CN112346337A - Vehicle stability control method based on active steering of rear wheels under limit working condition - Google Patents

Vehicle stability control method based on active steering of rear wheels under limit working condition Download PDF

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CN112346337A
CN112346337A CN202010964939.5A CN202010964939A CN112346337A CN 112346337 A CN112346337 A CN 112346337A CN 202010964939 A CN202010964939 A CN 202010964939A CN 112346337 A CN112346337 A CN 112346337A
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model
tire
angle
rear wheel
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王萍
丁晓东
刘胜涛
陈虹
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Jilin University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
    • B60L15/00—Methods, circuits, or devices for controlling the traction-motor speed of electrically-propelled vehicles
    • B60L15/20—Methods, circuits, or devices for controlling the traction-motor speed of electrically-propelled vehicles for control of the vehicle or its driving motor to achieve a desired performance, e.g. speed, torque, programmed variation of speed
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
    • B60L2240/00—Control parameters of input or output; Target parameters
    • B60L2240/40—Drive Train control parameters
    • B60L2240/42—Drive Train control parameters related to electric machines
    • B60L2240/423—Torque
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    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
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Abstract

A vehicle stability control method based on active steering of rear wheels under extreme working conditions belongs to the technical field of control. The invention aims to effectively improve the vehicle stability control method based on the active steering of the rear wheels under the limit working condition of the operation stability of the electric vehicle under the limit working condition. The method comprises the following steps: building a high-fidelity vehicle model, designing a two-degree-of-freedom reference model, designing an MPC controller, and calculating the torque of a lower-layer motor and converting the torque of a rear wheel. The invention improves the accuracy of the prediction model, thereby improving the control performance, ensuring the stability of the vehicle and improving the stability of the vehicle.

Description

Vehicle stability control method based on active steering of rear wheels under limit working condition
Technical Field
The invention belongs to the technical field of control.
Background
With the rapid development of science and technology, automobiles become essential vehicles for people to go out, and with the great popularization of automobiles, the improvement of the driving safety of the automobiles and the reduction of traffic accidents become important subjects of automobile development. Particularly, under extreme working conditions (such as low-speed working conditions), the tire cannot provide enough tire force due to low road adhesion coefficient, and the vehicle is extremely unstable, thereby causing accidents. For the four-wheel hub drive electric automobile, the characteristic that wheels of the four-wheel hub drive electric automobile are independently controllable is utilized, and driving/braking torque can be added to each wheel respectively, so that the motion state of the automobile can be better controlled. The rear wheel steering technology is an effective means for further improving the stability of the four-wheel hub drive electric automobile, can effectively reduce the turning radius when the automobile runs at low speed, and improves the stability when the automobile runs at high speed. However, current research on rear wheel steering has some disadvantages:
1. the existing research mainly simplifies the vehicle into a linear model, but with the continuous improvement of the control performance requirement, the traditional method for carrying out linear approximation near the working point ignores the nonlinear characteristic of the tire and cannot meet the precision requirement;
2. the control methods adopted in the existing research mainly comprise PID control, sliding film control and the like, but because the vehicle stability margin is small under the limit working condition, the traditional methods cannot consider the constraint problem and generally cannot ensure the vehicle stability.
3. Most of the existing active rear wheel steering systems only introduce one control quantity of a rear wheel steering angle and cannot simultaneously meet the ideal characteristics of a mass center slip angle and a yaw rate.
Disclosure of Invention
The invention aims to design a Model Predictive Controller (MPC) based on a vehicle two-degree-of-freedom model and a Fiala tire model considering tire nonlinear characteristics, wherein the reference value of yaw velocity generated by a tracking second-order reference value module and the reference value of the inhibition mass center lateral deviation are taken as control targets, and limit working conditions such as low-adhesion road surface, high vehicle speed and the like are comprehensively considered, and a control strategy of rear wheel active steering and additional yaw moment is applied by the MPC, so that a vehicle stability control method based on the rear wheel active steering under the limit working condition of the operation stability of an electric vehicle under the limit working condition is effectively improved.
