CN109552312A - Intact stability model predictive control method - Google Patents
Intact stability model predictive control method Download PDFInfo
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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, or advanced driver assistance systems for ensuring comfort, stability and safety or drive control systems for propelling or retarding the vehicle
- B60W30/02—Control of vehicle driving stability
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60L—PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES; SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL; MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
- B60L15/00—Methods, circuits, or devices for controlling the traction-motor speed of electrically-propelled vehicles
- B60L15/20—Methods, circuits, or devices for controlling the traction-motor speed of electrically-propelled vehicles for control of the vehicle or its driving motor to achieve a desired performance, e.g. speed, torque, programmed variation of speed
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T10/00—Road transport of goods or passengers
- Y02T10/60—Other road transportation technologies with climate change mitigation effect
- Y02T10/72—Electric energy management in electromobility
Abstract
A kind of intact stability model predictive control method, belongs to control technology field.The purpose of the present invention is establish the Vehicular yaw kinetic model for considering road roughness, then performance model predictive control algorithm designs sideway stability controller, it effectively prevent electric car in the case where bad working environments and zig zag, vehicle occurs to roll, the intact stability model predictive control method of whipping.Step of the invention is: consider the electric car mechanics of road roughness and kinetic model build, sideway stability controller.The present invention is during carrying out Torque-sharing strategy formulation, considering vehicle safety (prevents skidding or locking, roll or whipping), vehicle performance (accelerate and braking ability), driver comfort (moment variations cannot be too big, and vertical force changing value cannot be too big), save control energy (energy is saved under the premise of meeting performance).Improve Full Vehicle Dynamics performance.
Description
Technical field
The invention belongs to control technology fields.
Background technique
Recently as the increasingly exacerbation of environmental pollution and energy crisis, energy-saving and emission-reduction become domestic or even the world the weight
Want target.Electric car due to its high energy efficiency, low emission, low noise, can be carried out the advantages such as energy regenerating already and become current vapour
The great direction of vehicle industrial development, country have also put into effect a large amount of preferential policy and have supported business research electric car.
Electric car using In-wheel motor driving is the hot spot of recent researches, because hub motor is directly installed on by it
On wheel, space is saved, and being capable of lightweight automobile.Four-wheel wheel hub drives the driving force of each driving wheel of electric car can
Be directly independently accurately controlled, so that controlling more flexible, conveniently, the driving force for rationally controlling each Electric Motor Wheel can be with
Improve driving performance of the electric car under severe pavement conditions, improves vehicle operating stability.Consider the electronic of uneven road surface
Basic control system one of of the automobile stability control system as electric car, its key task are examined in uneven road surface
Consider the vertical dynamics performance of vehicle, the drivings of four wheels of coordinated control, braking moment realize vehicle yaw stability
Control target combines the ride comfort of electric car.Better sideway is obtained compared with traditional combustion engine automobile to stablize
Performance.Locking when wheel being effectively prevent excessively to trackslip or brake when driving in straight-line travelling, while guaranteeing output torque
Validity, that is, obtain good acceleration and braking ability；In negotiation of bends, it is ensured that the Yaw stability of vehicle
Can, prevent vehicle roll, whipping.For electric car, since its is relatively simple for structure, the available appropriate letter of control problem
Change, meanwhile, the fast response time of motor, the torque and revolving speed of motor is easy to obtain, this is the control system of this research
Provide good basic condition.It is directed to the sideway stability contorting for considering the four-wheel wheel hub driving electric car of uneven road surface,
Mainly there are following problems:
1. the sideway of current Vehicular yaw stability contorting, mainly integrated active steering and direct yaw moment control is steady
Fixed control, mainly consideration longitudinal direction of car, transversal dynamic performance, there is no consideration vehicle vertical dynamics performances, and consider
The electric car Yaw stability of vertical performance controls, and using Active suspension, increases the number of suspension motor, simultaneously
The motor oscillating of Active suspension, and the principal element of vehicle riding comfort is influenced, therefore, considered not using passive suspension
It is a complicated system that the Vehicular yaw of flat road surface, which stablizes integrated control, has in control and acquires a certain degree of difficulty.
