division diagram according to the embodiment of the present invention;

[0063] Figure 6 It is the trajectory tracking and stability control target weight diagram according to the embodiment of the present invention;

[0064] Figure 7 It is the characteristic curve diagram of the Dugoff tire model according to the embodiment of the present invention;

[0065] Figure 8 It is the look-up table diagram of the cornering stiffness saturation angle and lateral force saturation angle of the tire according to the embodiment of the present invention;

[0066] Figure 9 It is the AFS / DYC weight distribution curve diagram according to the embodiment of the present invention. Detailed Embodiment

[0067] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of them. The components of the embodiments of the present invention usually described and illustrated in the accompanying drawings here can be arranged and designed in various different configurations. In the description of the present invention, it should be noted that the orientation or positional relationship indicated by terms such as "upper", "lower", "inner", "outer", etc. is based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship when the product of this invention is usually placed. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation to the present invention.

[0068] Embodiment

[0069] As Figure 1 shown, the present invention provides a multi-actuator coordinated control method for distributed drive electric vehicles based on the phase plane. The steps include:

[0070] S1. Establish a vehicle model and a trajectory tracking model. The vehicle model is a seven-degree-of-freedom double-track vehicle dynamics model. The seven degrees of freedom include vehicle longitudinal, lateral, yaw around the z-axis of the body coordinate system, and four rotations of the wheels. The trajectory tracking model includes the X and Y coordinate positions of the vehicle center of mass and the heading angle.

[0071] Establishing the vehicle model includes:

[0072] Based on the vehicle coordinate system, the dynamic equations for the three dimensions of vehicle longitudinal, lateral, and yaw are expressed as:

[0073] Longitudinal along the x-axis:

[0074]

[0075] Lateral along the y-axis:

[0076]

[0077] Yaw around the z-axis:

[0078]

[0079] In the formulas, m represents the total vehicle mass, u represents the longitudinal speed at the vehicle center of mass, v represents the lateral speed at the vehicle center of mass, ω r represents the yaw angular velocity, respectively represent the first-order derivatives of the variables u, v, ω r F xfl , F xfr , F xrl, F xrr represent the longitudinal forces of the front left, front right, rear left, and rear right tires of the vehicle, and F yfl , F yfr , F yrl , F yrr similarly represent the lateral forces of the four tires of the vehicle, δ is the steering angle of the front wheels of the vehicle, I z represents the moment of inertia of the vehicle about the z-axis, a represents the distance from the vehicle's center of mass position to the front axle, b represents the distance from the vehicle's center of mass position to the rear axle, and d represents the wheelbase. The specific vehicle body parameters are shown in Table 1.

[0080] Table 1 Vehicle Body Parameters

[0081]

[0082] For a distributed in-wheel motor electric vehicle, when its wheels rotate, a force analysis is carried out on it, and the rotational motion equation can be expressed as:

[0083]

[0084] In the formula, J w is the moment of inertia of the wheel, ω w is the rotational speed of the wheel, represents the first derivative of the ω w variable, T di is the driving torque applied to the wheel, F fi is the rolling resistance of the wheel, F xi is the longitudinal force of the wheel, R w is the tire radius;

[0085] A trajectory tracking model is established. The trajectory tracking model represents the relationship between the vehicle's motion state and its position and attitude in the earth coordinate system. The displacement and yaw angle change of the vehicle's center of mass are expressed as:

[0086]

[0087] Among them, X and Y represent the position of the vehicle's center of mass in the earth coordinate system, are the first derivatives of X and Y respectively, is the yaw angle of the vehicle, represents the yaw angular velocity of the vehicle, ψ is the vehicle's heading angle, is the vehicle's heading angular velocity, β is the sideslip angle of the vehicle's center of mass, is the sideslip angular velocity of the vehicle's center of mass.

[0088] According to the small angle assumption v = βu, it can be simplified as follows:

[0089]

[0090] S2. Use the double-line method and the dynamic relationship between vehicle speed and road surface adhesion coefficient to divide the boundary of the phase-plane stability region of vehicle driving, calculate the vehicle instability factor, and use fuzzy logic to adjust the proportion of the transition region for trajectory tracking and stability target judgment.