The method comprises the following steps:
step one, building a high-fidelity vehicle model;
step two, designing a two-degree-of-freedom reference model:
a two-degree-of-freedom linear model of yaw angular velocity and centroid slip angle:
Figure BDA0002681930020000011
Figure BDA0002681930020000012
where β and γ represent the centroid slip angle and yaw rate of the vehicle, respectively, m represents the mass of the vehicle, V represents the speed of the vehicle, and I representszRepresenting the moment of inertia, L, of the vehicle about its centre of massfAnd LrDistances from the centre of mass of the vehicle to the front and rear axles, respectively, Δ MzFor adding yaw moment, deltafIs the angle of rotation of the front wheel, deltarIs the rear wheel steering angle;
based on the equation (1), the transient response obtained by the model is taken as an expectation, and the frequency response analysis can obtain the value of deltafDesired response gamma to yaw rate*：
Figure BDA0002681930020000021
Setting the distance from the front shaft to the rear shaft:
L＝Lf+Lr (3)
defining a stability factor of the vehicle:
Figure BDA0002681930020000022
defining yaw rate steady state gain:
Figure BDA0002681930020000023
the differential coefficient is defined as
Figure BDA0002681930020000024
Oscillation frequency omega of systemnAnd damping coefficient ζ:
Figure BDA0002681930020000025
Figure BDA0002681930020000026
limiting the Low road Friction coefficient the upper limit value of the yaw Rate is defined as
Figure BDA0002681930020000027
The upper limit value of the centroid slip angle is betaup| arctan (0.02 μ g) |, where g is the acceleration of gravity and μ is the coefficient of friction of the tire road surface;
step three, designing an MPC controller:
two-freedom vehicle model
Figure BDA0002681930020000028
Figure BDA0002681930020000029
In the formula FyfAnd FyrRespectively representing the tire lateral force of the front tire and the rear tire;
② tire model
When the tire slip angle α is small, there is tan (α) ≈ α, after which the tire model is:
Figure BDA0002681930020000031
in the formula FyIs the lateral force of the tire, mu is the road adhesion coefficient, FzCornering stiffness C of the tyre for vertical loadsiDividable into front wheel cornering stiffness CfAnd rear wheel cornering stiffness CrAnd alpha is a tire slip angle and can be divided into a front wheel slip angle alphafAnd rear wheel side slip angle alpharSide deflection angle of tireThe following formula gives:
Figure BDA0002681930020000032
Figure BDA0002681930020000033
in the formula offIs the angle of rotation of the front wheel, deltarIs the rear wheel steering angle;
③ forecasting model
The two-freedom vehicle dynamic model (8) and the tire model (9) can obtain a prediction model designed for a controller, the state quantity x of the prediction model consists of a mass center slip angle and a yaw angular velocity, and the mass center slip angle and the yaw angular velocity are subjected to normalization processing, namely
x＝[x1 x2]T＝[β/βup γ/γup]TWherein the controlled variable u is the additional yaw moment and the rear wheel steering angle
Figure BDA0002681930020000034
Figure BDA0002681930020000035
And (3) performing Euler dispersion and normalization on the equation (8) at the sampling moment to obtain a prediction equation:
Figure BDA0002681930020000036
Figure BDA0002681930020000037
in the formula TsIn order to be a discrete time,
Figure BDA0002681930020000039
is the maximum rear wheel steering angle, Δ MmaxIs the maximum value of the additional yaw moment;
and fourthly, defining the following objective functions and constraints:
L1(ki)＝||x2(ki)-γ*/γup||2
L2(ki)＝||x1(ki)||2
L3(ki)＝||u1(ki-1)||2
L4(ki)＝||u2(ki-1)||2 (12)
the vehicle should be subjected to safety constraint in the running process under the limit working condition, and due to the normalization processing, the constraint of the state quantity and the control quantity is changed into: | xi|≤1，|uiI ≦ 1, so the optimization problem is described as:
Figure BDA0002681930020000038
in the formulaβAnd ΓγWeight coefficients, Γ, of the centroid slip angle and yaw angular velocity, respectively1And Γ2Respectively are weight coefficients of the controlled variable, and N is a prediction time domain;
step four, calculating the torque of the lower layer motor and converting the rear wheel steering angle:
torque of electric machine
The actual additional torque is calculated as shown in equation 14 combining the dynamics of the additional yaw moment with the vehicle additional torque, where TiAdditional torque for in-wheel motor
Figure BDA0002681930020000041
② conversion of rear wheel steering angle
Because the angle units in Carsim and Simulink are different, an angle conversion module needs to be built to complete the conversion of the units.
