Distributed driving electric vehicle adaptive cruise and torque distribution cooperative control method

Abstract

A self-adaptive cruise and torque distribution cooperative control method for a distributed driving electric vehicle comprises the following steps: establishing a two-degree-of-freedom vehicle dynamics model, combining a nonlinear tire model and a longitudinal load transfer effect, establishing a longitudinal motion control model, adopting a permanent magnet synchronous motor, introducing a motor efficiency MAP graph, and predicting a control algorithm by using a multi-target optimization model. And constructing a multi-state variable optimization model, dynamically adjusting a weight coefficient, introducing a relaxation factor, converting a problem into a quadratic programming problem, and generating an optimization control instruction. And designing a nonlinear model predictive controller to calculate an optimal direct yaw moment, determining a torque distribution coefficient, solving a target function for minimizing the total loss power of the motor through quadratic programming, and finding an optimal torque distribution coefficient to be applied to the motor. And a dynamic model, a longitudinal motion control model and a nonlinear model predictive controller are integrated to form a comprehensive vehicle control system and realize closed-loop control iteration, so that the safety, comfort and energy efficiency of the vehicle under complex working conditions are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of intelligent electric vehicle control, and particularly relates to a distributed drive electric vehicle adaptive cruise control and torque distribution collaborative control method. BACKGROUND

[0002] With the transformation of global energy structure and the increasingly stringent environmental regulations, new energy vehicle technology is experiencing unprecedented rapid development. In this process, distributed drive electric vehicles stand out with their innovative powertrain architecture and become one of the most promising technology routes in the field of intelligent transportation. This kind of vehicle uses in-wheel motors or wheel hub motors to realize four-wheel independent drive, completely abandoning traditional mechanical components such as transmission shafts and differentials. Not only does it improve the transmission efficiency, but also increases the utilization rate of chassis space through modular design. This unique driving form brings revolutionary possibilities for vehicle dynamics control. Each wheel can independently adjust the driving torque, which theoretically enables more accurate trajectory tracking and more flexible control response than traditional architectures. However, this innovative architecture, while bringing technical advantages, also introduces control complexity that traditional vehicles do not have. Especially in complex traffic scenarios such as urban roads and highways, how to collaboratively optimize the three mutually restrictive target parameters of following safety, ride comfort and energy efficiency has become a key problem restricting the technology to land. Existing research shows that in unstructured road environments including sharp turns and slopes, traditional control methods often fail to meet the performance requirements of these three aspects simultaneously, resulting in vehicles either sacrificing comfort to ensure safety distance or reducing energy efficiency to maintain stability.

[0003] The current control technology of distributed drive electric vehicles mainly faces two-dimensional core challenges. In the longitudinal control aspect, the performance bottleneck of adaptive cruise control (ACC) is increasingly prominent. The traditional ACC algorithm is developed based on centralized drive architecture, and its control model fails to fully consider the nonlinear characteristics brought by four-wheel independent drive. Specifically, in the following vehicle on curve condition, due to the failure to consider the coupling effect of tire side slip characteristics and longitudinal force distribution, the vehicle is prone to periodic fluctuation of following distance; in the emergency braking scenario, the average distribution of braking torque will cause acceleration to change suddenly, which seriously affects the ride comfort. More importantly, the existing system lacks targeted optimization of motor response characteristics, and in the urban working condition of frequent start-stop, the frequent switching of motor working state will cause obvious energy waste. In the lateral control dimension, the limitation of torque distribution strategy is more prominent. Although the distributed architecture can realize active yaw control through differential torque in theory, the existing methods mostly adopt fixed distribution ratio or simply optimize a single indicator, which cannot optimize energy efficiency while ensuring vehicle stability. For example, when driving at high speed on a curve, excessive increase of the inner side wheel braking force to ensure lateral stability will cause the motor operating point to deviate from the high efficiency interval, and the measured data shows that the energy loss in this condition cannot be ignored. In the low adhesion road condition, the traditional distribution strategy is more likely to cause tire force saturation, further aggravating energy waste and handling risk.

[0004] In summary, the adaptive cruise control of distributed drive electric vehicles faces the contradiction between insufficient lateral stability, comfort and energy efficiency, and the single target optimization limitation of torque distribution strategy and the lack of coordination with longitudinal control, which makes it difficult to fully convert the hardware advantages of the vehicle into comprehensive performance improvement. In view of these key challenges, it is urgent to explore the cooperative control strategy of deep integration of adaptive cruise control and torque distribution of distributed drive electric vehicles, in order to solve the multi-objective coordinated control problem of safety, comfort and energy efficiency optimization of distributed drive electric vehicles. SUMMARY

[0005] In view of the problems existing in the prior art, the present application provides a distributed drive electric vehicle adaptive cruise control and torque distribution cooperative control method, which aims to realize the deep cooperation of longitudinal following control and lateral stability regulation through a hierarchical multi-objective optimization architecture, while considering energy efficiency optimization, and adopts a model predictive control framework combined with a motor efficiency dynamic distribution strategy, which significantly improves the comprehensive performance of the vehicle in complex working conditions, to solve the balance problem between following stability, handling safety and energy efficiency of the traditional strategy, and to improve the comprehensive performance of the vehicle.

[0006] In order to achieve the above-mentioned purpose, the specific scheme of the present application is as follows:

[0007] The distributed drive electric vehicle adaptive cruise control and torque distribution cooperative control method comprises the following steps:

[0008] Step 1: Construct a two-degree-of-freedom vehicle dynamics model that includes lateral motion and yaw motion, introduce a nonlinear tire model to calculate tire lateral force, and consider the longitudinal load transfer effect to calculate the vertical load on the front and rear axles.

[0009] Step 2: Using the vehicle's driving traction force and driving resistance, based on the two-degree-of-freedom vehicle dynamics model described in Step 1 and the calculation results of the vertical loads on the front and rear axles, establish a longitudinal motion control model. Track the vehicle's longitudinal speed through feedforward control and PI-based feedback control, and calculate the total longitudinal traction force.

[0010] Step 3: Select a permanent magnet synchronous motor as the drive motor, establish a motor model, input the total longitudinal traction force calculated in Step 2 into the motor model, calculate the power required by the motor, and import the motor efficiency MAP chart.

[0011] Step 4, Multi-objective optimization model predictive control algorithm to realize adaptive cruise control: Using the longitudinal motion control model in Step 2, an extended state space model of adaptive cruise control is constructed. The extended state space model of adaptive cruise control includes the characteristic parameters of the vehicle's longitudinal speed, acceleration, vehicle distance deviation and relative speed. The vehicle's longitudinal speed error, relative speed, longitudinal acceleration and acceleration change rate are selected as optimization state variables. Combined with safety, comfort and energy efficiency, a multi-objective optimization problem objective function is constructed. Based on the discretized result of the longitudinal following extended state space model (16), the vehicle's longitudinal speed error, relative speed, longitudinal acceleration and acceleration change rate are selected as optimization state variables. Using acceleration and the rate of change of acceleration as optimization state variables, a multi-objective optimization problem objective function is constructed. By dynamically adjusting the weight coefficients of safety boundary control, dynamic following optimization, and comfort constraints, a comprehensive optimization function is formed. A relaxation factor is introduced into the comprehensive optimization function, and the comprehensive optimization function and the constraints softened by adding the relaxation factor are transformed into a constrained quadratic programming problem. By solving the quadratic programming problem, a series of optimized control commands are generated. The first control command in the sequence is selected for vehicle control at the current moment, and the optimization iteration is performed cyclically in the subsequent time domain until the control task for the entire time period is completed, realizing the closed-loop control of vehicle adaptive cruise.

[0012] Step 5: Based on the two-degree-of-freedom vehicle dynamics model and nonlinear tire model described in Step 1, design a nonlinear model predictive controller as the core algorithm of the active safety controller, and calculate the optimal direct yaw moment.

[0013] Step 6, determine the current torque distribution coefficient according to the optimal direct yaw moment obtained in step 5, calculate the motor no-load loss power, calculate the motor loss power during driving and braking according to the energy flow characteristics of the motor during vehicle driving, and establish a motor total loss power model, calculate and compare the motor total loss power under different torque distribution coefficients, determine the torque distribution coefficient with the minimum loss power, and minimize the total loss power of the motor, determine the constraint conditions in the optimization process, including the maximum output limit of the torque, the speed limit and the related limit of the motor efficiency, use quadratic programming to solve the objective function, find the optimal torque distribution coefficient, verify whether the optimal torque distribution coefficient found meets all the constraint conditions, and apply the optimal torque distribution coefficient found to the driving motor;

[0014] Step 7, integrate the two-degree-of-freedom vehicle dynamics model constructed in step 1, the longitudinal motion control model established in step 2, and the nonlinear model predictive controller designed in step 5 to form a comprehensive vehicle control system, which uses the optimal control command generated by the multi-objective optimization model predictive control algorithm in step 4 to adjust the longitudinal speed of the vehicle, adjusts the torque distribution of the front and rear axles according to the optimal torque distribution coefficient identified in step 6, and applies the optimal torque distribution coefficient to the permanent magnet synchronous motor in step 3, monitors the longitudinal speed, lateral stability and motor operating state of the vehicle in real time during vehicle driving, dynamically adjusts the torque distribution coefficient and control command according to the monitoring results to adapt to changing driving conditions and optimize vehicle performance, and repeats steps 4 to 7 in each control period to form a closed-loop control iteration.

[0015] Further, the motion differential equation of the two-degree-of-freedom vehicle dynamics model in step 1 is:

[0016] (1),

[0017] In the formula: represents the lateral acceleration; represents the total lateral force provided by the front wheels to the vehicle; represents the total lateral force provided by the rear wheels to the vehicle; is the total mass of the vehicle; , is the distance from the front and rear axles of the vehicle to the center of mass; is the moment of inertia of the vehicle; is the longitudinal speed; is the yaw rate, represents the yaw angular acceleration;

[0018] The nonlinear tire model is the Fiala model, and the tire lateral force F y The calculation formula is:

[0019] (2),

[0020] wherein: is the tire cornering stiffness; is the road adhesion coefficient; is the tire vertical load; is the tire cornering angle; is the tire saturation cornering angle;

[0021] The calculation formula of the vertical load of the front and rear axles is as follows:

[0022] (5),

[0023] wherein: F zf represents the vertical load of the front axle; F zr represents the vertical load of the rear axle; L r represents the distance from the rear axle to the center of mass; L f represents the distance from the front axle to the center of mass; is the height to the center of mass of the vehicle; is the total mass of the vehicle; is the acceleration of gravity; is the wheelbase of the vehicle; is the longitudinal acceleration of the vehicle.

[0024] Further, the formula of the longitudinal motion control model in step 2 is as follows:

[0025] (6),

[0026] (7),

[0027] wherein, represents the product of the mass m of the vehicle and the longitudinal acceleration of the vehicle; is the total traction provided by the motor; is the running resistance; T ei represents the traction torque provided by the motor; is the equivalent tire radius, for the convenience of the design of the feedforward controller, set ; represents the inverse of the running resistance; F res represents the running resistance; represents the acceleration resistance; represents the air resistance, wherein the influence of the slope resistance on the result is small, and therefore not considered; is the total mass of the vehicle; is the acceleration of gravity; is the longitudinal speed; 、 、 、 respectively represent the rolling coefficient, air density, wind resistance coefficient and windward area of the vehicle;

[0028] The total longitudinal traction force is calculated as follows:

[0029] (9),

[0030] (10),

[0031] wherein, represents the feedback control traction force component; s represents the Laplace operator; represents the proportional gain coefficient of the PI controller; represents the integral gain coefficient of the PI controller; represents the total longitudinal traction force; represents the feedforward control traction force component; represents the desired longitudinal speed; is the longitudinal speed.

[0032] Further, the calculation formula of the power required by the motor in step 3 is as follows:

[0033] (11),

[0034] wherein, is the motor power, is the motor torque, is the motor speed.