[0091] Use the double-line method and the dynamic relationship between vehicle speed and road surface adhesion coefficient to divide the boundary of the phase-plane stability region of vehicle driving, and calculate the vehicle instability factor, specifically as follows:

[0092] First, establish a model in Simulink, set the vehicle speed, road surface adhesion coefficient, and front wheel steering angle of the vehicle. At the same time, give the initial values of the vehicle's sideslip angle and yaw rate state variables, and generate a phase trajectory starting from the initial value points of the sideslip angle and yaw rate. This phase trajectory will subsequently show the final convergence or divergence form according to the state of the system. When different initial numerical settings are given, characteristic phase trajectories will be derived. Numerous different phase trajectories jointly form the complete phase plane diagram, as Figure 2 shown.

[0093] Then, use the double-line method to divide the boundary of the vehicle phase-plane stability region. The double-line method formula is:

[0094]

[0095] In the formula, k β is the slope of the straight line of the stability region boundary, and b 0 is the intercept of the straight line on the positive half-axis of the vertical axis. Among them, the two-dimensional look-up table of the slope and intercept of the straight line of the stability region boundary for different vehicle states based on the characteristics of the phase plane is as Figure 3 shown.

[0096] The phase-plane stability region of vehicle driving is mainly related to vehicle speed, front wheel steering angle, and road surface adhesion coefficient. Among them, vehicle speed and road surface adhesion coefficient have the greatest impact on the change of the stability region. The front wheel steering angle mainly affects the translation of the stability region on the horizontal axis. On the one hand, it is based on the small-angle assumption, and on the other hand, the transition region will be further expanded in the subsequent stability region division process. The influence of the front wheel steering angle on the initial stability region boundary is relatively small. Therefore, determine the stability region boundary parameters according to vehicle speed and road surface adhesion coefficient.

[0097] Finally, in order to accurately judge the stable state of the vehicle and facilitate the subsequent control algorithm to make full use of the judgment result, introduce the vehicle instability factor κ to characterize the stable state of the vehicle, and quantify the vehicle stability state according to the magnitude of κ. The formula is:

[0098]

[0099]

[0100] In the formula, as Figure 4As shown, D c is the current state point of the vehicle to the distance of this straight line, D sat is the distance from the boundary of the stability domain (solid line) to the straight line (dashed line) passing through the origin and parallel to it.

[0101] Adjusting the proportion of the transition region using fuzzy logic includes:

[0102] Setting the transition domain according to the phase plane, adjusting the proportion of the transition region using fuzzy logic according to the current vehicle speed and road adhesion coefficient, obtaining the transition region by shrinking the boundary of the stability domain using the inner contraction method, and the distance is D t , as Figure 5 shown, the proportion q of the transition region relative to the initial stability domain is expressed as:

[0103]

[0104] The magnitude of the instability factor and the vehicle control target situation can be expressed as:

[0105] (1) In the stable region within the blue dashed line, the instability factor κ < 1 - q, and trajectory tracking control is performed;

[0106] (2) At the position of the blue dashed line, the instability factor κ = 1 - q, and stability control starts to intervene;

[0107] (3) In the transition region between the blue dashed line and the red solid line, the instability factor 1 - q < κ < 1, the control target undergoes a transition, the weight of trajectory tracking gradually decreases, and the weight of stability control gradually increases;

[0108] (4) At the position of the red solid line, κ = 1, and trajectory tracking completely exits;

[0109] (5) In the unstable region outside the red straight line, κ > 1, and stability control is fully performed.

[0110] The fuzzy logic inference rule table is shown in Table 2, where L is large, M is medium, S is small, SS is extremely small, and LL is extremely large.

[0111] Table 2 Fuzzy Logic Rule Table

[0112]

[0113] Based on the trajectory tracking model, the weight functions of trajectory tracking and stability control targets can be designed according to the instability factor κ and the proportion q of the transition domain. At the same time, the sigmoid function is used to achieve weight coordination, and the coordinated weight function after translation and scaling is:

[0114]

[0115] Obtain the trajectory tracking control weight parameter q according to the weight function tt and the stability control weight parameter q sc , and obtain the trajectory tracking and stability control objective weight diagram as shown in Figure 6 . The weight coordination is respectively:

[0116]

[0117] In the formula, q ttmax and q scmax are respectively the maximum weights of trajectory tracking and stability control, that is, the control amounts relatively preferentially applied to achieve this goal in the controller.

