CN111391822A - 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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CN111391822A
CN111391822A CN202010228385.2A CN202010228385A CN111391822A CN 111391822 A CN111391822 A CN 111391822A CN 202010228385 A CN202010228385 A CN 202010228385A CN 111391822 A CN111391822 A CN 111391822A
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slip
vehicle
longitudinal
tire
lateral
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CN111391822B (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)
  • Mechanical Engineering (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 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.

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 calculation of the tire force 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, but although control is possible, such a method has a complicated dynamic model and makes it difficult to set a reasonable expected slip ratio value.
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;
thirdly, designing an upper-layer NMPC controller, namely establishing a composite slip L uGre tire model by considering the composite slip characteristic of a tire based on a three-degree-of-freedom vehicle dynamic model, designing a prediction model, enabling the yaw velocity and the lateral velocity of the vehicle to track the expected values of the yaw velocity and the lateral velocity of the vehicle, inhibiting the longitudinal slip of the tire, and taking the tire slip rate and the slip angle as virtual control quantities, and optimally solving the obtained virtual control quantity as the expected value of lower-layer control;
step four, calculating the lower additional torque: according to the actual slip ratio and deviation amount between the slip angle and the expected value given by the upper layer, the dynamic relation between the longitudinal force of the tire, the slip ratio and the slip angle is utilized, the additional torque of the hub motor is calculated based on the change of the longitudinal force, and the additional torque is sent to the electric automobile as the input amount.
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 to ensure better lateral stability of the vehicle.
2. According to the method, when the tire longitudinal and lateral forces are fitted, a composite slip L uGre tire model is adopted, the composite slip characteristic of the tire is considered, the tire force under the limit working condition can be better calculated, and therefore 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 tire longitudinal force verification according to the present invention, wherein the solid line represents the longitudinal force calculated using the composite slip L uGre tire model, the dashed line represents the tire longitudinal force output by the CarSim port, and the ordinate is in units of N, and the abscissa is time and in units of s;
FIG. 4 is a graph of tire lateral force verification according to the present invention, wherein the solid line represents the lateral force calculated using the composite slip L uGre tire model, the dashed line represents the tire lateral force output by the CarSim port, and the ordinate is in units of N, and the abscissa is time in units of 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 cooperative control method flow is shown in figure 1, the input of an upper layer NMPC controller in the figure is an expected yaw velocity, an expected vehicle lateral velocity and a controlled object output measured value, the expected longitudinal slip rate and a lateral slip angle of four tires are output, deviation amounts of the slip rate and the lateral slip angle of the tires are obtained through calculation of a lower layer additional torque according to an expected value obtained by an upper layer and an actual value output by the controlled object, an additional motor torque is calculated based on changes of longitudinal force by using dynamic relations among longitudinal force, the slip rate and the lateral slip angle of the tires, calculation modules of the upper layer NMPC controller and the lower layer additional torque are built in MAT L AB/Simulink, and the controlled object is a four-wheel hub driving 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
The simulation models of the controller and the controlled object of the control system are respectively built through MAT L AB/Simulink and CarSim, the software versions are MAT L AB R2016a and CarSim 2016.1, the simulation step length is 0.001s, wherein the CarSim software is a commercial simulation software specially aiming at vehicle dynamics, the simulation system mainly has the effects of providing a high-fidelity vehicle dynamics model, replacing a real four-wheel hub drive electric automobile as an implementation object of a control method in a simulation experiment and providing a simulation environment of a limit working condition, and the MAT L AB/Simulink is used for building the 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 combined simulation of MAT L AB/Simulink and CarSim, firstly, the working path of CarSim is set as the designated Simulink Model, then the set vehicle Model in CarSim is added into Simulink, and Simulink is operated to realize the combined simulation and communication of the two.
3. Four-wheel hub drive electric automobile model building in combined simulation software
The 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, wherein a four-wheel drive vehicle is selected, a power device of the vehicle is four hub motors, additional torque input of the four hub motors 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 Table 1.
TABLE 1 electric vehicle parameter table
Figure BDA0002428434130000041
Figure BDA0002428434130000051
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 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 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 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.
