阅读说明：本技术 基于自适应反推控制器的电动汽车横摆稳定性控制方法 (Electric automobile yaw stability control method based on self-adaptive reverse pushing controller ) 是由 庞辉 姚睿 王鹏 王明祥 于 2021-07-23 设计创作，主要内容包括：本发明公开了基于自适应反推控制器的电动汽车横摆稳定性控制方法,包括以下步骤：构建电动汽车侧向动力学模型；开发基于屏障李雅普诺夫函数的自适应反推控制器,用作上层控制器来生成期望的附加横摆力矩；开发基于最小目标函数的最优转矩分配算法作为下层控制器,对附加横摆力矩进行分配；本发明方法能够最终实现自适应反推控制器设计和力矩分配算法,对电动汽车的横摆稳定性控制具有重大意义,解决了电动汽车在危险工况下可能出现的轮胎侧滑等问题,有效地提高了电动汽车的操纵性和行驶安全性。(The invention discloses an electric automobile yaw stability control method based on a self-adaptive reverse pushing controller, which comprises the following steps of: constructing a lateral dynamic model of the electric automobile; developing an adaptive back-pushing controller based on a barrier Lyapunov function, and using the adaptive back-pushing controller as an upper-layer controller to generate a desired additional yaw moment; developing an optimal torque distribution algorithm based on a minimum objective function as a lower-layer controller to distribute the additional yaw moment; the method can finally realize the design of the self-adaptive back-pushing controller and the moment distribution algorithm, has great significance for controlling the yaw stability of the electric automobile, solves the problems of tire sideslip and the like which can occur to the electric automobile under dangerous working conditions, and effectively improves the maneuverability and the driving safety of the electric automobile.)

1. The electric vehicle yaw stability control method based on the adaptive reverse-pushing controller is characterized by comprising the following steps of:

step 1, constructing a lateral dynamics model of the electric automobile;

step 2, designing a self-adaptive reverse-pushing controller based on a barrier Lyapunov function, and taking the self-adaptive reverse-pushing controller as an upper-layer controller to generate an expected additional yaw moment;

and 3, designing an optimal torque distribution algorithm based on a minimum objective function as a lower-layer controller to distribute the expected additional yaw moment.

2. The adaptive-reactive-controller-based yaw stability control method for the electric vehicle according to claim 1, wherein the electric vehicle lateral dynamics model comprises electric vehicle lateral dynamics equations, rotational dynamics equations of wheels, lateral acceleration and lateral acceleration.

3. The yaw stability control method of the electric vehicle based on the adaptive back-pushing controller according to claim 2, characterized in that the step 1 is implemented by the following specific processes:

according to Newton's second law, the lateral dynamic equation of the electric vehicle is as follows:

in the formula (1), m is the vehicle body mass, I_zRepresenting the rotational inertia of the vehicle body; f_yfAs lateral force of the front wheel, F_yrIs the lateral force of the rear wheel; beta and r are respectively a centroid slip angle and a yaw rate; l_fAnd l_rThe distances from the front and rear axes to the center of mass respectively; m_zAn additional yaw moment; v is the vehicle speed;

wherein, F_yfAnd F_yrThe expressions are respectively:

in the formula (2), C_fFor front wheel cornering stiffness, C_rIs rear wheel cornering stiffness; alpha is alpha_fIs a front wheel side slip angle, α_rIs a rear wheel side slip angle; alpha is alpha_fAnd alpha_rRespectively expressed as:

substituting equations (2) and (3) into (1) yields:

wherein the content of the first and second substances,a₂＝2l_rC_r-2l_fC_f，c₂＝2C_fl_f；

the rotational dynamics equation for a wheel is expressed as:

wherein R is the rolling radius of the wheel, w_ijIs the angular velocity of the wheel, I_wIs the moment of inertia of the wheel, T_ijIs the wheel moment;

lateral acceleration a_xAnd lateral acceleration a_yRespectively as follows:

