阅读说明：本技术 一种机械弹性电动轮车辆纵横向协同控制方法 (Longitudinal and transverse cooperative control method for mechanical elastic electric wheel vehicle ) 是由 钱程亮 林棻 马守刚 于 2021-07-30 设计创作，主要内容包括：本发明公开了一种机械弹性电动轮车辆纵横向协同控制方法,通过采集驾驶员的方向盘转角和油门/制动踏板信息,规划出便于驾驶员操纵的期望动力学响应；基于李雅普诺夫方法利用积分滑模算法计算机械弹性电动轮车辆纵向运动、侧向运动和横摆运动的控制律,克服了车辆纵横向运动中的强耦合、参数不确定性等问题；考虑电动轮滑移能量根据车辆行驶状态利用轮胎力分配规则,为每个轮胎动态规划最优纵向力和最优横向力；驱动各机械弹性电动轮和主动前轮转向子系统,将理论最优轮胎力进行实现。(The invention discloses a longitudinal and transverse cooperative control method for a mechanical elastic electric wheel vehicle, which plans an expected dynamic response convenient for a driver to operate by acquiring the steering wheel angle and accelerator/brake pedal information of the driver; based on the Lyapunov method, the control laws of longitudinal movement, lateral movement and transverse movement of the mechanical elastic electric wheel vehicle are calculated by utilizing an integral sliding mode algorithm, so that the problems of strong coupling, parameter uncertainty and the like in longitudinal and transverse movement of the vehicle are solved; dynamically planning an optimal longitudinal force and an optimal transverse force for each tire by considering the electric wheel slip energy and utilizing a tire force distribution rule according to the vehicle running state; and driving each mechanical elastic electric wheel and the driving front wheel steering subsystem to realize the theoretical optimal tire force.)

1. The longitudinal and transverse cooperative control method for the mechanical elastic electric wheel vehicle adopts a front wheel to actively steer, and four tires all adopt electric wheels, and is characterized by comprising the following steps of:

step 1), collecting steering wheel angle and accelerator/brake pedal information of a driver, and calculating an expected dynamic response convenient for the driver to operate:

step 1.1), obtaining the steering wheel angle delta of the vehicle_{steering_wheel}According to the steering gear ratio i of the steering sub-system_wCalculating the expected value of the front wheel steering angle

Step 1.2), calculating the steady state response of the yaw rateWherein v is_xIs the longitudinal speed of the vehicle,m is the mass of the vehicle, l_f、l_rThe distances of the centroid to the front and rear axes, k_r、k_fRespectively equivalent lateral deflection stiffness of the front shaft and the rear shaft;

step 1.3), setting the desired yaw rateWherein, tau_γIs a time coefficient, s is a differential operator,mu is the road surface adhesion coefficient, g is the gravity acceleration;

step 1.4), calculating the expected longitudinal speeda_xdIn order to obtain the desired acceleration using the pedal position sensor,the current vehicle speed;

step 1.5), setting the desired lateral velocity v_yd＝0；

Step 2), calculating the control laws of longitudinal movement, lateral movement and yaw movement of the mechanical elastic electric wheel vehicle based on the Lyapunov theory:

step 2.1), select [ v_x v_y γ]^TAs state variables, where v_yThe lateral speed of the vehicle and gamma is the yaw rate of the vehicle, and the three state variables are used as the input of sliding mode control, and the control laws of longitudinal motion, lateral motion and yaw motion are defined as F_xd F_yd M_zd]^TAs an output of the sliding mode control;

step 2.2), selecting three integral sliding mode surfaces, wherein the formulas are as follows:

S₁＝e₁+Λ₁ξ₁、S₂＝e₂+Λ₂ξ₂、S₃＝e₃+Λ₃ξ₃

wherein S is₁Sliding form surface for longitudinal control law, S₂Sliding form surface for transverse control law, S₃Deviation e of longitudinal speed from desired value for sliding mode surface of yaw control law₁＝v_xd-v_x(ii) a Deviation e of lateral velocity from desired value₂＝v_yd-v_y(ii) a Deviation e of yaw rate from desired value₃＝γ_d- γ; longitudinal velocity error integralTransverse velocity error integralIntegral of yaw motion errorΛ₁、Λ₂、Λ₃Positive coefficients of integral terms in sliding mode surfaces of a longitudinal control law, a transverse control law and a transverse control law respectively;

step 2.3), setting a longitudinal motion control law, a transverse motion control law and a yaw motion control law as shown in the following formula:

F_yd＝m(v_yd+v_xγ+Λ₂e₂-k₁₂S₂-k₂₂sat(S₂/κ₂))

in the formula (I), the compound is shown in the specification, k₁₁、k₂₁respectively S preset in the longitudinal control approach rate₁Term, sat (S)₁/κ₁) Coefficient of term, k₁₂、k₂₂Respectively S preset in the lateral control approach rate₁Term, sat (S)₁/κ₁) Coefficient of term, k₁₃、k₃₁For controlling preset S in approach rate of yaw movement₁Term, sat (S)₁/κ₁) Coefficient of term, κ₁，κ₂，κ₃The boundary layer thicknesses of longitudinal control, transverse control and transverse swing control are respectively adopted;

and 3), dynamically calculating the target longitudinal force and the target transverse force of each tire according to the control laws of longitudinal motion, lateral motion and yaw motion and by combining the driving state of the vehicle:

step 3.1), defining the load factor gamma of the tyre respectively_ijCost function J composed of the sum of the mean and variance of the load rate₁And constraint condition I:

constraint condition I:

with a cost function J₁Solving the optimal tire force by adopting a quasi-Newton iteration method for the objective function and the constraint condition I as the constraint condition

Step 3.2), defining the longitudinal slip force X of the mechanical elastic tyre_sAnd lateral slip force Y_sRespectively as follows:

wherein the content of the first and second substances,c_exand c_eyRespectively representing the longitudinal stiffness and the lateral stiffness of the mechanical elastic tire, alpha is the tire slip angle, a₁，a₂，a₃In order to be a coefficient of fit,

defining the longitudinal slip velocity v of a mechanically resilient wheel_sxAnd lateral slip velocity v_syRespectively as follows:

v_sx＝r_wω_w-v_xcosα

v_sy＝-v_xsinα

in the formula, r_w、ω_wEffective rolling radius of the wheel and wheel speed, respectively;

defining the longitudinal slip power P of a mechanically resilient wheel_sxPower P of lateral slip_syAnd total power P of slip_sRespectively as follows:

P_sx＝X_s·v_sx

P_sy＝Y_s·v_sy

P_s＝X_s·v_sx+Y_s·v_sy

cost function J for defining tire slip power square sum composition₂：

Wherein: p_sxij,t-1Power of longitudinal slip at a moment on the wheel, P_syij,t-1Power of lateral slip at a moment on the wheel, X_ij,t-1Is the longitudinal tire force on the wheel at a moment, Y_ij,t-1Is the lateral tire force on the wheel at a time,

defining a constraint II:

with a cost function J₂Calculating the optimal tire force by using a sequential quadratic programming method for the objective function and the constraint condition II as the constraint condition

Step 3.3), taking epsilon and | delta gamma | as the input of the fuzzy rule, setting the fuzzy rule according to the principle that the more stable the vehicle, the larger the fuzzy output eta, wherein,|Δγ|＝|γ_d-γ|，B₁、B₂of vehicles with mechanically-elastic electric wheelsBoundary parameters of a phase plane self-stabilization area and an unstable area, wherein beta is a mass center slip angle of the vehicle;

step 3.4), calculating epsilon and | delta gamma | according to the current state of the vehicle, solving fuzzy output eta by using the fuzzy rule belonging to the step 3.3, and further solving dynamic distribution output of tire force

Step 4), each electric wheel of the vehicle is driven so that the actual longitudinal force is equal to the target longitudinal force and the actual transverse force is equal to the target transverse force:

step 4.1), the actual control signal of each electric wheel is as follows:

in the formula, τ₁₁、τ₂₁、b₁Correction coefficient 1, correction coefficient 2, correction time constant, tau, controlled by left front electric wheel₁₂、τ₂₂、b₂Correction coefficient 1, correction coefficient 2, correction time constant, tau, controlled for the front right electric wheel₁₃、τ₂₃、b₃Correction coefficient 1, correction coefficient 2, correction time constant, tau, controlled by left and rear electric wheels₁₄、τ₂₄、b₄Respectively is a correction coefficient 1, a correction coefficient 2 and a correction time constant controlled by the right rear electric wheel; j. the design is a square_wIs the moment of inertia of the electric wheel; omega_{w_fl}、ω_{w_fr}、ω_{w_rl}、ω_{w_rr}The rotating speeds of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel are respectively; f_zfl、F_zfr、F_zrl、F_zrrVertical forces of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel are respectively;

step 4.2), solving the solution alpha of the following formula by three times of Newton iterative solution_ij,3：

