Real-time control method of additional yaw torque for distributed drive electric vehicles

Abstract

The present invention relates to a real-time control method for the additional yaw moment of a distributed drive electric vehicle, comprising the following steps: obtaining the vehicle's real-time motion state and inputting it into a vehicle dynamics model; using the vehicle's yaw rate and center-of-mass slip angle as tracking targets, suppressing actuation energy, optimizing the additional yaw moment, and obtaining the distribution of the additional yaw moment to each tire; during the optimization calculation, linear expressions of the vehicle's center-of-mass slip angle and the vehicle's yaw rate with respect to the additional yaw moment are constructed, thereby optimizing the additional yaw moment. Compared with existing technologies, the present invention achieves better control effects for both tracking the desired yaw rate and suppressing the center-of-mass slip angle, while also reducing calculation time and meeting real-time requirements.

Description

Technical Field

[0001] The present invention relates to the field of chassis control of distributed drive electric vehicles, and in particular to a real-time control method for an additional yaw torque of a distributed drive electric vehicle. Background Art

[0002] Driving stability control for electric vehicles is a crucial aspect of vehicle safety. Distributed drive electric vehicles have attracted widespread attention within the industry due to their high degree of control freedom and flexible and efficient control performance. To ensure stable vehicle driving, distributed drive electric vehicles track the desired additional yaw torque determined by the upper-level controller to implement additional torque control compensation for the four-wheel motor drive torque, thereby regulating the vehicle's motion state and maintaining stable driving. Therefore, the additional yaw torque decision method for distributed drive electric vehicles is extremely important for achieving vehicle stability control. However, existing additional yaw torque decision methods for distributed drive electric vehicles have the following problems:

[0003] 1. Existing research on yaw moment decision methods, such as those in patents CN 111959288 B and CN 113147422 A, mostly employ sliding film controllers to calculate the desired additional yaw moment for the vehicle. However, these yaw moment decision methods based on sliding film theory are essentially error-tracking feedback control methods. They derive an explicit expression for the additional yaw moment based on the error between the desired and actual vehicle states. Consequently, the resulting control variable is not optimal for the entire system, making it difficult to guarantee optimal control results.

[0004] 2. Existing optimization-based research on distributed electric vehicle additional yaw moment decision-making methods employs model predictive control (MPC) to optimize the additional yaw moment. Due to the characteristics of MPC's rolling optimization, solving MPC-based additional yaw moment optimization problems often takes a long time. Furthermore, model complexity significantly impacts solution time. For nonlinear models, solving MPC optimization problems requires specialized solvers, which further increases the demand for computing power and time. Summary of the Invention

[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a real-time control method for additional yaw torque of distributed drive electric vehicles, so as to ensure better control effect and reduce calculation time.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] A real-time control method for additional yaw torque of a distributed drive electric vehicle comprises the following steps:

[0008] The real-time vehicle motion state is acquired and input into a pre-built vehicle dynamics model. The vehicle's yaw rate and sideslip angle at the center of mass are used as tracking targets. The actuation energy is suppressed, and the additional yaw moment is optimized and calculated to obtain the distribution of the additional yaw moment to each tire.

[0009] During the optimization calculation process, a linear expression of the vehicle's center of mass sideslip angle with respect to the additional yaw moment and a linear expression of the vehicle's yaw angular velocity with respect to the additional yaw moment are constructed respectively, thereby performing an optimization calculation of the additional yaw moment.

[0010] Furthermore, the vehicle dynamics model is expressed as:

[0011]

[0012]

[0013]

[0014]

[0015]

[0016] Where, is the rate of change of the sideslip angle at the center of mass, is the rate of change of yaw rate, x1 is the normalized sideslip angle of the center of mass, x2 is the normalized yaw rate, g1(x) and g2(x) are both intermediate quantities, β up is the upper limit of the sideslip angle, γ up is the upper limit of the yaw rate, ΔM zup is the upper limit of the additional yaw moment, β is the sideslip angle of the center of mass; γ is the yaw angular velocity, F yf , F yr are the lateral forces of the front and rear axle tires, m is the mass of the vehicle, V x Indicates the longitudinal speed, L f , L r are the distances from the vehicle's center of mass to the front and rear axles, I z is the vehicle's moment of inertia about the Z axis.

[0017] Furthermore, the linear expression of the center of mass sideslip angle with respect to the additional yaw moment is:

[0018]

[0019] Where, are the partial derivatives of the function g1(x) with respect to the state variables yaw rate and sideslip angle of the center of mass, respectively. x1(t+h) is the sideslip angle of the center of mass at time t+h, h is the step size, and x1(t) is the sideslip angle of the center of mass at time t.