4. the yaw stability control method of the electric vehicle based on the adaptive reverse-thrust controller according to claim 3, characterized in that the step 2 is implemented by the following specific processes:

selecting psi as the desired virtual control variable and r as the actual control variable, if r is satisfied psi, the error e between the actual centroid slip angle and the preset centroid slip angle₁＝β-β_dConvergence to 0 or a limit value, wherein_dIs the centroid slip angle reference trajectory; definition e₂As error of actual and virtual control variables, i.e. e₂＝r-ψ；

For error e₁The derivation yields:

the desired virtual control variables are designed as:

in the formula, k₁，γ₁The adjustment coefficients in the design of the controller are positive numbers;

defining a semi-positive lyapunov function as:

deriving (9) to obtain:

to e₂The first derivative is calculated to obtain:

wherein θ is 1/I_z，θ_min＝1/I_zmax，θ_max＝1/I_zmin，I_zmin，I_zmaxAre the lower and upper bounds of the moment of inertia respectively,

designing additional yaw moment M_zComprises the following steps:

in the formula, k₂Is a normal number, and is,is an estimate of the value of theta that,

the self-adaptive control rate is as follows:

an adaptive reactive controller satisfying the adaptive control rate is used as an upper controller to generate a desired additional yaw moment.

5. The yaw stability control method of the electric vehicle based on the adaptive back-pushing controller according to claim 1, characterized in that the step 3 of designing the optimal torque distribution algorithm based on the minimum objective function comprises the following specific processes:

total longitudinal force F of the tire_xAnd respective tire longitudinal forces F_xijThe relationship between them is:

F_x＝F_xfl+F_xfr+F_xrl+F_xrr (21)

F_xflindicating front left wheel longitudinal force, F_xfrRepresenting front right wheel longitudinal force, F_xrlIndicating the rear left wheel longitudinal force, F_xrrRepresenting the rear right wheel longitudinal force;

the maximum driving force that the in-wheel motor can provide does:

F_xijmax＝μF_zij (22)

wherein mu is the friction coefficient of the road surface;

converting the four-wheel torque distribution into a quadratic programming standard form to be used as an objective function of the optimal torque distribution, and using the minimum objective function as an optimal torque distribution calculation function, wherein the minimum objective function is expressed as:

wherein p ═ F_xfl F_xfr F_xrl F_xrr]^T，lb＝[-μF_zfl -μF_zrl -μF_zrl -μF_rrl]^T，A₁＝0,b＝0，f^T＝0，beq＝M_z，ub＝[μF_zfl μF_zrl μF_zrl μF_rrl]^T。

Technical Field

The invention belongs to the technical field of electric automobile yaw stability control, and particularly relates to an electric automobile yaw stability control method based on an adaptive back-pushing controller.

Background

An electric vehicle, which is a clean energy vehicle, has been developed vigorously in recent years, and safety thereof is a problem of great concern, because when the electric vehicle runs on a road surface with a low adhesion coefficient at a high speed, traffic problems such as tire sideslip and the like are more likely to occur.

In order to avoid such traffic accidents, more and more trainees have proposed various control methods, such as an anti-lock system and an active front wheel steering system, in order to improve the steering stability and the driving quality of the electric vehicle. It should be noted that direct yaw moment control is one of the most effective methods for improving the stability of an electric vehicle, and has a better ability to stabilize the vehicle motion than control methods such as an anti-lock system and an active front steering system. One of the main problems with direct yaw moment control is how to calculate the ideal control moment.

Another problem with direct yaw moment control is how to generate a moment to drive. The traditional centralized driving electric automobile and the internal combustion engine automobile have similar driving structures, the internal combustion engine is replaced by the electric motor and relevant components, and the torque output by the electric motor is transmitted to wheels through a mechanical transmission device. Therefore, the traditional centralized driving electric automobile has the defects of large volume, heavy weight, low efficiency and the like. The motors and the speed reducers of the hub motor distributed driving electric automobile are arranged in wheels, the control algorithm calculates the required additional yaw moment, and the additional yaw moment is directly distributed into the four hub motors by the distribution algorithm, so that a transmission shaft and a differential mechanism can be omitted, a transmission system is simplified, the efficiency is improved, and the hub motor driven electric automobile also has the advantages of quick response, small volume and weight, flexible distribution and low cost. Therefore, more and more researchers have conducted research on in-wheel motor driven electric vehicles.

