CN111391822B - Automobile transverse and longitudinal stability cooperative control method under limit working condition - Google Patents

Automobile transverse and longitudinal stability cooperative control method under limit working condition Download PDF

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CN111391822B
CN111391822B CN202010228385.2A CN202010228385A CN111391822B CN 111391822 B CN111391822 B CN 111391822B CN 202010228385 A CN202010228385 A CN 202010228385A CN 111391822 B CN111391822 B CN 111391822B
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longitudinal
vehicle
tire
slip
wheel
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CN111391822A (en
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王萍
李梓涵
张曦月
胡云峰
陈虹
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Jilin University
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Jilin University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W30/00—Purposes of road vehicle drive control systems not related to the control of a particular sub-unit, e.g. of systems using conjoint control of vehicle sub-units
    • B60W30/02—Control of vehicle driving stability
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
    • B60W50/0098—Details of control systems ensuring comfort, safety or stability not otherwise provided for
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
    • B60W2050/0001—Details of the control system
    • B60W2050/0019—Control system elements or transfer functions
    • B60W2050/0028—Mathematical models, e.g. for simulation
    • B60W2050/0031—Mathematical model of the vehicle
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
    • B60W2520/00—Input parameters relating to overall vehicle dynamics

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  • Automation & Control Theory (AREA)
  • Transportation (AREA)
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Abstract

The invention discloses a cooperative control method for the transverse and longitudinal stability of an automobile under a limit working condition, which comprises the following steps of firstly, obtaining a four-wheel hub motor driven electric automobile model by using simulation software CarSim; secondly, designing a two-degree-of-freedom reference model, and deducing expected values of the lateral speed and the yaw rate of the vehicle through the two-degree-of-freedom reference model; secondly, a double-layer control structure is adopted for reducing solving complexity, an NMPC controller is adopted on the upper layer to ensure that the transverse and longitudinal stability of the vehicle is taken as a control target, and optimization solving is carried out by considering transverse and longitudinal safety constraints to obtain virtual control quantity, namely expected values of the tire slip rate and the slip angle; finally, the lower layer obtains additional torque to act on the hub motor according to the actual slip ratio and the deviation between the slip angle of the tire and the expected value given by the upper layer, and therefore the stability of the vehicle in the transverse direction and the longitudinal direction is guaranteed.

Description

Automobile transverse and longitudinal stability cooperative control method under limit working condition
Technical Field
The invention relates to a cooperative control method for the transverse and longitudinal stability of an automobile under a limit working condition, in particular to a cooperative control method for the transverse and longitudinal stability with low computation complexity designed under a model prediction control framework aiming at the problem that the transverse and longitudinal motion of a four-wheel hub drive electric automobile is unstable under the limit working condition, and belongs to the technical field of vehicle safety control.
Background
Under the limit driving condition, the vehicle is easy to destabilize to cause traffic accidents, at the moment, a transverse and longitudinal dynamic system of the vehicle presents a strong coupling nonlinear characteristic, but the existing active safety system usually only focuses on the stability of longitudinal or lateral movement, does not consider the mutual influence and coupling effect of other systems, and is difficult to play a role due to control target conflict, actuator interference and the like under the limit working condition, so that the cooperative control research on the transverse and longitudinal stability of the vehicle is required to be developed. 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 prior cooperative control of the transverse and longitudinal stability of the automobile under the limit working condition has the following problems:
1. the indexes for evaluating the lateral stability of the vehicle are mainly the lateral speed and the yaw rate of the vehicle, and are mainly reflected in the tracking of expected values of the lateral speed and the yaw rate. Most conventional control algorithms simply set the desired value of lateral velocity to zero or track only yaw rate, so that the design of the reference model is not completely rational and affects the controller control performance.
2. Under the limit working condition, the longitudinal force and the lateral force of the tire can influence each other, and the longitudinal force and the lateral force are in a coupling nonlinear relation with the slip ratio and the slip angle. Most of traditional control algorithms do not consider the composite slip characteristic of the tire when the tire model is used for calculating the longitudinal and lateral forces of the tire, so that the tire force calculation is inaccurate, and the accuracy of a prediction model is influenced.
3. Tire slip ratio is an index for evaluating the longitudinal stability of a vehicle, and most control methods track the tire slip ratio as a state variable, and can control the tire slip ratio.