[0020] Furthermore, the linear expression of the vehicle yaw rate with respect to the additional yaw moment is:

[0021]

[0022] Where x2(t+h) is the yaw rate at time t+h, h is the step size, and x2(t) is the yaw rate at time t.

[0023] Furthermore, the optimization problem of the optimization calculation is:

[0024]

[0025] stu min ≤u≤u max

[0026]

[0027] Where J is the objective function, Φ γ is the weight coefficient of the yaw rate, x2(t+h) is the yaw rate at time t+h, h is the step size, and is the intermediate quantity, Φ β is the weight coefficient of the sideslip angle of the center of mass, Φ u is the weight coefficient of the additional yaw moment, u is the control quantity, i.e. the additional yaw moment, β ref is the desired vehicle center of mass sideslip angle, γ ref is the desired yaw rate, u min is the minimum additional yaw moment, u max is the maximum value of the additional yaw moment, β up is the upper limit of the sideslip angle, γ up is the upper limit of the yaw rate.

[0028] Furthermore, during the optimization calculation, the linear expression of the vehicle's sideslip angle with respect to the additional yaw moment and the linear expression of the vehicle's yaw angular velocity with respect to the additional yaw moment are substituted into the optimization problem, and the objective function expression obtained is:

[0029] J=J1+J2+J3

[0030]

[0031]

[0032]

[0033]

[0034] Where x2 is the yaw rate, x1(t) is the sideslip angle of the center of mass at time t, are the partial derivatives of the function g1(x) with respect to the state variables yaw rate and sideslip angle of the center of mass, respectively.

[0035] Furthermore, during the optimization calculation process, the optimal solution of the additional yaw moment is calculated by solving the extreme point. The extreme point expression of the objective function is:

[0036] P1(x)u+P2(x)+P3(x)=0

[0037]

[0038]

[0039]

[0040] Where P1(x), P2(x) and P3(x) are all intermediate quantities;

[0041] The expression of the extreme point is:

[0042]

[0043] The obtained extreme point is denormalized to obtain the optimal solution of the additional yaw moment. The calculation expression of the optimal solution is:

[0044] u * =uΔM zup

[0045] Where u * is the optimal solution for the additional yaw moment.

[0046] Furthermore, the method further includes setting an additional yaw moment range for the optimal solution of the additional yaw moment to obtain an optimal additional yaw moment. The optimal additional yaw moment is used to distribute the additional yaw moment to each tire. The calculation expression of the optimal additional yaw moment is:

[0047]

[0048] Where, is the optimal additional yaw moment, is the minimum additional yaw moment, is the maximum value of the additional yaw moment.

[0049] Furthermore, the distribution expression of the distribution amount of the additional yaw moment of each tire is:

[0050]

[0051]

[0052] Where, ΔT fl , ΔT fr , ΔT rl and ΔT rr The distribution of the additional yaw moment to the left front wheel, right front wheel, left rear wheel and right rear wheel, R e is the tire rolling radius; d is the vehicle wheelbase.

[0053] Furthermore, the obtained distribution amount of the additional yaw moment of each tire is transmitted to the layer controller for execution, and each tire of the electric vehicle is driven respectively.

[0054] Compared with the prior art, the present invention has the following advantages:

[0055] The present invention first solves the state quantity based on the vehicle dynamics model and approximates the state quantity function. By combining the vehicle differential equation, a linear expression of the state quantity with respect to the control quantity is obtained. Finally, the optimization problem is reconstructed and the approximate expression of the state quantity is used to solve the extreme value point. This expression is the optimal additional yaw moment decision result.

[0056] This solution achieves excellent control results for tracking the desired yaw rate and suppressing the sideslip angle, comparable to nonlinear model predictive control. Furthermore, computational time comparisons show that the proposed real-time optimization decision method for additional yaw moment generates an explicit expression for the optimal additional yaw moment, resulting in a shorter computation time and meeting real-time requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 This is an architecture diagram of a real-time control method for additional yaw torque of a distributed drive electric vehicle provided in an embodiment of the present invention;

[0058] Figure 2 A schematic diagram of a two-degree-of-freedom model of a vehicle provided in an embodiment of the present invention;

[0059] Figure 3 A schematic diagram of a vehicle yaw rate curve under the solution of the present invention during a simulation process provided in an embodiment of the present invention;

[0060] Figure 4 A schematic diagram of a vehicle center of mass sideslip angle curve under a solution of the present invention during a simulation process provided in an embodiment of the present invention;