It is noteworthy that the body mass and the driving moment of inertia of the vehicle may vary due to the number of passengers and the payload, which are generally determined as uncertain inertial parameters, which may reduce the vehicle stability performance and cause certain difficulties in the design of the controller. To address these challenges, in the past decades, adaptive back-thrust control has been chosen by many scholars for use in controller designs with rigorous output feedback systems with uncertain parameters because of its advantages of input saturation resistance, higher tracking accuracy, and better robustness to external disturbances.

One difficulty in electric vehicle control is that when alleviating lateral stability problems caused by vehicle steering, there are difficult constraints to meet, requiring performance criteria to be limited to a certain range.

Disclosure of Invention

The invention aims to provide an electric automobile yaw stability control method based on an adaptive reverse thrust controller, which can effectively improve the operation stability of a vehicle.

The technical scheme adopted by the invention is that the electric automobile yaw stability control method based on the self-adaptive reverse pushing controller comprises the following steps:

step 1, constructing a lateral dynamics model of the electric automobile;

step 2, designing a self-adaptive reverse-pushing controller based on a barrier Lyapunov function, and taking the self-adaptive reverse-pushing controller as an upper-layer controller to generate an expected additional yaw moment;

and 3, designing an optimal torque distribution algorithm based on a minimum objective function as a lower-layer controller to distribute the expected additional yaw moment.

The electric vehicle lateral dynamic model comprises an electric vehicle lateral dynamic equation, a wheel rotation dynamic equation, a transverse acceleration and a lateral acceleration.

The invention is also characterized in that:

the specific process of the step 1 is as follows:

according to Newton's second law, the lateral dynamic equation of the electric vehicle is as follows:

in the formula (1), m is the vehicle body mass, I_zRepresenting the rotational inertia of the vehicle body; f_yfAs lateral force of the front wheel, F_yrIs the lateral force of the rear wheel; beta and r are respectively a centroid slip angle and a yaw rate; l_fAnd l_rThe distances from the front and rear axes to the center of mass respectively; m_zAn additional yaw moment; v is the vehicle speed;

wherein, F_yfAnd F_yrThe expressions are respectively:

in the formula (2), C_fFor front wheel cornering stiffness, C_rIs rear wheel cornering stiffness; alpha is alpha_fIs a front wheel side slip angle, α_rIs a rear wheel side slip angle; alpha is alpha_fAnd alpha_rRespectively expressed as:

substituting equations (2) and (3) into (1) yields:

wherein the content of the first and second substances,a₂＝2l_rC_r-2l_fC_f，c₂＝2C_fl_f；

the rotational dynamics equation for a wheel is expressed as:

wherein R is the rolling radius of the wheel, w_ijIs the angular velocity of the wheel, I_wIs the moment of inertia of the wheel, T_ijIs the wheel moment;

lateral acceleration a_xAnd lateral acceleration a_yRespectively as follows:

the specific process of the step 2 is as follows:

selecting psi as the desired virtual control variable and r as the actual control variable, if r is satisfied psi, the error e between the actual centroid slip angle and the preset centroid slip angle₁＝β-β_dConvergence to 0 or a limit value, wherein_dIs the centroid slip angle reference trajectory; definition e2 as the error between the actual and virtual controlled variables, i.e. e₂＝r-ψ；

For error e₁The derivation yields:

the desired virtual control variables are designed as:

in the formula, k₁，γ₁The adjustment coefficients in the design of the controller are positive numbers;

defining a semi-positive lyapunov function as:

deriving (9) to obtain:

taking the first derivative of e2 yields:

wherein θ is 1/I_z，θ_min＝1/I_zmax，θ_max＝1/I_zmin，I_zmin，I_zmaxAre the lower and upper bounds of the moment of inertia respectively,

designing additional yaw moment M_zComprises the following steps:

in the formula, k₂Is a normal number, and is,is an estimate of the value of theta that,

the self-adaptive control rate is as follows:

the adaptive control rate (13) ensures that the estimated parameters are always within known limits, i.e. theta_min≤θ≤θ_maxFor all τ, inequalityThis is true.

