CN113221257A - Vehicle transverse and longitudinal stability control method under extreme working condition considering control area - Google Patents

Vehicle transverse and longitudinal stability control method under extreme working condition considering control area Download PDF

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CN113221257A
CN113221257A CN202110657208.0A CN202110657208A CN113221257A CN 113221257 A CN113221257 A CN 113221257A CN 202110657208 A CN202110657208 A CN 202110657208A CN 113221257 A CN113221257 A CN 113221257A
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tire
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CN113221257B (en
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李梓涵
王萍
许娟
林佳眉
胡云峰
陈虹
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Jilin University
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Abstract

A method for controlling the stability of a vehicle in the transverse direction and the longitudinal direction under the limit working condition considering a control area belongs to the technical field of vehicle safety control. The invention aims to design a stability controller under a framework of model predictive control according to different stability control requirements of different regions where vehicle states are located, obtain additional torque to act on a hub motor, and adjust the driving posture of a vehicle, thereby ensuring the stability of the vehicle in the transverse and longitudinal directions under the limit working condition of the control region. The method comprises the following steps: constructing a limit driving condition; different control requirements for driving safety need to be met in different areas; mapping to different control objectives and constraint changes in the stability controller design; acting on the hub motor to form a closed loop system. The method ensures the solving real-time performance of the controller while ensuring the accurate description characteristics of the model.

Description

Vehicle transverse and longitudinal stability control method under extreme working condition considering control area
Technical Field
The invention belongs to the technical field of vehicle safety control.
Background
With the increase of the automobile holding capacity, the appearance of the electric automobile effectively improves the problems of energy shortage and environmental pollution. The four-wheel hub drive electric automobile has greater potential in the aspect of vehicle stability control because each wheel is independently controllable and can be respectively additionally provided with driving/braking torque through vehicle dynamics control. Under the extreme working condition, the vehicle is easy to be unstable and causes traffic accidents, and the coupled vehicle transverse and longitudinal dynamics influence each other at the moment, so that the existing active safety system is difficult to exert the control function, and the control algorithm is necessary to improve the vehicle transverse and longitudinal stability. The control areas of the yaw rate and the centroid slip angle are introduced and divided in the stability control, and different control performances are considered in different areas, so that the overall stability and the driving safety of the vehicle can be improved better.
The existing vehicle transverse and longitudinal stability control under the limit working condition considering the control area has the following problems:
1. even though the vehicle may be in different control areas at different time states during the driving process, most control methods still consider the same control requirement in each area, but do not change in real time according to the stability control requirement required by the current state, although the control methods can be more effectively controlled, the control performance of the control methods cannot be fully exerted, and the application potential of the control areas in the vehicle stability control is limited.
2. In the existing transverse and longitudinal stability control method for most four-wheel hub drive electric vehicles, when a tire model is used for fitting tire force, the composite slip characteristic of the tire under the limit working condition is not considered, and the coupling nonlinear relation between longitudinal and lateral forces and slip rate and slip angle is neglected, so that the calculation of the tire force is not accurate enough, and the accuracy of a prediction model is influenced.
3. Most of the existing vehicle stability control methods under the extreme working conditions use a complex nonlinear model in order to accurately describe the dynamics of the vehicle and the tire, and the solving complexity is increased, so that the solving of the controller can only select a complex solving tool, and the real-time performance of a control system cannot be ensured.
Disclosure of Invention
The invention aims to design a stability controller under a framework of model predictive control according to different stability control requirements of different regions where vehicle states are located, obtain additional torque to act on a hub motor, and adjust the driving posture of a vehicle, thereby ensuring the stability of the vehicle in the transverse and longitudinal directions under the limit working condition of the control region.
The method comprises the following steps:
s1, building a four-wheel hub motor driving electric automobile model by using simulation software CarSim, and constructing a limit driving working condition;
the method is characterized in that:
s2, according to current driving behaviors and road condition information, considering vehicle transverse-longitudinal-vertical dynamic characteristics, giving boundary conditions of an online vehicle control area, dividing the boundary conditions into a stable area, a critical stable area and an unstable area, and meeting different control requirements for driving safety in different areas;
the control demand setting obtains control areas related to the yaw velocity gamma and the centroid side offset angle beta on line according to driver behaviors and road condition information, the current vehicle state (beta, gamma) judges the position of the area, and the control demands to be met are changed along with the situation that the vehicle state may be in different areas, wherein the different areas are a stable area R1, a critical stable area R2 and an unstable area R3;
as the vehicle state gradually moves away from the stable region, i.e., transitions from the stable region R1 to the critical stable region R2 to the unstable region R3, the respective objective function weight values change in the form of an S-curve as follows:
Figure BDA0003113592830000021
wherein k is 0.7, q1＝0.1，q2＝7，
Figure BDA0003113592830000022
βain,βaout,βbin,βboutRespectively represent the boundary ain,aaout,bin,boutA centroid sideslip angle value corresponding to the current gamma above; determining a weight initial value gammainiTerminal value ΓterAnd beta is from the current betainThe weight value in the current state can be determined according to the distance;