[0061] Figure 5 A schematic diagram of a vehicle yaw rate curve under an additional yaw moment decision method based on nonlinear model predictive control during a simulation process provided in an embodiment of the present invention;

[0062] Figure 6 A schematic diagram of a vehicle center of mass sideslip angle curve under an additional yaw moment decision method based on nonlinear model predictive control during a simulation process provided in an embodiment of the present invention;

[0063] Figure 7 Schematic diagram of comparison curves of additional yaw moments determined by two methods provided in an embodiment of the present invention;

[0064] Figure 8 A schematic diagram of the calculation time consumption of the two methods provided in the embodiments of the present invention. DETAILED DESCRIPTION

[0065] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0066] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0067] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0068] In the description of the present invention, it should be noted that the terms "center", "up", "down", "left", "right", "vertical", "horizontal", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, or are the orientation or position relationship in which the product of the invention is usually placed when in use. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, they should not be understood as limiting the present invention.

[0069] It should be noted that the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of the technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of this application, "plurality" means two or more, unless otherwise specifically defined.

[0070] Furthermore, terms such as "horizontal" and "vertical" do not necessarily mean that a component must be absolutely horizontal or overhanging, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but rather that it can be slightly tilted.

[0071] Example 1

[0072] This embodiment provides a real-time control method for additional yaw torque of a distributed drive electric vehicle, comprising the following steps:

[0073] The real-time vehicle motion state is acquired and input into a pre-built vehicle dynamics model. The vehicle's yaw rate and sideslip angle at the center of mass are used as tracking targets. The actuation energy is suppressed, and the additional yaw moment is optimized and calculated to obtain the distribution of the additional yaw moment to each tire.

[0074] During the optimization calculation process, the linear expression of the vehicle's sideslip angle with respect to the additional yaw moment and the linear expression of the vehicle's yaw angular velocity with respect to the additional yaw moment were constructed respectively, so as to perform the optimal calculation of the additional yaw moment.

[0075] Specifically, the proposed solution consists of three parts. The first part solves the desired state variables based on a second-order reference model of the vehicle. The second part, based on knowledge of vehicle dynamics, approximates the state variable function using Taylor expansion theory. By combining the vehicle differential equations, a linear expression of the state variable with respect to the control variable is obtained. The third part constructs an optimization problem and uses the approximate state variable expression to obtain an explicit expression of the extreme point. This expression is the optimal additional yaw moment decision result. By constructing an explicit solution for the optimal additional yaw moment, the optimal real-time decision of the additional yaw moment can be achieved.

[0076] Preferably, in order to verify the effectiveness of the method described in this embodiment, a simulation condition was designed for comparison and verification with a traditional algorithm. The simulation condition was selected to solve the vehicle driving stability problem on a low-adhesion road, and the algorithm used for comparison was an additional yaw moment decision method based on model predictive control.

[0077] The specific steps of the above scheme include:

[0078] Step S1: Building a high-fidelity vehicle dynamics model.

[0079] In Carsim dynamics simulation software, a vehicle model was selected, vehicle parameters were configured, and input and output variable interfaces were defined. A multi-constraint torque vectoring optimization allocation algorithm was constructed based on MATLAB / Simulink. The algorithm input was the real-time vehicle motion state from Carsim dynamics simulation software, and the algorithm output was fed into the vehicle control input interface within Carsim dynamics simulation software. Based on the selected vehicle model and parameters, a simulation condition for stable vehicle driving on a low-adhesion road surface was constructed, and the effectiveness of the proposed method was verified through simulation.

[0080] Step S2: Expected state quantity reference solution

[0081] Aiming at the handling stability control problem of distributed drive electric vehicles, a second-order reference model is used to solve the desired state reference:

[0082]

[0083] Among them, δ f is the front wheel steering angle; H(s) is the transfer function from the front wheel steering angle to the vehicle's desired state reference.

[0084] The tire force of the vehicle is limited by the road adhesion limit during driving. Therefore, when calculating the expected state reference, it should be limited to a certain extent to adapt to the road adhesion limit. The upper limit of the expected state reference is defined as Then the expected state constraint is:

[0085]

[0086] Step S3: Use Taylor expansion theory to approximate the state differential equation

[0087] The specific steps include:

[0088] Step S3.1: Construct vehicle dynamics equations

[0089]

[0090] Among them, x is the system state quantity, which is a multidimensional vector, and the dimension is consistent with the degree of freedom of the vehicle dynamics model; u is the control quantity, which is the additional yaw moment in the present invention; g is the symbol representing the functional relationship.