The invention has the beneficial effects that:
1. because the vehicle is a complex nonlinear system, and the requirement on the control performance is continuously improved, the traditional method for carrying out linear approximation near a working point can not meet the precision requirement, a Fiala tire model is adopted in the invention for calculating the tire force, the model considers the nonlinearity of the tire force under the limit working condition, the precision of a prediction model is improved, and the control performance is improved;
2. aiming at the problem of small vehicle stability margin under the extreme working condition, the MPC can predict the future state of the system according to the model, consider the system safety constraint, and simultaneously can take uncertainty caused by model mismatch, time variation, interference and the like into consideration to make up in time so as to ensure the vehicle stability;
3. the method comprehensively considers the limit working conditions of low adhesion road surface and high vehicle speed, provides a cooperative control strategy of active rear wheel steering and additional yaw moment, solves the problem that the single control quantity of an underactuated system can not enable two state quantities to reach ideal characteristics, improves the centroid side slip angle by utilizing the rear wheel steering angle, improves the yaw characteristic by adding the yaw moment, and corrects the motion attitude of the vehicle by adopting a real-time feedback tracking method, thereby improving the stability of the vehicle.
Drawings
FIG. 1 is a block diagram of the overall control of the method of the present invention;
FIG. 2 is a two degree-of-freedom vehicle model schematic of a vehicle;
FIG. 3 is a schematic diagram of a rear-wheel active steering automobile model;
FIG. 4 is a graph comparing three experimental evaluation indexes;
fig. 5 is a diagram of yaw-rate tracking effect;
fig. 6 is a diagram showing the effect of suppressing the centroid slip angle.
Detailed Description
FIG. 1 is a schematic structural diagram of a system of a control method for maintaining vehicle stability based on active steering of a rear wheel under extreme conditions, wherein the system mainly comprises a vehicle two-degree-of-freedom vehicle model, a tire model, a reference model and a model prediction controller. The input of the MPC controller at the upper layer in the figure is the desired yaw rate and the measured value of the controlled object output, and the output is respectively the rearWheel turning angle and additional yaw moment; the lower layer computing module computes an actual additional torque and acts on the hub motor by utilizing the dynamic relation between the additional yaw moment and the vehicle torque according to the control quantity output by the upper layer; and the rear wheel steering angle is output through the angle conversion module and acts on the vehicle. In the figure TiIs the torque distributed to each in-wheel motor. The upper-layer MPC controller and the lower-layer motor torque calculation and rear wheel steering angle conversion module are all built in MATLAB/Simulink; the controlled object is a four-wheel hub drive electric automobile model constructed by using CarSim.
The stability control of the vehicle in the driving process is realized by the combined simulation of a software system.
1. Software selection
The simulation models of the rear wheel active steering controller and the controlled object are respectively built through software Matlab/Simulink and high-fidelity vehicle dynamics simulation software CarSim, the software versions are Matlab R2016a and CarSim2016.1, the solver is selected to be ODE1, and the simulation step length is 0.001s, wherein the CarSim software is a commercial high-fidelity vehicle dynamics simulation platform; MATLAB/Simulink software is used for building a controller, namely the operation of the controller in the method is completed through Simulink programming.
2. Joint simulation setup
To realize the joint simulation of MATLAB/Simulink and CarSim, firstly, a path of CarSim needs to be added in the path setting of Matlab; secondly, adding an output interface module in the CarSim interface; then the model information in CarSim is kept in Simulink in the form of CarSimS-function after system compilation, and finally the parameter setting of the CarSim module in Simulink is carried out. When the Simulink simulation model is operated, the CarSim model is also used for calculating and solving at the same time, and data exchange is continuously carried out between the CarSim model and the Simulink simulation model in the simulation process. If the model structure or parameter settings in the CarSim are modified, recompilation is required, and then the new CarSim module containing the latest setting information is sent back to Simulink.
3. Four-wheel hub drive electric automobile model building in combined simulation software
The complete vehicle model of the CarSim electric vehicle mainly comprises a vehicle body, a transmission system, a steering system, a braking system, tires, a suspension, aerodynamics, working condition configuration and other systems. A four-wheel drive vehicle is selected, the power device of the four-wheel drive vehicle is four hub motors, the additional torque input of the four-wheel drive vehicle is selected from IMP _ MYUSM _ L1, IMP _ MYUSM _ L2, IMP _ MYUSM _ R1 and IMP _ MYUSM _ R2, and the parameters of the electric vehicle are shown in Table 1.