[0035] Further, the objective function of the multi-objective optimization problem in step 4 is as follows: (33),

[0036] wherein, , , and is a constant term, the value of which has no influence on the solution of the optimal value of the quadratic programming problem; is the performance index at time k; represents the prediction matrix between the control increment and the output; represents the same meaning as , and the mathematical form is the transpose matrix form thereof; ΔU(k) represents the future control increment sequence vector; represents the same meaning as ΔU(k), and the mathematical form is the transpose matrix form thereof; represents the error vector between the reference trajectory and the free response; represents the same meaning as The same, the mathematical form is the transpose matrix form thereof; Q represents a weight matrix; R represents a weight matrix; T represents a matrix transpose symbol; k represents a sampling time index, has no unit, and identifies the serial number of a current control period (such as k=1, 2, 3,...), and is used for optimization iteration in a time domain; represents a linear term vector; represents the same meaning as The same, the mathematical form is the transpose matrix form thereof;

[0037] The formula of the safety boundary control is as follows:

[0038] (23),

[0039] In the formula, is an actual vehicle spacing, is a preset safety vehicle spacing threshold;

[0040] The following is a following performance target function of the dynamic following optimization:

[0041] (24),

[0042] In the formula, is a spacing error weight coefficient, is a relative speed error weight coefficient; represents an expected spacing error; represents an expected relative speed error;

[0043] The formula of the comfort constraint is as follows:

[0044] (26),

[0045] In the formula, is an expected acceleration increment weight coefficient, represents an expected acceleration increment;

[0046] The formula of the comprehensive optimization function is as follows:

[0047] (28),

[0048] In the formula, is a following performance target function; is a multi-objective comfort index; represents an expected spacing error; represents an expected relative speed error; is a spacing error weight coefficient, is a relative speed error weight coefficient; is an expected acceleration increment weight coefficient, represents an expected acceleration increment;

[0049] The formula of introducing the relaxation factor into the comprehensive optimization function is as follows:

[0050] (34),

[0051] In the formula, is a relaxation factor; has the same meaning as , and the mathematical form is the transpose matrix form thereof; is a relaxation factor weight; denotes a prediction matrix between a control increment and an output; ΔU(k) denotes a future control increment sequence vector; denotes an error vector between a reference trajectory and a free response; Q denotes a weight matrix; R denotes a weight matrix; T is a matrix transpose symbol; k denotes a sampling time index, has no unit, and identifies the serial number of a current control period (for example, k = 1, 2, 3,...), and is used for optimization iteration in a time domain;

[0052] The formula of the quadratic programming problem with constraints is as follows:

[0053] (36),

[0054] In the formula, denotes a control increment vector at k time; denotes an extended Hessian matrix; denotes an extended optimization vector; denotes an extended linear term vector; s denotes a lower bound vector of a constraint condition; t denotes an upper bound vector of a constraint condition; a coefficient matrix of a linear inequality constraint; a constant vector of a linear inequality constraint; T is a matrix transpose symbol;

[0055] Further, the calculation step of the optimal direct yaw moment in step 5 comprises:

[0056] Step 51, a state space model of active safety control is established. This step constructs a lateral stability linearization state space model, the state variables of which include lateral velocity , yaw rate , and center of mass side slip angle β, and the control input is direct yaw moment . The model is specially designed for the NMPC algorithm and is the core of the nonlinear model predictive controller (NMPC). The nonlinear characteristics of vehicle lateral dynamics are processed by online linearization, which provides a prediction model support for subsequent optimal direct yaw moment solving, and ensures the lateral stability of the vehicle in scenarios such as curves and low adhesion road surfaces. The expression is as follows:

[0057] (37),

[0058] where: is the state equation of the system; is the state variable; is the control variable, is the first derivative of the state variable;

[0059] Step 52, define the system output equation as follows:

[0060] (40),

[0061] (41);

[0062] where, denotes the state variable; denotes the system output; C is the output matrix; is the lateral velocity; is the yaw rate; is a 2x2 identity matrix;

[0063] Step 53, set the control horizon and prediction horizon as and respectively, at the sampling time the control variable sequence and the system output variable sequence are respectively:

[0064] (42),

[0065] (43),

[0066] where, denotes the future control sequence predicted at time k; denotes the control input applied at time k; denotes the control input applied at time k+1 predicted at time k; denotes the control input applied at time k+Nc-1 predicted at time k; Nc is the control horizon; denotes the future output sequence predicted at time k; denotes the system output at time k; denotes the subsystem index; k denotes the current time sampling; T denotes the matrix transpose symbol; denotes the system output at time k+1 predicted at time k; denotes the system output at time k+Np predicted at time k; N p is the prediction horizon.

[0067] Step 54, at the sampling time , the prediction control starting point is equal to Predict the future dynamic changes of the system as the initial value of the system state, define the system state and output prediction as formula (44) and formula (45) respectively:

[0068] (44),

[0069] (45),

[0070] In the formula, represents the linearized system equation at time k; is the output matrix; is the discrete time step; Nc is the control time domain, and Np is the prediction time domain; represents the system state at time k; represents the control input applied at time k; represents the system state at time k+1 predicted at time k; represents the system state at time k+2 predicted at time k; represents the control input applied at time k+1 predicted at time k; represents the process noise or disturbance at time k+j predicted at time k; represents the system state at time k+Nc predicted at time k; represents the system state at time k+Nc-1 predicted at time k; represents the control input applied at time k+Nc-1 predicted at time k; represents the system output at time k+Nc-1 predicted at time k; represents the system output at time k+1 predicted at time k; represents the system output at time k+2 predicted at time k; represents the system output at time k+Np predicted at time k; represents the system state at time k+Np predicted at time k; k represents the current discrete time index; k+1, k+2 represent the future discrete time index; represents the subsystem index;

[0071] Step 55, considering the lateral velocity and yaw rate, the expression of the target function J1 is as follows:

[0072] (46),

[0073] In the formula: is the weight of the lateral velocity, is the weight of yaw rate control, denotes the output tracking weight matrix, and are the desired lateral velocity and yaw rate, respectively, denotes the system output at time k+1 predicted at time k, denotes the desired output reference value at time k+j, denotes the lateral velocity at time k+i predicted at time k, denotes the desired lateral velocity at time k+i, denotes the desired yaw rate at time k+i, the yaw rate at time k+i predicted at time k, p denotes the upper limit of summation, and i, j denote the prediction step index;

[0074] To avoid a large rate of change of the control signal, the expression of the objective function J2 is as follows:

[0075] (47),

[0076] In the formula, denotes the control increment at time k+i predicted at time k, denotes the yaw moment increment at time k+i predicted at time k, R denotes the control increment weight coefficient, m denotes the upper limit of summation, and i denotes the prediction step index;

[0077] To prevent the problem of variables being unsolvable in the solving process, the expression of the slack variable and the corresponding cost function J3 is as follows:

[0078] (48),

[0079] In the formula, is the weight matrix representing the importance of the slack variable;

[0080] Step 56, constructing the optimization problem: according to the nonlinear control model equation and the objective function equation, the formula of the optimization problem is as follows:

[0081] (49),

[0082] In the formula: is the linear inequality bundle; is the nonlinear inequality bundle; J(u) denotes the total objective function of the nonlinear model predictive control (NMPC) optimization problem; J1 denotes the performance tracking objective function; J2 denotes the control cost objective function; J3 denotes the constraint violation penalty function; s denotes the lower bound vector of the constraint condition; and t denotes the upper bound vector of the constraint condition;

[0083] Step 57, solving the optimization problem: using the sequential quadratic programming method to solve the optimization problem to obtain the optimal control input;

[0084] Step 58, QP algorithm flow:

[0085] Step 581, take a reasonable initial solution ;

[0086] Step 582, solve the quadratic programming sub-problem:

[0087] (50),

[0088] In the formula, denotes the first order derivative of the objective function J at the point , denotes the second order derivative of the objective function J at the point , d represents the search direction vector, , denotes the inequality constraint function, , denotes the gradient of the constraint function at the point , denotes the current solution at the kth iteration, k represents the main iteration number of the SQP algorithm, and T represents the matrix transpose symbol;

[0089] The search direction is obtained;

[0090] Step 583, if or , stop, otherwise continue to the next step;

[0091] Step 584, find the step size satisfying and

[0092] Step 585, let , , go to step (2);

[0093] Step 59, calculate the direct yawing moment: at each sampling time, the system prediction variables are updated using the real-time measured vehicle state information, and an optimization is performed to obtain the optimal direct yawing moment.

[0094] Further, the formula of the current torque distribution coefficient in step 6 is as follows:

[0095] (51),

[0096] In the formula, , are the front and rear motor torques, respectively, Total torque required. Torque distribution coefficient 0 to 1, when Only front axle drive, Only rear axle drive, and other values represent the front and rear axle motors jointly drive;

[0097] The formula for calculating the motor no-load loss power is as follows:

[0098] (52),

[0099] In the formula, represents the motor no-load loss power; represents the motor no-load loss torque; n represents the motor speed

[0100] The formula for calculating the motor loss power during driving and braking is as follows:

[0101] (53),

[0102] (54),

[0103] In the formula, represents the motor loss power during driving; represents the motor loss power during braking; is the efficiency of the motor at the current torque and speed; represents the motor power; represents the motor torque; represents the motor speed;

[0104] The formula for establishing the motor total loss power model, calculating and comparing the motor total loss power under different torque distribution coefficients is as follows:

[0105] (57),

[0106] (58),

[0107] In the formula, and represent the front and rear axle motor no-load loss power when the speed is represents the rear axle motor efficiency; represents the front axle motor efficiency; represents the total loss power of the motor system under driving conditions, represents the total required driving torque of the vehicle, represents the motor speed, represents the torque distribution coefficient, represents the total loss power of the motor system under braking conditions;​

[0108] The objective function of minimizing the total loss power of the motor is as follows:

[0109] (59),

[0110] The constraint conditions are as follows:

[0111] Constraint conditions: (60),

[0112] In the formula, , respectively represent the maximum torque of the front and rear shaft motors at the current speed; is the maximum speed of the motor, represents the torque distribution coefficient, represents the efficiency of the rear shaft motor; represents the efficiency of the front shaft motor, represents the total demand driving torque of the vehicle;

[0113] The quadratic programming is used to solve the objective function, and the formula of the optimal torque distribution coefficient is as follows:

[0114] (65),

[0115] In the formula: , is the weight matrix satisfying the equality condition, , respectively are the weight of the total demand driving torque of the vehicle and the direct yawing torque; is the optimization vector of the solver, is the expected value of the total demand driving torque of the vehicle and the direct yawing torque; is the relaxation weight matrix; is the gain matrix, is the tire load rate weight matrix; is the wheel rolling radius; is the road adhesion rate coefficient; , is the motor torque constraint vector; is the optimization variable vector; T is the matrix transpose symbol; represents the vertical load of wheel i, wherein , respectively correspond to the left front wheel, the right front wheel, the left rear wheel and the right rear wheel; s represents the lower bound vector of the constraint condition; t represents the upper bound vector of the constraint condition.

[0116] Advantages of the present application

[0117] 1. Multi-objective optimization adaptive cruise control: The distributed drive electric vehicle adaptive cruise and torque distribution collaborative control method of the application balances the control accuracy of following distance and acceleration mutation suppression by constructing a multi-state variable optimization model containing vehicle distance error, relative speed, acceleration and acceleration change rate, and solving the quadratic programming with relaxation factor, so that the control performance of the vehicle in complex scenes such as curves and slopes is significantly improved. The upper multi-objective optimization adaptive cruise control is based on the model predictive control framework, and the expected acceleration command is generated by solving the quadratic programming problem with relaxation factor, so as to realize the dynamic balance of safety, following and comfort.

[0118] 2. Safety-energy efficiency collaborative torque distribution control: The application optimizes torque distribution based on motor efficiency MAP in real time, reduces no-load loss through low-load single-axis driving mode while ensuring lateral stability, so that the average working efficiency of the motor system is improved by more than 5%. The lower safety-energy efficiency collaborative torque distribution control calculates the direct yaw moment to ensure lateral stability by using nonlinear model predictive control, and dynamically adjusts the front and rear axle torque distribution coefficient based on the motor efficiency MAP, so as to avoid no-load loss through low-load single-axis driving and optimize energy efficiency through high-load dual-axis collaborative operation.

[0119] 3. Hierarchical collaborative control architecture: The application adopts a hierarchical collaborative control architecture to deeply couple the upper adaptive cruise control and the lower torque distribution strategy, realizes the dynamic coordination of longitudinal following and lateral stability through real-time data interaction, shortens the system response time and improves the real-time performance of control. The upper controller outputs the expected acceleration command with a period of 10ms, and the lower controller completes the torque distribution calculation with a period of 20ms, so as to ensure the real-time performance of the system through priority scheduling mechanism.