4. The additional torque is used as a control quantity which directly influences the motion state of the vehicle, and most control methods mainly distribute the total additional torque obtained by solving to each wheel, while neglecting that each wheel may be in different driving/braking states, so that the obtained additional torque is not accurate enough; or designing the controller separately for each wheel according to the state quantity of each tire results in additional torque, which makes the control system more complicated in structure.
Disclosure of Invention
Aiming at the problem of cooperative control of the transverse and longitudinal stability of the automobile under the limit working condition, the invention adopts a double-layer control structure, the upper layer utilizes an NMPC controller to enable the yaw angular velocity and the lateral velocity of the automobile to track the reference signals of the automobile, inhibit the longitudinal sliding of the automobile, ensure the transverse and longitudinal stability of the automobile, and solve to obtain the virtual control quantity which is the expected value of the slip rate and the lateral deviation angle of the automobile; the lower layer calculates additional torque to act on the hub motor based on the change of longitudinal force by using the dynamic relation among the longitudinal force of the tire, the slip ratio and the slip angle according to the actual slip ratio and the deviation between the slip angle of the tire and the expected value given by the upper layer, thereby ensuring the stability of the vehicle in the transverse and longitudinal directions.
In order to solve the technical problems, the invention is realized by adopting the following technical scheme:
a method for cooperatively controlling the transverse and longitudinal stability of an automobile under a limit working condition 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 expected values of the yaw velocity and the lateral velocity of the vehicle, which are limited by considering the road adhesion coefficient, and determining an ideal motion state of the vehicle;
step three, designing an upper NMPC controller: based on a three-degree-of-freedom vehicle dynamics model, a composite slip LuGre tire model is established by considering the composite slip characteristic of a tire, a prediction model is designed, the expected value of the yaw velocity and the expected value of the lateral velocity of the vehicle can be tracked, the longitudinal slip of the tire is restrained, the tire slip rate and the lateral slip angle are used as virtual control quantities, and the virtual control quantity obtained by optimization solution is used as the expected value of lower-layer control;
step four, calculating the lower additional torque: according to the actual slip ratio and deviation amount between the slip angle and the expected value given by the upper layer, the dynamic relation between the longitudinal force of the tire, the slip ratio and the slip angle is utilized, the additional torque of the hub motor is calculated based on the change of the longitudinal force, and the additional torque is sent to the electric automobile as the input amount.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention deduces the expected lateral speed and yaw rate signals of the vehicle based on a two-degree-of-freedom vehicle model, and simultaneously tracks the lateral speed and the yaw rate signals when designing the NMPC controller. Different from the traditional method that the expected value of the lateral speed is simply set to be zero or only the yaw rate is tracked, the ideal tracks of the lateral speed and the yaw rate are respectively designed, and the better lateral stability of the vehicle is ensured.
2. Most traditional control algorithms do not consider the mutual influence between the longitudinal force and the lateral force of the tire under the limit working condition, and neglect the coupling nonlinear relation between the longitudinal force and the lateral force and the slip ratio and the slip angle. When the method is used for fitting the longitudinal and lateral forces of the tire, the composite slip LuGre tire model is adopted, the composite slip characteristic of the tire is considered, and the tire force under the extreme working condition can be better calculated, so that the accuracy of a prediction model is improved.
3. The tire slip rate is used as a state variable to track by most of traditional control algorithms so as to ensure the longitudinal stability of the vehicle.
4. Compared with the traditional control algorithm for obtaining the additional torque by respectively designing a controller for each wheel, the method can reflect the influence of the change of the slip rate and the slip angle on the additional torque, can calculate the additional torque more accurately, and avoids the redundancy of multiple controllers.
Drawings
These and/or other aspects of the present invention will become apparent from the following further description of embodiments of the invention, when taken in conjunction with the accompanying drawings. Wherein:
FIG. 1 is a flow chart of a method for cooperatively controlling the lateral stability and the longitudinal stability of a four-wheel hub-driven electric vehicle according to the invention;
FIG. 2 is a schematic representation of a vehicle dynamics model according to the present invention;
FIG. 3 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. 4 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. 5 is a simulation plot of the longitudinal velocity of a vehicle in a double traverse line operating condition, with the unit of the ordinate being m/s and the unit of the abscissa being time and s;
FIG. 6 is a simulation of yaw rate under the double-traverse condition of the present invention, wherein the dotted line, the solid line, and the dashed line represent no controller action, and desired yaw rate, respectively, with rad/s on the ordinate and time on the abscissa;
FIG. 7 is a simulated plot of lateral velocity of a vehicle under a double-lane operating condition in accordance with the present invention, wherein the dotted, solid and dashed lines represent no controller action, and desired lateral velocity, respectively, with the ordinate in m/s and the abscissa in time, in s;
FIG. 8 is a simulation diagram of the additional moment under the double-shift-line working condition, wherein the unit of ordinate is Nm, and the unit of abscissa is time and s;
fig. 9 is a simulation diagram of the slip ratio of the tire under the double-shift-line working condition, in which the dashed line is the expected slip ratio calculated by the upper NMPC controller, the solid line is the actual slip ratio, and the abscissa is time and the unit is s.
