CN111391822A - A collaborative control method for vehicle lateral and longitudinal stability under extreme working conditions - Google Patents

Abstract

The invention discloses a coordinated control method for vehicle lateral and longitudinal stability under extreme working conditions. First, a four-wheel hub motor-driven electric vehicle model is obtained by using the simulation software CarSim; secondly, a two-degree-of-freedom reference model is designed, and the two-degree-of-freedom reference model is The expected values of lateral speed and yaw angular velocity of the vehicle are deduced; then, a two-layer control structure is adopted to reduce the complexity of the solution, and the upper layer adopts an NMPC controller to ensure the lateral and longitudinal stability of the vehicle as the control objective, and consider the lateral and longitudinal safety constraints for optimization Solve to get the virtual control variable - the expected value of tire slip rate and side slip angle; finally, the lower layer obtains the additional torque acting on the hub according to the deviation between the actual slip rate and side slip angle of the tire and the expected value given by the upper layer The motor ensures the stability of the vehicle in the horizontal and vertical directions.

Description

A collaborative control method for vehicle lateral and longitudinal stability under extreme working conditions

technical field

The invention relates to a coordinated control method for the lateral and longitudinal stability of an automobile under extreme working conditions. Under the present invention, a collaborative control method for lateral and longitudinal stability with low computational complexity is designed, which belongs to the technical field of vehicle safety control.

Background technique

Under extreme driving conditions, the vehicle is easily unstable and causes traffic accidents. At this time, the lateral and longitudinal dynamic systems of the vehicle exhibit strong coupling and nonlinear characteristics, and the existing active safety systems often only focus on the stability of longitudinal or lateral motion. , without considering the mutual influence and coupling effect of other systems, it is difficult to function under extreme conditions due to control target conflict, actuator interference and other reasons. Therefore, it is necessary to carry out collaborative control research on vehicle lateral and longitudinal stability. For a four-wheel-wheel-drive electric vehicle, with the independent controllability of its wheels, the driving/braking torque can be added to each wheel, so as to better control the motion state of the vehicle. At present, there are the following problems in the coordinated control of lateral and longitudinal stability of vehicles under extreme working conditions:

1. The indicators for evaluating the lateral stability of the vehicle are mainly the lateral speed and yaw angular velocity of the vehicle, which are mainly reflected in the tracking of its expected value. Most traditional control algorithms simply set the expected value of lateral velocity to zero, or only track the yaw angular velocity, which makes the design of the reference model not completely reasonable and affects the control performance of the controller.

2. Under the extreme working conditions, the longitudinal and lateral forces of the tires will affect each other, and there is a coupled nonlinear relationship between the longitudinal and lateral forces, the slip rate and the slip angle. Most of the traditional control algorithms do not consider the composite slip characteristics of the tire when using the tire model to calculate the tire longitudinal and lateral force, which makes the tire force calculation inaccurate and affects the accuracy of the prediction model.

3. The tire slip rate is used as an index to evaluate the longitudinal stability of the vehicle. Most control methods track the tire slip rate as a state variable. Although it can be controlled, the dynamic model of this method is complex and it is difficult to set a reasonable slip rate. expected value.

4. As a control quantity that directly affects the motion state of the vehicle, most control methods calculate the additional torque by distributing the total additional torque obtained by the solution to each wheel, ignoring that each wheel may be in different driving/ Braking state, the additional torque obtained in this way is not accurate; or the additional torque is obtained by designing a controller for each wheel separately according to the state quantity of each tire, which makes the control system structure more complicated.

SUMMARY OF THE INVENTION

Aiming at the problem of coordinated control of the vehicle's lateral and longitudinal stability under extreme working conditions, the invention adopts a double-layer control structure. The upper layer uses an NMPC controller to make the vehicle yaw rate and lateral speed track its reference signal, and suppress the longitudinal sliding of the vehicle to ensure that the vehicle Transverse and longitudinal stability, the virtual control variables obtained are the expected values of tire slip rate and sideslip angle; the lower layer uses the tire longitudinal force according to the deviation between the actual tire slip rate and sideslip angle and the expected value given by the upper layer. Based on the dynamic relationship between the slip rate and the slip angle, the additional torque is calculated based on the change of the longitudinal force and acts on the in-wheel motor, thereby ensuring the stability of the vehicle in the lateral and longitudinal directions.