TABLE 1 electric vehicle parameter table
Symbol Physical description Numerical value/Unit
m Vehicle mass 1430/kg
Re Radius of wheel 0.325/m
Lf Distance from vehicle center of mass to front axle 1.05/m
Lr Distance from vehicle center of mass to rear axle 1.61/m
d Left and right wheel track 1.55/m
Cf Sidewall deflection stiffness for front wheel tires 90700/N·rad-1
Cr Sidewall deflection stiffness of rear wheel 109000/N·rad-1
Iz Moment of inertia of vehicle about z-axis 2059.2/kg·m-2
4. Principle for controlling stability of automobile under limit working condition
According to the vehicle stability control method based on the active steering of the rear wheels under the limit working condition, firstly, a dynamic model capable of correctly describing the yaw motion state of a vehicle is deduced; secondly, selecting a proper vehicle model from high-fidelity vehicle dynamics simulation software CarSim and acquiring corresponding parameters; then, establishing a simulation working condition based on the selected vehicle model; then designing a prediction model to predict the future dynamics of a system based on a two-degree-of-freedom vehicle dynamics model and a Fiala tire model considering the tire nonlinear characteristic, selecting an objective function according to a set control target and system performance, wherein the magnitude of weights in the objective function is different due to the different magnitudes of yaw velocity, centroid slip angle, rear wheel turning angle and additional yaw moment, adopting a normalization method to enable the objective function to be in the same magnitude, considering that the vehicle is subjected to safety constraint, converting the objective function into a mathematical optimization problem by using a Casadi tool box, solving the optimization problem to obtain a controlled quantity rear wheel steering angle and an additional yaw moment, and then carrying out inverse normalization on the controlled quantity to obtain the input of a conversion module of motor torque calculation and rear wheel steering angle. And finally, the lower layer calculation module calculates the actual additional torque according to the dynamic relation between the additional yaw moment and the vehicle torque, the actual additional torque acts on the hub motor, and the rear wheel rotation angle is output through the angle conversion module and acts on the vehicle. And a real-time feedback tracking method is adopted to correct the motion attitude of the vehicle, so that the stability of the vehicle is improved.
The invention specifically comprises the following steps:
step one, building a high-fidelity vehicle model:
obtaining a four-wheel hub motor driven electric automobile model by using simulation software CarSim: the four-wheel hub motor-driven electric automobile model simulates a real controlled object, mainly has the functions of providing various state information of a vehicle in real time and changing the motion state of the vehicle by taking the additional torque of the motor and the angle of a rear wheel as input quantities.
Selecting a typical passenger car model, modifying and acquiring relevant parameters of the model, and adding vehicle model parameters into a Simulink simulation model. The main model parameters of the vehicle are vehicle mass, wheelbase, tire cornering stiffness, etc. After selecting the corresponding vehicle model and parameters, corresponding simulation working conditions need to be constructed, the driving route, the driving environment, the driver model and the like of the vehicle can be selected in the simulation working conditions, and the motion state parameters of the vehicle are read into Simulink.
Step two, designing a two-degree-of-freedom reference model:
in order to obtain an ideal yaw motion state of a vehicle, a front wheel corner, a rear wheel corner and a speed of the vehicle are used as input, a transient response obtained by a model is used as an expectation on the basis of a two-degree-of-freedom model of the vehicle, a two-degree-of-freedom reference model is designed according to frequency response analysis, and an expected value of the yaw velocity of the vehicle is obtained by considering road adhesion coefficient limit.
The vehicle yaw rate reference value in the present invention is determined by the current front wheel steering angle, rear wheel steering angle and speed, if assumed
Figure BDA0002681930020000061
And β ═ 0, a first order linear reference model can be obtained. However, during actual vehicle steering, the vehicle's centroid slip angle may not be equal to zero. Neglecting the non-linear terms of the tire lateral force, a two-degree-of-freedom linear model about the yaw rate and the centroid slip angle can be obtained:
Figure BDA0002681930020000062
where β and γ represent the centroid slip angle and yaw rate of the vehicle, respectively, m represents the mass of the vehicle, V represents the speed of the vehicle, and I representszRepresenting the moment of inertia, L, of the vehicle about its centre of massfAnd LrRespectively, the center of mass of the vehicle to the frontDistance between axle and rear axle, Δ MzFor adding yaw moment, deltafIs the angle of rotation of the front wheel, deltarIs the rear wheel steering angle.