[0118] S3. Divide the linear region, transition region and saturation region according to the tire cornering characteristics, and use the Sigmoid function to allocate the weights of AFS and DYC. Specifically:

[0119] According to the curve characteristics of the Dugoff tire model, the acting range of the tire lateral force is divided into three regions: linear region, non-linear region and saturation region. Among them, the linear region is the region of the linear cornering stiffness of the tire, the non-linear region is the region after the tire cornering stiffness starts to enter the non-linear stage until the tire lateral force reaches the maximum saturation value, and the saturation region is the region after the tire lateral force reaches the maximum value. The curve of the Dugoff model tire lateral force coefficient is as shown in Figure 7 .

[0120] Define the cornering angle at the critical point of the linear region as the cornering stiffness saturation angle α ksat , and the cornering angle at the critical point of the non-linear region and the saturation region as the lateral force saturation angle α Fsat . During normal use of AFS for vehicle trajectory tracking and stability control in the linear region of the tire stiffness; perform the transition between AFS and DYC between the cornering stiffness saturation angle α ksat and the lateral force saturation angle α Fsat ; finally, fully use DYC for trajectory tracking and stability control after the front wheel lateral force is completely saturated. Among them, the two-dimensional table diagram of the cornering stiffness saturation angle and the lateral force saturation angle is as shown in Figure 8 .

[0121] Design the tire cornering saturation factor:

[0122]

[0123] In the formula, α is the front wheel cornering angle;

[0124] Use the sigmoid function to coordinate the weights, and obtain the weight coordination diagram as shown in Figure 9 . The formula for coordinating the weights of the sigmoid function is:

[0125]

[0126] According to the weight ratio factor calculation formula, the weight r AFS of the active front wheel steering control quantity DYC and the weight r

[0127]

[0128] of the direct yaw moment control quantity AFSmax are respectively DYCmax where r

[0129] and r

[0130] are the maximum weights of AFS and DYC respectively, that is, the control quantities that are relatively preferentially applied to achieve this goal in the controller

[0131]

[0132] where M z is the direct yaw moment, F y1 is the front wheel side force, F y2 is the rear wheel side force

[0133]

[0134] Finally, the dynamic equations of vehicle sideslip and yaw are expressed as

[0135]

[0136] Determine the state of the prediction model according to the state space equation, that is, x(t)=[β,ω r ,X,Y,ψ] T , the inputs of the prediction model are the ideal vehicle trajectory, the ideal vehicle dynamic parameters based on the two-degree-of-freedom vehicle model and road surface constraints, the control target weight parameters obtained from step S2, and the AFS and DYC weight parameters obtained from step S3 as the inputs of the prediction model, and the outputs are the direct yaw moment M z and the front wheel steering angle δ f .

[0137] Combining the inputs, outputs and state variables of the prediction model, the continuous state space equation of the system is obtained as

[0138]

[0139] Among them,

[0140]

[0141] In the formula, k r is the cornering stiffness of the rear wheels of the two-degree-of-freedom vehicle model, and k f is the cornering stiffness of the front wheels of the two-degree-of-freedom vehicle model;

[0142] Since this state space is a continuous model, while MPC performs iterative calculations in a discrete form, it is necessary to discretize the continuous model. Here, the forward Euler method is used. Assuming the sampling time is T, the discrete system state can be expressed as:

[0143]

[0144] Among them, ξ(k), u(k), and η(k) are the state quantity, control quantity, and output quantity of the system at the current moment, respectively. In the matrix In the formula, I is the identity matrix, and T s is the sampling time. A c , B c , C c are the state matrices in the continuous state space equation of the system, respectively, used to represent the characteristics of this continuous system. They are the state matrices in the discrete state space equation of the system, respectively, used to represent the characteristics of this discrete system.

[0145] In the MPC control architecture, the control time domain is set to N c , and the prediction time domain is N p . Through iterative calculations, based on the state information, control increment, and control quantity at time k, the output within the prediction time domain is calculated as:

[0146]

[0147] They are the state matrices in the discrete state space equation of the system, respectively, used to represent the characteristics of this discrete system. ξ(k), u(k), and η(k) are the state quantity, control quantity, and output quantity of the system at the current moment, respectively. η(k + 1)Lη(k + N p ) is the output of the system from time k + 1 to time K + Np; u(k)Lu(k + N c - 1) is the control quantity of the system from time k to time K + Nc - 1.