In order to solve the above-mentioned technical problems, the present invention adopts the following technical solutions to realize:

A coordinated control method for vehicle lateral and longitudinal stability under extreme working conditions, comprising the following steps:

Step 1. Use the simulation software CarSim to obtain a model of an electric vehicle driven by a four-wheel in-wheel motor, and provide various status information of the vehicle in real time;

Step 2: Designing a two-degree-of-freedom reference model to obtain the expected values of the vehicle yaw angular velocity and the vehicle lateral velocity considering the limitation of the road adhesion coefficient, and determine the ideal motion state of the vehicle;

Step 3. Design of the upper-layer NMPC controller: Based on the three-degree-of-freedom vehicle dynamics model, a compound-slip LuGre tire model is established considering the compound-slip characteristics of the tire, and a prediction model is designed, so that the yaw rate and lateral speed of the vehicle can track the tire. the expected value, and suppress the longitudinal slip of the tire, take the tire slip rate and the slip angle as the virtual control variables, and the virtual control variables obtained by the optimization solution are used as the expected value of the lower layer control;

Step 4. Calculation of the additional torque of the lower layer: According to the deviation between the actual slip rate and slip angle of the tire and the expected value given by the upper layer, the dynamic relationship between the tire longitudinal force and the slip rate and the slip angle is used. , which calculates the additional torque of the in-wheel motor based on the change of the longitudinal force and sends it to the electric vehicle as an input.

Compared with the prior art, the beneficial effects of the present invention are:

1. The present invention derives the desired lateral speed and yaw rate signals of the vehicle based on the two-degree-of-freedom vehicle model, and simultaneously tracks both when designing the NMPC controller. Instead of simply setting the expected value of the lateral velocity to zero, or only tracking the yaw angular velocity, the ideal trajectories of the two are designed separately to ensure better lateral stability of the vehicle.

2. Most traditional control algorithms do not consider the interaction between longitudinal and lateral tire forces under extreme conditions, and ignore the coupled nonlinear relationship between longitudinal and lateral forces, slip rate and slip angle. When fitting the longitudinal and lateral force of the tire, the present invention adopts the compound slip LuGre tire model and considers the compound slip characteristic of the tire to better calculate the tire force under extreme working conditions, thereby improving the accuracy of the prediction model .

3. Most traditional control algorithms track the tire slip rate as a state variable to ensure the longitudinal stability of the vehicle. The present invention adopts a double-layer control structure, which reduces the order of the prediction model, and takes the tire slip rate and the expected value of the side slip angle as the expected value. The virtual control variables obtained by the NMPC controller can control them while reducing the computational complexity and improving the solution speed.

4. The calculation of the additional torque in the present invention is obtained by transforming the deviation between the expected tire slip rate and the slip angle and the actual value, compared with the calculation of the additional torque obtained by designing a controller for each wheel separately. Compared with the traditional control algorithm, the calculation method of the present invention can better reflect the influence of the change of the slip rate and the slip angle on the additional torque, calculate the additional torque more accurately, and avoid the redundancy of multiple controllers.

Description of drawings

The specific embodiments of the present invention will be further described below with reference to the accompanying drawings, and these and/or other aspects of the present invention will be more clearly understood. in:

Fig. 1 is the flow chart of the coordinated control method for lateral and longitudinal stability of a four-wheel hub-driven electric vehicle according to the present invention;

Fig. 2 is the schematic diagram of the vehicle dynamics model of the present invention;

Fig. 3 is the tire longitudinal force verification diagram of the present invention, wherein the solid line is the longitudinal force calculated by using the compound slip LuGre tire model, the dotted line represents the tire longitudinal force output by the CarSim port, the ordinate unit is N, and the abscissa is time , the unit is s;

Fig. 4 is the tire lateral force verification diagram of the present invention, wherein the solid line is the lateral force calculated by using the composite slip LuGre tire model, the dotted line represents the tire lateral force output by the CarSim port, the ordinate unit is N, the horizontal axis The coordinates are time, and the unit is s;