The actual control signals for the steered wheels are as follows:

2. the longitudinal-transverse cooperative control method for the mechano-elastic electric-wheel vehicle as claimed in claim 1, characterized in that the optimal tire force is solved by using a quasi-Newton iteration methodAnd solving the optimal tire force by adopting a sequential quadratic programming methodThe tire forces during the solution should also satisfy the following constraints:

-T_maxr_ij≤X_ij≤T_maxr_ij

-Y_max≤Y_ij≤Y_max

in the formula (I), the compound is shown in the specification,error relaxation factors preset to ensure the calculation of real-time.

Technical Field

The invention relates to the field of chassis control of electric automobiles, in particular to a longitudinal and transverse cooperative control method for a mechanical elastic electric wheel vehicle.

Background

The electric automobile has the advantages of small influence on the environment, quick driving response, high energy utilization rate and the like, and becomes a main solution for future traffic electrification. As one of the prominent configurations of electric vehicles, electric wheel vehicles have become a current research focus. Compared with the conventional internal combustion engine-driven vehicle and the centralized-drive electric vehicle, the electric wheel vehicle has the main advantages that more actuators can be independently controlled, and additional yaw moment can be generated through control redundancy, so that the vehicle obtains better stability performance and the operating limit of the vehicle is expanded. The direct yaw moment control can be combined with the active front wheel steering control, so that the longitudinal force of the four wheels and the transverse force of the front axle are effectively controlled, and the operation stability of the electric wheel vehicle is further improved. In the aspect of the control of the steering stability of the automobile, a driving/braking system and a steering system have advantages respectively. From a vehicle stability point of view, conventional control strategies separate the lateral and longitudinal stability studies, which makes optimal control of vehicle dynamics difficult. Therefore, optimization to achieve more goals by coordinating longitudinal and lateral motion is the focus of future research.

However, the current research on cooperative control of the automobile chassis still has obvious shortcomings, including the following points:

1. currently, a performance index is mostly used for distributing vehicle tire force, for example, document 1(o.mokhiamar, m.abe, simulation optimal distribution of lateral and longitudinal properties for the model following Control, Journal of Dynamic Systems Measurement and Control-Transactions of the same, 126(2004) 753-. Document 2(b.zhao, n.xu, h.chen, k.guo, y.huang, Design and Experimental evaluation on Energy-Efficient Control for4WIMD-EVs conditioning Tire Energy, IEEE trans.veh.technol.,69 (1462020) 14631-14644.) distribution of Tire forces is achieved with the aim of minimizing the longitudinal Slip Energy loss of four-wheel drive vehicle tires, and it does not consider that the lateral Slip Energy of tires is not sufficient for the current Tire force distribution strategy of a driving redundancy system such as a distributed drive chassis equipped with active front wheel steering, and cannot achieve the compromise of multiple objectives.

2. In order to solve the problem that the conventional pneumatic tire is easy to burst, the provided puncture-resistant high-bearing-capacity non-pneumatic mechanical elastic electric wheel has no related research on matching the longitudinal and transverse coordinated motion control directions of the whole vehicle.

The torque and rotating speed information of the four wheels of the electric wheel vehicle are easy to obtain, the four wheels can be independently and accurately controlled respectively, so that the control is more flexible and convenient, and meanwhile, the motor has two working modes of driving and braking, and the characteristics lay a solid foundation for the application of an advanced control algorithm to the electric vehicle. The control dimensionality is further increased after the active front wheel steering is added, and favorable conditions are provided for optimizing the system performance of the vehicle under the condition of realizing longitudinal and transverse cooperative control. The longitudinal and transverse cooperative control method for the mechanical elastic electric wheel vehicle can well solve the problems and realize the balance between the vehicle stability and the utilization rate of the output energy of the motor.