Detailed Description
For the purpose of illustrating the technical contents, constructional features, objects and the like of the present invention in detail, the present invention will be fully explained with reference to the accompanying drawings.
The flow of the cooperative control method of the invention is shown in figure 1, the input of an upper NMPC controller in the figure is the expected yaw velocity, the expected vehicle lateral velocity and the output measured value of a controlled object, and the output is respectively the expected longitudinal slip rate and the expected lateral slip angle of four tires; calculating the lower-layer additional torque to obtain the deviation amount of the tire slip rate and the slip angle according to the expected value obtained by the upper layer and the actual value output by the controlled object, and calculating the additional motor torque based on the change of the longitudinal force by using the dynamic relation among the longitudinal force of the tire, the slip rate and the slip angle; the upper NMPC controller and the lower additional torque calculation module are both built in MATLAB/Simulink; the controlled object is a four-wheel hub drive electric automobile model constructed by using CarSim.
The control system utilizes the deviation between the expected tire slip rate and the slip angle obtained by the upper layer controller and the actual value according to the real-time feedback signal, considers the dynamic relation between the longitudinal force of the tire and the slip rate and the slip angle, obtains additional torque acting on four hub motors based on the change of the longitudinal force, controls the transverse and longitudinal stability of the vehicle, enables the actual yaw velocity and the actual vehicle lateral velocity to track the expected values respectively, inhibits the longitudinal slip rate of the tire, limits and restricts the vehicle slip rate and the rear wheel side slip angle, and ensures the driving safety of the vehicle.
The invention provides a set of combined simulation model based on the operation principle and the operation process, which is constructed and operated as follows:
1. software selection
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. The CarSim software is a commercial simulation software specially aiming at vehicle dynamics, and the CarSim software mainly plays a role in providing a high-fidelity vehicle dynamics model, replaces a real four-wheel hub drive electric automobile as an implementation object of a control method in a simulation experiment, and provides a simulation environment of a limit working condition; 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.
2. Joint simulation setup
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 in CarSim is 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.
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 parameters of the electric vehicle are shown in the table 1.
TABLE 1 electric vehicle parameter table
Figure GDA0003589285630000041
Figure GDA0003589285630000051
4. Principle for controlling transverse and longitudinal stability of automobile under limit working condition
The controlled object of the invention is a four-wheel hub drive electric automobile, and the control target is to improve the transverse and longitudinal stability of the four-wheel hub drive electric automobile under the limit working condition. The main design process of the control method is described as follows: firstly, obtaining a four-wheel hub motor driving electric automobile model by using simulation software CarSim; secondly, designing a two-degree-of-freedom reference model, and deducing expected values of the lateral speed and the yaw rate of the vehicle through the two-degree-of-freedom reference model; secondly, a double-layer control structure is adopted for reducing the solving complexity, an NMPC controller is adopted on the upper layer to ensure that the transverse and longitudinal stability of the vehicle is taken as a control target, and the transverse and longitudinal safety constraints are considered for carrying out optimization solving to obtain the expected values of virtual control quantity, namely the tire slip rate and the slip angle; finally, the lower layer obtains additional torque to act on the hub motor according to the actual slip ratio and the deviation between the slip angle of the tire and the expected value given by the upper layer, and therefore the stability of the vehicle in the transverse direction and the longitudinal direction is guaranteed.
The specific steps of the control method of the invention are introduced as follows:
a cooperative control method for the transverse and longitudinal stability of an automobile under a limit working condition comprises the following steps:
the method comprises the following steps of obtaining a four-wheel hub motor drive 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 the vehicle in real time and changing the motion state of the vehicle by taking the additional torque of the motor as an input quantity.
Step two, designing a two-degree-of-freedom reference model: the desired values of the yaw rate of the vehicle and the lateral speed of the vehicle are obtained in consideration of the road adhesion coefficient limit, and the ideal motion state of the vehicle is determined.