Fig. 5 is a simulation diagram of the longitudinal speed of the vehicle under the double line shifting condition of the present invention, the unit of the ordinate is m/s, the unit of the abscissa is time, and the unit is s;

6 is a simulation diagram of the yaw angular velocity under the double line shifting condition of the present invention, wherein the dotted line, the solid line, and the dashed line represent respectively no controller function, controller function, and expected yaw angular velocity, ordinate The unit is rad/s, the abscissa is time, and the unit is s;

Fig. 7 is a simulation diagram of the lateral speed of the vehicle under the double line shifting condition of the present invention, wherein the dotted line, the solid line, and the dashed line respectively represent no controller function, a controller function, and the desired lateral speed, and the vertical The coordinate unit is m/s, the abscissa is time, and the unit is s;

Fig. 8 is a simulation diagram of additional torque under the double line shifting condition of the present invention, the unit of ordinate is Nm, the unit of abscissa is time, and the unit is s;

9 is a simulation diagram of the tire slip rate under the double-line shifting condition of the present invention, wherein the dotted line is the expected value of the slip rate calculated by the upper-layer NMPC controller, the solid line is the actual slip rate, and the abscissa is the time, The unit is s.

Detailed ways

In order to describe in detail the technical content, structural features, realization purpose, etc. of the present invention, the present invention will be fully explained below with reference to the accompanying drawings.

The flow of the collaborative control method of the present invention is shown in Figure 1. The input of the upper-layer NMPC controller in the figure is the expected yaw angular velocity, the expected lateral velocity of the vehicle, and the output measurement value of the controlled object, and the outputs are the expected longitudinal slip of the four tires respectively. The calculation of the additional torque of the lower layer is based on the expected value obtained by the upper layer and the actual value output by the controlled object, and the deviation of the tire slip rate and sideslip angle is obtained. The dynamic relationship between the angles, the additional motor torque is calculated based on the change of the longitudinal force; the upper-layer NMPC controller and the lower-layer additional torque calculation module are built in MATLAB/Simulink; the controlled object is a four-dimensional structure constructed by CarSim Wheel hub drive electric car model.

The control objective of the present invention is that, according to the real-time feedback signal, the control system uses the deviation between the expected tire slip rate, the side slip angle and the actual value obtained by the upper controller, and considers the relationship between the tire longitudinal force and the slip rate and the side slip angle. Based on the change of the longitudinal force, the additional torque acting on the four in-wheel motors is obtained to control the lateral and longitudinal stability of the vehicle, so that the actual yaw angular velocity and the actual lateral velocity of the vehicle track their expected values respectively, restraining the tires. The longitudinal slip rate of the vehicle is limited, and the vehicle slip rate and rear wheel slip angle are limited and restricted to ensure the driving safety of the vehicle.

The present invention provides a set of co-simulation models based on the above operating principles and operating processes, and the building and operating processes are as follows:

1. Software selection

The simulation models of the controller and the controlled object of the control system are built by the software MATLAB/Simulink and CarSim respectively. The software versions are MATLAB R2016a and CarSim 2016.1 respectively, and the simulation step size is 0.001s. Among them, CarSim software is a commercial simulation software specially aimed at vehicle dynamics. Its main function in the present invention is to provide a high-fidelity vehicle dynamics model and replace the real four-wheel hub-driven electric vehicle as a control method in the simulation experiment. MATLAB/Simulink is used to build the simulation model of the controller, that is, the operation of the controller in the control system is completed through Simulink programming.

2. Co-simulation settings

To realize the co-simulation of MATLAB/Simulink and CarSim, first set the working path of CarSim to the specified Simulink Model, then add the set vehicle model in CarSim to Simulink, and run Simulink to realize the co-simulation of the two with communication. If the model structure or parameter settings in CarSim are modified, it needs to be resent.

3. Construction of four-wheel hub-driven electric vehicle model in co-simulation software

CarSim electric vehicle model is mainly composed of body, drive train, steering system, braking system, tires, suspension, aerodynamics, working condition configuration and other systems. A four-wheel drive vehicle is selected, and its power unit is four in-wheel motors, and its additional torque input selects IMP_MYUSM_L1, IMP_MYUSM_L2, IMP_MYUSM_R1, and IMP_MYUSM_R2. The parameters of the electric vehicle are shown in Table 1.