s3, judging the current position of the area where the vehicle is located according to the current vehicle mass center side slip angle and the current yaw velocity based on the control area divided in the S2, and mapping different control targets and constraint changes in the stability controller design for the switching of different control requirements when the vehicle is located in each area; designing a model predictive controller based on a dynamic model reflecting yaw motion, lateral motion, longitudinal slip of the vehicle, and a tire model considering composite slip characteristics of the tire, wherein control target weight values and constraint conditions are changed according to S3;
MPC controller design
Vehicle dynamics model
Considering the yaw and lateral motion of the vehicle, a vehicle dynamics model is obtained as follows:
Figure BDA0003113592830000023
Figure BDA0003113592830000024
wherein, VyAs the lateral speed of the vehicle, deltafFor turning the front wheel, FxAnd FyRepresenting the longitudinal and lateral forces of the tyre, respectively, Δ T representing the additional torque, the subscript i ∈ { f, r }, the combination of j ∈ { l, r }, ij ∈ { fl, fr, rl, rr } representing the left front and right front, respectivelyFront, left rear and right rear wheels. In addition to the rolling of the wheels,
Figure BDA0003113592830000031
dynamics hold, where ω represents wheel speed. Longitudinal slip ratio of known tire
Figure BDA0003113592830000032
The change in slip rate can be expressed kinetically as follows:
Figure BDA0003113592830000033
② tire model
Longitudinal force F on tirexAnd a lateral force FyThe description is as follows:
Figure BDA0003113592830000034
wherein σ0x,σ0yRespectively representing longitudinal and lateral stiffness coefficients, σ2x,σ2yRespectively representing longitudinal and lateral viscous damping, kx,κyLongitudinal and lateral load distribution coefficients respectively;
Figure BDA0003113592830000035
the synthetic slip ratio; g(s)res) Is the Sterbek equation for slip ratio and slip angle, calculated as g(s)res)≈C1-C2λ-C3α, wherein C1＝1,C2＝0.64,C30.1; vertical load of tyre
Figure BDA0003113592830000036
The calculation takes into account the load redistribution on the slope when the vehicle is turning, where ax,ayRespectively represent the longitudinal acceleration and the lateral acceleration,
Figure BDA0003113592830000037
in order to be the side inclination angle,eta, zeta represents the side and longitudinal road slope, respectively;
extracting changes in longitudinal and lateral forces into forms related to slip ratio and yaw angle changes
Figure BDA0003113592830000038
The partial derivatives of the longitudinal force and the lateral force of the tire to the slip ratio and the slip angle are respectively as follows:
Figure BDA0003113592830000039
Figure BDA00031135928300000310
Figure BDA0003113592830000041
Figure BDA0003113592830000042
in the formula
Figure BDA0003113592830000043
The known tire slip angle α is calculated as follows:
Figure BDA0003113592830000044
the changes are described in terms of yaw rate and lateral velocity in the following manner:
Figure BDA0003113592830000045
wherein
Figure BDA0003113592830000046
Combining equation (6) with equation (8) yields the final form describing the variation of the longitudinal force and the front/rear axle lateral resultant force of each wheel as follows:
Figure BDA0003113592830000047
Figure BDA0003113592830000048
according to the formulas (9) and (10), the longitudinal and lateral forces calculated by the tire model are compared with the longitudinal and lateral forces output by the ports of the CarSim under the same low-adhesion double-shift-line working condition, so that the tire model can more accurately calculate the longitudinal and lateral forces of the tire under the extreme working condition, can describe the nonlinear characteristic of the tire during steering and meets the model precision;
③ forecasting model
According to the dynamic models (2) and (3) and the tire models (9) and (10), a prediction model designed for a controller is obtained, the state quantity x of the prediction model is composed of vehicle yaw velocity, lateral velocity, front-rear axis lateral force, tire slip ratio and longitudinal force, and the state quantity x is subjected to normalization processing, namely normalization processing
Figure BDA0003113592830000051
Where the subscript max represents the upper limit of the quantity, Vymax＝Vx·βlim，γmax＝γlim(ii) a The control amount u is an additional torque, and since normalization is performed, the control amount is
Figure BDA0003113592830000052
In summary, the prediction equation is described in the following state space form:
Figure BDA0003113592830000053
wherein the parameter matrix is:
Figure BDA0003113592830000054
Figure BDA0003113592830000055
Figure BDA0003113592830000056
Figure BDA0003113592830000061
based on equations (9) and (10), the calculation expression for each element in matrix M is as follows:
Figure BDA0003113592830000062
Figure BDA0003113592830000063
Figure BDA0003113592830000064
Figure BDA0003113592830000065
discretizing the model (11) to obtain a discrete model as follows:
x(k+1)＝A(k)x(k)+Bu(k)u(k)+Bd(k) (12)
wherein
Figure BDA0003113592830000066
Representing the current time, TsIs the sampling time;
objective function and constraint
In order to ensure the lateral stability of the vehicle under the extreme conditions, the main control targets of the controller are the tracking of the yaw rate and the lateral speed to their reference values, so that the following objective functions are provided:
Figure BDA0003113592830000067
wherein x1(t) is the predicted output of yaw rate, x2(t) is the predicted output of lateral velocity,. gammarefAnd VyrefRespectively obtaining a yaw angular velocity reference signal value and a lateral velocity reference signal value obtained by a two-degree-of-freedom reference model; defining the slip ratio set of four wheels as lambdax＝[x5,x6,x7,x8]TIn order to ensure the longitudinal stability of the vehicle and to suppress the longitudinal slip of the wheels to ensure the driving safety, the following control targets are designed:
J3＝||λx(t)||2 (14)
setting an objective function J regarding a control amount4＝||u(t)||2To reduce torque energy consumption;
for vehicle longitudinal safety, there are the following constraints on the longitudinal slip rate of the tire, where λlimTo the constraint value:
Figure BDA0003113592830000068
for lateral safety and stability of the vehicle, constraints on lateral speed are set as follows:
Figure BDA0003113592830000071
wherein VylimIs a constrained value of lateral velocity, andlimand VylimAccording toDifferent requirements of the control areas are changed;
considering the actuator saturation problem, setting a control quantity constraint:
u(t)∈[-I4×1 I4×1] (17)
wherein I represents a matrix with all 1 elements;
the optimization problem is summarized as follows:
Figure BDA0003113592830000072
s.t.(12),(15),(16),(17)
wherein gamma isv,Γx,ΓuIs a weight coefficient and is changed according to the formula (1) in different areas according to different control requirements; the optimization problem (18) is solved by utilizing a quadratic sequence programming algorithm, and the obtained control quantity is an additional torque to act on the hub motor.