Disclosure of Invention

The invention aims to solve the technical problem of providing a longitudinal and transverse cooperative control method for a mechanical elastic electric wheel vehicle, aiming at the defects involved in the background technology, and the method can coordinate each actuator of a redundant actuator chassis.

The invention adopts the following technical scheme for solving the technical problems:

the longitudinal and transverse cooperative control method for the mechanical elastic electric wheel vehicle adopts front wheels to actively steer, four tires all adopt electric wheels, and the longitudinal and transverse cooperative control method for the mechanical elastic electric wheel vehicle comprises the following steps:

step 1), collecting steering wheel angle and accelerator/brake pedal information of a driver, and calculating an expected dynamic response convenient for the driver to operate:

step 1.1), obtaining the steering wheel angle delta of the vehicle_{steering_wheel}According to the steering gear ratio i of the steering sub-system_wCalculating the expected value of the front wheel steering angle

Step 1.2), calculating the steady state response of the yaw rateWherein v is_xIs the longitudinal speed of the vehicle,m is the mass of the vehicle, l_f、l_rThe distances of the centroid to the front and rear axes, k_r、k_fRespectively equivalent lateral deflection stiffness of the front shaft and the rear shaft;

step 1.3), setting the desired yaw rateWherein, tau_γIs a time coefficient, s is a differential operator,mu is the road surface adhesion coefficient, g is the gravity acceleration;

step 1.4), calculating the expected longitudinal speeda_xdIn order to obtain the desired acceleration using the pedal position sensor,the current vehicle speed;

step 1.5), setting the desired lateral velocity v_yd＝0；

Step 2), calculating the control laws of longitudinal movement, lateral movement and yaw movement of the mechanical elastic electric wheel vehicle based on the Lyapunov theory:

step 2.1), select [ v_x v_y γ]^TAs state variables, where v_yIs the lateral speed of the vehicle, gamma isYaw rate of vehicle, and control law [ F ] of longitudinal motion, lateral motion and yaw motion by using the three state variables as input of sliding mode control_xd F_yd M_zd]^TAs an output of the sliding mode control;

step 2.2), selecting three integral sliding mode surfaces, wherein the formulas are as follows:

S₁＝e₁+Λ₁ξ₁、S₂＝e₂+Λ₂ξ₂、S₃＝e₃+Λ₃ξ₃

wherein S is₁Sliding form surface for longitudinal control law, S₂Sliding form surface for transverse control law, S₃Deviation e of longitudinal speed from desired value for sliding mode surface of yaw control law₁＝v_xd-v_x(ii) a Deviation e of lateral velocity from desired value₂＝v_yd-v_y(ii) a Deviation e of yaw rate from desired value₃＝γ_d- γ; longitudinal velocity error integralTransverse velocity error integralIntegral of yaw motion errorΛ₁、Λ₂、Λ₃Positive coefficients of integral terms in sliding mode surfaces of a longitudinal control law, a transverse control law and a transverse control law respectively;

step 2.3), setting a longitudinal motion control law, a transverse motion control law and a yaw motion control law as shown in the following formula:

F_yd＝m(v_yd+v_xγ+Λ₂e₂-k₁₂S₂-k₂₂sat(S₂/κ₂))

in the formula (I), the compound is shown in the specification, k₁₁、k₂₁respectively S preset in the longitudinal control approach rate₁Term, sat (S)₁/κ₁) Coefficient of term, k₁₂、k₂₂Respectively S preset in the lateral control approach rate₁Term, sat (S)₁/κ₁) Coefficient of term, k₁₃、k₃₁For controlling preset S in approach rate of yaw movement₁Term, sat (S)₁/κ₁) Coefficient of term, κ₁，κ₂，κ₃The boundary layer thicknesses of longitudinal control, transverse control and transverse swing control are respectively adopted;

and 3), dynamically calculating the target longitudinal force and the target transverse force of each tire according to the control laws of longitudinal motion, lateral motion and yaw motion and by combining the driving state of the vehicle:

step 3.1), defining the load factor gamma of the tyre respectively_ijCost function J composed of the sum of the mean and variance of the load rate₁And constraint condition I:

constraint condition I:

with a cost function J₁Solving the optimal tire force by adopting a quasi-Newton iteration method for the objective function and the constraint condition I as the constraint condition