In order to obtain the ideal yaw and lateral motion state of the vehicle, a two-degree-of-freedom reference model is established, and the two-degree-of-freedom reference model is a linear vehicle model which ignores the nonlinear characteristic of tire force. The equation is as follows:
Figure GDA0003589285630000052
where β is the vehicle's centroid slip angle, γ is the yaw rate, δ is the driver's steering wheel angle, and VxRepresenting the vehicle longitudinal speed. Taking the transient response obtained by the model as expectation, and obtaining the expected response beta from delta to the centroid slip angle and the yaw velocity according to frequency response analysis*And gamma*：
Figure GDA0003589285630000061
Wherein, Kβ,KγRespectively represent the steady-state gain of the centroid slip angle andyaw rate steady state gain, τβ,τγDifferential coefficients, ω, of two types respectivelynRepresenting the oscillation frequency of the system, ξ the damping coefficient and s the complex variable of the transfer function. Their calculation formula is as follows:
Figure GDA0003589285630000062
wherein L is Lf+LrRepresenting the distance from the front axle to the rear axle,
Figure GDA0003589285630000063
a vehicle system stability number. While the desired centroid slip angle β*And yaw angular velocity gamma*Are limited by the road adhesion coefficient, and their upper limits are:
Figure GDA0003589285630000064
wherein mu represents a road adhesion coefficient, and g is 9.8m/s2. The reference centroid yaw angle and the reference yaw rate can then be found as follows:
Figure GDA0003589285630000065
when the centroid slip angle is small, the value can be regarded as the ratio of the lateral speed to the longitudinal speed of the vehicle, so that the value is based on betarefThe reference value V of the lateral speed can be obtainedyrefThe following were used:
Vyref＝sgn(δ)Vx·min{|β*|,βlim} (6)
step three, designing an upper NMPC controller: based on a three-degree-of-freedom vehicle dynamics model, a composite slip LuGre tire model is established by considering the composite slip characteristics of tires, a prediction model is designed, the expected values of the yaw velocity and the lateral velocity of the vehicle can be tracked, the longitudinal slip of the tires is restrained, the tire slip rate and the lateral slip angle are used as virtual control quantities, and the virtual control quantity obtained by optimization solution is used as the expected value of lower-layer control.
Three-freedom vehicle dynamic model
The schematic diagram of the vehicle dynamics model of the invention is shown in fig. 2, and the three-degree-of-freedom vehicle dynamics model is obtained by considering the longitudinal, lateral and yaw motions of the vehicle:
Figure GDA0003589285630000071
wherein, VyAs the lateral speed of the vehicle, FxAnd FyThe longitudinal and lateral forces of the tire are represented, respectively, and the subscripts fl, fr, rl, rr represent the left front, right front, left rear and right rear wheels, respectively. The slip angle α of the tire is calculated as follows:
Figure GDA0003589285630000072
longitudinal slip ratio of tire
Figure GDA0003589285630000073
Wherein VxRepresenting the longitudinal speed of the vehicle, ReRepresenting the wheel radius and omega representing the wheel speed.
② tire model
Under the limit working condition, the longitudinal force and the lateral force of the tire are mutually influenced, the longitudinal force of the tire is not only obtained by calculating the longitudinal slip ratio, but also is related to the slip angle of the tire in the same way, so that the longitudinal force and the lateral force of the tire are in a coupling nonlinear relation with the slip ratio and the slip angle. Thus, the longitudinal and lateral forces of the tire are described using the compound slip LuGre tire model.
When the vehicle is in a steady state, the composite slip LuGre tire model is used for resisting longitudinal force FxAnd a lateral force FyThe description of (A) is as follows:
Figure GDA0003589285630000081
wherein σ0xAnd σ0yRespectively representing longitudinal and lateral stiffness coefficients, σ2xAnd σ2yRespectively representing longitudinal and lateral viscous damping, kxAnd kappayLongitudinal and lateral load distribution coefficients respectively; alpha is the slip angle of the tire,
Figure GDA0003589285630000082
the synthetic slip ratio; g(s)res) Is a Sterbek equation for slip ratio and slip angle, and can be approximated as g(s)res)≈C1-C2λ-C3α, wherein C1＝1,C2＝0.64,C3＝0.1；FzIs the vertical load of the tire.
According to the formula (9), 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 the CarSim are compared, for example, as shown in FIGS. 3 and 4, as can be seen from FIGS. 3 and 4, the tire model can more accurately calculate the longitudinal and lateral forces of the tire under the extreme working condition, and can also describe the nonlinear characteristic of the tire during steering.