The invention has the beneficial effects that:
1. in the invention, when the vehicle is in different control areas, different control requirements are considered, the control requirements are mapped into control targets and constraint conditions in the controller design, and the switching of the control requirements is reflected by the change of weight values and constraint values of the control targets in different areas;
2. most control methods ignore the coupled nonlinear relationship between the longitudinal and lateral forces of the tire under extreme conditions and the slip ratio and the slip angle. When the method is used for fitting the longitudinal and lateral forces of the tire, a composite slip LuGre tire model is adopted, the common influence of the slip rate and the slip angle on the tire force is considered, the tire force under the extreme working condition can be more accurately calculated, and the accuracy of a prediction model is improved;
3. most control methods use complex non-linear models to describe the dynamics under extreme conditions, which, although more accurate, increases the complexity of the solution. The invention extracts the changes of the lateral movement and the longitudinal sliding of the vehicle to describe the changes of the longitudinal force and the lateral force of the tire, thereby establishing a linear prediction model, ensuring the accurate description characteristics of the model and simultaneously ensuring the solving real-time performance of the controller.
Drawings
FIG. 1 is a control block diagram of a lateral and longitudinal stability control system of a four-wheel hub-drive electric vehicle with consideration of a control area according to the present invention;
FIG. 2 is a schematic diagram of the boundary and the division of the control area according to the present invention, wherein the vehicle runs on a straight road with a road surface adhesion coefficient of 0.35, and the vehicle speed is in the range of 60-65km/h, wherein the solid line is the controllable boundary, the double-dashed line is the inner boundary of the stable condition obtained at a speed of 60km/h, the dash-dot line is the outer boundary of the stable condition obtained at a speed of 65km/h, the area formed by the inner boundary and the controllable boundary is the stable area R1, the area formed by the inner and outer boundaries is the critical stable area R2, and the other parts are all regarded as the unstable area R3;
FIG. 3 is a schematic diagram illustrating the variation of the weighting values in the region variation according to the present invention, wherein the weighting values are the initial value and the terminal value in the stable region R1 and the unstable region R3, respectively, and the weighting values are associated with β and β in the critical stable region R2inThe distance of (a) is changed in an S shape;
FIG. 4 is a schematic representation of a vehicle dynamics model according to the present invention;
FIG. 5 is a graph of a tire longitudinal force verification according to the present invention, wherein the solid line represents the longitudinal force calculated using the LuGre composite slip tire model, the dotted line represents the tire longitudinal force output from the CarSim port, and the ordinate is in units of N, and the abscissa is time and s;
FIG. 6 is a graph of lateral force verification for a tire according to the present invention, wherein the solid line represents the lateral force calculated using the LuGre tire model, the dotted line represents the tire lateral force output from the CarSim port, and the ordinate is in units of N, and the abscissa is time and s; FIG. 7 is a simulation diagram of the yaw rate under the double-shift-line condition according to the present invention, in which the solid line, the double-dashed line, the dot-dash line, and the dashed line represent the yaw rate under the variable-coefficient control, the desired constant-coefficient control, and the no-controller action, respectively, and the ordinate is rad/s, and the abscissa is time and s;
FIG. 8 is a simulated lateral velocity of a vehicle under a double-traverse condition in accordance with the present invention, wherein the solid, double-dashed, and dashed lines represent the lateral velocities of variable-coefficient control, desired, constant-coefficient control, and no-controller action, respectively, with the ordinate in m/s and the abscissa in time and in s;
FIG. 9 is a simulation diagram of the tire slip ratio under the double-shift-line working condition of the present invention, in which the solid line and the double-dashed line represent the tire slip ratio under the control of the variable coefficient and the constant coefficient, respectively, and the abscissa is time and the unit is s;
FIG. 10 is a simulation diagram of additional torques obtained by variable-coefficient control under the double-traverse working condition, in which a solid line, a double-traverse line, a dot-dash line, and a dotted line represent additional torques acting on the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel hub motors, respectively, and the ordinate is Nm, and the abscissa is time and s;
fig. 11 is a simulation diagram comparing the variation of the control area under the condition of the double-shift line, in which the solid line and the broken line respectively represent the control areas under the variable coefficient control and the non-control action, and the abscissa is time and the unit is s.
Detailed Description
Aiming at the problem of controlling the transverse and longitudinal stability of the automobile under the limit working condition, different stability control requirements are considered according to different regions where the automobile state is located, and a stability controller is designed under the framework of model prediction control, wherein the weight value and the state constraint of each control target are respectively changed in real time according to different control regions, so that the transverse and longitudinal speeds of the automobile track the reference signals of the automobile, the longitudinal sliding of the automobile is inhibited, the optimization problem is solved, the additional torque is obtained and acts on a hub motor, and the driving posture of the automobile is adjusted, so that the transverse and longitudinal stability of the automobile is ensured.