Step 3.2), defining the longitudinal slip force X of the mechanical elastic tyre_sAnd lateral slip force Y_sRespectively as follows:

wherein the content of the first and second substances,a＝a₁F_z ²+a₂F_z+a₃，c_exand c_eyRespectively representing the longitudinal stiffness and the lateral stiffness of the mechanical elastic tire, alpha is the tire slip angle, a₁，a₂，a₃In order to be a coefficient of fit,

defining the longitudinal slip velocity v of a mechanically resilient wheel_sxAnd lateral slip velocity v_syRespectively as follows:

v_sx＝r_wω_w-v_xcosα

v_sy＝-v_xsinα

in the formula, r_w、ω_wEffective rolling radius of the wheel and wheel speed, respectively;

defining the longitudinal slip power P of a mechanically resilient wheel_sxPower P of lateral slip_syAnd total power P of slip_sRespectively as follows:

P_sx＝X_s·v_sx

P_sy＝Y_s·v_sy

P_s＝X_s·v_sx+Y_s·v_sy

cost function J for defining tire slip power square sum composition₂：

Wherein: p_sxij,t-1Power of longitudinal slip at a moment on the wheel, P_syij,t-1Power of lateral slip at a moment on the wheel, X_ij,t-1Is the longitudinal tire force on the wheel at a moment, Y_ij,t-1Is the lateral tire force on the wheel at a time,

defining a constraint II:

with a cost function J₂Calculating the optimal tire force by using a sequential quadratic programming method for the objective function and the constraint condition II as the constraint condition

Step 3.3), taking epsilon and | delta gamma | as the input of the fuzzy rule, setting the fuzzy rule according to the principle that the more stable the vehicle, the larger the fuzzy output eta, wherein,|Δγ|＝|γ_d-γ|，B₁、B₂of vehicles with mechanically-elastic electric wheelsBoundary parameters of a phase plane self-stabilization area and an unstable area, wherein beta is a mass center slip angle of the vehicle;

step 3.4), calculating epsilon and | delta gamma | according to the current state of the vehicle, solving fuzzy output eta by using the fuzzy rule belonging to the step 3.3, and further solving dynamic distribution output of tire force

Step 4), each electric wheel of the vehicle is driven so that the actual longitudinal force is equal to the target longitudinal force and the actual transverse force is equal to the target transverse force:

step 4.1), the actual control signal of each electric wheel is as follows:

in the formula, τ₁₁、τ₂₁、b₁Correction coefficient 1, correction coefficient 2, correction time constant, tau, controlled by left front electric wheel₁₂、τ₂₂、b₂Correction coefficient 1, correction coefficient 2, correction time constant, tau, controlled for the front right electric wheel₁₃、τ₂₃、b₃Correction coefficient 1, correction coefficient 2, correction time constant, tau, controlled by left and rear electric wheels₁₄、τ₂₄、b₄Respectively is a correction coefficient 1, a correction coefficient 2 and a correction time constant controlled by the right rear electric wheel; j. the design is a square_wIs the moment of inertia of the electric wheel; omega_{w_fl}、ω_{w_fr}、ω_{w_rl}、ω_{w_rr}The rotating speeds of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel are respectively; f_zfl、F_zfr、F_zrl、F_zrrVertical forces of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel are respectively;

step 4.2), solving the solution alpha of the following formula by three times of Newton iterative solution_ij,3：

The actual control signals for the steered wheels are as follows:

as a further optimization scheme of the longitudinal and transverse cooperative control method of the mechanical elastic electric wheel vehicle, the optimal tire force is solved by adopting a quasi-Newton iteration methodAnd solving the optimal tire force by adopting a sequential quadratic programming methodThe tire forces during the solution should also satisfy the following constraints:

-T_maxr_ij≤X_ij≤T_maxr_ij

-Y_max≤Y_ij≤Y_max

in the formula (I), the compound is shown in the specification,error relaxation factors preset to ensure the calculation of real-time.