[0120] 4. Dynamic adjustment and real-time optimization: The multi-objective optimization function introduces an adaptive relaxation factor to dynamically adjust the weight of the constraint boundary, converts the rigid safety distance constraint into the boundary condition of the feasible region of the quadratic programming, so as to control the acceleration change rate within 2.5m / s³. In the curve working condition, the distribution coefficient is dynamically corrected in combination with the tire attachment ellipsoid theory, so as to control the centroid side slip angle error within 0.5°, and at the same time ensure that the motor works in the interval with efficiency higher than 80%. BRIEF DESCRIPTION OF DRAWINGS

[0121] Figure 1 The flowchart of the distributed drive electric vehicle adaptive cruise and torque distribution collaborative control method of the application.

[0122] Figure 2 The figure is a two-degree-of-freedom vehicle dynamics schematic diagram of the application.

[0123] Figure 3is the motor efficiency MAP of the present application, including two subgraphs: (a) the graph is the efficiency distribution of the front axle motor at different rotating speeds and torques. (b) is the efficiency distribution of the rear axle motor at different rotating speeds and torques.

[0124] Figure 4 is the model predictive control principle block diagram of the present application.

[0125] Figure 5 is the longitudinal vehicle distance model diagram of the present application.

[0126] Figure 6 is the proposed torque distribution control strategy block diagram of the present application.

[0127] Figure 7 is the torque distribution coefficient MAP of the present application, wherein: (a) the graph is the change of the torque distribution coefficient with the rotating speed and torque under the consideration of motor no-load loss; (b) the graph is the change of the torque distribution coefficient with the rotating speed and torque without considering the motor no-load loss.

[0128] Figure 8 is the multi-objective cooperative control strategy block diagram.

[0129] Figure 9 is the performance comparison of the multi-objective cooperative control and the model predictive control (MPC) under the sinusoidal variable speed cruise following vehicle working condition of the present application. Among them: (a) the graph is the following distance: the vehicle speed change with time under the two control methods is compared, and compared with the front vehicle speed; (b) the graph is the following distance error: the vehicle speed error change with time under the two control methods is shown; (c) the graph is the speed: the vehicle speed change with time under the two control methods is compared, and compared with the front vehicle speed; (d) the graph is the speed error: the vehicle speed error change with time under the two control methods is shown; (e) the graph is the acceleration: the vehicle acceleration change with time under the two control methods is compared; (f) the graph is the energy consumption: the energy consumption under the two control methods is compared, wherein the energy consumption of the MPC method is 1532 kJ, and the energy consumption of the multi-objective cooperative control method is 1321 kJ.

[0130] Figure 10is a working condition result diagram of the serpentine curve following vehicle of the present application: it shows the performance comparison of the multi-objective collaborative control and model predictive control (MPC) methods in the serpentine curve following vehicle working condition. Among them: (a) the figure is the following distance: it shows the following distance changes with time under the multi-objective collaborative control and MPC method, and the comparison with the reference value; (b) the figure is the following distance error: it shows the following distance error changes with time under the two control methods; (c) the figure is the yaw angle: it compares the yaw angle changes with time under the two control methods; (d) the figure is the vehicle speed: it shows the vehicle speed changes with time under the two control methods; (e) the figure is the acceleration: it compares the vehicle acceleration changes with time under the two control methods; (f) the figure is the energy consumption: it compares the energy consumption under the two control methods, and shows that the energy consumption of the multi-objective collaborative control is lower.

[0131] Figure 11 is the performance comparison of the multi-objective collaborative control and MPC (model predictive control) two control strategies of the present application in the CHTC variable speed cruise following vehicle working condition. Among them, (a) the figure shows the following distance changes with time; (b) the figure shows the vehicle speed changes; (c) the figure depicts the acceleration changes; (d) the figure shows the energy consumption changes; (e) the figure shows the MPC torque distribution; (f) the figure shows the multi-objective collaborative control torque distribution. DETAILED DESCRIPTION

[0132] The present application will be further explained and described in conjunction with the accompanying drawings and specific embodiments, it should be noted that the specific embodiments are not used to limit the scope of the present application.

[0133] As Figures 1 to 11 shown, the distributed drive electric vehicle adaptive cruise and torque distribution collaborative control method provided by the specific embodiment includes the following steps:

[0134] Step 1, a two-degree-of-freedom vehicle dynamics model including lateral motion and yaw motion is constructed, a nonlinear tire model is introduced to calculate the tire lateral force, and the vertical load of the front and rear axles is calculated considering the longitudinal load transfer effect;

[0135] Step 11, a two-degree-of-freedom vehicle dynamics model including lateral motion and yaw motion is constructed:

[0136] Since the two-degree-of-freedom vehicle model can fully capture the key dynamic characteristics, has low calculation complexity and is matched with the optimization framework, based on the trade-off between the problem requirements and the algorithm implementation, the two-degree-of-freedom vehicle dynamics model considering lateral motion and yaw motion is adopted in the embodiment, as Figure 2 shown, including lateral motion and yaw motion, the motion differential equation of the two-degree-of-freedom vehicle dynamics model is as follows:

[0137] (1),

[0138] where: denotes lateral acceleration; denotes total lateral force provided by front wheels; denotes total lateral force provided by rear wheels; is the vehicle mass; , is the distance between the front and rear axles and the center of mass; is the moment of inertia of the vehicle; is the longitudinal velocity; is the yaw rate, denotes yaw angular acceleration;

[0139] Step 12, to expand the application range of the vehicle model, the Fiala nonlinear tire model is introduced, and the tire lateral force F y The calculation formula is as follows:

[0140] (2),

[0141] (3),

[0142] where: is the tire cornering stiffness; is the road adhesion coefficient; is the tire vertical load; is the tire slip angle; is the tire saturation slip angle.

[0143] The front and rear tire slip angle calculation formula is:

[0144] (4),

[0145] In formula (4), denotes the front wheel slip angle; , is the distance between the front and rear axles and the center of mass; is the yaw rate; is the center of mass slip angle; denotes the front wheel steering angle; denotes the rear wheel slip angle; is the longitudinal velocity.

[0146] Step 13, vehicle acceleration and braking will cause dynamic changes in tire vertical load. According to the nonlinear tire model, the change in vertical load affects the tire lateral force, and further affects the vehicle lateral dynamics. Considering the longitudinal load transfer effect, the front and rear axle vertical load formula is:

[0147] (5),

[0148] In the formula: F zf Indicates the vertical load on the front axle; F zr Indicates the vertical load on the rear axle; L r L represents the distance from the rear axle to the center of mass. f Indicates the distance from the front axle to the center of mass; It is the height of the vehicle's center of gravity; For the overall vehicle weight; It is gravitational acceleration; It is the vehicle's wheelbase; It is the longitudinal acceleration of the vehicle.

[0149] Step 2: Using the vehicle's driving traction force and driving resistance, and based on the two-degree-of-freedom vehicle dynamics model described in Step 1 and the calculation results of the vertical loads on the front and rear axles, a longitudinal motion control model is established. Through feedforward control and PI-based feedback control, the vehicle's longitudinal velocity is tracked, ultimately yielding the total longitudinal traction force. The specific steps are as follows:

[0150] First, using the vehicle's driving traction force and driving resistance (including acceleration resistance and air resistance), a longitudinal dynamic model is established based on the two-degree-of-freedom vehicle dynamics model and the calculation results of the vertical loads on the front and rear axles.

[0151] Design a control strategy: Design a control strategy consisting of feedforward control and PI-based feedback control. Feedforward control directly calculates the required driving force based on model predictions, while feedback control adjusts according to the deviation between the actual speed and the desired speed.

[0152] Achieving longitudinal vehicle speed tracking: The designed control strategy is applied to the longitudinal dynamics model, and accurate tracking of the vehicle's longitudinal speed is achieved through feedforward control and PI-based feedback control.

[0153] Longitudinal dynamics control enables the vehicle to track a reference longitudinal velocity. It consists of feedforward control and PI-based feedback control, and the formula for the longitudinal dynamics model, utilizing driving traction and driving resistance, is as follows:

[0154] (6),

[0155] (7),

[0156] In the formula, This represents the relationship between the vehicle's mass m and its longitudinal acceleration. The product; Total traction force provided to the motor; T represents the driving resistance; ei This indicates the traction torque provided by the motor; For the equivalent tire radius, and to facilitate the design of the feedforward controller, let... ; F represents the reciprocal of the resistance to movement; res Indicates driving resistance; Indicates acceleration drag; This represents air resistance, where ramp resistance has a relatively small impact on the results, so its influence is not considered. For the overall vehicle weight; It is gravitational acceleration; Longitudinal velocity; , , , These represent the vehicle's rolling coefficient, air density, drag coefficient, and frontal area, respectively.

[0157] Feedforward controller: Due to the discrepancy between the theoretical torque requirement and the torque requirement used by the feedforward controller in equation (8), a feedforward controller is used to resolve this issue. The calculation formula for the feedforward control is as follows:

[0158] (8),

[0159] In the formula, Indicates the feedforward control traction force component; It is the proportional gain; T ei This indicates the traction torque provided by the motor; For the overall vehicle weight; Let be the equivalent tire radius; s represents the Laplace operator; Longitudinal velocity;

[0160] This embodiment uses a proportional-integral (PI) controller with feedback to eliminate static deviations in longitudinal velocity, ultimately obtaining the total longitudinal traction force. :

[0161] (9),

[0162] (10)

[0163] In the formula, The traction force component represents the feedback control; s represents the Laplace operator. This represents the proportional gain coefficient of the PI controller; This represents the integral gain coefficient of the PI controller; Indicates the total longitudinal traction force; Indicates the feedforward control traction force component; Indicates the desired longitudinal velocity; This represents the longitudinal velocity.

[0164] Step 3: Since permanent magnet synchronous motors have the advantages of high power density, high efficiency and large torque range, permanent magnet synchronous motors are selected as drive motors. A motor model is established, and the total longitudinal traction force calculated in Step 2 is input into the motor model to calculate the power required by the motor at time t. The motor efficiency MAP diagram is then introduced.

[0165] For a distributed drive electric vehicle, the formula for calculating the motor power at time t is as follows:

[0166] (11),

[0167] in, For motor power, This is the motor torque. This represents the motor speed.

[0168] This embodiment focuses on the energy consumption of the inter-shaft drive force distribution, and therefore does not consider the working efficiency of the battery and other components.

[0169] During the operation of a motor, it is desirable for the motor to operate within its high-efficiency range as much as possible. Introducing, for example... Figure 3 The MAP diagrams shown above illustrate the motor efficiency of the front and rear axle motors, visually representing the relationship between motor efficiency, motor torque, and motor speed.

[0170] Step 4: For the longitudinal following scenario of distributed drive electric vehicles, a multi-objective optimization model predictive control algorithm is proposed to realize adaptive cruise control. Using the longitudinal motion control model in Step 2, an extended state space model for adaptive cruise control is constructed. The extended state space model for adaptive cruise control includes characteristic parameters of the vehicle's longitudinal speed, acceleration, distance deviation, and relative rate. Based on the discretization results of the longitudinal following extended state space model, as shown in Equation 16, the vehicle-to-vehicle time distance error, relative speed, longitudinal acceleration, and rate of change of acceleration are selected as optimization state variables to construct the objective function of the multi-objective optimization problem. By dynamically adjusting the weight coefficients of safety boundary control, dynamic following optimization, and comfort constraints, a comprehensive optimization function is formed. The relaxation factor is introduced into the comprehensive optimization function to dynamically adjust the constraint boundary weights. The comprehensive optimization function and the constraint condition of the rigid safety distance softened by the relaxation factor are transformed into the feasible domain boundary condition of a constrained quadratic programming problem. The objective function weight coefficients are optimized in real time by combining a rolling time domain strategy. By solving a quadratic programming problem, a series of optimized control commands are generated. The first control command in the sequence is selected for vehicle control at the current moment, and the optimization iteration is performed repeatedly in the subsequent time domain until the control task for the entire time period is completed, thus realizing closed-loop control of the vehicle's adaptive cruise control. The specific content is as follows:

[0171] By nonlinearizing vehicle dynamics, an NMPC controller was designed to control the front wheel steering angle and calculate the direct yaw moment, enabling the vehicle to achieve smooth and safe trajectory tracking control.