The research method of the invention is a control system designed aiming at the control problem of the transverse and longitudinal stability of the vehicle under the limit working condition, and comprises the following steps:
s1, building a four-wheel hub motor driving electric automobile model by using simulation software CarSim, and constructing an ultimate driving working condition;
s2, according to current driving behaviors and road condition information, considering vehicle transverse-longitudinal-vertical dynamic characteristics, giving boundary conditions of an online vehicle control area, dividing the boundary conditions into a stable area, a critical stable area and an unstable area, and meeting different control requirements for driving safety in different areas;
s3, judging the current position of the area where the vehicle is located according to the current vehicle mass center side slip angle and the current yaw velocity based on the control area divided in the S2, and mapping different control targets and constraint changes in the stability controller design for the switching of different control requirements when the vehicle is located in each area;
s4, designing a model predictive controller based on a dynamic model reflecting the yaw motion, the lateral motion and the longitudinal sliding of the vehicle and a tire model considering the composite sliding characteristic of the tire, wherein the control target weight value and the constraint condition are changed according to S3;
and S5, obtaining the control quantity additional torque by solving the optimization problem, and acting the control quantity additional torque on the hub motor to form a closed-loop system.
In order to solve the technical problems, the invention is realized by adopting the following technical scheme:
the cooperative control of the transverse and longitudinal stability of the automobile under the extreme working condition considering the stable region is realized by the combined simulation of a software system MATLAB/Simulink and a CarSim, wherein the CarSim software is a commercial simulation software specially aiming at the vehicle dynamics, replaces a real four-wheel hub driving electric automobile as an implementation object of a control method, provides a simulation environment of the extreme working condition and collects road condition information; MATLAB/Simulink is used for building a simulation model of the controller, namely the operation of the controller in the control system is completed through Simulink programming.
Functionally, the present invention may include the following: the system comprises a four-wheel hub motor driven electric automobile model, a control area division and judgment module, a reference model and a transverse and longitudinal stability controller based on MPC.
The function of each part is explained in detail as follows:
the four-wheel hub motor-driven electric automobile model simulates a real controlled object, mainly has the functions of providing various state information and road condition information of a vehicle in real time and changing the motion state of the vehicle by taking the additional torque of the motor as an input quantity.
The control area dividing and judging module is mainly used for dividing the control area according to the current road condition information and the driver behaviors (steering, acceleration/deceleration), and judging the position of the area where the vehicle is located and the current control requirement according to the current yaw velocity and the centroid side deviation angle, so that different target function weight values and constraint conditions are provided for the controller.
The main function of the reference model is to determine an ideal motion state of the vehicle by a two-degree-of-freedom vehicle model, resulting in a desired yaw rate and a vehicle lateral velocity that take into account road adhesion coefficient constraints.
The MPC controller is mainly used for ensuring the transverse and longitudinal stability of the vehicle as a control target, and performing optimization solution by considering transverse and longitudinal safety constraints to obtain additional torque which is used as the input quantity of the hub motor of the electric automobile.
For the purpose of illustrating the technical contents, constructional features, objects and the like of the invention in detail, the invention will be fully explained with reference to the accompanying drawings, wherein:
the system control block diagram of the invention is shown in figure 1, the control area dividing and judging part in the figure obtains the control area on line according to the current driver behavior and road condition information, and then judges the current area position of the vehicle according to the yaw velocity and the centroid side slip angle, thereby providing real-time weight value and constraint condition for the controller; the input of the transverse and longitudinal stability controller based on the MPC comprises an expected yaw velocity and an expected lateral velocity obtained by a reference model in addition to the weight value and the constraint value, and the input is output as additional torque acting on the four hub motors respectively; the above parts are all built in MATLAB/Simulink, and a four-wheel hub drive electric automobile model constructed by using CarSim is used as a controlled object and outputs a vehicle state and road surface information feedback signal.
The control target of the invention is to control the vehicle motion by the additional torque obtained by solving the control requirement by the controller in consideration of the change of the control requirement in different control areas, ensure the operation stability and the lateral stability of the vehicle under the extreme working condition, and inhibit the sliding of the tire on the low-adhesion road surface, thereby improving the overall stability performance of the vehicle.
The invention provides a set of devices based on the operation principle and the operation process. The construction and operation processes are as follows:
1. software selection and co-simulation setup
A simulation model of a controller and a controlled object of the control system is respectively built through software MATLAB/Simulink and CarSim, the software versions are MATLAB R2016a and CarSim 2016.1, and the simulation step length is 0.001 s.
To realize the joint simulation of MATLAB/Simulink and CarSim, firstly, the working path of CarSim is set as a specified Simulink Model, then the set vehicle Model and road information in CarSim are added into Simulink, and Simulink is operated so as to realize the joint simulation and communication of the two. If the model structure or parameter settings in the CarSim are modified, a retransmission is required.
2. Four-wheel hub drive electric automobile model building
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. Four-wheel drive vehicles are selected, the power units are four hub motors, and the additional torque inputs are selected from IMP _ MYUSM _ L1, IMP _ MYUSM _ L2, IMP _ MYUSM _ R1 and IMP _ MYUSM _ R2. The electric automobile model used in the invention is constructed based on east wind A60, and the parameters are shown in Table I.