Based on the equation (1), the transient response obtained by the model is taken as an expectation, and the frequency response analysis can obtain the value of deltafDesired response gamma to yaw rate*：
Figure BDA0002681930020000071
Distance from front axle to rear axle:
L＝Lf+Lr (3)
defining a stability factor of the vehicle:
Figure BDA0002681930020000072
defining yaw rate steady state gain:
Figure BDA0002681930020000073
the differential coefficient is defined as
Figure BDA0002681930020000074
Oscillation frequency omega of systemnAnd damping coefficient ζ:
Figure BDA0002681930020000075
the upper limit value of the yaw rate is defined in consideration of the limit of the low road surface friction coefficient
Figure BDA0002681930020000076
The upper limit value of the centroid slip angle is betaupOr | arctan (0.02 μ g) |, where g isThe gravitational acceleration, μ, is the tire road friction coefficient.
Step three, designing an MPC controller:
designing a prediction model to predict the future dynamics of the system based on a two-degree-of-freedom vehicle dynamics model and a Fiala tire model considering the nonlinear characteristics of tires; selecting an objective function according to a set control target (the yaw velocity tracks the expected value of the yaw velocity, the mass center slip angle is restrained, and the energy consumption is as small as possible); the magnitude difference of the yaw velocity, the mass center slip angle, the rear wheel corner and the additional yaw moment can cause the difference of the weight magnitude in the objective function, the objective function is enabled to be in the same magnitude by adopting a normalization method, the safety constraint of the vehicle is considered at the same time, the objective function is converted into a mathematical optimization problem by using a Casadi tool box, the optimization problem is solved at the same time to obtain the controlled variable rear wheel corner and the additional yaw moment, and then the controlled variable is subjected to inverse normalization.
Two-freedom vehicle model
The controller of the invention adopts a two-degree-of-freedom vehicle model, only the lateral motion and the yaw motion of the vehicle are considered in the two-degree-of-freedom model, and as shown in figure 2, the tires of a front axle and the tires of a rear axle are respectively simplified into one tire. The driver can only rotate the front wheels, and the rotation angles of the two front wheels are equal, so that the vehicle model can be simplified into a two-degree-of-freedom vehicle model, which can be described by the following equation:
Figure BDA0002681930020000077
in the formula FyfAnd FyrRespectively, the tire lateral forces of the front and rear tires.
② tire model
In the invention, because the vehicle is in the limit working condition, in order to improve the model accuracy, the nonlinear characteristic of the tire force under the limit working condition needs to be considered, and the Fiala tire model is adopted for description. In this model, the tire slip angle is used as an internal variable. When the tire slip angle α is small, there is tan (α) ≈ α, and then the tire model can be approximated as:
Figure BDA0002681930020000081
in the formula FyIs the lateral force of the tire, mu is the road adhesion coefficient, FzCornering stiffness C of the tyre for vertical loadsiDividable into front wheel cornering stiffness CfAnd rear wheel cornering stiffness CrAnd alpha is a tire slip angle and can be divided into a front wheel slip angle alphafAnd rear wheel side slip angle alphar；
The tire slip angle can be calculated by the following equation:
Figure BDA0002681930020000082
in the formula offIs the angle of rotation of the front wheel, deltarIs the rear wheel steering angle.
③ forecasting model
The two-freedom vehicle dynamic model (8) and the tire model (9) can obtain a prediction model designed for a controller, the state quantity x of the prediction model consists of a mass center slip angle and a yaw angular velocity, and the mass center slip angle and the yaw angular velocity are subjected to normalization processing, namely
x＝[x1 x2]T＝[β/βup γ/γup]TWherein the controlled variable u is the additional yaw moment and the rear wheel steering angle
Figure BDA0002681930020000083
Figure BDA0002681930020000084
Euler discretization and normalization are carried out on the formula (8) at the sampling moment, and a prediction equation can be obtained
Figure BDA0002681930020000085
In the formula TsIn order to be a discrete time,
Figure BDA0002681930020000086
is the maximum rear wheel steering angle, Δ MmaxIs the maximum value of the additional yaw moment.