An adaptive reactive controller satisfying the adaptive control rate is used as an upper controller to generate a desired additional yaw moment.

Step 3, designing an optimal torque distribution algorithm based on a minimum objective function, which comprises the following specific processes:

total longitudinal force F of the tire_xAnd respective tire longitudinal forces F_xijThe relationship between them is:

F_x＝F_xfl+F_xfr+F_xrl+F_xrr (21)

F_xflindicating front left wheel longitudinal force, F_xfrRepresenting front right wheel longitudinal force, F_xrlIndicating the rear left wheel longitudinal force, F_xrrRepresenting the rear right wheel longitudinal force;

the maximum driving force that the in-wheel motor can provide does:

F_xijmax＝μF_zij (22)

wherein mu is the friction coefficient of the road surface;

converting the four-wheel torque distribution into a quadratic programming standard form to be used as an objective function of the optimal torque distribution, and using the minimum objective function as an optimal torque distribution calculation function, wherein the minimum objective function is expressed as:

wherein p ═ F_xfl F_xfr F_xrl F_xrr]^T，lb＝[-μF_zfl -μF_zrl -μF_zrl -μF_rrl]^T，A₁＝0，b＝0，f^T＝0，beq＝M_z，ub＝[μF_zfl μF_zrl μF_zrl μF_rrl]^T。

The invention has the beneficial effects that:

according to the method, a corresponding self-adaptive control law is designed according to a self-adaptive back-stepping method aiming at the uncertainty in the electric automobile model, the uncertain parameters in the model can be estimated on line in real time so as to adjust the influence of the uncertain parameters on the automobile, meanwhile, the output response of the mass center slip angle and the yaw rate of the automobile is obviously reduced, and the operation stability is effectively improved.

Compared with a general direct distribution algorithm, the optimal torque distribution algorithm provided by the invention has a better control effect, and can ensure that the output torque is less than the maximum driving force which can be provided by the hub motor.

The method is simple and easy to realize, the system does not need redundant hardware, and the cost is lower.

Drawings

FIG. 1 is a flow chart of the operation of the yaw stability control method of the electric vehicle based on the adaptive back-pushing controller;

FIG. 2 is a lateral dynamics model of an electric vehicle according to the present invention;

FIG. 3 is a schematic block diagram of an adaptive back-stepping control system according to the present invention;

FIG. 4 is a front wheel steering angle input graph in accordance with the present invention;

FIG. 5 is a graph of centroid slip angle response of the present invention;

FIG. 6 is a graph of yaw rate response according to the present invention;

FIG. 7 is a graph of the front left wheel torque response of the present invention;

FIG. 8 is a graph of the right front wheel torque response of the present invention;

FIG. 9 is a graph of the torque response of the left rear wheel of the present invention;

FIG. 10 is a graph illustrating a torque response of the right rear wheel of the present invention;

FIG. 11 is a graph of vehicle tracking path response in accordance with the present invention.

Detailed Description

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

The invention discloses an electric automobile yaw stability control method based on an adaptive reverse-pushing controller, which comprises the following steps as shown in figure 1:

step 1, constructing a lateral dynamics model of the electric automobile; the lateral dynamic model of the electric automobile is widely applied to the field of yaw stability control of the electric automobile due to the fact that the lateral dynamic model of the electric automobile comprises main characteristics of lateral dynamics of the electric automobile and is simple in structure. The invention provides an electric automobile lateral dynamics model, which is shown in figure 2. The electric vehicle lateral dynamics model comprises an electric vehicle lateral dynamics equation, a wheel rotation dynamics equation, a transverse acceleration and a lateral acceleration; the specific process is as follows:

according to Newton's second law, the lateral dynamic equation of the electric vehicle is as follows:

in the formula (1), m is the vehicle body mass, I_zRepresenting the rotational inertia of the vehicle body; f_yfAs lateral force of the front wheel, F_yrIs the lateral force of the rear wheel; beta and r are respectively a centroid slip angle and a yaw rate; l_fAnd l_rThe distances from the front and rear axes to the center of mass respectively; m_zAn additional yaw moment; v is the vehicle speed;

wherein, F_yfAnd F_yrThe expressions are respectively:

in the formula (2), C_fFor front wheel cornering stiffness, C_rIs rear wheel cornering stiffness; alpha is alpha_fIs a front wheel side slip angle, α_rIs a rear wheel side slip angle; alpha is alpha_fAnd alpha_rRespectively expressed as:

substituting equations (2) and (3) into (1) yields:

wherein the content of the first and second substances,a₂＝2l_rC_r-2l_fC_f，c₂＝2C_fl_f；

the rotational dynamics equation for a wheel is expressed as:

wherein R is the rolling radius of the wheel, w_ijIs the angular velocity of the wheel, I_wIs the moment of inertia of the wheel, T_ijIs the wheel moment;

lateral acceleration a_xAnd lateral acceleration a_yRespectively as follows:

step 2, designing a self-adaptive reverse-pushing controller based on a barrier Lyapunov function, and taking the self-adaptive reverse-pushing controller as an upper-layer controller to generate an expected additional yaw moment; the specific process of the step 2 is as follows:

selecting psi as the desired virtual control variable and r as the actual control variable, if r is satisfied psi, the error e between the actual centroid slip angle and the preset centroid slip angle₁＝β-β_dConvergence to 0 or a limit value, wherein_dIs the centroid slip angle reference trajectory; definition e2 as the error between the actual and virtual controlled variables, i.e. e₂＝r-ψ；

For error e₁The derivation yields:

the desired virtual control variables are designed as:

in the formula, k₁，γ₁The adjustment coefficients in the design of the controller are positive numbers;

defining a semi-positive lyapunov function as:

deriving (9) to obtain:

to e₂The first derivative is calculated to obtain:

wherein θ is 1/I_z，θ_min＝1/I_zmax，θ_max＝1/I_zmin，I_zmin，I_zmaxAre the lower and upper bounds of the moment of inertia respectively,

designing additional yaw moment M_zComprises the following steps:

in the formula, k₂Is a normal number, and is,is an estimate of the value of theta that,

the self-adaptive control rate is as follows:

the adaptive control rate (13) ensures that the estimated parameters are always within known limits, i.e. theta_min≤θ≤θ_maxFor all τ, inequalityThis is true.

Another semi-positive lyapunov function is defined as:

the derivation of equation (14) yields:

integrating equation (15) from 0 to t gives:

the above formula shows e₁And e₂Is bounded throughout the time domain, i.e.:

further, it can be obtained from formula (17):

that is, the following formula (19) holds:

a₂β+b₂r+c₂δ+M_z∈L_∞ (19)

therefore, the temperature of the molten metal is controlled,it can further be derived that:

thus, the method can obtain the product,is also bounded, thereforeAre consistent and continuous, and as can be seen from the Barbalt's theorem, with t → ∞Further obtaining e₁→0，e₂→ 0, so e₁And e₂Is progressively stable;

an adaptive reactive controller satisfying the adaptive control rate is used as an upper controller to generate a desired additional yaw moment.

And 3, designing an optimal torque distribution algorithm based on a minimum objective function as a lower-layer controller to distribute the expected additional yaw moment. The specific process of designing the optimal torque distribution algorithm based on the minimum objective function is as follows:

in order to make a reasonable distribution of the additional yaw moment generated in the upper level controller, the moment distribution algorithm is widely used. The invention provides an optimal torque distribution algorithm. The algorithm is designed to:

F_x＝F_xfl+F_xfr+F_xrl+F_xrr (21)