[0148] When rewritten in matrix form, it becomes:

[0149] Y(k) = Ψ(k)ξ(k) + Θ(k)U(k);

[0150] Among them, Y(k), Ψ(k), Θ(k), and U(k) are the system output in augmented form, the system state quantity coefficient, the system control quantity coefficient, and the system control quantity, respectively.

[0151]

[0152] For the stability control problem, a reference model is required as the ideal value input of the controller. Simplify the vehicle dynamics model and use a linear two-degree-of-freedom vehicle reference model to select the ideal sideslip angle β d and the ideal yaw rate ω rd as the stability control objectives [β d , ω rd T , and the motion equations of the vehicle in the lateral and yaw directions are:

[0153]

[0154] Among them, L = a + b, and K is the stability factor used to characterize the vehicle stability response state. The formula is:

[0155]

[0156] To ensure the stable driving of the vehicle, consider the limit of the road surface adhesion. The formula is:

[0157]

[0158] For the trajectory tracking accuracy control problem, based on the trajectory tracking model, use the ideal path as the reference trajectory of the MPC controller [X d , Y d , ψ d T .

[0159] The main objective of the controller is to complete trajectory tracking and stability control. To achieve accurate trajectory tracking and effective stability control, it is necessary to design a cost function according to the MPC model. The cost function is expressed as:

[0160]

[0161] In the formula, η(t + i|t) is the state quantity of the vehicle dynamics prediction model [β, ω r , X, Y, ψ] T , and η ref (t + i|t) is the reference model z state quantity matrix [β d , ω rd , X d , Y d ​​, ψ d T , where Q and R respectively represent the control objective and control quantity weight matrices, ρ represents the relaxation factor weight, and ε represents the relaxation factor.

[0162] According to the calculated control objective coordination strategy (trajectory tracking control weight parameter and stability control weight parameter) and control quantity weights (active front wheel steering control quantity weight and direct yaw moment control quantity weight), the weight matrices in the cost function are as follows:

[0163]

[0164] For rolling optimization, it is transformed into the standard quadratic form:

[0165]

[0166] G t = [2E(t) T QΘ t , E(t) = Ψξ(t) - Y ref (t).

[0167] In the formula, H t represents the coefficient vector of the quadratic form part; G t represents the coefficient vector of the linear part; E(t) represents the system output error vector.

[0168] During the optimization process, constraint conditions are added to the output control quantity, and the formula is:

[0169] U min ≤ U t ≤ U max ;

[0170] In the formula, U t is the control quantity at the current time, U min is the minimum value of the control quantity, and U max is the maximum value of the control quantity.

[0171] At this time, vehicle trajectory tracking and stability control are transformed into quadratic programming with constraints. After solving, the output quantity sequence within the control time domain is obtained:

[0172] U t = [u(t), u(t + 1), L, u(t + N c - 1)] T .

[0173] Taking the first item of the control sequence as the actual output quantity and applying it to the system, the yaw moment M z and the front wheel steering angle δ f are obtained at this moment.​

[0174] The lower - layer controller defines the tire load ratio, and uses the quadratic programming algorithm to solve the driving torque according to the direct yaw moment and the tire load ratio, obtaining the minimized four - wheel driving torque distribution.

[0175] For vehicle stability margin, when the vehicle turns, the tire is in a combined state of longitudinal slip and lateral deformation because the total force of the tire is restricted by the tire friction ellipse. To maintain vehicle stability under extreme conditions, the distribution of longitudinal and lateral forces must be considered. The longitudinal and lateral forces are restricted by the ground friction force as follows:

[0176]

[0177] Among them, F x represents the tire longitudinal force, F y represents the tire lateral force, and μ represents the road surface adhesion coefficient. On this basis, the tire load coefficient is set to represent the vehicle stability. The tire load ratio is defined as:

[0178]

[0179] The simplified tire load ratio is:

[0180]

[0181] Using the quadratic programming algorithm to solve the driving torque, the objective function based on the tire load ratio is defined as follows:

[0182]

[0183] In the formula, E(ρ i ) represents the mean value of the tire load ratio, k ρ represents the weight factor of the average value of the tire load ratio; the first term on the right - hand side of the equal sign is the variance of the load ratios of the four wheels, and the second term is the average value of the load ratios of the four wheels. Optimizing the load ratio variance can comprehensively utilize the driving torques of the four wheels to avoid excessive or too small load ratio of a certain tire among the four wheels; optimizing the average value of the load ratios can reduce the overall tire load ratio of the vehicle and improve safety and stability.