Table 1 Electric vehicle parameter table

4. The control principle of vehicle lateral and longitudinal stability under extreme working conditions of the present invention

The controlled object of the present invention is a four-wheel hub-driven electric vehicle, and the control objective is to improve its lateral and longitudinal stability under extreme working conditions. The main design process of the control method is described as follows: First, the four-wheel in-wheel motor-driven electric vehicle model is obtained by using the simulation software CarSim; secondly, the two-degree-of-freedom reference model is designed, and the vehicle lateral speed and yaw angular velocity are derived from the two-degree-of-freedom reference model. Then, in order to reduce the complexity of the solution, a double-layer control structure is adopted, and the upper layer adopts an NMPC controller to ensure the lateral and longitudinal stability of the vehicle as the control goal, and consider the lateral and longitudinal safety constraints to optimize the solution to obtain a virtual control variable - tire slippage The expected value of slip rate and slip angle; finally, the lower layer obtains additional torque to act on the in-wheel motor according to the deviation between the actual slip rate and slip angle of the tire and the expected value given by the upper layer, so as to ensure the stability of the vehicle in the lateral and longitudinal directions .

The specific steps of the control method of the present invention are introduced below:

A coordinated control method for vehicle lateral and longitudinal stability under extreme working conditions, comprising the following steps:

Step 1. Use the simulation software CarSim to obtain the four-wheel in-wheel motor-driven electric vehicle model: The four-wheel in-wheel motor-driven electric vehicle model simulates the real controlled object. The moment is used as the input quantity to change the vehicle motion state.

Step 2: Design of a two-degree-of-freedom reference model: obtain the expected values of the vehicle yaw angular velocity and the vehicle lateral velocity considering the limitation of the road adhesion coefficient, and determine the ideal motion state of the vehicle.

In order to obtain the ideal yaw and lateral motion states of the vehicle, a two-degree-of-freedom reference model is established, which is a linear vehicle model that ignores the nonlinear characteristics of tire forces. Its equation is as follows:

Among them, β is the sideslip angle of the center of mass of the vehicle, γ is the yaw rate, δ is the steering wheel angle given by the driver, and V _x represents the longitudinal speed of the vehicle. Taking the transient response obtained by this model as the expectation, according to the frequency response analysis, the expected responses β ^* and γ ^* from δ to the center of mass slip angle and yaw rate can be obtained:

Among them, K _β , K _γ represent the steady-state gain of the center of mass slip angle and the steady-state gain of the yaw rate, respectively, τ _β , τ _γ are the differential coefficients of the two formulas, respectively, ω _n represents the oscillation frequency of the system, and ξ represents the damping coefficient. Their calculation formulas are as follows:

为车辆系统稳定数。而期望的质心侧偏角β^*和横摆角速度γ^*都会受到有关路面附着系数的限制，它们的上限值分别为：In the formula, L=L _f +L _r represents the distance from the front axle to the rear axle,

is the vehicle system stability number. The expected center of mass slip angle β ^* and yaw rate γ ^* will be limited by the relevant road adhesion coefficient, and their upper limits are:

Among them, μ represents the road adhesion coefficient, and the gravity coefficient g=9.8m/s ² . Then the reference centroid sideslip angle and reference yaw rate can be obtained as follows:

When the center of mass slip angle is small, its value can be regarded as the ratio of the lateral speed of the vehicle to the longitudinal speed, so the reference value V _yref of the lateral speed can be obtained according to β _ref as follows:

V _yref =sgn(δ)V _x ·min{|β ^* |,β _lim } (6)

Step 3. Design of the upper-layer NMPC controller: Based on the three-degree-of-freedom vehicle dynamics model, a compound-slip LuGre tire model is established considering the compound-slip characteristics of the tire, and a prediction model is designed, so that the yaw rate and lateral speed of the vehicle can track the tire. The expected value is obtained, and the longitudinal slip of the tire is suppressed. The tire slip rate and the slip angle are used as virtual control variables, and the virtual control variables obtained by the optimization solution are used as the expected value of the lower layer control.