[0091] Step S3.2: Build tire model

[0092]

[0093] Among them, f x , f y All are symbols representing functional relationships.

[0094] Step S3.3: Approximate the vehicle state function using Taylor expansion theory

[0095] Analysis of the vehicle dynamics equations reveals that the vehicle state is a nonlinear differential equation expressing the control variable, making it difficult to solve the optimization problem. To obtain an explicit solution to the optimization problem, an approximate step size of h is used, and Taylor expansions of different orders are performed on the state at the current time t. The order is selected based on the ability to obtain a linear expression for the control variable.

[0096] Combined with the vehicle dynamics differential equation (3), the vehicle state function is approximated by Taylor expansion to obtain the linear expression of the state with respect to the control quantity:

[0097] x(t+h)=G(x(t))+Ku(t) (5)

[0098] Among them, K is the coefficient vector; t represents the current time; G is the symbol representing the functional relationship.

[0099] Step S4: Construct the optimization problem and obtain the explicit expression of the extreme point

[0100] The specific steps include:

[0101] Step S4.1: Construct the optimization problem objective function

[0102] In the study of vehicle driving stability control, the construction of the objective function usually considers the tracking of the desired state quantity and the suppression of the actuation energy. Therefore, the objective function is constructed as follows:

[0103]

[0104] Among them, x ref is the state quantity reference; Φ1 and Φ2 are the weight coefficients of the state quantity and the control quantity respectively.

[0105] Step S4.2: Substitute the Taylor expansion approximate expression of the state quantity into the objective function

[0106] Substituting equation (5) into equation (6), we can obtain the objective function expression containing only the variable to be optimized u(t):

[0107]

[0108] Step S4.3: Solve the explicit expression of the extreme point

[0109] From the analysis of formula (7), we can see that the objective function is a quadratic function of the variable to be optimized u(t). Therefore, the extreme point of the objective function is the optimal solution of the variable to be optimized.

[0110] make

[0111]

[0112] The explicit optimal solution of the variable to be optimized is

[0113] u * (t) = -Φ1(Φ1K+Φ2) -1 [G(x(t))-x ref ] T (9)

[0114] In practical applications, after obtaining the explicit solution of the control quantity, it is also necessary to consider the upper and lower limits of the control quantity constraints, and set the additional yaw moment range to The optimal additional yaw moment is:

[0115]

[0116] Once the optimal additional yaw torque is obtained, it can be transmitted to the lower-level controller for execution. By adopting a suitable distribution method to distribute the additional yaw torque, the additional torque on the four wheels is obtained, thus achieving stability control for the distributed drive electric vehicle.

[0117] The following is an example to introduce the specific implementation process of the above solution.

[0118] The architecture diagram of the real-time optimization decision method for the additional yaw moment in this example is as follows: Figure 1 As shown in the figure, the expected vehicle state reference calculation module receives the front wheel angle input δ from the driver. f Then, the expected state reference value x of the vehicle is calculated based on the vehicle's two-degree-of-freedom reference model ref This reference value is fed into the real-time optimal additional yaw moment decision module. In this module, the vehicle and tire models are first constructed. The state function is then approximated based on Taylor expansion theory. Combined with the vehicle dynamics differential equation, a linear expression of the state with respect to the control variable is obtained. Next, an optimization objective function is constructed based on the vehicle's driving stability requirements. The approximated state differential equation is then substituted into the function to obtain a quadratic function with respect to the control variable. Finally, an explicit expression for the optimal additional yaw moment is derived based on the extreme value theorem. Because the determined additional yaw moment is an explicit expression, it meets real-time computational requirements.

[0119] The real-time optimization decision-making method for the additional yaw moment in this example is implemented and verified through software system co-simulation. The specific process is as follows:

[0120] 1. Software Selection

[0121] The proposed real-time optimization algorithm for the additional yaw moment and the construction of the controlled vehicle simulation model were implemented using Matlab / Simulink R2020a and CarSim 2019.1, respectively, using high-fidelity vehicle dynamics simulation software. Matlab / Simulink was used to build the algorithm, which was implemented through modular programming within Simulink. CarSim provided a high-fidelity vehicle dynamics model and corresponding simulation conditions. This model replaced the actual vehicle in the simulation experiments as the target for the designed real-time optimization algorithm.