F_xflindicating front left wheel longitudinal force, F_xfrRepresenting front right wheel longitudinal force, F_xrlIndicating the rear left wheel longitudinal force, F_xrrRepresenting the rear right wheel longitudinal force;

the maximum driving force that the in-wheel motor can provide does:

F_xijmax＝μF_zij (22)

wherein mu is the friction coefficient of the road surface;

converting the four-wheel torque distribution into a quadratic programming standard form to be used as an objective function of the optimal torque distribution, and using the minimum objective function as an optimal torque distribution calculation function, wherein the minimum objective function is expressed as:

wherein p ═ F_xfl F_xfr F_xrl F_xrr]^T，lb＝[-μF_zfl -μF_zrl -μF_zrl -μF_rrl]^T，A₁＝0，b＝0，f^T＝0，beq＝M_z，ub＝[μF_zfl μF_zrl μF_zrl μF_rrl]^T。

Verifying the adaptive back-pushing controller developed in the step 2 and the optimal torque distribution algorithm developed in the step 3 based on a CarSim model:

uncertainty of rotational inertia of lateral dynamics systemThe description is as follows: i is not less than 1250_z≤1450；

Selecting a front wheel steering angle as input;

introducing a CarSim model into Simulink as a controlled object, building a self-adaptive back-pushing controller and a torque distribution algorithm, further verifying by combining corresponding parameters, and discussing and analyzing the following three modes:

1) PS: without a controller;

2) ADA: the lower controller is a direct distribution algorithm;

3) ODA: the lower layer controller adopts an optimal torque distribution algorithm;

4) ref: a reference curve;

in order to verify the effectiveness of the constructed controller, the invention establishes the lateral dynamics model of the electric automobile in the MATLAB/Simulink environment, and the accuracy of the controller is verified through simulation in the above way. FIG. 4 is a front wheel steering angle input curve; the performance index of the system is shown in the response curves of fig. 5-11 under different modes. As can be seen from the graphs in FIGS. 5 and 6, the controller provided by the invention can obviously reduce the centroid slip angle and the yaw rate, and the tracking precision and the performance of the optimal torque distribution algorithm are superior to those of the direct distribution algorithm, thereby effectively improving the yaw stability of the vehicle. As can be seen from fig. 7, 8, 9, 10, the torque response of the optimal torque split algorithm is smoother than the torque response of the direct split algorithm, as shown in the close-up views. On the other hand, while the even distribution algorithm is simpler and easier to implement, the distributed torque may be greater than the limit that may exceed the maximum driving force provided by the motor, and the optimal torque distribution algorithm may avoid this, proving that the problem with the optimal torque distribution strategy is better than the even distribution algorithm. As can be seen from fig. 7-11, the tracking trajectories of both controllers are much smoother than for the vehicle without control, and the optimal torque distribution algorithm is much closer to the reference trajectory than the average distribution algorithm, indicating that the proposed optimal torque distribution algorithm can achieve maintaining better steering stability performance.

Simulation shows that the adaptive back-pushing controller provided by the invention can reduce the performance index of the lateral dynamics of the electric automobile, and the optimal distribution algorithm can reasonably distribute the additional yaw moment to four tires, so that the effectiveness and the accuracy of the composite controller are verified, the yaw stability and the safety of the automobile are improved, and the adaptive back-pushing controller has great significance for controlling the yaw stability of the lateral dynamics of the electric automobile.

By the mode, the electric vehicle yaw stability control method based on the self-adaptive reverse-pushing controller is characterized in that a corresponding self-adaptive control law is designed according to the self-adaptive reverse-pushing method aiming at the uncertainty in an electric vehicle model, the uncertain parameters in the model can be estimated on line in real time so as to adjust the influence of the uncertain parameters on a vehicle, and meanwhile, the output response of the mass center yaw angle and the yaw rate of the vehicle is obviously reduced, so that the control stability is effectively improved; compared with a general direct distribution algorithm, the provided optimal torque distribution algorithm has a better control effect and can ensure that the output torque is smaller than the maximum driving force which can be provided by the hub motor; the method is simple and easy to realize, the system does not need redundant hardware, and the cost is lower.