Thirdly, predicting model
The three-degree-of-freedom vehicle dynamics model (7) and the tire model (9) can obtain a prediction model designed for a controller, the state quantity x of the prediction model is composed of the longitudinal speed, the lateral speed and the yaw rate of the vehicle, and the state quantity x is subjected to normalization processing, namely
Figure GDA0003589285630000083
Wherein Vxmax,Vymax,γmaxUpper limit values of vehicle longitudinal speed, lateral speed, yaw rate, Vymax＝Vx·βlim，γmax＝γlim(ii) a The control quantity u is the expected slip rate and slip angle of the tire, and is normalized to obtain a virtual control quantity
Figure GDA0003589285630000084
Wherein
Figure GDA0003589285630000085
Respectively the expected slip rates of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel,
Figure GDA0003589285630000086
desired slip angles, λ, of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel, respectivelymax,αfmax,αrmaxUpper limit values of the wheel slip ratio, the front wheel side slip angle, and the rear wheel side slip angle, respectively.
The above prediction equation can be described as
Figure GDA0003589285630000087
Objective function and constraint
In order to ensure the lateral stability of the vehicle in extreme operating conditions, the NMPC controller has as its main control targets the tracking of the yaw rate and the lateral speed with respect to their reference values, so that there are the following control targets
Figure GDA0003589285630000091
Wherein, tkRepresenting the current time, tpTo predict the time domain, x2(t) is the predicted output of lateral velocity, x3(t) is a prediction output of the yaw rate. In addition, for the control amount, define
Figure GDA0003589285630000092
In order to ensure the longitudinal stability of the vehicle, inhibit the longitudinal sliding of the wheels and ensure the driving safety, the following control targets are designed:
Figure GDA0003589285630000093
the vehicle is subject to safety constraint in the running process under the limit working condition, and for the longitudinal safety of the vehicle, the longitudinal slip rate of the tire is constrained as follows:
ux(t)∈[-I4×1 I4×1] (13)
definition of
Figure GDA0003589285630000094
αmaxFor the maximum value of the tire slip angle alpha, the rear wheel slip angle can be calculated from equation (8), and the centroid slip angle is known
Figure GDA0003589285630000095
Left rear wheel slip angle alpharlAnd the right rear wheel slip angle alpharrCan be calculated by the following formula:
Figure GDA0003589285630000096
then there are
Figure GDA0003589285630000097
Beta and gamma are indexes for evaluating the lateral stability of the vehicle, and in order to better ensure the lateral safety of the vehicle, the rear wheel side slip angle is restrained as follows:
uy(t)∈[-I2×1 I2×1] (15)
I2×1is a full 1 matrix with 2 rows and 1 column; I.C. A4×1Is a full 1 matrix with 4 rows and 1 column;
the objective function is obtained as follows:
Figure GDA0003589285630000098
wherein, gamma isv,ΓxAre weight coefficients. And (4) optimally solving the objective function by using a GRAMPC tool box to obtain the slip rate and the slip angle of the tire with the virtual control quantity as expected.
Step four, calculating the lower additional torque: according to the actual slip ratio and deviation amount between the slip angle and the expected value given by the upper layer, the dynamic relation between the longitudinal force of the tire, the slip ratio and the slip angle is utilized, the additional torque of the hub motor is calculated based on the change of the longitudinal force, and the additional torque is sent to the electric automobile as the input amount.
The virtual control quantity obtained by the optimization solution of the upper NMPC controller needs to be converted into an input quantity which can be actually acted on the vehicle, and the input quantity is converted into an additional torque acted on each hub motor. According to the previous analysis of the tire force under the limit condition, the calculation of the longitudinal force of the tire is related to the slip ratio and the slip angle, so the change delta F of the longitudinal force of the tirexAlso related to the change in slip ratio Δ λ and the change in slip angle Δ α, the relationship between them can be expressed as:
Figure GDA0003589285630000101
wherein, Δ Fxfl,ΔFxfr,ΔFxrl,ΔFxrrRespectively represent the change values of longitudinal forces of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel, delta lambdafl,Δλfr,Δλrl,ΔλrrRespectively represent the change values of the slip rates of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel, delta alphafl,Δαfr,Δαrl,ΔαrrRespectively representing the change values of the slip angles of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel;
Figure GDA0003589285630000102
respectively are partial derivatives of longitudinal force of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel to the slip ratio,
Figure GDA0003589285630000103
respectively are the partial derivatives of the longitudinal force of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel to the side deflection angle.