[0172] Model Predictive Control (MPC), a core technology in industrial process control and intelligent driving, consists of three main functional modules: predictive model construction based on state equations, a rolling time-domain strategy for multi-objective optimization, and a feedback correction mechanism based on real-time measurement. A block diagram of the MPC principle is shown below. Figure 4 As shown, the system consists of an MPC controller, a distributed drive electric vehicle, and a state estimation unit operating collaboratively. The MPC controller constructs a dynamic state equation based on a predictive model and solves a constrained quadratic programming problem through a multi-objective collaborative optimization framework to generate the optimal control sequence in the future time domain. After implementation by the distributed drive electric vehicle, the vehicle state data is transmitted to the state estimation unit. This unit can use a Kalman filter algorithm to estimate unmeasurable parameters such as the road adhesion coefficient. The corrected state data is fed back to the MPC controller, dynamically adjusting the prediction time domain forward to form a closed-loop "prediction-execution-observation-correction" link, ensuring that the control commands match the actual vehicle state in real time.

[0173] Constructing a longitudinal following distance model: Based on longitudinal following characteristics, a longitudinal following extended state space model is constructed. This model is a simplified and processed vehicle longitudinal dynamics model specifically designed for adaptive cruise control (ACC) systems. Its continuous state equation is shown in equation (14), and after discretization, a discrete state space equation is obtained, as shown in equation (16). A following control model is constructed by selecting vehicle longitudinal dynamics characteristic parameters. The core characteristic parameters include: the speed difference between the preceding vehicle and the current vehicle, the acceleration difference, the vehicle distance deviation, and the relative speed fluctuation. Figure 5 The longitudinal driving distance model shown establishes an adaptive cruise control following model by dynamically relating the motion state parameters of the two vehicles with the control target parameters.

[0174] The motion relationship between the two vehicles can be seen from the longitudinal driving distance motion model as follows:

[0175] (12),

[0176] In the formula, Indicates the distance error between vehicles; Indicates the actual vehicle spacing; Indicates the desired safe vehicle spacing; This refers to the headway; v h(t) Indicates the speed of the vehicle itself; The minimum safe distance when the two vehicles are stopped; Represents relative velocity; Indicates the speed of the other vehicle; This represents the speed of the vehicle at time t-1; d represents the actual acceleration of the vehicle; d represents the distance between the two vehicles; t represents the time.

[0177] Due to the inherent inertial characteristics of the vehicle's transmission system, there is a dynamic lag between the desired acceleration command and the actual acceleration. Therefore, a first-order inertial transfer function model needs to be established, its mathematical expression being:

[0178] (13)

[0179] In the formula, For the actual acceleration, The desired acceleration command is given. This represents the gain factor of the inertial element, set to 1. represents the time constant of the inertial element; s represents the Laplace operator.

[0180] Based on formulas (12) and (13), the longitudinal control equations of the vehicle are constructed using a state-space modeling method. The deviation between the two vehicles is selected. Relative speed Real-time speed of this vehicle and actual acceleration Using the desired acceleration command as the control input, the vehicle dynamic state equation is established as follows:

[0181] (14)

[0182] In the formula: The first derivative of a state variable; Represents the system matrix; Indicates the output matrix; The input matrix represents the disturbance; x represents the state variable. To control input and ; For external interference and ; y is the output vector; This represents the output matrix.

[0183] ,

[0184] In the formula, △d represents the workshop error margin; Represents relative velocity; v h Indicates the vehicle's speed; The actual acceleration is represented by 'th'; 'th' represents the headway. The time constant representing the inertial element; It is a 4x4 identity matrix.

[0185] Given the discrete execution characteristics of model predictive control algorithms, a discretization transformation of the continuous system is required. The computationally efficient forward Euler method is used to discretize equation (14) to adapt to the discrete execution environment of model predictive control. The specific discretization results are as follows:

[0186] (15)

[0187] In the formula, This represents the vehicle spacing error at time k+1; This represents the vehicle spacing error at time k; represents the relative velocity at time k; th represents the headway. This represents the actual acceleration of the vehicle at time k; The sampling period; This represents the relative velocity at time k+1; This represents the acceleration of the vehicle in front at time k; Let k represent the vehicle speed at time k; This represents the actual acceleration of the vehicle at time k+1; This represents the vehicle's speed at time k+1; This represents the desired acceleration command at time k; This represents the inertial time constant of the actuator.

[0188] The discrete state-space equation can be derived using formula (15):

[0189] (16)

[0190] In the formula, x(k+1) represents the state vector at time K+1; A is the state transition matrix; B is the control input matrix; and G is the disturbance output matrix. , ; Let k be the state vector at time k; This is the control input at time k; The external disturbance at time k; Let C be the system output at time k; C is the output matrix.

[0191] , , , , .

[0192] In the formula, Let k be the state vector at time k; This represents the system output at time k. This represents the vehicle spacing error at time k; Represents the relative velocity at time k; Let k represent the vehicle speed at time k; This represents the actual acceleration of the vehicle at time k; is the sampling period; G is the interference output matrix; th represents the headway. A represents the inertial time constant of the actuator; B is the state transition matrix; G is the control input matrix; C is the disturbance output matrix; and D is the output matrix.

[0193] This embodiment uses a state-space modeling method to define the system's dynamic parameters: state variables. Characterizes the longitudinal motion state of the vehicle, output variable After sensor fusion, the data is mapped to the output of an observable system, which then acts as the input. Discretized control commands. Predictive time domain. With control time domain satisfy Relationship. Core assumptions include: observation consistency, and the state vector and disturbance vector being within the same sampling period. It can observe and predict external disturbances at all times within the time domain in real time. All are consistent with the current measured values Equivalence; control continuity, ensuring that control commands outside the control time domain remain consistent with the last command within the control time domain, i.e. Based on this, through Step-by-step recursive generation of state prediction equations:

[0194] (17)

[0195] In the formula, Let A represent the system state predicted at time k+1 from time k; A, B, and G are discrete state-space matrices. This represents the predicted system state at time k; k represents the current discrete-time index; k+1 and k+2 represent future discrete-time indices. This represents the absolute control quantity predicted at time k; The external disturbance at time k; This represents the system state predicted at time k+2 from time k. This represents the prediction of k+ at time k. The system state at any given moment; To control the time domain; A Nc This represents the free response of the system state after Nc sampling periods; This represents the prediction of k+ at time k. The absolute control quantity applied at time -2; This represents the prediction of k+ at time k. The absolute control quantity applied at time -1; A Nc-1A represents the free response of the system state after Nc-1 sampling periods; Nc-2 A represents the free response of the system state after Nc-2 sampling periods; 2 I represents the free response of the system state after 2 sampling periods; I is the identity matrix.

[0196] To improve the engineering applicability of the control strategy, this embodiment adopts an incremental control framework, which increments the control... Defined as an optimization variable, its recursive relationship is as follows:

[0197] (18)

[0198] In the formula, This represents the absolute control quantity to be applied at time k+j, predicted at time k. This represents the control increment predicted at time k+j from time k. This represents the absolute control quantity predicted at time k+j-1;

[0199] Based on the state variable recursion mechanism, when Prior control input at time Given that the future state of the system can be predicted, it can be expressed as:

[0200] (19)

[0201] In the formula, This represents the absolute control quantity predicted at time k; This represents the control quantity predicted at time k; This represents the prior control input at time k; This represents the absolute control quantity predicted at time k+1; This represents the control increment predicted at time k+1 from time k. This represents the prediction of k+ at time k. The absolute control quantity applied at time -1; This represents the prediction of k+ at time k. The control quantity applied at time -1; To control the time domain;

[0202] By combining formula (17) and formula (19), the recursive formula can be transformed into a form with incremental control effect:

[0203] (20)

[0204] In the formula, This represents the system state predicted at time k+1 from time k. This represents the predicted system state at time k; This represents the control quantity predicted at time k; A, B, and G are discrete state-space matrices. This represents the prior control input at time k; The external disturbance at time k;

[0205] I represents the system state predicted at time k+2 from time k; I is the identity matrix.

[0206] This represents the prediction of k+ at time k. The system state at a given time; A Nc A represents the free response of the system state after Nc sampling periods; Nc-1 This represents the free response of the system state after Nc-1 sampling periods; This represents the prediction of k+ at time k. The control quantity applied at time -1;

[0207] This represents the prediction of k+ at time k. The system state at time +1; A Nc+1 This represents the free response of the system state after Nc+1 sampling periods;

[0208] A represents the system state predicted at time k+Np+1 from time k; Np A represents the free response of the system state after Np sampling periods; Np-1 A represents the free response of the system state after Np-1 sampling periods; Np-Nc This represents the free response of the system state after Np-Nc sampling periods; k represents the current discrete-time index; k+1 and k+2 represent the future discrete-time indices. for Prior control input at time t; Nc is the control time domain; Np is the prediction time domain; A 2 This represents the free response of the system state after two sampling periods;

[0209] The predicted state equation of the system model is obtained from formula (20):

[0210] (twenty one),

[0211] In the formula, Predicting a sequence of states for the future time domain; This is the initial condition matrix for state prediction; Let be the current state vector at time k; To control the coefficient matrix of the input history items; The prior control input at time k; The coefficient matrix for controlling the increment term; This is the coefficient matrix of external disturbances; The external disturbance at time k; For future control of incremental sequence vectors;

[0212] , , ,

[0213] , , .

[0214] In the formula, Predicting a sequence of states for the future time domain; This is the initial condition matrix for state prediction; For future control of incremental sequence vectors; This represents the system state predicted at time k+1 from time k. This represents the system state predicted at time k+2 from time k. This represents the prediction of k+ at time k. The system state at any given moment; This represents the prediction of k+ at time k. The system state at time +1; A represents the system state predicted at time k+Np from time k. Nc A represents the free response of the system state after Nc sampling periods; Nc+1 A represents the free response of the system state after Nc+1 sampling periods; Np This represents the free response of the system state after Np sampling periods; This represents the control quantity predicted at time k; This represents the control increment predicted at time k+1 from time k. This represents the prediction of k+ at time k. The control quantity applied at time -1; A 2 This represents the free response of the system state after two sampling periods;

[0215] A, B, and G are discrete state-space matrices; k represents the current discrete-time index; k+1 and k+2 represent future discrete-time indices. The coefficient matrix for controlling the input history terms; N c To control the time domain, N p For prediction in the time domain; A i This represents the free response of the system state after i sampling periods; This is the coefficient matrix of external disturbances; The coefficient matrix for controlling the increment term;

[0216] Formula (16) can be used to determine that in The predicted output at time step is:

[0217] (twenty two),

[0218] In the formula, Predict the output sequence for the future time domain; This is the initial condition matrix for state prediction; Let be the current state vector at time k; To control the coefficient matrix of the input history items; The prior control input at time k; The coefficient matrix for controlling the increment term; For future control of incremental sequence vectors; This is the coefficient matrix of external disturbances; The external disturbance at time k;

[0219] , , , ,

[0220] .

[0221] In the formula, Predict the output sequence for the future time domain; This represents the system output predicted at time k+1 from time k. This represents the system output predicted at time k+2 from time k. This represents the system output predicted at time k+Np from time k. A is the initial condition matrix for state prediction; A, B, C, and G are discrete state space matrices; A 2 Indicates the free response of the system state after 2 sampling periods; A Nc A represents the free response of the system state after Nc sampling periods; Nc+1 A represents the free response of the system state after Nc+1 sampling periods; Np This represents the free response of the system state after Np sampling periods; A is the coefficient matrix for controlling the input history items; i This represents the free response of the system state after i sampling periods; This is the coefficient matrix of external disturbances; The coefficient matrix for controlling the increment term;

[0222] Adaptive cruise control systems need to strike a balance between following responsiveness, safety, comfort, and energy efficiency. Overemphasizing response speed leads to frequent switching between drive and braking, impacting comfort and energy consumption; conversely, overemphasizing smoothness reduces following performance, affecting driving safety and traffic efficiency. Model predictive control, through a multi-objective optimization framework, can effectively coordinate these mutually constraining performance indicators, ensuring system responsiveness while also considering ride comfort and energy efficiency.

[0223] The core of the multi-dimensional performance coordination of adaptive cruise control systems lies in balancing the triple coupling relationship between safety constraints, dynamic following, and comfort needs:

[0224] (1) Safety boundary control

[0225] The safety protection mechanism of an adaptive cruise control system needs to construct a dynamic safety threshold system. The key is to ensure that the actual vehicle distance meets the safety boundary through a real-time constraint mechanism. The system prevents rear-end collisions caused by uncontrolled distance by forcibly constraining the actual vehicle distance. The formula for the safety boundary control is as follows:

[0226] (twenty three),

[0227] In the formula, This is the actual vehicle spacing. This is a preset safe vehicle spacing threshold.