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 BDA0002428434130000052
where β is the vehicle centroid slip angle, γ is the yaw rate, is the driver-given steering wheel angle, VxRepresenting the vehicle longitudinal speed. Taking the transient response obtained by the model as an expectation, and according to frequency response analysis, the lateral deviation from the center of mass can be obtainedDesired response β of yaw and angular velocity*And gamma*：
Figure BDA0002428434130000061
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, their calculation is as follows:
Figure BDA0002428434130000062
Figure BDA0002428434130000063
wherein L-Lf+LrRepresenting the distance from the front axle to the rear axle,
Figure BDA0002428434130000064
desired centroid slip angle β for vehicle system stabilization number*And yaw rate γ*Are limited by the road adhesion coefficient, and their upper limits are:
Figure BDA0002428434130000065
Figure BDA0002428434130000066
wherein mu represents the 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 BDA0002428434130000067
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 according to βrefThe reference value V of the lateral speed can be obtainedyrefThe following were used:
Vyref＝sgn()Vx·min{|β*|,βlim} (6)
and thirdly, designing an upper-layer NMPC controller, namely establishing a composite slip L uGre tire model by considering the composite slip characteristic of the tire based on a three-degree-of-freedom vehicle dynamic model, designing a prediction model, enabling the yaw velocity and the lateral velocity of the vehicle to track the expected values of the yaw velocity and the lateral velocity of the vehicle, inhibiting the longitudinal slip of the tire, and taking the tire slip rate and the slip angle as virtual control quantities and optimally solving the obtained virtual control quantities as the expected values of lower-layer control.
① three-degree-of-freedom vehicle dynamics model
The vehicle dynamics model schematic diagram 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 BDA0002428434130000071
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 front left, front right, rear left, and rear right wheels, respectively the slip angle α of the tire is calculated as follows:
Figure BDA0002428434130000072
longitudinal slip ratio of tire
Figure BDA0002428434130000073
Where ω represents wheel speed.
② tire model
Under the limit 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 not only 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, and then, the longitudinal force and the lateral force of the tire are described by utilizing a composite slip L uGre tire model.
Composite slip L uGre tire model vs. longitudinal force F when the vehicle is at steady statexAnd a lateral force FyThe description of (A) is as follows:
Figure BDA0002428434130000081
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;
Figure BDA0002428434130000082
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.
③ predictive 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 BDA0002428434130000083
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 BDA0002428434130000084
Wherein λmax,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 BDA0002428434130000085
④ 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 BDA0002428434130000091
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 BDA0002428434130000092
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 BDA0002428434130000093
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)∈[-I4×1I4×1](13)
definition of
Figure BDA0002428434130000094
The side slip angle of the rear wheel can be calculated according to the formula (8), and the side slip angle of the mass center is known
Figure BDA0002428434130000095
The rear wheel side slip angle can be calculated by the following equation:
Figure BDA0002428434130000096
then there are
Figure BDA0002428434130000097
β 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)∈[-I2×1I2×1](15)
the objective function is obtained as follows:
Figure BDA0002428434130000098
wherein,v,xare 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 the input quantity which can actually act on the vehicle, and the input quantity is converted into the additional torque acting 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 BDA0002428434130000101
according to the L uGre composite slip tire model (9), the partial derivatives of the tire longitudinal force to the slip ratio and the slip angle can be obtained as follows:
Figure BDA0002428434130000102
in which we define
Figure BDA0002428434130000103
Desired slip ratio by upper NMPC controller
Figure BDA0002428434130000104
And slip angle
Figure BDA0002428434130000105
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 that occurs when the controller control objectives and constraints are desired, is then the following relationship:
Figure BDA0002428434130000106
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 embodiment simulation experiments:
in order to verify the effectiveness of the control method, a simulation experiment is designed under the combined simulation environment of CarSim and MAT L AB/Simulink, the simulation test working condition is set to be a double-line-shifting working condition, 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 2.
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 Upper limit value of additional torque 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 a vehicle in real time;
designing a two-degree-of-freedom reference model to obtain expected values of the yaw velocity and the lateral velocity of the vehicle, which are limited by considering the road adhesion coefficient, and determining an ideal motion state of the vehicle;
thirdly, designing an upper-layer NMPC controller, namely establishing a composite slip L uGre tire model by considering the composite slip characteristic of a tire based on a three-degree-of-freedom vehicle dynamic model, designing a prediction model, enabling the yaw velocity and the lateral velocity of the vehicle to track the expected values of the yaw velocity and the lateral velocity of the vehicle, inhibiting the longitudinal slip of the tire, and taking the tire slip rate and the slip angle as virtual control quantities, and optimally solving the obtained virtual control quantity as the expected value of lower-layer control;
step four, calculating the lower additional torque: according to the actual slip ratio and deviation amount between the slip angle and the expected value given by the upper layer, the dynamic relation between the longitudinal force of the tire, the slip ratio and the slip angle is utilized, the additional torque of the hub motor is calculated based on the change of the longitudinal force, and the additional torque is sent to the electric automobile as the input amount.