Compared with the prior art, the invention adopting the technical scheme has the following technical effects:

1. an overdrive electronic chassis longitudinal and transverse cooperative motion control algorithm is designed, so that the work among different chassis electronic control systems can be effectively coordinated, and the respective advantages can be exerted; on the premise of overcoming the difficulties brought by strong coupling and parameter uncertainty to the longitudinal and transverse control of the mechanical elastic electric wheel vehicle, the characteristics of the driving redundancy of the chassis are fully utilized by considering the tire slip energy;

2. the dynamic coordination method of the vehicle stability and the tire slip energy dissipation is provided, the coordination weight is calculated by using the phase track of the centroid slip angle-centroid slip angular velocity and the yaw angular velocity error through a fuzzy rule, the tire slip energy dissipation is effectively reduced on the premise of ensuring the vehicle stability through the dynamic distribution of the tire force, the utilization rate of the mechanical elastic electric wheel output energy is improved, and the driving mileage of the electric vehicle is increased;

3. the advanced control of the torque of the mechanical elastic electric wheel is realized, and the delay of torque transmission of the mechanical elastic tire caused by the existence of the hinge group and the elastic ring structure is overcome.

Drawings

FIG. 1 is a schematic diagram of a longitudinal and transverse cooperative control method for a mechanical elastic electric wheel vehicle according to the present invention;

FIG. 2 is a diagram of a dynamic model of a mechano-elastic electric-wheeled vehicle according to an embodiment of the present invention;

FIG. 3 is a diagram showing a result of a yaw rate simulation;

FIG. 4 is a diagram of a simulation result of centroid slip angles;

FIG. 5 is a graph of a result of a simulation of the slip energy of a mechano-elastic electric wheel using the controller of the present invention;

FIG. 6 is a graph of the simulation results of the slip energy of the mechanically elastic electric wheel without the controller.

Detailed Description

The technical scheme of the invention is further explained in detail by combining the attached drawings:

the present invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. In the drawings, components are exaggerated for clarity.

As shown in FIG. 1, the invention discloses a longitudinal and transverse cooperative control method for a mechanical elastic electric wheel vehicle, which specifically comprises the following steps

Step 1), collecting steering wheel angle and accelerator/brake pedal information of a driver, and calculating an expected dynamic response convenient for the driver to operate:

step 1.1), acquiring steering wheel corner delta by using a steering wheel angle sensor_{steering_wheel}According to the steering gear ratio i of the steering sub-system_wCalculating the expected value of the front wheel steering angle

Step 1.2), using the desired value delta of the front wheel steering angle_fCalculating the Steady State response of yaw Rate with two degree of freedom vehicle modelWhereinm is the mass of the vehicle, l_fAnd l_rRespectively representing the distance of the centre of mass to the front and rear axes, k_rAnd k_fRespectively equivalent lateral deflection stiffness of the front shaft and the rear shaft;

step 1.3), designing a reference yaw rate according to the road adhesion coefficient muThe danger caused by the fact that sufficient tire force cannot be provided due to the limitation of road adhesion and the danger caused by tracking of an excessively high reference yaw velocity is avoided. Since the reference yaw rate is treated as a piecewise function, although continuous, there may be points that are not differentiable. In order to make the reference yaw rate microminiaturible and facilitate the design of a control law, a first-order inertia link is added, and finally the expected yaw rate is set as follows:whereinτ_γIs a time coefficient, s is a differential operator, mu is a road surface adhesion coefficient, and g is a gravity acceleration;

step 1.4), obtaining expected acceleration a by using a pedal position sensor_xdAccording to the current vehicle speedCalculable to desired longitudinal vehicle speed

Step 1.5), in order to guarantee the stability of the vehicle in extreme conditions, the invention sets the desired lateral speed to zero, i.e. v_yd＝0；

Step 2), calculating the control laws of longitudinal movement, lateral movement and yaw movement of the mechanical elastic electric wheel vehicle based on the Lyapunov theory:

step 2.1), selecting longitudinal vehicle speed, lateral vehicle speed and yaw angular speed [ v ]_x v_y γ]^TAs state variables, the three state variables are simultaneously used as the input of sliding mode control, and the control laws of longitudinal motion, lateral motion and yaw motion are defined as [ F_xdF_yd M_zd]^TAs an output of the sliding mode control;

step 2.2), selecting three integral sliding modes, wherein the integral sliding modes are represented by the formula (1):