2. solving under the conditions of bad road attachment or when the dangerous working conditions such as high speed sharp turn, electric car is easy to produce sideslip
Or the problem of whipping, in order to keep vehicle stabilization and good maneuverability, it is required that it is expected mould on the output tracking of system
Type solves vehicle wheel when suddenly accelerating or emergency braking and needs there is a situation where skidding or locking by wheel slip
Control is in stability range；In order to guarantee that the comfort property of vehicle, vertical force changing value cannot be excessive；And motor torque is not
It can excessive, Yao Jieyue energy；The actual conditions for considering performer motor simultaneously, keep smooth steering and motor driven behavior,
Control amount variation should be reduced.This four control targets are contradictory, it is therefore desirable to compromise processing.
3. four-wheel torque can be distributed independently due to four-wheel driving electric vehicle, electric vehicle dynamics can be promoted
Can, but there are certain difficulty for the formulation of torque allocation rule, torque distribution is uncoordinated easily to cause electric car to be in danger
Operating condition, therefore the torque distribution of electric car is also a problem urgently to be resolved.
4. four wheels of four-wheel driving electric vehicle drive independently of one another, it is therefore desirable to while four wheels of control
Torque, and be contemplated that vehicle itself constraint condition, such as motor maximum output torque and vehicle safety
Property constraint etc..This is really the complex optimization control problem of a multiple target belt restraining.Common traditional algorithm has been difficult to
It meets the requirements.
Summary of the invention
The purpose of the present invention is establishing the Vehicular yaw kinetic model for considering road roughness, then performance model is predicted
Control algolithm designs sideway stability controller, effectivelying prevent electric car in the case where bad working environments and zig zag,
The intact stability model predictive control method of inclination, whipping occurs for vehicle.
Step of the invention is:
One, consider that the electric car mechanics of road roughness and kinetic model are built
(1) consider the mechanics of vehicles model buildings of road roughness
Formula (1) (2) are obtained according to the force analysis at vehicle body and wheel:
Vehicle body, suspension and wheel force analysis obtain:
Vehicle can generate pitching movement in uneven road surface traveling, can be obtained according to equalising torque at vehicle body:
Force analysis obtains tire force at tire:
Fti=kti(xwi-xoi) (6)
To progress mechanical analysis at suspension:
Wherein, i=f, r respectively represent the front wheels and rear wheels of vehicle, mwiFor wheel mass, m is car body mass, xwiIt hangs down for wheel
To displacement, xbiFor car body front and back end vertical deviation, xoiFor road excitation, ksiFor suspension flexibility coefficient, csiFor suspension damping system
Number, ktiFor tire spring rate, ctiFor tire damped coefficient, FtiFor tire force, FsiFor suspension power, IhbIt is body car body around y-axis
Rotary inertia, θ are the pitch angle of pitching movement, and a, b are respectively wheel base；
Equation (3)-equation (6) is arranged available:
Wherein,
By above-mentioned equation, tire pressure in model of vibration can be obtained are as follows:
(2) vehicle dynamic model is built
Controller model
Wherein, β is side slip angle yaw angle, represents the angle between the vehicle longitudinal axis and speed direction vector, γ
It is the yaw-rate of vehicle body；β and γ represents two freedom degrees for simplifying two degrees of freedom vehicle dynamic model；Fyf,FyrRespectively
Two degrees of freedom auto model front-wheel lateral force and rear-wheel lateral force are represented, m represents complete vehicle quality, and V represents longitudinal speed, Lf,Lr
Respectively represent vehicle centroid to front axle distance and mass center to rear axle distance；MzIt is vehicle yaw moment, is expressed as follows
Wherein, d represents uniaxial left and right sides wheelspan, Fxfl Fxfr Fxrl FxrrRepresent the near front wheel, left rear wheel, off-front wheel and off hind wheel
Longitudinal force；
The magic formula model of side force of tire:
Fyi=Dsin (Carctan (B αi-E(Bαi-arctanBαi))) (13)
Wherein, i=f, r represent front wheels and rear wheels, and B, C, D and E have vertical load decision, so side force of tire FyiIt is one