According to the LuGre composite slip tire model (9), the partial derivatives of the longitudinal force of the tire to the slip ratio and the slip angle can be obtained as follows:
Figure GDA0003589285630000104
in which we define
Figure GDA0003589285630000105
κxIs the longitudinal load distribution coefficient.
Desired slip ratio by upper NMPC controller
Figure GDA0003589285630000106
And slip angle
Figure GDA0003589285630000107
The amount of deviation from the actual slip ratio λ and slip angle α of the vehicle, which can be seen as the change in slip ratio and slip angle when the controller control objective and constraints are desired to be met, is then in the following relationship:
Figure GDA0003589285630000111
the deviation is converted into the required longitudinal force change Δ F according to equation (14)xThe additional torque Δ T acting on each in-wheel motor is then calculated as follows and limited taking into account the saturation of the actuator:
ΔT＝sgn(ΔFx)min{|ΔFxRe|,Tmax} (20)
in the formula TmaxIs the upper limit value of the additional torque that can be applied to the in-wheel motor.
The effectiveness of the control method of the invention is verified by the following simulation experiments of the embodiment:
in order to verify the effectiveness of the control method, a simulation experiment is designed under the combined simulation environment of CarSim and MATLAB/Simulink. Setting the simulation test working condition as a double-line shifting working condition, wherein the road surface friction coefficient mu is 0.35, and the vehicle speed is kept at 60 km.h-1In the neighborhood, as shown in FIG. 5, the sampling time is set to 5ms, and the time domain t is predictedpThe parameters and weighting factors used in the simulation experiment are shown in table 102。
Table 2 simulation experiment parameter table
(symbol) Definition of Numerical value/Unit
Vxmax Upper limit value of longitudinal speed of vehicle 120/km·h-1
λmax Upper limit value of tire slip ratio 0.1
αfmax Upper limit of front wheel side slip angle 0.4/rad
αrmax Upper limit value of tire slip angle 0.1/rad
Tmax Additional torque upper limit value of hub motor 800/N·m-1
Γv Lateral velocity tracking weight in NMPC 0.05
Γu Tire slip ratio suppression weight in NMPC 0.25
Fig. 6 and 7 are simulation curves of the yaw rate and the lateral speed of the vehicle under the low-adhesion double-lane-shifting condition, respectively, and it can be seen that compared with a system without controller intervention, under the action of the NMPC controller, the yaw rate of the vehicle can track the expected value of the vehicle, and the lateral speed is effectively suppressed, so that the lateral stability of the vehicle is ensured.
The lower layer utilizes the tire slip ratio and the additional torque calculated by the deviation amount of the slip angle as shown in fig. 8, in the first 1s, as the vehicle is in an accelerating state, in order to ensure the vehicle speed, the four hub motors need to be added with driving torque, after the speed is kept stable, the additional torque approaches zero, and the vehicle starts to turn at 4 s.
The actual slip rates of the tires and the expected slip rates obtained by the upper NMPC controller are shown in FIG. 9, and in the first 1s, the slip rates of the four tires can be gradually reduced and approach to zero in the process of accelerating and keeping the vehicle stable, and in the whole double-shifting process, the slip rates of the tires can be limited in a small range, and the longitudinal sliding of the vehicle on a low-adhesion road surface is effectively inhibited, so that the longitudinal stability of the vehicle is ensured. Through verification of simulation experiments, the transverse and longitudinal stability cooperative control method can effectively improve the transverse and longitudinal stability of the four-wheel hub drive electric automobile under the limit working condition, and ensure the driving safety.

Claims (4)

1. A method for cooperatively controlling the transverse and longitudinal stability of an automobile under a limit working condition is characterized by comprising the following steps:
the method comprises the following steps of firstly, obtaining a four-wheel hub motor driven electric automobile model by using simulation software CarSim, and providing each state information of the automobile in real time;
designing a two-degree-of-freedom reference model to obtain expected values of the yaw velocity and the lateral velocity of the vehicle, which are limited by considering the road adhesion coefficient, and determining an ideal motion state of the vehicle;
step three, designing an upper NMPC controller: based on a three-degree-of-freedom vehicle dynamics model, a composite slip LuGre tire model is established by considering the composite slip characteristic of a tire, a prediction model is designed, the expected value of the yaw velocity and the expected value of the lateral velocity of the vehicle can be tracked, the longitudinal slip of the tire is restrained, the tire slip rate and the lateral slip angle are used as virtual control quantities, and the virtual control quantity obtained by optimization solution is used as the expected value of lower-layer control;
step four, calculating the lower additional torque: according to the actual slip ratio and deviation amount between the slip angle and the expected value given by the upper layer, the dynamic relation among the longitudinal force of the tire, the slip ratio and the slip angle is utilized, the additional torque of the in-wheel motor is calculated based on the change of the longitudinal force, and the additional torque is sent to the electric automobile as an input amount.