[0228] (2) Dynamic following optimization

[0229] The core of vehicle tracking performance lies in building a real-time response mechanism, enabling the vehicle to dynamically adjust its tracking strategy based on the motion state of the vehicle ahead. Its performance indicators focus on maintaining synchronization between the desired vehicle distance and the target vehicle speed, achieving real-time compensation for tracking errors through dynamic weight adjustments. Under ideal conditions, tracking performance must meet the distance error... With relative velocity The dual convergence constraints are used to construct a dynamic following optimization objective function for tracking performance. The formula is as follows:

[0230] (twenty four),

[0231] In the formula, This is the weighting coefficient for the spacing error. Δd represents the weighting coefficient for relative velocity error; Δv represents the expected spacing error; Δv represents the expected relative velocity error.

[0232] In actual operation, deviations in control parameters can easily lead to two extreme conditions: first, excessive spacing reduces road traffic efficiency and increases the probability of lane changes in adjacent lanes; second, insufficient spacing increases the collision risk index and reduces passenger comfort. To achieve safe following, the system uses dynamic threshold constraints to forcibly maintain the stability of spacing and speed.

[0233] (25)

[0234] In the formula, and An adaptive safety threshold for spacing error. and This is the safety threshold for relative speed.

[0235] (3) Comfort constraints

[0236] Under the premise of meeting safety constraints and tracking accuracy, ride comfort has become a core evaluation indicator for user acceptance. Studies have shown that a constant-speed driving mode can significantly reduce ride discomfort, primarily by suppressing drastic fluctuations in acceleration variables. Therefore, a multi-objective comfort constraint index is defined. The formula is as follows:

[0237] (26)

[0238] In the formula, The weighting coefficient is the expected acceleration increment. It represents the expected acceleration increment.

[0239] This indicator achieves dynamic compensation through a third-order constraint framework:

[0240] (27)

[0241] In the formula, and This indicates the allowable range of the expected acceleration increment. and This represents the desired acceleration safety threshold. and Indicates the actual acceleration execution boundary; Characterizes the expected acceleration increment; a des Indicates the desired acceleration; a s Indicates actual acceleration;

[0242] To construct a multi-objective performance system suitable for adaptive cruise control, it is necessary to dynamically adjust the weighting coefficients of safety boundaries, tracking accuracy, and comfort characteristics, and to weight and fuse multi-dimensional performance indicators to form a comprehensive optimization function. Through adaptive parameter adjustment, synergistic optimization of safety threshold constraints, tracking error suppression, and ride comfort improvement is achieved. The final formula for the system's comprehensive optimization function is as follows:

[0243] (28)

[0244] In the formula, To follow the performance objective function; For multi-objective comfort indicators; Indicates the expected spacing error; This represents the expected relative velocity error; This is the weighting coefficient for the spacing error. This is the weighting coefficient for the relative velocity error; The weighting coefficient is the expected acceleration increment. Characterizes the expected acceleration increment;

[0245] In the model predictive control architecture, the objective function supports multiple mathematical forms, including the 1-norm, quadratic form, or infinite norm. Since the quadratic form has the advantage of avoiding differences between positive and negative values ​​in computation, this embodiment chooses it as the basis for constructing the objective function. For the actual needs of vehicle dynamic following scenarios, the system performance index design focuses on two core objectives: first, to improve tracking accuracy by minimizing the deviation between the predicted trajectory and the actual output; and second, to limit the adjustment range of control commands and reduce the frequency of actuator actions. The second objective is to constrain the actuator action range and suppress abrupt changes in control input caused by frequent mode switching. Specifically:

[0246] (29)

[0247] In the formula, , This indicates the output tracking weight matrix. R controls the incremental weight matrix; In order to be in Performance metrics at any given time To control the incremental sequence, To output the predicted sequence, Expected reference trajectory sequence; .

[0248] To set the increment of the control quantity as the control input, the deviation is now defined. as follows:

[0249] (30)

[0250] In the formula, The desired reference trajectory sequence; This represents the reference output for time k+1 of the plan at time k; This represents the reference output for time k+2 of the plan at time k. This represents the reference output for time k+Np of the plan at time k; is the initial condition matrix for state prediction; x(k) is the state vector at the current time step; To control the coefficient matrix of the input history items; The prior control input at time k; This is the coefficient matrix of external disturbances; The external disturbance at time k;

[0251] Based on the tracking error constraint of equation (22), the performance index definition of equation (29), and the control input increment model of equation (30), the advanced mathematical expression of the system objective function is derived through the fusion of a multi-objective optimization framework as follows:

[0252] (32),

[0253] In the formula, Let k be the system performance index at time k; The coefficient matrix for controlling the increment term; ² represents the weighted sum of squares of the control increments at all times within the entire control time domain Np in the future; For future control of incremental sequence vectors; Meaning and The same applies; its mathematical form is its transpose matrix form; Q represents the output tracking weight matrix. The meaning is the same as ΔU(k), and its mathematical form is its transpose matrix form; R represents the control vector weight matrix; The reference trajectory and the free response error vector; Meaning and The same applies; its mathematical form is its transpose matrix form. ² represents the weighted sum of squares of the reference trajectory and free response errors at all times throughout the entire prediction time domain Np; T is the matrix transpose symbol.

[0254] To satisfy the convergence condition for the optimization solution, the objective function needs to be reconstructed into the standard mathematical paradigm of a quadratic programming (QP) problem, specifically expressed as follows:

[0255] (33),

[0256] In the formula, , ,and This is a constant term, and its value does not affect the solution of the optimal value in the quadratic programming problem. The performance metric at time k; This represents the prediction matrix between the control increment and the output; Meaning and The same applies; its mathematical form is its transpose matrix form; ΔU(k) ​​represents the future control increment sequence vector. The meaning is the same as ΔU(k), and its mathematical form is its transpose matrix form; This represents the error vector between the reference trajectory and the free response; Meaning and The same applies; its mathematical form is its transpose matrix form; Q represents the weight matrix; R represents the weight matrix; T represents the transpose of the matrix; k represents the sampling time index, which is unitless and identifies the sequence number of the current control cycle (e.g., k=1,2,3...), used for optimization iteration in the time domain; Represents a vector of linear terms; Meaning and The same applies; its mathematical form is its transpose matrix form.

[0257] To avoid unsolvable optimization scenarios, the constraints need to be flexible to expand the feasible region while maintaining the original rigid boundaries of the safety constraints. While ensuring the system safety threshold remains unchanged, the tolerance for vehicle dynamic tracking accuracy and the fluctuation threshold for ride comfort need to be dynamically adjusted. Strict limits are maintained for safety-related hard constraints, while tracking error and comfort indicators are allowed to expand flexibly within acceptable user ranges. By introducing a dynamic adjustment factor, the original hard constraints are transformed into scalable soft constraints, and this factor is embedded as a penalty term in the initial objective function to construct a new objective function to balance constraint rigidity. The formula for introducing the relaxation factor into the comprehensive optimization function is as follows:

[0258] (34),

[0259] In the formula, This represents the prediction matrix between the control increment and the output; Indicates the future control increment sequence; The vector represents the error between the reference trajectory and the free response; Q represents the weight matrix. It is a relaxation factor; Meaning and The same applies; its mathematical form is its transpose matrix form. R represents the relaxation factor weight; T represents the transpose of the matrix; k represents the sampling time index, which is unitless and identifies the sequence number of the current control cycle (e.g., k=1,2,3...), used for optimization iteration in the time domain.

[0260] Accordingly, the constraints softened by adding a relaxation factor are as follows:

[0261] (35),

[0262] In the formula, , , As slack variables, , , , , , These are the relaxation coefficients for the corresponding constraints, and their values ​​can be adjusted as needed; , Indicates the lower and upper limits of the control increment; , Indicates the lower and upper limits of the control quantity; , Indicates the lower and upper limits of the output quantity; This indicates the output selection matrix; This represents the control increment predicted at time k+j from time k. This represents the absolute control quantity to be applied at time k+j, predicted at time k. This represents the system output predicted at time k+j from time k; Nc is the control time domain, and Np is the prediction time domain.

[0263] , , .

[0264] In the formula, , This represents the lower and upper limits of the expected spacing error; , Indicates the lower and upper limits of vehicle speed; , Indicates the lower and upper limits of vehicle acceleration; , Indicates the lower and upper limits of the output quantity; This indicates the output selection matrix;

[0265] Based on formulas (34) and (35), the formula for the constrained quadratic programming problem is as follows:

[0266] (36)

[0267] In the formula, This represents the control increment vector at time k; This represents the extended Hessian matrix; This represents the expanded optimized vector; represents the expanded linear term vector; s represents the constraint condition bound vector; t represents the constraint condition upper bound vector. The coefficient matrix of linear inequality constraints; The constant vector of the linear inequality constraint, where T is the matrix transpose symbol.

[0268] in, , , ,

[0269] , ,

[0270] , ,

[0271] , ,

[0272] , ,

[0273] , , .

[0274] In the formula, The vector represents the extended optimization vector; △U represents the future control increment sequence vector. It is a relaxation factor; Represents the extended Hessian matrix; Represents the control increment Hessian matrix; The weights are relaxation factor weights; The extended error gradient vector is represented by f;

[0275] The coefficient matrix of the linear inequality constraint; II and Γ represent the cumulative control increment matrices; Ψ represents the control increment transformation matrix; I is the identity matrix; The coefficient matrix for controlling the increment term; , , , , , These are the relaxation coefficients for the corresponding constraints, and their values ​​can be adjusted as needed;

[0276] The constant vector of linear inequality constraints; , Indicates the lower and upper limits of the control increment; , Indicates the lower and upper limits of the control quantity; , Indicates the lower and upper limits of the output quantity; This is the initial condition matrix for state prediction; To control the coefficient matrix of the input history items; This is the coefficient matrix of external disturbances; The external disturbance at time k; The prior control input at time k;

[0277] Represents the upper limit boundary vector of the control increment; T is the matrix transpose symbol; Nc is the control time domain. This represents the lower bound boundary vector of the control increment;

[0278] Represents the upper limit boundary vector of the control quantity; Represents the lower limit boundary vector of the control quantity;

[0279] This represents the upper bound vector of the output boundary; Np is the prediction time domain; represents the lower bound vector of the output boundary; p represents the dimension controlling the input.

[0280] An optimized control command sequence is generated by performing a quadratic programming solution. The first control command in the sequence is extracted and applied to the distributed drive electric vehicle to complete the control task at the current moment. The optimization iteration is then performed repeatedly in the subsequent time domain until full-time control is achieved, thus realizing closed-loop control of the vehicle's adaptive cruise control.

[0281] Step 5: Based on the two-degree-of-freedom vehicle dynamics model and nonlinear tire model described in Step 1, design a nonlinear model predictive controller as the core algorithm of the active safety controller, and calculate the optimal direct yaw moment; the specific content is as follows:

[0282] A simplified framework for torque distribution control of distributed drive electric vehicles, considering safety and energy consumption, such as... Figure 6 As shown, the active safety controller uses nonlinear model predictive control (NMPC) to calculate the direct yaw torque, improving system safety and stability. The torque distribution optimizer employs a multi-objective optimization-based torque distribution method, with objectives including minimizing motor power loss and no-load motor loss, ensuring the motor operates in its high-efficiency region. This method achieves optimal torque distribution with minimal energy consumption while ensuring vehicle stability and safety.

[0283] Active safety controller: By nonlinearizing vehicle dynamics, an NMPC controller was designed to control the front wheel steering angle and calculate the optimal direct yaw moment, enabling the vehicle to achieve smooth and safe trajectory tracking control.