A and side drift angle αiWith vertical load FzRelevant function；
Lateral force is changed to obtain the cubic term expression formula of side force of tire:
Wherein, Cf,CrFor front-and rear-wheel steer rigidity, Ka,KbFor fitting coefficient, front and rear wheel side drift angle is as follows:
Wherein, δfFor front wheel angle；
The vertical force load simultaneous of tire is
Wherein, hcgVehicle centroid height is represented, g represents acceleration of gravity, axRepresent longitudinal acceleration, ayRepresent longitudinal acceleration；
Obtain vertical force suffered by wheel reality:
By longitudinal movement and pitching movement, establish the following equation:
By the rotary motion of two wheels, following formula is obtained:
Wherein, ωiFor front and rear wheel angular velocity of rotation, TeiFor front-wheel drive torque, TbiFor rear wheel drive torque, R has for wheel
Imitate radius, JiFor the rotary inertia of wheel；
According to the definition of slip rate, the calculation expression such as following formula (26) of straight skidding rate is obtained, above formula is the cunning in accelerator
Shifting rate calculating formula, following formula are the slip rate calculating formula in braking process
Wherein, ε is the constant value set,
By formula (26) both sides derivation, the formula that formula (24) (25) is brought into after derivation is obtained:
When only considering driving situation, formula is expressed are as follows:
Formula (1) (14), which is arranged to obtain system model, is
Two, sideway stability controller
System model is to be arranged the state-space model for obtaining system shown in formula (29)
Using the slip rate of yaw velocity γ, side slip angle β and four wheels as system state variable x=[β, γ,
λfl,λfr,λrl,λrr]T, control amount is u=[δf,Tfl,Tfr,Trl,Trr]TRespectively front wheel steering angle, four wheel driving electricity
The torque command of machine, system export y=[beta, gamma]T；
Discretization is carried out using Euler's formula, obtained discrete-time system model is as follows:
Wherein, k indicates sampling instant, TsFor sampling time, matrix
Derive p step predicted state and prediction output:
Mutual specific gravity is adjusted by weighting coefficient, to realize the compromise optimization between vehicle different performance index.
Optimization aim of the present invention:
(1) main optimization aim is
Q in formula1,Q2It is the weighting coefficient in optimization aim；
(2) quadratic sum of control amount is small as far as possible,
R in formula1,R2It is the weighting coefficient in optimization aim；
(3) by control slip rate, guarantee longitudinal performance of vehicle, while realizing the control to vertical load
(4) reduce the variation of control amount
S in formula1,S2It is the weighting coefficient in optimization aim；
Obtain total objective function
Constraint:
Motor constraint of saturation:
The torque of four motors and it should be equal to total driving torque T from driving pedalt,
The present invention compared with prior art the beneficial effects of the present invention are:
1. the present invention establishes the influence for considering Uneven road to Vehicular yaw stability contorting, using the electronic vapour of passive suspension
Vehicle, it is possible to reduce the motor number of suspension, lightweight automobile, while more existing sideway stabilizing control system is compared, due to examining
Yaw stability energy can be improved in the influence for having considered vertical force, while improving certain comfort level.
2. during carrying out Torque-sharing strategy formulation, it is contemplated that vehicle safety (prevents skidding or locking, side
Incline or whipping), vehicle performance (accelerate and braking ability), (moment variations cannot be too big, vertical force variation for driver comfort
Value cannot be too big), save control energy (energy is saved under the premise of meeting performance).Improve Full Vehicle Dynamics performance.
3. the sideway stabilizing control system designed in the present invention can control four wheels simultaneously, and consider maximum biography
Defeated torque and motor maximum output torque firm constraints, traditional control algolithm can not effective processing system constraint, and
Model Predictive Control Algorithm can effectively handle the Optimal Control Problem of multiple-input and multiple-output belt restraining, effectively realize vehicle
Compromise optimization between safety and vehicle performance, while under the premise of meeting performance requirement, it is also contemplated that driver's is comfortable
Property and save control energy.