[0184] Taking the longitudinal forces of the four tires as independent variables x = [F xfl , F xfr , F xrl , F xrr T the objective function is transformed into the standard quadratic programming form as follows:

[0185]

[0186] ​After derivation, the matrix of quadratic programming can be expressed as:

[0187]

[0188] Considering the constraint conditions of the total driving torque and the total yaw moment during distribution, as well as the tire force and the maximum motor torque limit, the constraint conditions of quadratic programming are obtained, and the formula is:

[0189]

[0190] Therefore, the present invention adopts the above-mentioned multi-actuator coordinated control method for distributed drive electric vehicles based on the phase plane. Through dynamic stability domain division, fuzzy logic boundary adjustment, and tire cornering characteristic analysis, the smooth switching and weight optimization of AFS and DYC are realized, and finally the coordinated control of multiple controllers is achieved.

[0191] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions of the present invention or make equivalent replacements, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A phase plane-based distributed drive electric vehicle multi-actuator coordinated control method, characterized in that the steps include: S1. Establish vehicle model and trajectory tracking model; S2. Use the two-line method and the vehicle speed and road adhesion coefficient to dynamically divide the boundary of the phase plane stability domain of the vehicle, calculate the vehicle instability factor, and use fuzzy logic to adjust the transition area ratio to perform trajectory tracking and stability target judgment; S3, dividing the tire into linear region, transition region and saturation region according to its side slip characteristics, and using Sigmoid function to allocate AFS and DYC weights; S4, based on the weight parameters of step S2 and step S3, coordinate the control objectives and control the multiple actuators, optimize the front wheel steering angle and yaw moment through the hierarchical controller, and distribute the four-wheel drive torque by minimizing the tire load rate.

2. The phase plane-based distributed drive electric vehicle multi-actuator coordinated control method according to claim 1 is characterized in that: The vehicle model in step S1 is a seven-degree-of-freedom dual-track vehicle dynamics model, where the seven degrees of freedom include the vehicle's longitudinal, lateral, yaw around the z-axis of the vehicle body coordinate system, and four rotations of the wheels. The trajectory tracking model includes the vehicle's center of mass X, Y coordinate positions and heading angle.

3. The phase plane-based distributed drive electric vehicle multi-actuator coordinated control method according to claim 2 is characterized in that: The process of establishing the vehicle model and the trajectory tracking model includes: Build the vehicle model: Based on the vehicle coordinate system, the dynamic equations of the vehicle in the longitudinal, lateral and yaw dimensions are expressed as: Longitudinal direction along the x-axis: Lateral direction along the y-axis: Yaw about the z-axis: In the formula, m represents the vehicle mass, u represents the longitudinal velocity at the center of mass of the vehicle, v represents the lateral velocity at the center of mass of the vehicle, ω r represents the yaw angular velocity, Represent u, v, ω respectively r First derivative of the variable, F xfl 、F xfr 、F xrl 、F xrr Indicates the longitudinal force of the tires of the front left, front right, rear left, and rear right of the vehicle, F yfl 、F yfr 、F yrl 、F yrr It also represents the lateral force of the four tires of the vehicle, δ is the steering angle of the front wheels of the vehicle, and I z represents the moment of inertia of the vehicle around the z-axis, a represents the distance from the center of mass of the vehicle to the front axle, b represents the distance from the center of mass of the vehicle to the rear axle, and d represents the wheelbase; The equation of rotational motion is expressed as: In the formula, J w is the wheel moment of inertia, ω w is the wheel speed, Represents ω w First derivative of variable, T di is the driving torque applied to the wheels, F fi is the wheel rolling resistance, F xi is the wheel longitudinal force, R w is the tire radius; A trajectory tracking model is established. The trajectory tracking model represents the relationship between the vehicle's motion state and the vehicle's position and posture in the geodetic coordinate system. The vehicle's center of mass displacement and heading angle change are expressed as: Among them, X and Y represent the position of the vehicle's center of mass in the geodetic coordinate system. are the first-order derivatives of X and Y, respectively, is the vehicle yaw angle, represents the vehicle's yaw rate, ψ is the vehicle's heading angle, is the vehicle heading angular velocity, β is the vehicle center of mass sideslip angle, is the vehicle's sideslip angular velocity.