Objective function and constraint
In order to improve the stability of the vehicle, the main control targets are to make the vehicle track the reference value of the yaw rate and suppress the centroid slip angle under the action of the controller, while taking the energy consumption into consideration. The following objective function is thus defined:
Figure BDA0002681930020000087
the vehicle should be subjected to safety constraint in the running process under the limit working condition, and due to the normalization processing, the constraint of the state quantity and the control quantity is changed into: | xi|≤1，|ui|≤1
The optimization problem can then be described as:
Figure BDA0002681930020000091
in the formulaβAnd ΓγWeight coefficients, Γ, of the centroid slip angle and yaw angular velocity, respectively1And Γ2The weight coefficients are respectively of the control quantity, and N is a prediction time domain.
Step four, calculating the torque of the lower layer motor and converting the rear wheel steering angle:
calculating actual additional torque by using the control quantity given by the upper layer, namely the rear wheel turning angle and the additional yaw moment, and combining the dynamic relation between the additional yaw moment and the vehicle torque, and acting the actual additional torque on the hub motor; and the rear wheel rotating angle is output through the angle conversion module and acts on the vehicle.
Firstly, the motor torque is calculated, because the control quantity additional yaw moment can not directly act on the hub motor, the actual additional torque is calculated by combining the dynamic relation of the additional yaw moment and the vehicle additional torque as shown in a formula 14, wherein TiBeing an in-wheel motorAdditional torque
Figure BDA0002681930020000092
Conversion of rear wheel turning angle
Because the angle units in Carsim and Simulink are different, an angle conversion module needs to be built to complete the conversion of the units.
The invention discloses a vehicle stability control method based on active steering of rear wheels under the limit working condition, which comprises 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 a vehicle yaw angular speed expected value considering the limit of the road adhesion coefficient and determine an ideal motion state of the vehicle;
step three, designing an upper-layer MPC controller: designing a prediction model based on a two-degree-of-freedom vehicle dynamic model and a Fiala tire model considering the nonlinear characteristics of tires, considering the safety constraint of a vehicle to enable the yaw velocity of the vehicle to track the reference value of the vehicle, simultaneously inhibiting the mass center side slip angle of the vehicle, and solving an optimization problem to obtain a controlled quantity rear wheel steering angle and an additional yaw moment;
step four, calculating the torque of the lower layer motor and converting the rear wheel steering angle: calculating actual additional torque by using the control quantity given by the upper layer, namely the rear wheel turning angle and the additional yaw moment, and combining the dynamic relation between the additional yaw moment and the vehicle torque, and acting the actual additional torque on the hub motor; and the rear wheel steering angle is output through the angle conversion module and acts on the vehicle.
Verifying and comparing by a simulation experiment:
joint simulation was performed using CarSim and Simulink, and a simulation experiment was performed under a double-shift line condition of V75 km/h and μ 0.35, and evaluation indexes were defined as in table 2 below for good evaluation of the simulation experiment.
TABLE 2 evaluation index
Figure BDA0002681930020000101
In table tmTo simulate time, yupThe lateral maximum deviation.
The method is characterized in that a plurality of groups of experiments are comprehensively considered to obtain a graph 4, and tau is selected in consideration of the tracking error, the energy consumption and the beta inhibition capability of the yaw angular velocity1The set of data represented. Because of tau1And the group data has smaller tracking error, tracking error and energy consumption of the centroid slip angle under the condition that the centroid slip angle is equivalent. The specific yaw rate tracking ability and the beta suppression effect are shown in fig. 5 and 6, and it can be seen from the figures that the vehicle stability control method based on the active steering of the rear wheels under the limit working condition can better track the reference value of the yaw rate, so that the maneuverability of the vehicle is effectively improved; the centroid slip angle of the vehicle can be suppressed within a small range, and the stability of the vehicle is greatly improved compared with the situation without the controller. As can be seen from the simulation example, the stability controller provided by the invention has a better control effect.