Detailed description of the invention
Fig. 1 is four-wheel wheel hub driving electric vehicle structure schematic diagram；
Fig. 2 is the intact stability model predictive control system structural block diagram for considering road roughness；
Fig. 3 is the two degrees of freedom bicycle model of Controller-oriented design；
Fig. 4 is 1/2 Vertical Vibration of Vehicle model；
The relational graph of Fig. 5 side force of tire and yaw angle, vertical force；
Fig. 6 is the relational graph of longitudinal force of tire and slip rate, vertical force；
Fig. 7 is fitting function and former magic formula contrast effect figure；
Fig. 8 is Model Predictive Control basic schematic diagram；
Fig. 9 polling power controlling device schematic illustration.
Specific embodiment
The considerations of present invention designs road roughness based on passive suspension electric car and Model Predictive Control Algorithm
Electric car sideway stabilizing control system can be well solved above 4 problems.The present invention, which establishes, considers road roughness
Vehicular yaw kinetic model, then performance model predictive control algorithm designs sideway stability controller, effectivelying prevent electricity
In the case where bad working environments and zig zag, inclination, whipping occur electrical automobile for vehicle, while vehicle guarantee is good vertical
Dynamic performance improves riding comfort.The present invention does not introduce Active suspension, does not increase the load burden of vehicle, light weight
Change automobile, save the cost.Model predictive control method can effectively handle multiple target complex optimization control problem, and dominant
Processing constraint, the present invention can consider motor, vehicle security constraint, maximum transmitted power using model predictive control method simultaneously
Square is also used as time-domain constraints to handle, and effectively realizes the compromise optimization between vehicle safety and vehicle performance, in linear rows
Locking when wheel being effectively prevent excessively to trackslip or brake when driving when sailing, while guaranteeing the validity of output torque, that is,
Obtain good acceleration and braking ability；In negotiation of bends, it is ensured that the Yaw stability energy of vehicle prevents vehicle side
Incline, whipping.By constructing cost function, optimizing solves the torque command signal of four wheels after being optimized, of the invention
Cost function consideration mainly includes four aspects, comprising: vehicle safety (preventing skid perhaps locking inclination or whipping),
Vehicle performance (accelerate and braking ability), driver comfort (moment variations cannot be too big, and vertical force changing value cannot be too big),
Save control energy (energy is saved under the premise of meeting performance).
The present invention is to provide for a kind of electric car sideway stable model Predictive Control System for considering road roughness.It builds
The vertical Vehicular yaw kinetic model for considering road roughness, then performance model predictive control algorithm is stablized to design sideway
Controller, to effectively prevent electric car in the case where bad working environments and zig zag, inclination, whipping occur for vehicle, simultaneously
Vehicle guarantees good vertical dynamics performance, improves riding comfort.The present invention does not introduce Active suspension, does not increase
The load burden of vehicle, lightweight automobile, save the cost.Multiple target complexity is effectively handled using model predictive control method
Optimal Control Problem, while considering motor, vehicle security constraint, maximum transmitted torque is also used as time-domain constraints to handle, has
Effect realizes the compromise optimization between vehicle safety and vehicle performance, excessive when effectivelying prevent wheel to drive in straight-line travelling
Locking when trackslipping or braking, while guaranteeing the validity of output torque, that is, obtain good acceleration and braking ability；
In negotiation of bends, it is ensured that the Yaw stability energy of vehicle prevents vehicle roll, whipping.