4. The phase plane-based distributed drive electric vehicle multi-actuator coordinated control method according to claim 1, characterized in that: In step S2, the two-line method and the vehicle speed and road adhesion coefficient are used to dynamically divide the boundary of the phase plane stability region of the vehicle, and the calculation of the vehicle instability factor includes: The phase plane diagram is established based on the vehicle model, and the two-line method is used to divide the boundary of the vehicle phase plane stability domain. The formula of the two-line method is: In the formula, k β is the slope of the boundary line of the stable region, b0 is the intercept of the line on the positive semi-axis of the vertical axis; Determine the boundary parameters of the stability region according to the vehicle speed and the road adhesion coefficient; The vehicle instability factor κ is introduced to characterize the vehicle stability state. The vehicle stability state is quantified according to the size of κ. The formula is: Where D c The current state point of the vehicle The distance to the line, D sat is the distance from the boundary of the stability domain to the straight line passing through the origin and parallel to it.

5. The phase plane-based distributed drive electric vehicle multi-actuator coordinated control method according to claim 4 is characterized in that: The method of adjusting the transition area ratio by using fuzzy logic includes: The transition region is set according to the phase plane. According to the current vehicle speed and road adhesion coefficient, the proportion of the transition region is adjusted using fuzzy logic. The transition region is obtained by shrinking the boundary of the stable region using the shrinkage method. The distance is D t , the proportion q of the transition region relative to the initial stable region is expressed as: Based on the trajectory tracking model, the trajectory tracking and stability control target weight functions are allocated according to the instability factor κ and the transition domain proportion q. At the same time, the sigmoid function is used to achieve weight coordination and realize the dynamic intervention of stability control. The coordinated weight function after translation and scaling is: According to the weight function, the trajectory tracking control weight parameter q is obtained tt and the stability control weight parameter q sc , respectively: In the formula, q ttmax and q scmax are the maximum weights for trajectory tracking and stability control, respectively.

6. The phase plane-based distributed drive electric vehicle multi-actuator coordinated control method according to claim 1, characterized in that: Step S3 specifically includes: The tire lateral force action range is divided into three regions: linear region, nonlinear region and saturation region. The linear region is the tire linear cornering stiffness region, the nonlinear region is the region after the tire cornering stiffness begins to enter nonlinearity and before the tire lateral force reaches the maximum value and saturation, and the saturation region is the region after the tire lateral force reaches the maximum value. Define the slip angle at the critical point of the linear region as the saturation angle of the slip stiffness α ksat , the side slip angle at the critical point between the nonlinear region and the saturation region is the saturation angle of the side force α Fsat In the linear region of tire stiffness, AFS is normally used for vehicle trajectory tracking and stability control; at the saturation angle α of the cornering stiffness ksat The saturation angle α Fsat AFS and DYC are transitioned between the two stages; finally, after the front wheel lateral force is fully saturated, DYC is fully used for trajectory tracking and stability control. The tire side saturation factor is designed to characterize whether the tire lateral force is saturated. The formula is: Where α is the front wheel slip angle; Use the sigmoid function to coordinate weights, the formula is: According to the weight proportional factor calculation formula, the active front wheel turn control weight r AFS and the direct yaw moment control weight r DYC They are: In the formula, r AFSmax and r DYCmax are the maximum weights of AFS and DYC respectively.

7. The phase plane-based distributed drive electric vehicle multi-actuator coordinated control method according to claim 1, characterized in that: In step S4, the hierarchical controller includes an upper controller and a lower controller. The upper controller is used to optimize the front wheel steering angle and yaw moment, and the lower controller distributes the four-wheel drive torque by minimizing the tire load rate to achieve coordinated control.

8. The phase plane-based coordinated control method for distributed drive electric vehicle multi-actuator according to claim 7 is characterized in that: Step S4 specifically includes: the upper controller determines the state x(t)=[β,ω r ,X,Y,ψ] T The ideal vehicle trajectory, the ideal vehicle dynamics parameters based on the two-degree-of-freedom model and road constraints, the control target weight parameters obtained in step S2, and the AFS and DYC weight parameters obtained in step S3 are used as the input of the prediction model, and the direct yaw moment M is output. z and the front wheel steering angle δ f The lower controller defines the tire load rate, and uses the quadratic programming algorithm to solve the driving torque according to the direct yaw moment and the tire load rate to obtain the minimized distributed four-wheel drive torque.

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