Meter-four-wheel hub driving electric vehicle parameter meter
Figure BDA0003113592830000101
3. Control system design
The controlled object of the invention is a four-wheel hub drive electric automobile, and the control target is to consider the change of a vehicle control area and improve the transverse and longitudinal stability of the vehicle under the limit working condition. The main design process of the control system is described below. Firstly, according to the behavior of a driver and the information of a driving road, based on the lateral-longitudinal-vertical dynamic characteristics of a vehicle, obtaining a control area about a centroid slip angle and a yaw velocity on line, dividing the control area into a stable area, a critical stable area and an unstable area, arranging different stability control requirements for each area, wherein the different requirements can be mapped into different control target weight values and constraint conditions in the design of a controller; secondly, a vehicle dynamic model is established in consideration of coupling nonlinearity of transverse and longitudinal movement of the vehicle under the limit working condition, the composite slip characteristic of tires is considered, a controller is designed under a model prediction control framework on the basis of the dynamic model, a control target comprises an expected value of tracking the yaw velocity of the vehicle, the lateral velocity of the vehicle and the slip rate of the tires are inhibited, and transverse and longitudinal safety constraints in the running process of the vehicle need to be considered; and then, based on different stability control requirements in each region, adjusting a control target weight value and a constraint condition according to the position of the region, sending the control target weight value and the constraint condition to the MPC controller, completing the design of the controller, solving an optimization problem to obtain additional torques acting on the four hub motors so as to adjust the motion of the vehicle under the limit working condition and improve the vehicle maneuverability and the transverse and longitudinal stability.
1) Controlling demand settings
As described above, the control region is introduced to better describe the vehicle handling stability performance, and the control region that can be changed in real time according to the driving state is more reliable than the off-line region. According to the invention, control areas related to the yaw velocity gamma and the centroid slip angle beta are obtained on line according to the behavior of a driver and road condition information, and are divided by utilizing stability boundary conditions, and the control areas are divided as shown in FIG. 2 by taking the case that a vehicle runs on a straight road with the road surface friction coefficient of 0.35 according to the speed of 60km/h, and the positions of the areas can be judged according to the current vehicle states (beta, gamma).
The control requirements to be met may also vary for situations where the vehicle conditions may be in different zones. In the stable region R1, where the maneuverability and lateral stability of the vehicle are ensured, wheel slip resistance and energy consumption may be considered; in the critical stability region R2, the control requirements regarding the steering stability and the lateral stability are increased, and as the vehicle state is gradually moved away from R1 in R2, the center of gravity of the requirements for wheel slip and energy consumption should be gradually shifted to the steering stability of the vehicle; in the unstable region R3, the primary control requirement is to ensure handling and lateral stability and thus driving safety. The switching of control requirements in different areas can be realized through an objective function and a weight value thereof in the design of the controller and the adjustment and change of the constraint conditions.
In the present invention, as the vehicle state gradually moves away from the stable region, i.e., transitions from the stable region R1 to the critical stable region R2 to the unstable region R3, the respective objective function weight values change in the form of an S-shaped curve as follows:
Figure BDA0003113592830000111
wherein k is 0.7, q1＝0.1，q2＝7，
Figure BDA0003113592830000112
βain,βaout,βbin,βboutRespectively represent the boundary ain,aaout,bin,boutUp to the corresponding centroid cornering angle value at the current γ.
The above formula is schematically shown in FIG. 3, and the weight initial value Γ is determinediniTerminal value ΓterAnd beta is from the current betainThe weight value in the current state can be determined according to the distance. As can be seen from fig. 3, the change is in the form of an S-curve, and may have a rising or falling trend depending on the magnitude of the initial value and the terminal value.
For the constraint conditions of each region, if (beta, gamma) ∈ R1 has no lateral constraint, and the constraint value V for the lateral velocity is obtained when (beta, gamma) ∈ R2-R3ylimAlso varies in an S-shaped function (1); similarly, for longitudinal anti-skid safety constraints, the constraint value λlimAnd also changes in an S-shaped function (1) as the vehicle state moves away from the stable region. In summary, the weight values and the constraint conditions of the objective function of the vehicle in each region can be realizedThe real-time online vehicle state is adjusted according to the change of the vehicle state, and the change is sent to the MPC controller to realize the switching of the control requirements in each area.
2) MPC controller design
Vehicle dynamics model
The schematic diagram of the vehicle dynamics model of the invention is shown in fig. 4, and the vehicle dynamics model is obtained by considering the yaw and the lateral movement of the vehicle as follows:
Figure BDA0003113592830000121
Figure BDA0003113592830000122
wherein, VyAs the lateral speed of the vehicle, deltafFor turning the front wheel, FxAnd FyRepresenting the longitudinal and lateral forces of the tire, respectively, Δ T representing the additional torque, the subscript i e { f, r }, the combination of j e { l, r }, ij e { fl, fr, rl, rr } representing the left front, right front, left rear and right rear wheels, respectively.