To achieve the above object, the present invention is as follows using technical solution:
The Vehicular yaw kinetic model for considering road roughness is established, then performance model predictive control algorithm designs sideway
Stability controller, to effectively prevent electric car in the case where bad working environments and zig zag, inclination, whipping occur for vehicle,
Vehicle guarantees good vertical dynamics performance simultaneously, improves riding comfort.The present invention does not introduce Active suspension, does not have
Increase the load burden of vehicle, lightweight automobile, save the cost.It is multiple that model predictive control method can effectively handle multiple target
Miscellaneous Optimal Control Problem, and dominant processing constrains, and the present invention can consider motor, whole using model predictive control method simultaneously
Vehicle security constraint, maximum transmitted torque are also used as time-domain constraints to handle, and effectively realize vehicle safety and vehicle performance
Between compromise optimization, locking when wheel being effectively prevent excessively to trackslip or brake when driving in straight-line travelling guarantees simultaneously
The validity of output torque, that is, obtain good acceleration and braking ability；In negotiation of bends, it is ensured that vehicle
Yaw stability energy prevents vehicle roll, whipping.By constructing cost function, optimizing solves four wheels after being optimized
Torque command signal.
For the technology contents that the present invention will be described in detail, construction features, realize purpose etc., with reference to the accompanying drawing to the present invention into
Row is explained comprehensively.
Realization platform of the invention is that four-wheel wheel hub drives electric car, and structure is as shown in Figure 1, the platform includes four
Independent hub motor 1,2,3,4 (motor obtains torque and wheel speed information by sensor measurement), four corresponding electricity
Machine controller 5,6,7,8, an entire car controller 10, and mentioned between entire car controller 10 and electric machine controller 5,6,7,8
For the CAN network 11 of communication, the operation of certain motor be unable to do without battery pack 9, and battery pack 9 provides power supply for four motors.Motor
The major function of controller 5,6,7,8 is that the torque of corresponding four wheels of acquisition and rotary speed information feed back to vehicle sideway and stablize
Controller, and the torque closed loop control of corresponding hub motor 1,2,3,4 is realized using the torque command that entire car controller 10 provides
System, exports desired torque；The effect of entire car controller 10 is exactly corresponding four provided according to electric machine controller 5,6,7,8
The torque of a wheel and rotary speed information respectively obtain the corresponding slip rate value of four wheels by calculating, and the time domain as system is about
Beam using Model Predictive Control Algorithm, while considering the maximum output torque and vertical force changing value of motor, passes through solution
The corresponding optimal control problem of cost function, the torque command of four wheels after being optimized simultaneously act on wheel, effectively anti-
Locking when perhaps braking of skidding when only wheel accelerates prevents Ackermann steer angle from lateral deviation or whipping occurs, and obtains good add
Speed, braking and turn performance, while improving the comfort property of vehicle.Electric car sideway stability contorting algorithm in the present invention
Exactly realized in such a closed loop procedure.
The intact stability model predictive control system structural block diagram of consideration road roughness of the invention is as shown in Figure 2.
Firstly, inputting δ and vehicle present speed V according to the steering wheel of driver obtains desired yaw velocity according to the reference module
γrWith side slip angle βrAnd the driving moment T of driver's inputtIt is given in Nonlinear Model Predictive Control device, passes through tune
Section control amount steering wheel angle and driving motor torque make the practical yaw velocity of vehicle and side slip angle fast and accurately
Desired value in tracking.Considering in stable control process, torque, which distributes, directly determines the movement of driver, and tire
Directly there is nuance in nonlinear characteristic, while considering the constraint of saturation of motor torque, and it is direct to design a whole controller
Torque needed for Optimization Solution obtains motor.Modules are described in detail respectively below.
Present invention is primarily based on the sideway dynamics of vehicle to be studied, main to consider vehicle roll and sideway two certainly
By the movement spent.Therefore, it is assumed here that speed is definite value, vehicle, which is simplified, becomes two degrees of freedom bicycle model, such as Fig. 3
It is shown.
1. considering that the electric car mechanics of road roughness and kinetic model are built
This part includes the mechanical model and kinetic model of vehicle, is the additional shadow for considering road excitation and generating to wheel respectively
Loud and Vehicular yaw dynamic analysis.