①Three degrees of freedom vehicle dynamics model

The schematic diagram of the vehicle dynamics model of the present invention is shown in Figure 2, considering the longitudinal, lateral and yaw motions of the vehicle, the three-degree-of-freedom vehicle dynamics model is obtained:

Among them, V _y is the lateral speed of the vehicle, F _x and F _y represent the longitudinal force and lateral force of the tire, respectively, and the subscripts fl, fr, rl, rr represent the front left, front right, rear left, and rear right wheels, respectively. The tire slip angle α is calculated as follows:

其中ω代表车轮转速。Longitudinal slip rate of tires

where ω represents the wheel speed.

②Tire model

Under the extreme conditions, the longitudinal force and lateral force of the tire affect each other. The longitudinal force of the tire is not only calculated by the longitudinal slip rate. Similarly, the lateral force is not only related to the tire slip angle. Both the thrust forces are coupled nonlinearly with slip rate and slip angle. Therefore, the composite slip LuGre tire model is used to describe the longitudinal and lateral forces of the tire.

When the vehicle is in steady state, the composite slip LuGre tire model describes the longitudinal force F _x and the lateral force F _y as follows:

为合成滑移率；g(s_res)是关于滑移率和侧偏角的斯特里贝克方程，可近似计算为g(s_res)≈C₁-C₂λ-C₃α，其中C₁＝1,C₂＝0.64,C₃＝0.1；F_z为轮胎的垂向载荷。Among them, σ _0x and σ _0y represent longitudinal and lateral stiffness coefficients, respectively, σ _2x and σ _2y represent longitudinal and lateral viscous damping, respectively, and κ _x and κ _y are longitudinal and lateral load distribution coefficients, respectively;

is the synthetic slip rate; g(s _res ) is the Strybeck equation for slip rate and slip angle, which can be approximately calculated as g(s _res )≈C ₁ -C ₂ λ-C ₃ α, where C ₁ = 1, C ₂ =0.64, C ₃ =0.1; F _z is the vertical load of the tire.

According to formula (9), the longitudinal and lateral forces calculated by the tire model are compared with the longitudinal and lateral forces output by the CarSim port under the same low-adhesion double-line shift condition, as shown in Figures 3 and 4. It can be seen from Figure 3 and Figure 4 that the tire model can more accurately calculate the longitudinal and lateral forces of the tire under extreme conditions, and can also describe the nonlinear characteristics of the tire during steering.

③Prediction model

其中V_xmax,V_ymax,γ_max分别为车辆纵向速度，侧向速度，横摆角速度的上限值，V_ymax＝V_x·β_lim，γ_max＝γ_lim；控制量u为轮胎期望的滑移率和侧偏角，由于进行了归一化，求解得到的虚拟控制量

其中λ_max,α_fmax,α_rmax分别为车轮滑移率、前轮侧偏角和后轮侧偏角的上限值。综上预测方程可描述为From the three-degree-of-freedom vehicle dynamics model (7) and the tire model (9), a prediction model for controller design can be obtained, and its state quantity x is composed of vehicle longitudinal velocity, lateral velocity and yaw angular velocity. processing, i.e.

Wherein V _xmax , V _ymax , γ _max are the upper limit values of vehicle longitudinal speed, lateral speed and yaw angular velocity respectively, V _ymax =V _x ·β _lim , γ _max =γ _lim ; the control variable u is the expected slippage of the tire The shift rate and the slip angle, due to the normalization, the virtual control quantity obtained by the solution

Where λ _max , α _fmax , α _rmax are the upper limit values of wheel slip ratio, front wheel slip angle and rear wheel slip angle, respectively. In summary, the prediction equation can be described as

④ Objective function and constraints

In order to ensure the lateral stability of the vehicle under extreme working conditions, the main control objective of the NMPC controller is the tracking of the yaw rate and lateral velocity to its reference value, so there are the following control objectives

为了保证车辆的纵向稳定，抑制车轮纵向滑动保证驾驶安全，设计下面控制目标：Among them, t _k represents the current moment, t _p is the prediction time domain, x ₂ (t) is the predicted output of the lateral velocity, and x ₃ (t) is the predicted output of the yaw rate. In addition, for the control quantity, define