In addition to the rolling of the wheels,
Figure BDA0003113592830000123
dynamics hold, where ω represents wheel speed. Longitudinal slip ratio of known tire
Figure BDA0003113592830000124
The change in slip rate can be expressed kinetically as follows:
Figure BDA0003113592830000125
② tire model
Under the limit working condition, the longitudinal force and the lateral force of the tire which are mutually influenced are in a coupling nonlinear relation with the slip rate lambda and the slip angle alpha, so that the tire force needs to be described by utilizing a composite slip tire model. The invention uses a composite sliding LuGre wheelTyre model, longitudinal force F on tyrexAnd a lateral force FyThe description is as follows:
Figure BDA0003113592830000131
wherein σ0x,σ0y＝195m-1Respectively representing longitudinal and lateral stiffness coefficients, σ2x,σ2y0.001s/m represents longitudinal and lateral viscous damping, respectively, κx,κy13.4 is the longitudinal and lateral load distribution coefficients respectively;
Figure BDA0003113592830000132
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,C30.1; vertical load of tyre
Figure BDA0003113592830000133
The calculation takes into account the load redistribution on the slope when the vehicle is turning, where ax,ayRespectively represent the longitudinal acceleration and the lateral acceleration,
Figure BDA0003113592830000134
the roll angle, η, ζ represents the lateral and longitudinal road slope, respectively.
As can be seen from equation (5), the longitudinal and lateral forces are functions with respect to the slip rate and the slip angle, and thus the changes in the longitudinal and lateral forces can be extracted in the form of changes with respect to the slip rate and the slip angle, which are described as follows:
Figure BDA0003113592830000135
the partial derivatives of the longitudinal force and the lateral force of the tire on the slip ratio and the slip angle are respectively calculated as follows:
Figure BDA0003113592830000136
Figure BDA0003113592830000137
Figure BDA0003113592830000138
Figure BDA0003113592830000139
in the formula
Figure BDA0003113592830000141
The known tire slip angle α is calculated as follows:
Figure BDA0003113592830000142
the changes can be described in terms of yaw rate and lateral velocity in the following form:
Figure BDA0003113592830000143
wherein
Figure BDA0003113592830000144
Combining equation (6) with equation (8), the final form describing the variation of the longitudinal force and the front/rear axle lateral resultant force of each wheel can be obtained as follows:
Figure BDA0003113592830000145
Figure BDA0003113592830000146
according to the formulas (9) and (10), the longitudinal and lateral forces calculated by the tire model and the longitudinal and lateral forces output by the ports under the same low-adhesion double-shift-line working condition of CarSim are compared as shown in the figures 5 and 6, so that the tire model can more accurately calculate the longitudinal and lateral forces of the tire under the limit working condition, can describe the nonlinear characteristic of the tire during steering and meets the model precision.
③ forecasting model
According to the dynamic models (2) and (3) and the tire models (9) and (10), a prediction model designed for a controller can be obtained, the state quantity x of the prediction model is composed of vehicle yaw velocity, lateral velocity, front-rear axis lateral force, tire slip ratio and longitudinal force, and the state quantity x is subjected to normalization processing, namely
Figure BDA0003113592830000147
Where the subscript max represents the upper limit of the quantity, Vymax＝Vx·βlim，γmax＝γlim(ii) a The control amount u is an additional torque, and since normalization is performed, the control amount is
Figure BDA0003113592830000148
In summary, the prediction equation can be described in the following state space form:
Figure BDA0003113592830000151
wherein the parameter matrix is:
Figure BDA0003113592830000152
Figure BDA0003113592830000153
Figure BDA0003113592830000154
Figure BDA0003113592830000155
based on equations (9) and (10), the calculation expression for each element in matrix M is as follows:
Figure BDA0003113592830000156
Figure BDA0003113592830000157
Figure BDA0003113592830000158
Figure BDA0003113592830000159
discretizing the model (11) to obtain a discrete model as follows:
x(k+1)＝A(k)x(k)+Bu(k)u(k)+Bd(k) (12)
wherein
Figure BDA0003113592830000161
k represents the current time, TsIs the sampling time.
Objective function and constraint
In order to ensure the lateral stability of the vehicle under the extreme conditions, the main control targets of the controller are the tracking of the yaw rate and the lateral speed to their reference values, so that the following objective functions are provided:
Figure BDA0003113592830000162
wherein x1(t) is the predicted output of yaw rate, x2(t) is the predicted output of lateral velocity,. gammarefAnd VyrefThe yaw rate and the lateral velocity reference signal values obtained from the two-degree-of-freedom reference model are respectively.
Defining the slip ratio set of four wheels as lambdax＝[x5,x6,x7,x8]TIn order to ensure the longitudinal stability of the vehicle and to suppress the longitudinal slip of the wheels to ensure the driving safety, the following control targets are designed:
J3＝||λx(t)||2 (14)
on the other hand, an objective function J with respect to the control amount is set4＝||u(t)||2To reduce torque energy consumption.
The vehicle is subject to safety constraints during extreme driving conditions, and for vehicle longitudinal safety there are the following constraints on the longitudinal slip rate of the tire, where λlimTo the constraint value:
Figure BDA0003113592830000163
for lateral safety and stability of the vehicle, constraints on lateral speed are set as follows:
Figure BDA0003113592830000164
wherein VylimIs a constrained value of lateral velocity, andlimand VylimAccording to the different requirements of the control areas.
In addition, the problem of actuator saturation is also considered, and a control quantity constraint is set:
u(t)∈[-I4×1 I4×1] (17)
wherein I represents a matrix with all 1 elements.
The optimization problem is summarized as follows:
Figure BDA0003113592830000165
s.t.(12),(15),(16),(17)
wherein gamma isv,Γx,ΓuAre weight coefficients and vary in different regions according to equation (1) according to different control requirements. The optimization problem (18) can be solved by utilizing a quadratic sequence programming (quadrprog) algorithm, and the obtained control quantity is an additional torque to act on the hub motor.