S₁＝e₁+Λ₁ξ₁、S₂＝e₂+Λ₂ξ₂、S₃＝e₃+Λ₃ξ₃ (1)

wherein S is₁Sliding form surface for longitudinal control law, S₂Sliding form surface for transverse control law, S₃Deviation e of longitudinal speed from desired value for sliding mode surface of yaw control law₁＝v_xd-v_x(ii) a Deviation e of lateral velocity from desired value₂＝v_yd-v_y(ii) a Deviation e of yaw rate from desired value₃＝γ_d- γ; longitudinal velocity error integralTransverse velocity error integralIntegral of yaw motion errorΛ₁、Λ₂、Λ₃Positive coefficients of integral terms in sliding mode surfaces of a longitudinal control law, a transverse control law and a transverse control law respectively;

derivation of equation (1) can give:

referring to the 7-degree-of-freedom vehicle model built in fig. 2, including longitudinal, lateral, yaw, and four-wheel rotation, the 7-degree-of-freedom kinetic equation is rewritten as:

in order to overcome the buffeting problem in actual control, the following exponential approach rate is adopted:

and 2.3), driving the formula (3) into the formula (4), and deducing a longitudinal motion control law, a transverse motion control law and a yaw motion control law as shown in the formula (5):

k₁₁、k₂₁respectively S preset in the longitudinal control approach rate₁Term, sat (S)₁/κ₁) Coefficient of term, k₁₂、k₂₂Respectively S preset in the lateral control approach rate₁Term, sat (S)₁/κ₁) Coefficient of term, k₁₃、k₃₁For controlling preset S in approach rate of yaw movement₁Term, sat (S)₁/κ₁) Coefficient of term, κ₁，κ₂，κ₃The boundary layer thicknesses of longitudinal control, transverse control and transverse swing control are respectively adopted;

and 3), dynamically calculating the target longitudinal force and the target transverse force of each tire according to the control laws of longitudinal motion, lateral motion and yaw motion and by combining the driving state of the vehicle:

step 3.1), defining the negativity of the tire respectivelyCharge rate gamma_ijCost function J composed of the sum of the mean and variance of the load rate₁，

Longitudinal force X of a wheel in a tire coordinate system_ijAnd a transverse force Y_ijAnd the longitudinal force F of the wheel in the vehicle coordinate system_xijAnd a transverse force F_yijThe following relationship is satisfied:

thus, the load factor γ of the tire_ijCan be rewritten as:

defining constraint I is shown in equation (11):

the optimal tire force is obtained by using a quasi-Newton iteration method with the formula (8) as an objective function and the formula (11) as a constraint condition

Step 3.2), defining the longitudinal slip force X of the mechanical elastic tyre_sAnd lateral slip force Y_sRespectively as follows:

wherein the content of the first and second substances,a＝a₁F_z ²+a₂F_z+a₃，c_exand c_eyRespectively representing the longitudinal stiffness and the lateral stiffness of the mechanical elastic tire, alpha is the tire slip angle, a₁，a₂，a₃In order to be a coefficient of fit,

defining the longitudinal slip velocity v of a mechanically resilient wheel_sxAnd lateral slip velocity v_syRespectively as follows:

in the formula, r_w、ω_wEffective rolling radius of the wheel and wheel speed, respectively;

defining the longitudinal slip power P of a mechanically resilient wheel_sxPower P of lateral slip_syAnd total power P of slip_sRespectively as follows:

cost function J for defining tire slip power square sum composition₂：

Wherein: p_sxij,t-1Power of longitudinal slip at a moment on the wheel, P_syij,t-1Power of lateral slip at a moment on the wheel, X_ij,t-1Is the longitudinal tire force on the wheel at a moment, Y_ij,t-1Is the lateral tire force on the wheel at a time,

defining a constraint II:

calculating the optimal tire force by using a sequential quadratic programming method by taking the formula (15) as an objective function and the formula (16) as a constraint condition

Solving for optimal tire force by using quasi-Newton iteration methodAnd solving the optimal tire force by adopting a sequential quadratic programming methodThe tire forces should take into account the following constraints:

the tire forces need to satisfy the constraint of the friction circle, namely:

the longitudinal tire force needs to satisfy the outer characteristic curve of the mechanical elastic electric wheel, namely: -T_maxr_ij≤X_ij≤T_maxr_ij，

Tire lateral force needs to be satisfied so that the steering subsystem can provide the maximum tire lateral force, namely: -Y_max≤Y_ij≤Y_max，