[0122] 2. Joint simulation settings

[0123] To achieve co-simulation between the two software programs, the input and output interface modules of CarSim are first configured, and the Simulink model path is added to the CarSim software to enable joint communication. CarSim is then compiled and the corresponding S-Function module is generated in Simulink. Finally, the S-Function parameters are configured and the input and output signal interfaces are derived. The co-simulation step size is set to 0.001s. While the Simulink model is running, the CarSim model is also performing calculations and solving. Data is continuously exchanged between the two during the simulation. If the model structure or parameter settings in CarSim are modified, it must be recompiled and the S-Function module must be regenerated to update the CarSim software configuration information.

[0124] To verify the effectiveness of the additional yaw moment real-time optimization decision-making method described in the present invention, the present invention selects vehicle stability control on low-adhesion roads for method verification. First, a joint simulation software platform based on MATLAB / Simulink and Carsim high-assurance dynamics software is built to select a vehicle model and configure parameters. Then, an additional yaw moment real-time optimization decision-making algorithm is built in MATLAB / Simulink and the input and output interfaces are defined to meet the joint simulation requirements. Finally, a low-adhesion road vehicle stability control test condition is set in Carsim to verify the method described in the present invention. At the same time, a comparison is made with the additional yaw moment decision-making method based on model predictive control to illustrate the beneficial effects of the present invention.

[0125] The specific method of the additional yaw moment real-time optimization decision-making method of the present invention is as follows:

[0126] Step S1: Building a high-fidelity vehicle dynamics model

[0127] The high-fidelity vehicle dynamics model is used to simulate a real controlled object, which is a distributed drive electric vehicle in the present invention. The high-fidelity vehicle dynamics model constructed here mainly simulates the yaw motion and lateral motion of the real vehicle.

[0128] In Carsim, first select the passenger car model and then configure its parameters. Since the present invention focuses on the real-time optimization decision-making method for the additional yaw moment, it focuses on important vehicle and tire parameters such as vehicle mass, the distance between the vehicle center of mass and the front and rear axles, and the tire cornering stiffness. Then, configure the vehicle driving conditions, mainly including the test route and road adhesion conditions. The vehicle driving route is controlled by the driver model provided by Carsim, and the driver model outputs the front wheel steering angle δ f After determining the additional yaw moment, the additional yaw moment is distributed using an average distribution method to obtain the additional torque on all four wheels. Finally, configure the input and output interfaces of Carsim. The input interface is for the additional torque on all four wheels, and the output interface is for important vehicle status information. After completing the above configuration, add Carsim to Simulink as an S-Function and match the algorithm with the input and output interfaces of the Carsim module.

[0129] Step S2: Calculate the expected state

[0130] For vehicle driving stability control, the vehicle yaw rate and vehicle center of mass sideslip angle are usually selected as tracking targets. For the yaw rate, the expected yaw rate reference value is calculated using the widely used vehicle second-order reference model. In the reference model, according to the current vehicle front wheel angle δ f and the corresponding transfer function to calculate the desired state, where the front wheel angle δ f The desired yaw rate γ of the vehicle ref The transfer function is

[0131]

[0132] The vehicle stability factor is

[0133]

[0134] In the above formula, L = L f +L r Indicates the vehicle's wheelbase.

[0135] The natural frequency of the system is:

[0136]

[0137] The system damping coefficient is:

[0138]

[0139] The steady-state yaw rate gain is

[0140]

[0141] Yaw rate differential coefficient

[0142]

[0143] The tire force of the vehicle is limited by the road adhesion limit during driving. Therefore, when calculating the expected yaw rate reference, it should be limited to a certain extent to adapt to the road adhesion limit. The upper limit of the expected yaw rate reference is defined as γ up , then

[0144]

[0145] The yaw rate reference value should be limited to the boundary range, that is:

[0146] |γ ref |≤γ up (18)

[0147] For the desired vehicle center of mass slip angle reference, since the center of mass slip angle represents the lateral motion ability of the vehicle, the larger the center of mass slip angle, the more violent the vehicle lateral motion, and the greater the possibility of vehicle instability and tail swing. Therefore, the desired vehicle center of mass slip angle reference is usually set to zero, that is:

[0148] β ref =0 (19)

[0149] Similarly, considering the tire adhesion limit on the center of mass slip angle, the upper limit of the center of mass slip angle β up for

[0150]

[0151] Step S3: Use Taylor expansion theory to approximate the state differential equation

[0152] The specific steps include:

[0153] Step S3.1: Construct vehicle dynamics equations

[0154] In this embodiment, a two-degree-of-freedom vehicle model is used to describe the vehicle's lateral and yaw motions. It is worth noting that, because the approximate step size selected in the Taylor expansion theory is typically small, the vehicle's longitudinal velocity can be assumed to remain constant within this approximate step size. In this case, the vehicle's longitudinal velocity is introduced into the model as a variable parameter and updated during each approximate calculation.