4. Simulation experiment verification
In order to verify the effectiveness of the control method (variable coefficient) provided by the invention, a simulation experiment is designed in a combined simulation environment of CarSim and MATLAB/Simulink, and is compared with an MPC controller (constant coefficient) with a weight value and a constraint value as constant values. Setting a simulation test working condition as a double-line-shifting working condition, setting the road surface friction coefficient mu to be 0.35, setting the initial vehicle speed to be 60km/h, and setting the sampling time TsPredicting the time domain t 10mspThe parameters used by the controller in the simulation are shown in table two, 10. The weights and constraint values of the MPC controller with fixed coefficients are the average values of the initial and terminal values in the variable coefficient control method.
Table two simulation experiment parameter table
Figure BDA0003113592830000171
Fig. 7 and 8 are simulation curves of the yaw rate and the lateral rate of the vehicle under the low-adhesion double-lane-shifting working condition, respectively, and it can be seen that the yaw rate of the vehicle can track the expected value thereof and the lateral rate is effectively inhibited under the action of the MPC controller compared with a system without controller intervention, and it can also be seen through comparison that the tracking and inhibiting effects under the variable coefficient control are better, so that the maneuverability and the lateral stability of the vehicle are better ensured.
Fig. 9 is a simulation comparison curve of the tire slip ratio of the vehicle under the double-traverse condition, and it can be seen that the tire slip ratio can be limited within a small range in the whole double-traverse process, and under the variable coefficient control, the longitudinal sliding of the vehicle on the low-adhesion road surface can be better inhibited by using the changed weight and the constraint value, so as to ensure the longitudinal stability of the vehicle.
The additional torque obtained by variable coefficient control under the double-shift-line working condition is shown in fig. 10, when the vehicle starts to turn, the controller can add reasonable driving/braking torque to the four hub motors to meet the control requirement of vehicle transverse and longitudinal stability, in the whole working condition driving process, the additional torque is mostly negative to inhibit wheel slip, and the left and right wheel torques are symmetrical to better assist the steering action of the vehicle under the limit working condition.
Fig. 11 shows the control region change of the vehicle in the double-traverse condition, and it can be seen that the vehicle state is in the unstable region R3 most of the time from the start of steering if no controller is operated, and the vehicle state can be pulled back to the stable region R1 and the critical stable region R2 as much as possible under the action of the variable coefficient controller, so that the driving safety of the vehicle is ensured more reliably. Through the verification and comparison of the simulation experiments, the control method for considering the transverse and longitudinal stability of the control area can effectively improve the maneuverability and the transverse and longitudinal stability of the four-wheel hub drive electric automobile under the limit working condition and ensure the driving safety.

Claims (1)

1. A control method for controlling the stability of a vehicle in the transverse direction and the longitudinal direction under the limit working condition considering a control area comprises the following steps:
s1, building a four-wheel hub motor driving electric automobile model by using simulation software CarSim, and constructing a limit driving working condition;
the method is characterized in that:
s2, according to current driving behaviors and road condition information, considering vehicle transverse-longitudinal-vertical dynamic characteristics, giving boundary conditions of an online vehicle control area, dividing the boundary conditions into a stable area, a critical stable area and an unstable area, and meeting different control requirements for driving safety in different areas;
controlling demand settings
Obtaining control areas related to the yaw velocity gamma and the centroid side deviation angle beta on line according to the behavior of a driver and road condition information, judging the positions of the areas according to the current vehicle states (beta, gamma), and changing control requirements to be met according to the conditions that the vehicle states may be in different areas, wherein the different areas are a stable area R1, a critical stable area R2 and an unstable area R3;
as the vehicle state gradually moves away from the stable region, i.e., transitions from the stable region R1 to the critical stable region R2 to the unstable region R3, the respective objective function weight values change in the form of an S-curve as follows:
Figure FDA0003113592820000011
wherein k is 0.7, q1＝0.1，q2＝7，
Figure FDA0003113592820000012
βain,βaout,βbin,βboutRespectively represent the boundary ain,aaout,bin,boutA centroid sideslip angle value corresponding to the current gamma above; determining a weight initial value gammainiTerminal value ΓterAnd beta is from the current betainThe weight value in the current state can be determined according to the distance;
s3, judging the current position of the area where the vehicle is located according to the current vehicle mass center side slip angle and the current yaw velocity based on the control area divided in the S2, and mapping different control targets and constraint changes in the stability controller design for the switching of different control requirements when the vehicle is located in each area; designing a model predictive controller based on a dynamic model reflecting yaw motion, lateral motion, longitudinal slip of the vehicle, and a tire model considering composite slip characteristics of the tire, wherein control target weight values and constraint conditions are changed according to S3;
MPC controller design
Vehicle dynamics model
Considering the yaw and lateral motion of the vehicle, a vehicle dynamics model is obtained as follows:
Figure FDA0003113592820000021
Figure FDA0003113592820000022