In order to ensure the longitudinal stability of the vehicle and suppress the longitudinal sliding of the wheels to ensure driving safety, the following control objectives are designed:

Vehicles should be subject to safety constraints during driving under extreme conditions. For vehicle longitudinal safety, the longitudinal tire slip rate constraints are as follows:

u _x (t)∈[-I _4×1 I _4×1 ] (13)

根据式(8)可计算后轮侧偏角，已知质心侧偏角

后轮侧偏角可通过下式计算：definition

According to formula (8), the rear wheel slip angle can be calculated, and the center of mass slip angle is known

The rear wheel slip angle can be calculated by the following formula:

β和γ都是评价车辆侧向稳定性的指标，为了更好地保证车辆侧向安全，对后轮侧偏角进行约束如下：So there is

β and γ are both indicators for evaluating the lateral stability of the vehicle. In order to better ensure the lateral safety of the vehicle, the rear wheel slip angle is constrained as follows:

u _y (t)∈[-I _2×1 I _2×1 ] (15)

In summary, the objective function is obtained as follows:

Among them, Γ _v , Γ _x are weight coefficients. Using the GRAMPC toolbox to optimize and solve the above objective function, the virtual control variables are obtained as the expected slip rate and slip angle of the tire.

Step 4. Calculation of the additional torque of the lower layer: According to the deviation between the actual slip rate and slip angle of the tire and the expected value given by the upper layer, the dynamic relationship between the tire longitudinal force and the slip rate and the slip angle is used. , which calculates the additional torque of the in-wheel motor based on the change of the longitudinal force and sends it to the electric vehicle as an input.

The virtual control quantity obtained by the optimization solution of the upper-layer NMPC controller needs to be converted into the input quantity that can actually act on the vehicle, and it is transformed into the additional torque acting on each in-wheel motor. According to the previous analysis of tire force under extreme conditions, the calculation of tire longitudinal force is related to slip rate and sideslip angle, so the change of tire longitudinal force ΔF _x is also related to the change of slip rate Δλ and sideslip angle The change Δα is related to the relationship between them can be expressed as:

According to the LuGre composite-slip tire model (9), the deflection of the tire longitudinal force to the slip rate and slip angle can be obtained as follows:

where we define

和侧偏角

与车辆实际的滑移率λ和侧偏角α之间存在的偏差量，可看作为滑移率和侧偏角在想要满足控制器控制目标及约束时所产生的变化，于是有下列关系：Desired slip rate obtained by the upper-level NMPC controller

and slip angle

The deviation from the actual slip rate λ and the sideslip angle α of the vehicle can be regarded as the change of the slip rate and sideslip angle when trying to meet the control objectives and constraints of the controller, so there is the following relationship :

According to formula (14), the deviation is converted into the required longitudinal force change ΔF _x , and then the additional torque ΔT acting on each in-wheel motor is calculated as follows, and the saturation of the actuator is considered to limit it:

ΔT=sgn(ΔF _x )min{|ΔF _{x Re} |,T _max } (20)

where T _max is the upper limit of the additional torque that can act on the in-wheel motor.

The validity of the control method of the present invention is verified by the following simulation experiments:

In order to verify the effectiveness of the control method described in the present invention, a simulation experiment is designed under the co-simulation environment of CarSim and MATLAB/Simulink. The simulation test condition is set as the double-line shift condition, the road friction coefficient μ=0.35, the vehicle speed is kept around 60km·h ^-1 as shown in Figure 5, the sampling time is set to 5ms, the prediction time domain _tp =10, the simulation experiment The parameters and weight coefficients used in Table 2.

Table 2 Simulation experiment parameter table

symbol definition value/unit V_xmax Vehicle longitudinal speed upper limit 120/km·h^-1 λ_max Upper limit of tire slip ratio 0.1 α_fmax Front wheel slip angle upper limit 0.4/rad α_rmax Tire slip angle upper limit 0.1/rad T_max In-wheel motor additional torque upper limit 800/N m^-1 Γ_v Lateral velocity tracking weights in NMPC 0.05 Γ_u Tire Slip Suppression Weights in NMPC 0.25

Figures 6 and 7 are the simulation curves of the yaw angular velocity and the lateral velocity of the vehicle under the low-adhesion double lane-shifting condition, respectively. It can be seen that compared with the system without the intervention of the controller, under the action of the NMPC controller, the vehicle's The yaw rate can track its desired value, and the lateral velocity is effectively suppressed, thereby ensuring the lateral stability of the vehicle.