[0155] The vehicle two-degree-of-freedom model is as follows Figure 2 As shown in the model diagram, F yf , F yr are the lateral forces of the front and rear axle tires respectively; F xf , F xr are the longitudinal forces of the front and rear axle tires respectively; α f , α r are the tire side slip angles of the front and rear axles respectively; L f , L r are the distances from the center of mass of the vehicle to the front and rear axles respectively; m is the mass of the vehicle; I z is the vehicle's moment of inertia around the Z axis; V x represents the longitudinal velocity; β represents the sideslip angle of the center of mass; γ represents the yaw rate; δ f Indicates the front wheel turning angle;

[0156] according to Figure 2 The vehicle two-degree-of-freedom model is established as:

[0157]

[0158] Among them, β up is the upper limit of the sideslip angle at the center of mass; γ up is the upper limit of the yaw rate; ΔM zup The purpose of introducing these quantities to add an upper limit value of the yaw moment is to normalize the state quantities and control quantities. They are all considered to be known quantities in the present invention.

[0159] Step S3.2: Build tire model

[0160] To improve model accuracy, the Fiala brush model is used here to describe the lateral forces on the front and rear axle tires. This nonlinear model can effectively improve tire force estimation accuracy compared to linear models. In this model, the tire slip angle is used as an internal variable. When the tire slip angle α is very small, tanα≈α. The tire model can then be approximated as:

[0161]

[0162] Wherein, μ is the road adhesion coefficient; F z is the vertical load; C α is the tire cornering stiffness. To distinguish the front and rear wheels, the front wheel cornering stiffness is recorded as C f , the rear wheel cornering stiffness is recorded as C r .

[0163] The tire slip angle is calculated as follows:

[0164]

[0165] Step S3.3: Approximate the vehicle state function using Taylor expansion theory

[0166] To facilitate derivation, the vehicle dynamics equation in Equation (21) is rewritten as follows:

[0167]

[0168] in,

[0169]

[0170] In order to obtain an explicit solution to the optimization problem, the approximate step size is taken as h, and Taylor expansions of different orders are performed on the state function. The order is selected based on the ability to obtain a linear expression of the state with respect to the control quantity.

[0171] Performing a second-order Taylor expansion on the center-of-mass slip angle function x1(t) and combining it with the vehicle dynamics differential equation (21), we can obtain the linear expression of the center-of-mass slip angle with respect to the control variable additional yaw moment:

[0172]

[0173] in, They are the partial derivatives of the function g1(x) with respect to the state variables yaw rate and center of mass sideslip angle, and the solution formula is as follows

[0174]

[0175] in, represents the derivative of the tire lateral force with respect to the tire slip angle and is determined by equation (22).

[0176] Performing a first-order Taylor expansion on the yaw rate function x2(t) and combining it with the vehicle dynamics differential equation (21), we can obtain the linear expression of the yaw rate with respect to the control variable additional yaw torque:

[0177]

[0178] Step S4: Construct the optimization problem and obtain the explicit expression of the extreme point

[0179] The specific steps include:

[0180] Step S4.1: Construct the optimization problem objective function

[0181] In the real-time optimization decision method for the additional yaw moment of the present invention, when setting the objective function, the tracking of the vehicle's desired yaw rate reference value, the desired center of mass sideslip angle reference value, and the suppression of actuation energy are considered. The optimization problem is thus constructed as follows:

[0182]

[0183] stu min ≤u≤u max

[0184] in,

[0185]

[0186] Step S4.2: Substitute the Taylor expansion approximate expression of the state quantity into the objective function

[0187] Substituting equations (26)-(28) into the objective function (29), we have

[0188]

[0189]

[0190]

[0191]

[0192] in,

[0193] Therefore, the objective function expression is

[0194] J=J1+J2+J3 (34)

[0195] Step S4.3: Solve the explicit expression of the extreme point

[0196] Analyzing equations (31)-(34), we can see that the objective function is a quadratic function of the variable to be optimized u. Therefore, the extreme point of the objective function is the optimal solution of the variable to be optimized.