Claims (1)

1. A vehicle stability control method based on active steering of rear wheels under extreme working conditions comprises the following steps:
step one, building a high-fidelity vehicle model;
step two, designing a two-degree-of-freedom reference model:
a two-degree-of-freedom linear model of yaw angular velocity and centroid slip angle:
Figure FDA0002681930010000011
Figure FDA0002681930010000012
wherein beta and gamma represent the centroid sideslip of the vehicleAngular and yaw rates, m represents the mass of the vehicle, V represents the speed of the vehicle, IzRepresenting the moment of inertia, L, of the vehicle about its centre of massfAnd LrDistances from the centre of mass of the vehicle to the front and rear axles, respectively, Δ MzFor adding yaw moment, deltafIs the angle of rotation of the front wheel, deltarIs the rear wheel steering angle;
based on the equation (1), the transient response obtained by the model is taken as an expectation, and the frequency response analysis can obtain the value of deltafDesired response gamma to yaw rate*：
Figure FDA0002681930010000013
The method is characterized in that:
setting the distance from the front shaft to the rear shaft:
L＝Lf+Lr (3)
defining a stability factor of the vehicle:
Figure FDA0002681930010000014
defining yaw rate steady state gain:
Figure FDA0002681930010000015
the differential coefficient is defined as
Figure FDA0002681930010000016
Oscillation frequency omega of systemnAnd damping coefficient ζ:
Figure FDA0002681930010000021
Figure FDA0002681930010000022
limiting the Low road Friction coefficient the upper limit value of the yaw Rate is defined as
Figure FDA0002681930010000023
The upper limit value of the centroid slip angle is
Figure FDA00026819300100000211
Wherein g is the gravitational acceleration and μ is the tire road friction coefficient;
step three, designing an MPC controller:
two-freedom vehicle model
Figure FDA0002681930010000024
Figure FDA0002681930010000025
In the formula FyfAnd FyrRespectively representing the tire lateral force of the front tire and the rear tire;
② tire model
When the tire slip angle α is small, there is tan (α) ≈ α, after which the tire model is:
Figure FDA0002681930010000026
in the formula FyIs the lateral force of the tire, mu is the road adhesion coefficient, FzCornering stiffness C of the tyre for vertical loadsiDividable into front wheel cornering stiffness CfAnd rear wheel cornering stiffness CrAnd alpha is a tire slip angle and can be divided into a front wheel slip angle alphafAnd rear wheel side slip angle alpharSide slip angle of tire from bottom to bottomThe formula is obtained:
Figure FDA0002681930010000027
Figure FDA0002681930010000028
in the formula offIs the angle of rotation of the front wheel, deltarIs the rear wheel steering angle;
③ forecasting model
The two-freedom vehicle dynamic model (8) and the tire model (9) can obtain a prediction model designed for a controller, the state quantity x of the prediction model consists of a mass center slip angle and a yaw angular velocity, and the mass center slip angle and the yaw angular velocity are subjected to normalization processing, namely
Figure FDA0002681930010000029
Wherein the controlled variable u is the additional yaw moment and the rear wheel steering angle
Figure FDA00026819300100000210
Figure FDA0002681930010000031
And (3) performing Euler dispersion and normalization on the equation (8) at the sampling moment to obtain a prediction equation:
Figure FDA0002681930010000032
Figure FDA0002681930010000033
wherein Ts is a discrete time in the formula,
Figure FDA0002681930010000034
is the largest rear wheelAngle of rotation,. DELTA.MmaxIs the maximum value of the additional yaw moment;
and fourthly, defining the following objective functions and constraints:
L1(ki)＝||x2(ki)-γ*/γup||2
L2(ki)＝||x1(ki)||2
L3(ki)＝||u1(ki-1)||2
L4(ki)＝||u2(ki-1)||2 (12)
the vehicle should be subjected to safety constraint in the running process under the limit working condition, and due to the normalization processing, the constraint of the state quantity and the control quantity is changed into: | xi|≤1，|uiI ≦ 1, so the optimization problem is described as:
Figure FDA0002681930010000035
in the formulaβAnd ΓγWeight coefficients, Γ, of the centroid slip angle and yaw angular velocity, respectively1And Γ2Respectively are weight coefficients of the controlled variable, and N is a prediction time domain;
step four, calculating the torque of the lower layer motor and converting the rear wheel steering angle:
torque of electric machine
The actual additional torque is calculated as shown in equation 14 combining the dynamics of the additional yaw moment with the vehicle additional torque, where TiAdditional torque for in-wheel motor
Figure FDA0002681930010000036
② conversion of rear wheel steering angle
Because the angle units in Carsim and Simulink are different, an angle conversion module needs to be built to complete the conversion of the units.
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