2. The cooperative control method for the transverse and longitudinal stability of the automobile under the limit condition as claimed in claim 1, wherein in the second step, a two-degree-of-freedom reference model is designed, and the equation is as follows:
Figure FDA0002428434120000011
Figure FDA0002428434120000012
where β is the vehicle centroid slip angle, γ is the yaw rate, is the driver-given steering wheel angle, VxRepresenting the vehicle longitudinal speed;
taking the transient response obtained by the son's finite reference model as the expectation, the expected response β from the centroid yaw angle and yaw rate is obtained*And gamma*：
Figure FDA0002428434120000013
Figure FDA0002428434120000014
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;
desired centroid slip angle β*And yaw rate γ*Are limited by the road adhesion coefficient, and their upper limits are:
Figure FDA0002428434120000021
Figure FDA0002428434120000022
wherein mu represents the road adhesion coefficient, and g is 9.8m/s2(ii) a The reference centroid slip angle and the reference yaw rate are obtained as follows:
βref＝sgn()min{|β*|,βlim}
γref＝sgn()min{|γ*|,γlim}
when the centroid slip angle is small, the value can be considered as the ratio of the vehicle lateral velocity to the longitudinal velocity, so according to βrefThe reference value V of the lateral speed can be obtainedyrefThe following were used:
Vyref＝sgn()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 1, wherein the third step comprises the following steps:
① the vehicle dynamics model is obtained by considering the longitudinal, lateral and yaw movement of the vehicle:
Figure FDA0002428434120000023
Figure FDA0002428434120000024
Figure FDA0002428434120000025
wherein, VyAs the lateral speed of the vehicle, FxAnd FyThe subscripts fl, fr, rl, rr represent the left front, right front, left rear and right rear wheels, respectively;
longitudinal slip ratio of tire
Figure FDA0002428434120000031
Wherein ω represents wheel speed;
② tire longitudinal force F using compound slip L uGre tire modelxAnd a lateral force FyThe description of (A) is as follows:
Figure FDA0002428434120000032
Figure FDA0002428434120000033
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;
Figure FDA0002428434120000034
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;
③ A predictive model for controller design is obtained from the three-degree-of-freedom vehicle dynamics model and the tire model:
Figure FDA0002428434120000035
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 FDA0002428434120000036
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 FDA0002428434120000037
Wherein λmax,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;
④ objective function and constraints:
the NMPC controller mainly controls the tracking of the yaw velocity and the lateral velocity on the reference value thereof, and the control targets are as follows:
Figure FDA0002428434120000038
Figure FDA0002428434120000039
wherein, tkRepresenting the current time, tpTo predict the time domain, x2(t) is the predicted output of lateral velocity, x3(t) is the predicted output of yaw rate;
for the controlled quantity, define
Figure FDA0002428434120000041
Designing a control target:
Figure FDA0002428434120000042
the tire longitudinal slip ratio is constrained as follows:
ux(t)∈[-I4×1I4×1]
definition of
Figure FDA0002428434120000043
Centroid slip angle
Figure FDA0002428434120000044
The rear wheel side slip angle is calculated by the following equation:
Figure FDA0002428434120000045
then there are
Figure FDA0002428434120000046
The rear wheel side slip angle is constrained as follows:
uy(t)∈[-I2×1I2×1]
the objective function is obtained as follows:
Figure FDA0002428434120000047
s.t.
Figure FDA0002428434120000048
ux(t)∈[-I4×1I4×1]
uy(t)∈[-I2×1I2×1]
wherein,v,xis a weight coefficient;
and optimally solving the objective function to obtain the slip rate and the slip angle of the tire with the virtual control quantity as expected.
4. The method for cooperatively controlling the transverse and longitudinal stability of the automobile under the limit condition of claim 1, wherein the step four of lower-layer additional torque comprises the following steps of:
change of tire longitudinal force Δ FxThe relationship between the change in slip ratio Δ λ and the change in slip angle Δ α can be expressed as:
Figure FDA0002428434120000049
the partial derivatives of the tire longitudinal force on the slip ratio and the slip angle are as follows:
Figure FDA0002428434120000051
Figure FDA0002428434120000052
in the formula (II)
Figure FDA0002428434120000053
Desired slip ratio by upper NMPC controller
Figure FDA0002428434120000054
And slip angle
Figure FDA0002428434120000055
The following relationship is present with respect to the actual slip ratio λ and slip angle α of the vehicle:
Figure FDA0002428434120000056
Figure FDA0002428434120000057
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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