[0197]

[0198] The expression of the extreme point is:

[0199] P1(x)u+P2(x)+P3(x)=0 (36)

[0200] in,

[0201]

[0202]

[0203]

[0204] Solving equation (36) yields the expression of the extreme point:

[0205]

[0206] After denormalizing the control quantity, we have

[0207] u * =uΔM zup (39)

[0208] In practical applications, after obtaining the explicit solution of the control quantity additional yaw moment, it is also necessary to consider the upper and lower limits of the control quantity constraints, and set the additional yaw moment range to [ΔM min ΔM max ], then the optimal additional yaw moment is:

[0209]

[0210] After obtaining the optimal additional yaw moment, it can be transmitted to the lower-level controller for execution. For example, the additional yaw moment can be distributed evenly, as shown in the following formula:

[0211]

[0212] Among them, fl, fr, rl, rr represent the left front wheel, right front wheel, left rear wheel, and right rear wheel respectively; R e is the tire rolling radius; d is the vehicle wheelbase;

[0213] In order to verify the effectiveness of the real-time optimization decision-making method for the additional yaw moment described in the present invention, vehicle stability control on a low-adhesion road was selected for method verification.

[0214] The comparison method used in the simulation process is an additional yaw moment decision method based on model predictive control. In this comparison method, the vehicle and tire models used are consistent with those in the embodiment of the present invention to ensure the effectiveness of the comparison experiment. Because the tire model used in the embodiment is nonlinear, the constructed additional yaw moment decision method based on model predictive control is a nonlinear control method and requires a specific solver for solution. In this simulation process, the Casadi nonlinear solver is used to solve the nonlinear model predictive control problem.

[0215] The parameters of the vehicle model used in the simulation are the vehicle's moment of inertia around the Z axis I z =2059.2kg.m 2 ; Vehicle mass m = 1430kg; Distance from vehicle center of mass to front axle L f =1.05m, distance from rear axle L r =1.61m; front tire cornering stiffness C f =43082N / rad, rear tire cornering stiffness C r=59950N / rad, vehicle wheelbase d = 1.55m. In the low-adhesion road condition setting, the road adhesion coefficient μ = 0.35, and the vehicle driving condition is a double lane change condition. For the developed additional yaw moment real-time optimization decision algorithm, the approximate step size h = 0.01 is taken; the yaw rate tracking weight is Φ γ =500, the center of mass sideslip angle suppression weight is Φ β =0.01; the actuation energy suppression weight is Φ u =2; additional yaw moment upper limit ΔM zup =5000Nm;

[0216] In the simulation test, the vehicle was driven in a dual-lane-change mode at a constant speed of 70 km / h. The vehicle's steering wheel angle was determined by Carsim's built-in driver model. The real-time optimization decision-making method for additional yaw moment determined the optimal additional yaw moment, which was then evenly distributed across all four wheels to generate additional torque, which was then applied to the high-fidelity vehicle dynamics model. The simulation results are shown in the accompanying figure.

[0217] Figure 3 This is the vehicle yaw rate tracking curve obtained by the real-time optimization decision-making method for the additional yaw moment described in the present invention during the simulation process. Analysis of the curve shows that the additional yaw moment obtained by the method proposed in the present invention can effectively ensure the vehicle yaw rate tracking accuracy after being applied to the vehicle. Figure 4 This is the vehicle center of mass sideslip angle curve obtained by the real-time optimization decision-making method for the additional yaw moment described in the present invention during the simulation process. Analysis of the curve shows that the additional yaw moment obtained by the method proposed in the present invention can effectively suppress the vehicle center of mass sideslip angle after being applied to the vehicle, ensuring stable vehicle driving. Figure 5 and Figure 6 The vehicle yaw rate curve and center of mass sideslip angle curve are obtained based on the additional yaw moment decision method of nonlinear model predictive control. Figure 5 and Figure 6 As a benchmark, compared Figure 3 and Figure 4 It can be found that the real-time optimization decision-making method for the additional yaw moment of the present invention has the same effect as the nonlinear model predictive control method in tracking the desired vehicle yaw rate and suppressing the sideslip angle. Figure 7 These are the additional yaw moment curves determined by the two methods. Analysis of the curves shows that the additional yaw moments obtained by the two methods are substantially the same, which fully demonstrates the effectiveness of the method of the present invention.

[0218] Figure 8The calculation time of the two methods is compared. The calculation time of the method described in the present invention is about 0.05ms, while the calculation time of the additional yaw moment decision method based on nonlinear model predictive control using the Casadi nonlinear solver is about 5ms. Therefore, the method described in the present invention can fully meet the requirements of real-time calculation, and the calculation time required is much less than the nonlinear model predictive control algorithm.

[0219] Simulations show that the proposed real-time optimization decision method for additional yaw moment achieves excellent control results for tracking the desired yaw rate and suppressing the sideslip angle, comparable to nonlinear model predictive control. Furthermore, computational time comparisons show that, because the proposed real-time optimization decision method for additional yaw moment generates an explicit expression for the optimal additional yaw moment, it consumes minimal computation time and meets real-time requirements. In summary, the proposed method effectively achieves all the benefits described herein.