wherein, VyAs the lateral speed of the vehicle, deltafFor turning the front wheel, FxAnd FyRepresenting the longitudinal and lateral forces of the tire, respectively, Δ T representing the additional torque, the subscript i e { f, r }, the combination of j e { l, r }, ij e { fl, fr, rl, rr } representing the left front, right front, left rear and right rear wheels, respectively. In addition to the rolling of the wheels,
Figure FDA0003113592820000023
dynamics hold, where ω represents wheel speed. Longitudinal slip ratio of known tire
Figure FDA0003113592820000024
The change in slip rate can be expressed kinetically as follows:
Figure FDA0003113592820000025
② tire model
Longitudinal force F on tirexAnd a lateral force FyThe description is as follows:
Figure FDA0003113592820000026
wherein σ0x,σ0yRespectively representing longitudinal and lateral stiffness coefficients, σ2x,σ2yRespectively representing longitudinal and lateral viscous damping, kx,κyRespectively longitudinal and lateralA coefficient of distribution to load;
Figure FDA0003113592820000027
the synthetic slip ratio; g(s)res) Is the Sterbek equation for slip ratio and slip angle, calculated as g(s)res)≈C1-C2λ-C3α, wherein C1＝1,C2＝0.64,C30.1; vertical load of tyre
Figure FDA0003113592820000028
The calculation takes into account the load redistribution on the slope when the vehicle is turning, where ax,ayRespectively represent the longitudinal acceleration and the lateral acceleration,
Figure FDA0003113592820000029
is the roll angle, η, ζ represents the lateral and longitudinal road slope, respectively;
extracting changes in longitudinal and lateral forces into forms related to slip ratio and yaw angle changes
Figure FDA00031135928200000210
The partial derivatives of the longitudinal force and the lateral force of the tire to the slip ratio and the slip angle are respectively as follows:
Figure FDA0003113592820000031
Figure FDA0003113592820000032
Figure FDA0003113592820000033
Figure FDA0003113592820000034
in the formula
Figure FDA0003113592820000035
The known tire slip angle α is calculated as follows:
Figure FDA0003113592820000036
the changes are described in terms of yaw rate and lateral velocity in the following manner:
Figure FDA0003113592820000037
wherein
Figure FDA0003113592820000038
Combining equation (6) with equation (8) yields the final form describing the variation of the longitudinal force and the front/rear axle lateral resultant force of each wheel as follows:
Figure FDA0003113592820000039
Figure FDA00031135928200000310
according to the formulas (9) and (10), the longitudinal and lateral forces calculated by the tire model are compared with the longitudinal and lateral forces output by the ports of the CarSim under the same low-adhesion double-shift-line working condition, so that the tire model can more accurately calculate the longitudinal and lateral forces of the tire under the extreme working condition, can describe the nonlinear characteristic of the tire during steering and meets the model precision;
③ forecasting model
According to the dynamic models (2) and (3) and the tire models (9) and (10), a prediction model designed for a controller is obtained, the state quantity x of the prediction model is composed of vehicle yaw velocity, lateral velocity, front-rear axis lateral force, tire slip ratio and longitudinal force, and the state quantity x is subjected to normalization processing, namely normalization processing
Figure FDA0003113592820000041
Where the subscript max represents the upper limit of the quantity, Vymax＝Vx·βlim，γmax＝γlim(ii) a The control amount u is an additional torque, and since normalization is performed, the control amount is
Figure FDA0003113592820000042
In summary, the prediction equation is described in the following state space form:
Figure FDA0003113592820000043
wherein the parameter matrix is:
Figure FDA0003113592820000044
Figure FDA0003113592820000045
Figure FDA0003113592820000051
Figure FDA0003113592820000052
based on equations (9) and (10), the calculation expression for each element in matrix M is as follows:
Figure FDA0003113592820000053
Figure FDA0003113592820000054
Figure FDA0003113592820000055
Figure FDA0003113592820000056
discretizing the model (11) to obtain a discrete model as follows:
x(k+1)＝A(k)x(k)+Bu(k)u(k)+Bd(k) (12)
wherein
Figure FDA0003113592820000057
Representing the current time, TsIs the sampling time;
objective function and constraint
In order to ensure the lateral stability of the vehicle under the extreme conditions, the main control targets of the controller are the tracking of the yaw rate and the lateral speed to their reference values, so that the following objective functions are provided:
Figure FDA0003113592820000058
wherein x1(t) is the predicted output of yaw rate, x2(t) is the predicted output of lateral velocity,. gammarefAnd VyrefRespectively obtaining a yaw angular velocity reference signal value and a lateral velocity reference signal value obtained by a two-degree-of-freedom reference model; defining the slip ratio set of four wheels as lambdax＝[x5,x6,x7,x8]TIn order to ensure the longitudinal stability of the vehicle and to suppress the longitudinal slip of the wheels to ensure the driving safety, the following control targets are designed:
J3＝||λx(t)||2 (14)
setting an objective function J regarding a control amount4＝||u(t)||2To reduce torque energy consumption;
for vehicle longitudinal safety, there are the following constraints on the longitudinal slip rate of the tire, where λlimTo the constraint value:
Figure FDA0003113592820000061
for lateral safety and stability of the vehicle, constraints on lateral speed are set as follows:
Figure FDA0003113592820000062
wherein VylimIs a constrained value of lateral velocity, andlimand VylimChanging according to different requirements of each control area;
considering the actuator saturation problem, setting a control quantity constraint:
u(t)∈[-I4×1 I4×1] (17)
wherein I represents a matrix with all 1 elements;
the optimization problem is summarized as follows:
Figure FDA0003113592820000063
s.t.(12),(15),(16),(17)
wherein gamma isv,Γx,ΓuIs a weight coefficient and is changed according to the formula (1) in different areas according to different control requirements; the optimization problem (18) is solved by utilizing a quadratic sequence programming algorithm, and the obtained control quantity is an additional torque to act on the hub motor.
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