The additional torque calculated by the lower layer using the deviation of the tire slip rate and the slip angle is shown in Figure 8. In the first 1s, since the vehicle is in the acceleration state, in order to ensure the vehicle speed, it is necessary to add additional driving torque to the four in-wheel motors. After the speed remains stable, the additional torque tends to zero, and the vehicle starts to turn at 4s. The control structure of the present invention can add a reasonable driving/braking torque to the four in-wheel motors to ensure the stability of the vehicle, and consider Saturation of the actuator.

The actual slip rate of the tires and the expected slip rate obtained by the upper-layer NMPC controller are shown in Figure 9. In the first 1s, the slip rates of the four tires will gradually decrease as the vehicle accelerates and remains stable. Small approaching zero, the tire slip rate can be limited to a small range during the entire double line shifting process, and the longitudinal sliding of the vehicle on the low-adhesion road surface is effectively suppressed, thereby ensuring the longitudinal stability of the vehicle sex. Through the verification of simulation experiments, the lateral and longitudinal stability cooperative control method of the present invention can effectively improve the lateral and longitudinal stability of the four-wheel hub-driven electric vehicle under extreme working conditions, and ensure driving safety.

Claims (4)

1. A method for cooperatively controlling the transverse and longitudinal stability of an automobile under a limit working condition is characterized by comprising the following steps:

the method comprises the following steps of firstly, obtaining a four-wheel hub motor driven electric automobile model by using simulation software CarSim, and providing each state information of a vehicle in real time;

designing a two-degree-of-freedom reference model to obtain expected values of the yaw velocity and the lateral velocity of the vehicle, which are limited by considering the road adhesion coefficient, and determining an ideal motion state of the vehicle;

thirdly, designing an upper-layer NMPC controller, namely establishing a composite slip L uGre tire model by considering the composite slip characteristic of a tire based on a three-degree-of-freedom vehicle dynamic model, designing a prediction model, enabling the yaw velocity and the lateral velocity of the vehicle to track the expected values of the yaw velocity and the lateral velocity of the vehicle, inhibiting the longitudinal slip of the tire, and taking the tire slip rate and the slip angle as virtual control quantities, and optimally solving the obtained virtual control quantity as the expected value of lower-layer control;

step four, calculating the lower additional torque: according to the actual slip ratio and deviation amount between the slip angle and the expected value given by the upper layer, the dynamic relation between the longitudinal force of the tire, the slip ratio and the slip angle is utilized, the additional torque of the hub motor is calculated based on the change of the longitudinal force, and the additional torque is sent to the electric automobile as the input amount.

2. The cooperative control method for the transverse and longitudinal stability of the automobile under the limit condition as claimed in claim 1, wherein in the second step, a two-degree-of-freedom reference model is designed, and the equation is as follows:

where β is the vehicle centroid slip angle, γ is the yaw rate, is the driver-given steering wheel angle, V_xRepresenting the vehicle longitudinal speed;

taking the transient response obtained by the son's finite reference model as the expectation, the expected response β from the centroid yaw angle and yaw rate is obtained^*And gamma^*：

Wherein, K_β,K_γRespectively representing the steady-state gain of the centroid slip angle and the steady-state gain of the yaw angular velocity, tau_β,τ_γDifferential coefficients, ω, of two types respectively_nRepresenting the oscillation frequency of the system, ξ representing the damping coefficient;

desired centroid slip angle β^*And yaw rate γ^*Are limited by the road adhesion coefficient, and their upper limits are:

wherein mu represents the road adhesion coefficient, and g is 9.8m/s²(ii) a The reference centroid slip angle and the reference yaw rate are obtained as follows:

β_ref＝sgn()min{|β^*|,β_lim}

γ_ref＝sgn()min{|γ^*|,γ_lim}

when the centroid slip angle is small, the value can be considered as the ratio of the vehicle lateral velocity to the longitudinal velocity, so according to β_refThe reference value V of the lateral speed can be obtained_yrefThe following were used:

V_yref＝sgn()V_x·min{|β^*|,β_lim}。

3. the cooperative control method for the transverse and longitudinal stability of the automobile under the limit condition as claimed in claim 1, wherein the third step comprises the following steps:

① the vehicle dynamics model is obtained by considering the longitudinal, lateral and yaw movement of the vehicle:

wherein, V_yAs the lateral speed of the vehicle, F_xAnd F_yThe subscripts fl, fr, rl, rr represent the left front, right front, left rear and right rear wheels, respectively;

longitudinal slip ratio of tire

Wherein ω represents wheel speed;

② tire longitudinal force F using compound slip L uGre tire model_xAnd a lateral force F_yThe description of (A) is as follows:

wherein σ_0xAnd σ_0yRespectively representing longitudinal and lateral stiffness coefficients, σ_2xAnd σ_2yRespectively representing longitudinal and lateral viscous damping, k_xAnd kappa_yLongitudinal and lateral load distribution coefficients respectively;

the synthetic slip ratio; g(s)_res) Is a Sterbek equation for slip ratio and slip angle, and can be approximated as g(s)_res)≈C₁-C₂λ-C₃α, wherein C₁＝1,C₂＝0.64,C₃＝0.1；F_zIs the vertical load of the tire;

③ A predictive model for controller design is obtained from the three-degree-of-freedom vehicle dynamics model and the tire model:

the state quantity x is composed of the longitudinal speed, the lateral speed and the yaw rate of the vehicle, and the state quantity x is subjected to normalization processing, namely:

wherein V_xmax,V_ymax,γ_maxUpper limit values V of the longitudinal speed, lateral speed and yaw rate of the vehicle_ymax＝V_x·β_lim，γ_max＝γ_lim(ii) a The control quantity u is a virtual control quantity obtained by solving the slip rate and the slip angle expected by the tire

Wherein λ_max,α_fmax,α_rmaxThe upper limit values of the wheel slip rate, the front wheel side deflection angle and the rear wheel side deflection angle are respectively;

④ objective function and constraints:

the NMPC controller mainly controls the tracking of the yaw velocity and the lateral velocity on the reference value thereof, and the control targets are as follows:

wherein, t_kRepresenting the current time, t_pTo predict the time domain, x₂(t) is the predicted output of lateral velocity, x₃(t) is the predicted output of yaw rate;

for the controlled quantity, define

Designing a control target:

the tire longitudinal slip ratio is constrained as follows:

u_x(t)∈[-I_4×1I_4×1]

definition of

Centroid slip angle

The rear wheel side slip angle is calculated by the following equation:

then there are

The rear wheel side slip angle is constrained as follows:

u_y(t)∈[-I_2×1I_2×1]

the objective function is obtained as follows:

s.t.

u_x(t)∈[-I_4×1I_4×1]

u_y(t)∈[-I_2×1I_2×1]

wherein,_v,_xis a weight coefficient;

and optimally solving the objective function to obtain the slip rate and the slip angle of the tire with the virtual control quantity as expected.

4. The method for cooperatively controlling the transverse and longitudinal stability of the automobile under the limit condition of claim 1, wherein the step four of lower-layer additional torque comprises the following steps of:

change of tire longitudinal force Δ F_xThe relationship between the change in slip ratio Δ λ and the change in slip angle Δ α can be expressed as:

the partial derivatives of the tire longitudinal force on the slip ratio and the slip angle are as follows:

in the formula (II)

Desired slip ratio by upper NMPC controller

And slip angle

The following relationship is present with respect to the actual slip ratio λ and slip angle α of the vehicle:

converting the deviation into the desired longitudinal force change Δ F_xThen, the additional torque Δ T acting on each in-wheel motor is calculated as follows:

ΔT＝sgn(ΔF_x)min{|ΔF_xR_e|,T_max}

in the formula, T_maxIs an upper limit value of the additional torque acting on the in-wheel motor.

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