[0220] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A real-time control method for additional yaw torque of a distributed drive electric vehicle, characterized in that: The following steps are involved: The real-time vehicle motion state is acquired and input into a pre-built vehicle dynamics model. The vehicle's yaw rate and sideslip angle at the center of mass are used as tracking targets. The actuation energy is suppressed, and the additional yaw moment is optimized and calculated to obtain the distribution of the additional yaw moment to each tire. During the optimization calculation process, a linear expression of the vehicle's sideslip angle with respect to the additional yaw moment and a linear expression of the vehicle's yaw angular velocity with respect to the additional yaw moment are constructed, thereby performing an optimal calculation of the additional yaw moment; The vehicle dynamics model is expressed as: Where, is the rate of change of the sideslip angle at the center of mass, is the rate of change of yaw angular velocity, is the normalized center of mass sideslip angle, is the normalized yaw rate, and All are intermediate amounts, is the upper limit of the sideslip angle at the center of mass, is the upper limit of the yaw angular velocity, is the upper limit of the additional yaw moment, represents the sideslip angle of the center of mass; represents the yaw angular velocity, are the lateral forces of the front and rear axle tires, is the mass of the vehicle, represents the longitudinal velocity, are the distances from the vehicle's center of mass to the front and rear axles, is the vehicle's moment of inertia around the Z axis; The linear expression of the center of mass sideslip angle with respect to the additional yaw moment is: Where, Function The partial derivatives of the state variables yaw rate and sideslip angle, for The sideslip angle of the center of mass at the moment, is the step length, for The sideslip angle of the center of mass at the moment; The linear expression of the vehicle yaw rate with respect to the additional yaw moment is: Where, for The yaw rate at time , is the step length, for The yaw rate at the moment The optimization problem of the optimization calculation is: Where, is the objective function, is the weight coefficient of yaw rate, for The yaw rate at time , is the step length, and is the intermediate amount, is the weight coefficient of the sideslip angle of the center of mass, is the weight coefficient of the additional yaw moment, is the control quantity, i.e. the additional yaw moment, is the desired vehicle sideslip angle, is the desired yaw rate, is the minimum additional yaw moment, is the maximum value of the additional yaw moment, is the upper limit of the sideslip angle at the center of mass, is the upper limit of the yaw rate.

2. The method for real-time control of additional yaw torque for a distributed drive electric vehicle according to claim 1, characterized in that: During the optimization calculation, the linear expression of the vehicle's sideslip angle with respect to the additional yaw moment and the linear expression of the vehicle's yaw rate with respect to the additional yaw moment are substituted into the optimization problem, and the objective function expression obtained is: Where, is the yaw angular velocity, for The sideslip angle of the center of mass at the moment, Function Partial derivatives of the state variables yaw rate and sideslip angle.

3. The method for real-time control of additional yaw torque for a distributed drive electric vehicle according to claim 2, characterized in that: During the optimization calculation process, the optimal solution of the additional yaw moment is calculated by solving the extreme point. The extreme point expression of the objective function is: Where, 、 and All are intermediate amounts; The expression of the extreme point is: The obtained extreme point is denormalized to obtain the optimal solution of the additional yaw moment. The calculation expression of the optimal solution is: Where, is the optimal solution for the additional yaw moment.

4. The method for real-time control of additional yaw torque for a distributed drive electric vehicle according to claim 3, characterized in that: The method further includes setting an additional yaw moment range for the optimal solution of the additional yaw moment to obtain an optimal additional yaw moment, wherein the optimal additional yaw moment is used to distribute the additional yaw moment to each tire. The calculation expression of the optimal additional yaw moment is: Where, is the optimal additional yaw moment, is the minimum additional yaw moment, is the maximum value of the additional yaw moment.

5. The method for real-time control of additional yaw torque for a distributed drive electric vehicle according to claim 4, characterized in that: The distribution expression of the distribution amount of the additional yaw moment of each tire is: Where, 、 、 and are the distribution of additional yaw moment to the left front wheel, right front wheel, left rear wheel and right rear wheel respectively, is the tire rolling radius; The wheelbase of the vehicle.

6. The method for real-time control of additional yaw torque for a distributed drive electric vehicle according to claim 5, characterized in that: The obtained distribution amount of the additional yaw moment of each tire is transmitted to the layer controller for execution, and each tire of the electric vehicle is driven separately.

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