[0284] The calculation steps for the optimal direct yaw moment include:

[0285] Step 51: Establish the state-space model of active safety control using equation (1); this step constructs a transversely stable linearized state-space model, whose state variables include transverse velocity. yaw rate The sideslip angle β of the center of gravity is controlled by a direct yaw torque. This model is specifically designed for the NMPC algorithm and is the core of the Nonlinear Model Predictive Controller (NMPC). It provides predictive model support for solving the optimal direct yaw moment by linearizing the nonlinear characteristics of the vehicle's lateral dynamics online, ensuring the vehicle's lateral stability in scenarios such as curves and low-adhesion surfaces. The expression is as follows:

[0286] (37)

[0287] In the formula: Here are the state equations of the system; For state variables; For control variables; It is the first derivative of the state variable;

[0288] As shown in the following formula:

[0289] (38),

[0290] (39)

[0291] Step 52, define the system output equation as follows:

[0292] (40)

[0293] (41),

[0294] In the formula, Represents the system output vector; C represents the state vector; C represents the output matrix; where, For lateral velocity; This refers to the yaw rate; It is a 2x2 identity matrix; This is the direct yaw moment;

[0295] Step 53, let the control time domain and prediction time domain be respectively and At the sampling time control variable sequence and system output variable sequence They are respectively:

[0296] (42),

[0297] (43),

[0298] In the formula, This represents the predicted future control sequence at time k; This represents the control input applied at time k; This represents the control input predicted at time k+1 from time k. This represents the control input predicted at time k+Nc-1; Nc is the control time domain. This represents the predicted future output sequence at time k; This represents the system output at time k; The subsystem index is represented by k; the sampled value at the current time is represented by t; and the matrix transpose symbol is represented by t. This represents the system output predicted at time k+1 from time k. This represents the system output at time k+Np predicted at time k; N p For prediction in the time domain.

[0299] Step 54, at the sampling time Predictive control start point equal As the initial values ​​of the system state to predict future dynamic changes of the system, the system state and output prediction are defined as Equations (44) and (45), respectively:

[0300] (44),

[0301] (45)

[0302] In the formula, The system equations are linearized at time k; This is the output matrix; Nc represents the discrete time step; Np represents the control time domain and Np represents the prediction time domain. This represents the system state at time k; This represents the control input applied at time k; This represents the system state predicted at time k+1 from time k. This represents the system state predicted at time k+2 from time k. This represents the control input predicted at time k+1 from time k. This represents the process noise or disturbance predicted at time k+j from time k. This represents the system state predicted at time k+Nc from time k. This represents the system state predicted at time k+Nc-1 at time k; This represents the control input predicted at time k+Nc-1; This represents the system output predicted at time k+Nc-1 at time k; This represents the system output predicted at time k+1 from time k. This represents the system output predicted at time k+2 from time k. This represents the system output predicted at time k+Np from time k. This represents the system state predicted at time k+Np from time k; k represents the current discrete-time index; k+1 and k+2 represent future discrete-time indices. Indicates a subsystem index;

[0303] Step 55: Vehicle stability control is achieved by tracking the driver's desired response. Taking into account both lateral velocity and lateral angular velocity, the expression for the objective function J1 is designed as follows:

[0304] (46)

[0305] In the formula, This represents the system output predicted at time k+1 from time k. This represents the expected output reference value at time k+j; This indicates the output tracking weight matrix; The weight for lateral velocity; This represents the lateral velocity predicted at time k+i from time k. Let represent the expected lateral velocity at time k+i; It is the weight for yaw rate control; and These are the desired lateral velocity and yaw rate, respectively. This represents the yaw rate predicted at time k+i from time k. This represents the expected yaw rate at time k+i; p represents the upper limit of the summation; i and j represent the prediction step indices;

[0306] To ensure safety and stability while avoiding excessive rate of change in the control signal, the objective function J2 is designed as follows:

[0307] (47)

[0308] In equation (47), This represents the control increment predicted at time k+i at time k. R represents the yaw moment increment predicted at time k+i, m represents the upper limit of the summation, and i represents the prediction step index.

[0309] To prevent unsolvable variables during the solution process, slack variables and the corresponding cost function J3 are designed as follows:

[0310] (48)

[0311] In the formula, It is a weight matrix that characterizes the importance of slack variables; The set of slack variables that represent the degree of strictness of dynamic adjustment constraints.

[0312] Step 56, Construct the optimization problem: Based on the nonlinear control model equations and the objective function equations, the formula for constructing the optimization problem is as follows:

[0313] (49)

[0314] In the formula: A bundle of linear inequalities; denoted as a nonlinear inequality bundle; J(u) represents the overall objective function of the nonlinear model predictive control (NMPC) optimization problem; J1 represents the performance tracking objective function; J2 represents the control cost objective function; J3 represents the constraint violation penalty function; s represents the constraint lower bound vector; t represents the constraint upper bound vector.

[0315] Step 57, Solve the optimization problem: The optimization problem is solved using the sequential quadratic programming method. At each iteration point, a quadratic programming subproblem is solved to obtain the search direction. Then, a one-dimensional search is performed to obtain a new iteration point until the optimal solution is obtained, so as to obtain the optimal control input.

[0316] Step 58, QP algorithm flow:

[0317] Step 581, select a reasonable initial solution u0;

[0318] Step 582, solve the quadratic programming subproblem:

[0319] (50),

[0320] In the formula, This indicates that the objective function J is at the point The first derivative at that point, This indicates that the objective function J is at the point The second derivative at point d, where d represents the search direction vector. , Represents the inequality constraint function. , Indicates the constraint function at the point gradient at, This represents the current solution at the k-th iteration, where k represents the major iteration number of the SQP algorithm, and T represents the matrix transpose symbol.

[0321] Get search direction ;

[0322] Step 583, if or If yes, stop; otherwise, proceed to the next step.

[0323] Step 584, find the step size ,satisfy and

[0324] Step 585, let , Proceed to step (2);

[0325] Step 59, Calculate the direct yaw moment: At each sampling time, the system prediction variables are updated using the real-time measured vehicle state information, and an optimization solution is performed to obtain the optimal direct yaw moment. This optimization process continues until the task ends.

[0326] NMPC obtains the optimal direct yaw moment by solving the optimization problem at each time step, thereby improving the vehicle's handling stability and active safety under extreme conditions.

[0327] Step 6: Determine the current torque distribution coefficient based on the optimal direct yaw torque obtained in Step 5, calculate the motor's no-load power loss, and calculate the motor's power loss during driving and braking based on the energy flow characteristics of the motor during vehicle operation. Establish a total motor power loss model, calculate and compare the total motor power loss under different torque distribution coefficients, determine the torque distribution coefficient that minimizes power loss, and define the objective function that minimizes the total motor power loss. Determine the constraints in the optimization process, including maximum torque output limits, speed limits, and motor efficiency limitations. Use quadratic programming to solve the objective function, find the optimal torque distribution coefficient, verify whether the found optimal torque distribution coefficient satisfies all constraints, and apply the found optimal torque distribution coefficient to the drive motor. Specific steps are as follows:

[0328] Torque Distribution Optimizer: The goal of the torque distribution optimizer is to optimize the energy distribution between the front and rear axles to meet the stability requirements of the safety controller. It emphasizes that reducing motor energy efficiency is the key factor in achieving optimization.

[0329] Considering the torque distribution model of motor no-load loss, the torque distribution between the front and rear axle motors is determined by the torque distribution coefficient. Based on the optimal direct yaw torque obtained in step 5, the current torque distribution coefficient is determined as follows:

[0330] (51),

[0331] In the formula, , These represent the torques of the front and rear motors, respectively. The required total torque. Torque distribution coefficient. The value range is from 0 to 1, when At that time, only the front axle was driven. The value indicates that only the rear axle is driven; all other values ​​indicate that both the front and rear axle motors are driven together.

[0332] In a distributed electric vehicle, the motor is directly connected to the axle. In single-motor drive mode, the non-working motor will be driven to rotate, and the resulting loss is called motor no-load loss. The formula for calculating the no-load power loss of a motor, which can be obtained by measuring it with a dynamometer, is as follows:

[0333] (52),

[0334] In the formula, This represents the no-load power loss of the motor; n represents the motor speed. This indicates the no-load loss torque of the motor.

[0335] Based on the energy flow characteristics of the motor during driving and braking of a vehicle, the motor power loss during driving and braking is calculated using the following formula:

[0336] (53),

[0337] (54),

[0338] In the formula, This represents the power loss of the motor during driving; This represents the power loss of the motor during braking. It is the efficiency of the motor at the current torque and speed; Indicates motor power; Indicates motor torque; Indicates the motor speed;

[0339] For ease of analysis, it is assumed that the vehicle wheel speeds are equal and the transmission ratios of the front and rear axle reducers are the same. Based on equations (53) and (54), a total power loss model for the motor is established:

[0340] (55),

[0341] (56),

[0342] In the formula, This represents the total power loss of the motor system under driving conditions. This represents the total required driving torque for the vehicle. Indicates the motor speed; Indicates the torque distribution coefficient. Indicates the efficiency of the rear axle motor; Indicates the efficiency of the front axle motor; This indicates the total power loss of the motor system under braking conditions.

[0343] When considering the no-load loss of the motor, a total power loss model of the motor needs to be established, and the objective function needs to be modified according to equation (52). When in single-motor mode (d... i When the torque distribution coefficient is 0 or 1, the no-load loss of the corresponding motor needs to be explained separately. The formulas for calculating and comparing the total power loss of the motor under different torque distribution coefficients are as follows:

[0344] (57),

[0345] (58),

[0346] In equations (57) and (58), This represents the total power loss of the motor system under driving conditions. This indicates the total power loss of the motor system under braking conditions; This represents the total required driving torque for the vehicle. Indicates the motor speed; Indicates the torque distribution coefficient; Indicates the efficiency of the front axle motor; Indicates the efficiency of the rear axle motor; and These represent the rotational speeds as follows: The no-load power loss of the front and rear axle motors.

[0347] Taking the minimum total power loss of the motor as the objective function, we can obtain the total required torque. and rotational speed Under these conditions, the total motor loss can be expressed as the torque distribution coefficient d. i The function. Based on this, an objective function that minimizes the total power loss of the motor, considering the no-load loss of the motor, can be established as follows:

[0348] (59),

[0349]

[0350] Constraints: (60)

[0351] In the formula, , These represent the maximum torque of the front and rear axle motors at the current speed; That is the maximum speed of the motor. Indicates the torque distribution coefficient; Indicates the efficiency of the rear axle motor; Indicates the efficiency of the front axle motor; This represents the total required driving torque for the vehicle.

[0352] Determination of torque distribution coefficient: Based on the mathematical model and efficiency MAP, the optimal torque distribution coefficient is determined offline. In dual-motor mode, the minimum total loss is calculated under different distribution coefficients. and corresponding Total losses of front and rear motors and By comparing the results, the optimal torque distribution coefficient that minimizes the total loss is determined.

[0353] (61),

[0354] Based on two objective functions, one considering no-load losses and the other not, equations (57)(58) and (55)(56) are used as objective functions to solve the problems for different total torque and speed conditions. The results are presented in the form of a MAP diagram, which can be used for real-time table lookup applications. Figure 7 The torque distribution coefficient MAP is shown for both cases.

[0355] As can be seen from the figure, total torque demand is the dominant factor in optimal torque distribution and has a significant impact, while motor speed has a relatively smaller impact. At low torque, using a single front axle motor drive can achieve higher efficiency and energy saving; at high torque, using a dual-motor operating mode allows the overall motor to operate in the high-efficiency range.

[0356] Torque distribution control method: Based on previous research, the operating mode of the drive motor is defined as follows:

[0357] (62),

[0358] In the formula, This represents the actual output torque of the motor; This represents the expected output speed of the motor; Here is the torque distribution coefficient, where These correspond to the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. Since this embodiment focuses on a dual-motor distributed drive electric vehicle with both front and rear axles, the torques of the left and right front axle wheels are equal, and the torques of the left and right rear axle wheels are also equal. , .

[0359] In the torque distribution controller, an optimization objective function based on minimizing tire adhesion utilization was established:

[0360] (63),

[0361] In the formula, Let be the motor torque of the i-th wheel; This refers to the yaw rate; This refers to the road surface adhesion coefficient. These correspond to the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. This represents the vertical load on the i-th wheel;

[0362] In the process of solving the optimization allocation algorithm, the effective solution must satisfy the total required torque. and direct yaw moment The requirements are also limited by the maximum output torque of the drive motor, and the constraints are as follows:

[0363] (64),

[0364] In the formula, Let be the motor torque of the i-th wheel; Wheelbase; These correspond to the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. Indicates the torque distribution coefficient; This refers to the yaw rate;

[0365] The objective function is solved using quadratic programming, and the formula for finding the optimal torque distribution coefficient is as follows:

[0366] (65),

[0367] In the formula: , It is a weight matrix that satisfies the equality conditions. , They are Total demand drive torque of the vehicle and Weight of direct yaw moment; It is the solver's optimization vector. for Total demand drive torque of the vehicle and The expected value of the direct yaw moment; It is a relaxation weight matrix; Here is the gain matrix. This is the tire load factor weight matrix; The radius of the wheel's rolling radius; This refers to the road surface adhesion coefficient. , This is the motor torque constraint vector; To optimize the variable vector; T is the matrix transpose symbol; This represents the vertical load on wheel i; , corresponding to the left front wheel, right front wheel, left rear wheel, and right rear wheel respectively; s represents the constraint condition bounding vector; t represents the constraint condition upper bounding vector;

[0368] (66),

[0369] In the formula, This is the direct yaw moment; This represents the total required driving torque of the vehicle; T is the matrix transpose symbol.