The lateral forces of the front left and right wheels need to satisfy the geometrical constraints of the steering trapezium arm, namely:

in the formula (I), the compound is shown in the specification,an error relaxation factor preset for ensuring the calculation real-time performance;

step 3.3), taking epsilon and | delta gamma | as the input of the fuzzy rule, selecting a Gaussian membership function, setting the fuzzy rule according to the principle that the more stable the vehicle is, the larger the fuzzy output eta is, and making the following fuzzy rule table:

wherein the content of the first and second substances,|Δγ|＝|γ_d-γ|，B₁、B₂for vehicles with mechanically-elastic electrically-powered wheelsBoundary parameters of a phase plane self-stabilization area and an unstable area, wherein beta is a mass center slip angle of the vehicle;

step 3.4), calculating epsilon and | delta gamma | according to the current state of the vehicle, solving fuzzy output eta by using the fuzzy rule belonging to the step 3.3, and further solving dynamic distribution output of tire force

Step 4), each electric wheel of the vehicle is driven so that the actual longitudinal force is equal to the target longitudinal force and the actual transverse force is equal to the target transverse force:

step 4.1), the actual control signal of each electric wheel is shown as the formula (17),

in the formula，τ₁₁、τ₂₁、b₁Correction coefficient 1, correction coefficient 2, correction time constant, tau, controlled by left front electric wheel₁₂、τ₂₂、b₂Correction coefficient 1, correction coefficient 2, correction time constant, tau, controlled for the front right electric wheel₁₃、τ₂₃、b₃Correction coefficient 1, correction coefficient 2, correction time constant, tau, controlled by left and rear electric wheels₁₄、τ₂₄、b₄Respectively is a correction coefficient 1, a correction coefficient 2 and a correction time constant controlled by the right rear electric wheel; j. the design is a square_wIs the moment of inertia of the electric wheel; omega_{w_fl}、ω_{w_fr}、ω_{w_rl}、ω_{w_rr}The rotating speeds of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel are respectively; f_zfl、F_zfr、F_zrl、F_zrrVertical forces of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel are respectively;

T_(s)is expressed by the formula (18),

step 4.2), the solution alpha of the formula (19) is determined by three times of Newton iterative solutions_ij,3，

The actual control signal for the steered wheels is as shown in equation (20).

In conclusion, the design flow of the longitudinal and transverse cooperative control method for the mechanical elastic electric wheel vehicle is completely explained, and through the design of the method, the optimal control of the movable chassis of the mechanical elastic electric wheel vehicle can be realized, the utilization rate of the output energy of the electric wheels is improved on the premise of ensuring the stability of the vehicle, the driving mileage of the electric vehicle is increased, and the abrasion of tires is effectively reduced.

Simulation result

And verifying the effectiveness of the controller on the vehicle control effect by adopting a 108km/h constant-speed single-line-shifting working condition, wherein the selected pavement adhesion coefficient is 0.3.

Fig. 3 and 4 represent the yaw rate and the centroid slip angle of the vehicle, respectively, the former reflecting the drivability of the vehicle and the latter reflecting the stability of the vehicle. Fig. 3 finds that the maximum yaw rate of the vehicle without control reaches-0.38 rad/s, and the longitudinal and transverse cooperative controller provided by the invention can make the vehicle be operated and linear in an extreme working condition as easily as possible, so that the difficulty of controlling the vehicle by a driver is greatly reduced. Fig. 4 shows that the vehicle centroid slip angle response using the proposed controller of the present invention does not exceed 0.004rad at maximum, whereas the vehicle centroid slip angle without the controller reaches 0.73rad, and the vehicle has been difficult to control by a normal driver. Fig. 5 shows that the slip energy dissipation of the two front wheels is almost equal and the slip energy dissipation of the two rear wheels is also almost equal under the tire force distribution strategy proposed by the invention, thereby ensuring the consistency of tire wear. Compared with the sliding energy dissipation when the controller is not arranged in the figure 6, the sliding energy dissipation of the tire is effectively controlled, and the driving efficiency of the electric wheel is improved.

It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.

The above-mentioned embodiments, objects, technical solutions and advantages of the present invention are further described in detail, it should be understood that the above-mentioned embodiments are only illustrative of the present invention and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.