2. The cooperative control method for the transverse and longitudinal stability of the automobile under the limit working condition as claimed in claim 1, wherein in the second step, a two-degree-of-freedom reference model is designed, and the equation is as follows:
Figure FDA0003617397400000011
Figure FDA0003617397400000012
where β is the vehicle's centroid slip angle, γ is the yaw rate, δ is the driver's steering wheel angle, and VxRepresenting the longitudinal speed of the vehicle, CfFor the tire sidewall deflection stiffness of the front wheel, CrFor rear wheel tire sidewall stiffness, LfIs the distance from the center of mass of the vehicle to the front axle, LrThe distance from the center of mass of the vehicle to the rear axle; i isZIs the moment of inertia of the vehicle about the z-axis;
taking the transient response obtained by the two-degree-of-freedom reference model as an expectation, and obtaining the expected response beta from delta to the centroid slip angle and the yaw velocity*And gamma*：
Figure FDA0003617397400000013
Figure FDA0003617397400000014
Wherein, Kβ,KγRespectively representing the steady-state gain of the centroid slip angle and the steady-state gain of the yaw angular velocity, tauβ,τγDifferential coefficients, ω, of two types respectivelynRepresenting the oscillation frequency of the system, ξ representing the damping coefficient, s representing the complex variable of the transfer function;
desired centroid slip angle β*And yaw rate γ*Are limited by the road adhesion coefficient, and their upper limits are:
Figure FDA0003617397400000021
Figure FDA0003617397400000022
where m represents the vehicle mass, μ represents the road adhesion coefficient, and g is 9.8m/s2，VxRepresenting the longitudinal speed of the vehicle, CrFor rear wheel tire sidewall stiffness, LfIs the distance from the center of mass of the vehicle to the front axle, LrIs the distance from the center of mass of the vehicle to the rear axle, L ═ Lf+LrBefore representingThe distance of the axle to the rear axle; the reference centroid slip angle and the reference yaw rate are obtained as follows:
βref＝sgn(δ)min{|β*|,βlim}
γref＝sgn(δ)min{|γ*|,γlim}
when the centroid slip angle is small, the value can be regarded as the ratio of the lateral speed to the longitudinal speed of the vehicle, so that the value is based on betarefThe reference value V of the lateral speed can be obtainedyrefThe following were used:
Vyref＝sgn(δ)Vx·min{|β*|,βlim}。
3. the cooperative control method for the transverse and longitudinal stability of the automobile under the limit condition as claimed in claim 2, wherein the third step comprises the following steps:
the method comprises the following steps of (1) considering longitudinal, lateral and transverse motions of a vehicle to obtain a three-degree-of-freedom vehicle dynamic model:
Figure FDA0003617397400000023
Figure FDA0003617397400000024
Figure FDA0003617397400000025
wherein d is the left and right wheel track, VyIs the vehicle lateral velocity; fxflRepresenting the longitudinal force of the left front tire, FxfrRepresenting the longitudinal force of the right front tyre, FxrlRepresenting the longitudinal force of the left rear tire, FxrrRepresents the longitudinal force of the right rear tire; fyflRepresenting the lateral force of the left front tyre, FyfrRepresenting the lateral force of the right front tyre, FyrlRepresenting the lateral force of the left rear tyre, FyrrRepresents to the rightThe lateral force of the rear tire;
longitudinal slip ratio of tire
Figure FDA0003617397400000031
Wherein, VxRepresenting the longitudinal speed of the vehicle, ReRepresents the wheel radius, ω represents the wheel speed;
② longitudinal force F of the tire by utilizing the composite slip LuGre tire modelxAnd a lateral force FyThe description of (A) is as follows:
Figure FDA0003617397400000032
Figure FDA0003617397400000033
wherein σ0xAnd σ0yRespectively representing longitudinal and lateral stiffness coefficients, σ2xAnd σ2yRespectively representing longitudinal and lateral viscous damping, kxAnd kappayLongitudinal and lateral load distribution coefficients respectively; alpha is the side slip angle of the tire,
Figure FDA0003617397400000034
the synthetic slip ratio; g(s)res) Is the Sterbek equation for slip ratio and slip angle, and can be approximated as g(s)res)≈C1-C2λ-C3α, wherein C1＝1,C2＝0.64,C3＝0.1；FzIs the vertical load of the tire;
obtaining a prediction model designed for the controller from the three-degree-of-freedom vehicle dynamics model and the tire model:
Figure FDA0003617397400000035
the state quantity x is composed of the longitudinal speed, the lateral speed and the yaw rate of the vehicle, and the state quantity x is subjected to normalization processing, namely:
Figure FDA0003617397400000036
wherein Vxmax,Vymax,γmaxUpper limit values V of the longitudinal speed, lateral speed and yaw rate of the vehicleymax＝Vx·βlim，γmax＝γlim(ii) a The control quantity u is a virtual control quantity obtained by solving the slip rate and the slip angle expected by the tire
Figure FDA0003617397400000037
Wherein
Figure FDA0003617397400000038
Respectively the expected slip rates of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel,
Figure FDA0003617397400000039
desired slip angles, λ, of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel, respectivelymax,αfmax,αrmaxThe upper limit values of the wheel slip rate, the front wheel side deflection angle and the rear wheel side deflection angle are respectively;
objective function and constraint:
the NMPC controller mainly controls the tracking of the yaw velocity and the lateral velocity on the reference value thereof, and the control targets are as follows:
Figure FDA0003617397400000041
Figure FDA0003617397400000042
wherein, tkRepresenting the current time, tpTo predictTime domain, x2(t) is the predicted output of lateral velocity, x3(t) is the predicted output of yaw rate;
for the control quantity, define
Figure FDA0003617397400000043
Designing a control target:
Figure FDA0003617397400000044
the tire longitudinal slip ratio is constrained as follows:
ux(t)∈[-I4×1 I4×1]
definition of
Figure FDA0003617397400000045
Centroid slip angle
Figure FDA0003617397400000046
αmaxThe maximum value of the tire slip angle alpha, left rear wheel slip angle alpharlAnd the right rear wheel slip angle alpharrCalculated by the following formula:
Figure FDA0003617397400000047
then there are
Figure FDA0003617397400000048
The rear wheel side slip angle is constrained as follows:
uy(t)∈[-I2×1 I2×1]
wherein, I2×1Is a full 1 matrix with 2 rows and 1 column; the objective function is obtained as follows:
Figure FDA0003617397400000049
Figure FDA00036173974000000410
ux(t)∈[-I4×1 I4×1]
uy(t)∈[-I2×1 I2×1]
wherein, gamma isv,ΓuIs a weight coefficient, I4×1A full 1 matrix with 4 rows and 1 column;
and optimally solving the objective function to obtain the slip ratio and the slip angle of the tire with the virtual control quantity as expected.
4. The cooperative control method for the transverse and longitudinal stability of the automobile under the limit condition as claimed in claim 3, wherein the step four lower layer additional torques comprise the following steps:
change of tire longitudinal force Δ FxThe relationship between the change Δ λ in slip ratio and the change Δ α in slip angle can be expressed as:
Figure FDA0003617397400000051
wherein, Δ Fxfl,ΔFxfr,ΔFxrl,ΔFxrrRespectively represent the change values of longitudinal forces of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel, delta lambdafl,Δλfr,Δλrl,ΔλrrRespectively represent the change values of the slip rates of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel, delta alphafl,Δαfr,Δαrl,ΔαrrRespectively representing the change values of the side deflection angles of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel;
Figure FDA0003617397400000052
respectively are partial derivatives of longitudinal force of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel to the slip ratio,
Figure FDA0003617397400000053
the partial derivatives of the longitudinal force of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel to the side deflection angle are respectively;
the partial derivatives of the tire longitudinal force on the slip ratio and the slip angle are as follows:
Figure FDA0003617397400000054
Figure FDA0003617397400000055
in the formula (II)
Figure FDA0003617397400000056
Wherein κxIs the longitudinal load distribution coefficient;
desired slip ratio by upper NMPC controller
Figure FDA0003617397400000057
And slip angle
Figure FDA0003617397400000058
The following relationship is established with the actual slip ratio λ and slip angle α of the vehicle:
Figure FDA0003617397400000059
Figure FDA00036173974000000510
converting the deviation into the desired longitudinal force change Δ FxThen, the additional torque Δ T acting on each in-wheel motor is calculated as follows:
ΔT＝sgn(ΔFx)min{|ΔFxRe|,Tmax}
in the formula, TmaxIs an upper limit value of the additional torque acting on the in-wheel motor.
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