[0370] The gain matrix can be represented as:

[0371] (67)

[0372] In the formula, Wheelbase; These correspond to the left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively. Indicates the torque distribution coefficient; ω represents the yaw rate.

[0373] Step 7: Integrate the two-degree-of-freedom vehicle dynamics model constructed in Step 1, the longitudinal motion control model established in Step 2, and the nonlinear model predictive controller designed in Step 5 to form a comprehensive vehicle control system. This comprehensive vehicle control system uses the optimized control commands generated by the multi-objective optimization model predictive control algorithm in Step 4 to adjust the longitudinal speed of the vehicle. Based on the optimal torque distribution coefficient identified in Step 6, it adjusts the torque distribution between the front and rear axles and applies the optimal torque distribution coefficient to the permanent magnet synchronous motor described in Step 3. During vehicle operation, the longitudinal speed, lateral stability, and motor operating status of the vehicle are monitored in real time. The torque distribution coefficient and control commands are dynamically adjusted based on the monitoring results to adapt to changing driving conditions and optimize vehicle performance. Steps 4 to 7 are repeated in each control cycle to form a closed-loop control iteration.

[0374] Specifically, this embodiment studies and designs adaptive cruise following control and torque distribution control for distributed drive electric vehicles, merging the two control methods into a hierarchical multi-objective cooperative control strategy. The framework diagram of this hierarchical multi-objective cooperative control strategy is shown below. Figure 8As shown, the upper layer is a multi-objective optimization MPC adaptive cruise control, and the lower layer is a multi-objective torque distribution control considering safety and energy consumption. The adaptive cruise and torque distribution coordinated control system of the distributed drive electric vehicle adopts a hierarchical architecture to achieve multi-objective optimization. The upper-layer controller is based on the model predictive control framework and generates the optimal acceleration command by fusing multi-objective functions of safety, following, and comfort. The lower-layer torque distribution system combines nonlinear model predictive control and motor efficiency optimization algorithms to dynamically adjust the front and rear axle torque distribution strategy. This system ensures lateral stability by calculating the direct yaw moment in real time, and intelligently switches between single / dual-axle drive modes according to the motor's operating characteristics. Under the premise of ensuring safe distance constraints, it achieves coordinated optimization of longitudinal tracking accuracy and lateral handling stability, while also taking into account energy efficiency and ride comfort. The entire control process forms a closed-loop optimization chain from objective analysis and constraint fusion to torque distribution execution, effectively solving the limitations of traditional control methods in multi-objective coordination.

[0375] To verify the effectiveness of the aforementioned adaptive cruise and torque distribution coordinated control method for distributed drive electric vehicles, a vehicle simulation model was constructed based on the MATLAB / Simulink simulation platform, and detailed simulation experiments were conducted.

[0376] The main parameter settings for the vehicle simulation model are shown in Table 1.

[0377] Table 1 Main parameters of the car simulation model

[0378]

[0379] 1. Sine wave cruise following mode:

[0380] The vehicle initially follows a target vehicle traveling at 95 km / h at an initial speed of 110 km / h, with an initial distance of 65 m. The target vehicle then travels at an average speed of 95 km / h with a fluctuation range of ±20 km / h, performing sinusoidal speed changes over a 30-second cycle for a total of 80 seconds. This test comprehensively verifies the system's following control performance under varying speed differences and distances.

[0381] Simulation results of sinusoidal variable speed cruise following conditions are as follows Figure 9As shown, the multi-objective cooperative control strategy exhibits excellent comprehensive performance under sinusoidal speed change conditions. In terms of following distance control, the integrated vehicle control system maintains a stable following distance within a safe range of 53-65m, with significantly reduced error fluctuations compared to the traditional MPC strategy, rapidly converging to a precise control range of ±0.5m within 10 seconds. Regarding speed tracking performance, the vehicle completes speed adjustment from 110km / h to 85km / h within 10 seconds, maintaining a stable tracking accuracy of ±1km / h. In terms of acceleration control, the integrated vehicle control system limits the maximum longitudinal acceleration to within 0.6m / s², ensuring smooth acceleration and deceleration. In terms of energy consumption, through dynamic torque distribution optimization, total energy consumption is reduced by 13.8%, and the average motor efficiency is increased to 82.1%, achieving synergistic optimization of performance and energy efficiency.

[0382] Table 2 Comparison of Energy Efficiency Results under Sine Wave Cruise Following Conditions

[0383]

[0384] 2. Snake-shaped bend following vehicle condition:

[0385] In serpentine curve following conditions, vehicles must not only maintain a suitable distance from the vehicle in front but also cope with continuous curves, placing high demands on the vehicle's lateral stability and longitudinal control coordination. The reference speed was set to 80 km / h, the initial following distance was 50 meters, and the total duration of the test was 120 seconds.

[0386] Simulation results of serpentine bend following vehicle condition are as follows: Figure 10 As shown. Regarding lateral stability, the system controls the peak yaw rate to within 0.8°, a 60% reduction compared to traditional MPC strategies, and effectively suppresses the risk of sideslip in corners through real-time torque distribution. In terms of longitudinal control performance, the following distance is stabilized within the 48-52m range, with error fluctuations reduced to ±0.8m, while the vehicle speed tracking error is controlled within ±1km / h. Comfort performance is outstanding, with the rate of acceleration change limited to ±0.3m / s³, significantly reducing passenger discomfort.

[0387] In terms of energy efficiency optimization, according to Figure 9 (f) Energy consumption comparison and energy efficiency comparison of serpentine curve following conditions Table 3 shows that the total energy consumption of the multi-objective strategy is 1426kJ, which is 13.0% lower than the 1640kJ of the MPC strategy, saving about 60Wh of electricity. The average efficiency of the motor is increased to 82.5%, thanks to the dynamic distribution of torque according to the tire adhesion state in the curve to reduce torque output when the inner wheel is under low load, reduce no-load loss, and make the motor work in the high efficiency range.

[0388] Table 3 Comparison of Energy Efficiency Results under the Snake-Beam Following Condition

[0389]

[0390] 3. CHTC Variable Speed ​​Cruise Control Following Vehicle Condition

[0391] The CHTC variable speed cruise following scenario is a comprehensive test scenario that closely reflects the actual traffic conditions in China. The initial speed of the vehicle is set to 0 km / h, the distance between vehicles is 5m, and the speed of the vehicle in front changes according to the CHTC scenario. The simulation time is 1600 seconds.

[0392] The simulation results of CHTC variable speed cruise control following the vehicle are as follows: Figure 11 As shown, the multi-objective cooperative control strategy exhibits superior comprehensive performance under CHTC mixed operating conditions. In terms of dynamic following control, the integrated vehicle control system achieves precise maintenance of a safe distance across the entire operating range: maintaining a stable following distance of 20-25m in low-speed congestion and controlling it within the 40-45m range in high-speed cruising, significantly reducing distance fluctuation by 10% compared to the traditional MPC strategy. Regarding speed tracking performance, the integrated vehicle control system controls the maximum speed error within ±5km / h and ensures smooth acceleration and deceleration by constraining the rate of change of acceleration (peak value ≤1.4m / s³). Energy efficiency optimization is outstanding, with total energy consumption reduced by 6% and the average motor efficiency increased to 83.1%. This is mainly due to the intelligent torque distribution mechanism, which uses a front axle single-drive mode to avoid no-load losses at low speeds and achieves dual-axle cooperative drive based on the efficiency MAP at high speeds. The torque distribution strategy creates a 50N·m level inter-axle torque difference under rapid acceleration conditions, ensuring that each motor always operates within its high-efficiency range.

[0393] Table 4 Comparison of energy efficiency results of CHTC cruise control under following conditions

[0394]

[0395] The results under the above three operating conditions show that the proposed cooperative control strategy effectively improves the vehicle's following stability, handling safety and energy utilization efficiency through hierarchical control coupling. Compared with the traditional single-objective strategy, it significantly improves the vehicle's overall performance and achieves a good balance between safety, comfort and economy.

Claims

1. A method for coordinated control of adaptive cruise and torque distribution in a distributed-drive electric vehicle, characterized in that, Includes the following steps: Step 1: Construct a two-degree-of-freedom vehicle dynamics model that includes lateral motion and yaw motion, introduce a nonlinear tire model to calculate tire lateral force, and consider the longitudinal load transfer effect to calculate the vertical load on the front and rear axles. Step 2: Using the vehicle's driving traction force and driving resistance, based on the two-degree-of-freedom vehicle dynamics model described in Step 1 and the calculation results of the vertical loads on the front and rear axles, establish a longitudinal motion control model. Track the vehicle's longitudinal speed through feedforward control and PI-based feedback control, and calculate the total longitudinal traction force. Step 3: Select a permanent magnet synchronous motor as the drive motor, establish a motor model, input the total longitudinal traction force calculated in Step 2 into the motor model, calculate the power required by the motor, and import the motor efficiency MAP chart. Step 4, Multi-objective optimization model predictive control algorithm to realize adaptive cruise control: Using the longitudinal motion control model in Step 2, an extended state space model of adaptive cruise control is constructed. The extended state space model of adaptive cruise control includes characteristic parameters of vehicle longitudinal speed, acceleration, vehicle distance deviation and relative speed. Based on the discretization results of the longitudinal following extended state space model, the vehicle-to-vehicle time distance error, relative speed, vehicle longitudinal acceleration and acceleration change rate are selected as optimization state variables, and the objective function of the multi-objective optimization problem is constructed. By dynamically adjusting the weight coefficients of safety boundary control, dynamic following optimization, and comfort constraints, a comprehensive optimization function is formed. A relaxation factor is introduced into the comprehensive optimization function, and the comprehensive optimization function and the constraints softened by adding the relaxation factor are transformed into a constrained quadratic programming problem. By solving the quadratic programming problem, a series of optimized control commands are generated. The first control command in the sequence is selected for vehicle control at the current moment, and optimization iterations are performed cyclically in the subsequent time domain until the control task for the entire time period is completed, thereby realizing the closed-loop control of vehicle adaptive cruise. Step 5: Based on the two-degree-of-freedom vehicle dynamics model and nonlinear tire model described in Step 1, design a nonlinear model predictive controller as the core algorithm of the active safety controller, and calculate the optimal direct yaw moment. Step 6: Determine the current torque distribution coefficient based on the optimal direct yaw torque obtained in Step 5, calculate the motor no-load power loss, calculate the motor power loss during driving and braking based on the energy flow characteristics of the motor during vehicle operation, establish a total motor power loss model, calculate and compare the total motor power loss under different torque distribution coefficients, determine the torque distribution coefficient with the minimum power loss, and the objective function for minimizing the total motor power loss, determine the constraints in the optimization process, including the maximum torque output limit, speed limit, and relevant motor efficiency limits, use quadratic programming to solve the objective function, find the optimal torque distribution coefficient, verify whether the found optimal torque distribution coefficient satisfies all constraints, and apply the found optimal torque distribution coefficient to the drive motor. Step 7: Integrate the two-degree-of-freedom vehicle dynamics model constructed in Step 1, the longitudinal motion control model established in Step 2, and the nonlinear model predictive controller designed in Step 5 to form a comprehensive vehicle control system. This comprehensive vehicle control system uses the optimized control commands generated by the multi-objective optimization model predictive control algorithm in Step 4 to adjust the longitudinal speed of the vehicle. Based on the optimal torque distribution coefficient identified in Step 6, it adjusts the torque distribution between the front and rear axles and applies the optimal torque distribution coefficient to the permanent magnet synchronous motor described in Step 3. During vehicle operation, the longitudinal speed, lateral stability, and motor operating status of the vehicle are monitored in real time. Based on the monitoring results, the torque distribution coefficient and control commands are dynamically adjusted to adapt to changing driving conditions and optimize vehicle performance. Steps 4 to 7 are repeated in each control cycle to form a closed-loop control iteration.

2. The method according to claim 1, characterized in that, The differential equations of motion for the two-degree-of-freedom vehicle dynamics model described in step 1 are: （1）， In the formula: Indicates lateral acceleration; This represents the total lateral force exerted by the front wheels on the vehicle. This indicates the total lateral force exerted by the rear wheels on the vehicle. For the overall vehicle weight; , This refers to the distance from the front and rear axles of the vehicle to its center of gravity. The moment of inertia of the car; Longitudinal velocity; The yaw rate is angular velocity. Indicates yaw acceleration; The nonlinear tire model is the Fiala model, and the tire lateral force... The calculation formula is: （2）， In the formula: This refers to the tire's lateral stiffness. The road surface adhesion coefficient; This refers to the vertical load on the tire; This refers to the tire slip angle; This refers to the tire saturation slip angle; The formulas for calculating the vertical loads on the front and rear axles are as follows: （5）， In the formula: F zf Indicates the vertical load on the front axle; F zr Indicates the vertical load on the rear axle; L r L represents the distance from the rear axle to the center of mass. f Indicates the distance from the front axle to the center of mass; It is the height of the vehicle's center of gravity; For the overall vehicle weight; It is gravitational acceleration; It is the vehicle's wheelbase; It is the longitudinal acceleration of the vehicle.

3. The method according to claim 1, characterized in that, The formula for the longitudinal motion control model described in step 2 is as follows: （6）， （7）， In the formula, This represents the relationship between the vehicle's mass m and its longitudinal acceleration. The product; Total traction force provided to the motor; T represents the driving resistance; ei This indicates the traction torque provided by the motor; For the equivalent tire radius, and to facilitate the design of the feedforward controller, let... ; Represents the reciprocal of the resistance to movement; Indicates acceleration drag; This represents air resistance, where ramp resistance has a relatively small impact on the results, so its influence is not considered. For the overall vehicle weight; It is gravitational acceleration; Longitudinal velocity; , , , These represent the vehicle's rolling coefficient, air density, drag coefficient, and frontal area, respectively. The formula for the total longitudinal traction force is as follows: （9）， （10）， In the formula, This indicates the traction force component of the feedback control; s represents the Laplace operator; This represents the proportional gain coefficient of the PI controller; This represents the integral gain coefficient of the PI controller; Indicates the total longitudinal traction force; Indicates the feedforward control traction force component; Indicates the desired longitudinal velocity; This represents the longitudinal velocity.

4. The method according to claim 1, characterized in that, The formula for calculating the power required by the motor in step 3 is as follows: （11）， in, For motor power, This is the motor torque. This represents the motor speed.

5. The method according to claim 1, characterized in that, The objective function of the multi-objective optimization problem described in step 4 is as follows: (33), In the formula, Let be the performance index at time k; ΔU(k) ​​represents the future control increment sequence vector; The meaning is the same as ΔU(k), and its mathematical form is its transpose matrix form; , ,and This is a constant term, and its value does not affect the solution of the optimal value in the quadratic programming problem. This represents the prediction matrix between the control increment and the output; Meaning and The same applies; its mathematical form is its transpose matrix form. This represents the error vector between the reference trajectory and the free response; Meaning and The same applies; its mathematical form is its transpose matrix form; Q represents the weight matrix; R represents the weight matrix; T represents the transpose of the matrix; k represents the sampling time index, which is unitless and identifies the sequence number of the current control cycle (e.g., k=1,2,3...), used for optimization iteration in the time domain; Represents a vector of linear terms; Meaning and The same applies; its mathematical form is its transpose matrix form. The formula for the safety boundary control is as follows: （23）， In the formula, This is the actual vehicle spacing. To preset a safe vehicle spacing threshold; The objective function for the dynamic following optimization is as follows: （24）， In the formula, J track This represents the performance objective function for following the target function; This is the weighting coefficient for the spacing error. This is the weighting coefficient for the relative velocity error; Indicates the expected spacing error; This represents the expected relative speed error; The formula for the comfort constraint is as follows: （26）， In the formula, For multi-objective comfort indicators; The weighting coefficient is the expected acceleration increment. Characterizes the expected acceleration increment; The formula for the comprehensive optimization function is as follows: （28）， In the formula, J represents the comprehensive optimization function; To follow the performance objective function; For multi-objective comfort indicators; Indicates the expected spacing error; This represents the expected relative velocity error; This is the weighting coefficient for the spacing error. This is the weighting coefficient for the relative velocity error; The weighting coefficient is the expected acceleration increment. Characterizes the expected acceleration increment; The formula for introducing the relaxation factor into the comprehensive optimization function is as follows: （34）， In the formula, It is a relaxation factor; Meaning and The same applies; its mathematical form is its transpose matrix form. The weights are relaxation factor weights; This represents the error vector between the reference trajectory and the free response; This represents the prediction matrix between the control increment and the output; This represents the control increment vector; The error vector between the reference trajectory and the free response is represented by Q; the weight matrix is ​​represented by R; the transpose of the T matrix is ​​represented by k; k represents the sampling time index, which is unitless and identifies the sequence number of the current control cycle (e.g., k=1,2,3...), used for optimization iteration in the time domain. The formula for the constrained quadratic programming problem is as follows: （36）， In the formula, This represents the control increment vector at time k; This represents the extended Hessian matrix; This represents the expanded optimized vector; represents the expanded linear term vector; s represents the constraint condition bound vector; t represents the constraint condition upper bound vector. The coefficient matrix of linear inequality constraints; The constant vector of linear inequality constraints.

6. The method according to claim 1, characterized in that, Step 5, the calculation steps for the optimal direct yaw moment, include: Step 51: Establish the state-space model of active safety control, whose expression is as follows: （37）， In the formula: Here are the state equations of the system; For state variables; For control variables; It is the first derivative of the state variable; Step 52, define the system output equation as follows: （40）， （41）， In the formula, Represents state variables; Indicates the system output; C is the output matrix; The lateral velocity; This refers to the yaw rate; It is a 2x2 identity matrix; Step 53, let the control time domain and prediction time domain be respectively and At the sampling time The control variable sequence and the system output variable sequence are as follows: （42）， （43）， In the formula, This represents the predicted future control sequence at time k; This represents the control input applied at time k; This represents the control input predicted at time k+1 from time k. This represents the control input predicted at time k+Nc-1; Nc is the control time domain. This represents the predicted future output sequence at time k; This represents the system output at time k; The subsystem index is represented by k; the sampled value at the current time is represented by t; and the matrix transpose symbol is represented by t. This represents the system output predicted at time k+1 from time k. This represents the system output at time k+Np predicted at time k; N p For prediction in the time domain; Step 54, at the sampling time Predictive control start point equal As the initial value of the system state to predict the future dynamic changes of the system, the system state and output prediction are defined as Equations (44) and (45), respectively: （44）， （45）， In the formula, The system equations are linearized at time k; This is the output matrix; Nc represents the discrete time step; Np represents the control time domain and Np represents the prediction time domain. This represents the system state at time k; This represents the control input applied at time k; This represents the system state predicted at time k+1 from time k. This represents the system state predicted at time k+2 from time k. This represents the control input predicted at time k+1 from time k. This represents the process noise or disturbance predicted at time k+j from time k. This represents the system state predicted at time k+Nc from time k. This represents the system state predicted at time k+Nc-1 at time k; This represents the control input predicted at time k+Nc-1; This represents the system output predicted at time k+Nc-1 at time k; This represents the system output predicted at time k+1 from time k. This represents the system output predicted at time k+2 from time k. This represents the system output predicted at time k+Np from time k. This represents the system state predicted at time k+Np from time k; k represents the current discrete-time index; k+1 and k+2 represent future discrete-time indices. Indicates a subsystem index; Step 55, taking into account both lateral velocity and yaw rate, the expression for the objective function J1 is designed as follows: （46）， In the formula: This represents the system output predicted at time k+1 from time k. This represents the expected output reference value at time k+j; This indicates the output tracking weight matrix; The weight for lateral velocity; This represents the lateral velocity predicted at time k+i from time k. Let represent the expected lateral velocity at time k+i; It is the weight for yaw rate control; and These are the desired lateral velocity and yaw rate, respectively. This represents the yaw rate predicted at time k+i from time k. This represents the expected yaw rate at time k+i; p represents the upper limit of the summation; i and j represent the prediction step indices; To avoid excessively large rates of change in the control signal, the expression for the objective function J2 is designed as follows: （47）， In the formula, This represents the control increment predicted at time k+i at time k. R represents the yaw moment increment predicted at time k+i; m represents the upper limit of the summation; and i represents the prediction step index. To prevent unsolvable variables during the solution process, slack variables and the corresponding cost function J3 are designed as follows: （48）， In the formula, It is a weight matrix that characterizes the importance of slack variables; Step 56, Construct the optimization problem: Based on the nonlinear control model equations and the objective function equations, the formula for constructing the optimization problem is as follows: （49）， In the formula: J1 represents the performance tracking objective function; J2 represents the control cost objective function; J3 represents the constraint violation penalty function; s represents the constraint lower bound vector; t represents the constraint upper bound vector; A bundle of linear inequalities; For nonlinear inequality bundles; J(u) represents the overall objective function of the nonlinear model predictive control (NMPC) optimization problem; Step 57, Solve the optimization problem: Use the sequential quadratic programming method to solve the optimization problem and obtain the optimal control input; Step 58, QP algorithm flow: Step 581: Select a reasonable initial solution ; Step 582, solve the quadratic programming subproblem: （50）， Get search direction ; In the formula, This indicates that the objective function J is at the point The first derivative at that point, This indicates that the objective function J is at the point The second derivative at point d, where d represents the search direction vector. , Represents the inequality constraint function. , Indicates the constraint function at the point gradient at, This represents the current solution at the k-th iteration, where k represents the major iteration number of the SQP algorithm, and T represents the matrix transpose symbol. Step 583, if or If yes, stop; otherwise, proceed to the next step. Step 584, find the step size ,satisfy and ; Step 585, let , Proceed to step (2); Step 59, Calculate the direct yaw moment: At each sampling time, update the system prediction variables using the real-time measured vehicle state information, perform an optimization solution, and obtain the optimal direct yaw moment.

7. The method according to claim 1, characterized in that, The formula for the current torque distribution coefficient mentioned in step 6 is as follows: （51）， In the formula, , These represent the torque of the front and rear motors, respectively. Total torque required; torque distribution factor The value range is from 0 to 1, when At that time, only the front axle was driven. When only the rear axle is driven, all other values ​​indicate that the front and rear axle motors drive together. The formula for calculating the no-load power loss of the motor is as follows: （52）， In the formula, This indicates the no-load power loss of the motor; This indicates the no-load loss torque of the motor; Indicates the motor speed; The formula for calculating the motor power loss during driving and braking is as follows: （53）， （54）， In the formula, This represents the power loss of the motor during driving; This represents the power loss of the motor during braking. It is the efficiency of the motor at the current torque and speed; Indicates motor power; Indicates motor torque; Indicates the motor speed; The formula for calculating and comparing the total power loss of the motor under different torque distribution coefficients is as follows: （57）， （58）， In equations (57) and (58), This represents the total power loss of the motor system under driving conditions. This indicates the total power loss of the motor system under braking conditions. This represents the total required driving torque for the vehicle. Indicates the motor speed; Indicates the torque distribution coefficient; Indicates the efficiency of the front axle motor; Indicates the efficiency of the rear axle motor; and These represent rotational speeds of 1000 and 1000 respectively. The no-load power loss of the front and rear axle motors; The objective function for minimizing the total power loss of the motor is established as follows: （59）， The constraints are as follows: （60）， In the formula, , These represent the maximum torque of the front and rear axle motors at the current speed; That is the maximum speed of the motor. Indicates the torque distribution coefficient. Indicates the efficiency of the rear axle motor; Indicates the efficiency of the front axle motor. This represents the total required driving torque for the vehicle. The objective function is solved using quadratic programming, and the formula for finding the optimal torque distribution coefficient is as follows: （65）， In the formula: , It is a weight matrix that satisfies the equality conditions. , They are Total demand drive torque of the vehicle and Weight of direct yaw moment; It is the solver's optimization vector. for Total demand drive torque of the vehicle and The expected value of the direct yaw moment; Here is the gain matrix. This is the tire load factor weight matrix; The radius of the wheel's rolling radius; This refers to the road surface adhesion coefficient. , This is the motor torque constraint vector; To optimize the variable vector; T is the matrix transpose symbol; Represents the vertical load on wheel i, where , respectively, correspond to the left front wheel, right front wheel, left rear wheel, and right rear wheel; s represents the constraint condition bounding vector; t represents the constraint condition upper bounding vector.

Images