(1) consider the mechanics of vehicles model buildings of road roughness
Pressure suffered by wheel in order to obtain establishes Vertical Vibration of Vehicle model.According to Newton's second law, three quality are utilized
Block respectively represents vehicle front and back wheel and car body, establishes vehicle and simplifies vibration maths model.1/2 Vertical Vibration of Vehicle model is such as
Shown in Fig. 4.
First precondition for establishing 1/2 vehicle vibration model is that 1/2 vehicle is reduced to front and back wheel and car body three
The mutual mechanical relationship of mass block, three mass blocks are constants；Another precondition is by two wheel connection bodies
Suspension and tire are reduced to spring and damper.Front and back wheel under the premise of having road excitation is known based on these assumed conditions
Mechanical relationship between three mass blocks of car body can be expressed by relationship, and then obtain 1/2 Vertical Vibration of Vehicle mould
Type.
According to Newton's second law, 1/2 Vertical Vibration of Vehicle model can be expressed as follows, the pressure as suffered by wheel, be come
Derived from road surface and suspension, and suspension is the medium for connecting vehicle body and wheel, it is therefore desirable to vehicle body and suspension, wheel and suspension
Carry out mechanical analysis.
Formula (1) (2) are obtained according to the force analysis at vehicle body and wheel:
Vehicle body, suspension and wheel force analysis obtain:
Vehicle can generate pitching movement in uneven road surface traveling, can be obtained according to equalising torque at vehicle body:
Force analysis obtains tire force at tire:
Fti=kti(xwi-xoi) (6)
To progress mechanical analysis at suspension:
Wherein, i=f, r respectively represent the front wheels and rear wheels of vehicle, mwiFor wheel mass, m is car body mass, xwiIt hangs down for wheel
To displacement, xbiFor car body front and back end vertical deviation, xoiFor road excitation, ksiFor suspension flexibility coefficient, csiFor suspension damping system
Number, ktiFor tire spring rate, ctiFor tire damped coefficient, FtiFor tire force, FsiFor suspension power, IhbIt is body car body around y-axis
Rotary inertia, θ are the pitch angle of pitching movement, and a, b are respectively wheel base.
Equation (3)-equation (6) is arranged available:
Wherein,
By above-mentioned equation, tire pressure in model of vibration can be obtained are as follows:
(2) vehicle dynamic model is built
As state variable, the driving torque and front wheel angle of four-wheel are used as input for vehicle centroid side drift angle and yaw velocity,
Obtain controller model.
Wherein, β is side slip angle yaw angle, represents the angle between the vehicle longitudinal axis and speed direction vector, and γ is vehicle body
Yaw-rate.β and γ represents two freedom degrees for simplifying two degrees of freedom vehicle dynamic model.Fyf,FyrRespectively represent two freely
Auto model front-wheel lateral force and rear-wheel lateral force are spent, m represents complete vehicle quality, and V represents longitudinal speed, Lf,LrRespectively represent vehicle
Mass center to front axle distance and mass center to rear axle distance.MzIt is vehicle yaw moment, is expressed as follows.
Wherein, d represents uniaxial left and right sides wheelspan, and .. represents the longitudinal force of the near front wheel, left rear wheel, off-front wheel and off hind wheel.
The magic formula model of side force of tire:
Fyi=Dsin (Carctan (B αi-E(Bαi-arctanBαi))) (13)
Wherein, i=f, r represent front wheels and rear wheels, and B, C, D and E have vertical load decision, so side force of tire FyiIt is one
A and side drift angle αiWith vertical load FzRelevant function, variation characteristic are as shown in Figure 5.
Longitudinal force of tire can equally be shown that characteristic curve is as shown in Figure 6 by magic formula model.
Due to being unfavorable for the design of System design based on model device, while Tire nonlinearity characteristic is retained again, so using
Taylor method is changed lateral force to obtain the cubic term expression formula of side force of tire:
Wherein, Cf,CrFor front-and rear-wheel steer rigidity, Ka,KbFor fitting coefficient, matched curve is as shown in Figure 7.Front and rear wheel lateral deviation
Angle is as follows:
Wherein, δfFor front wheel angle.
Due to being influenced by longitudinal acceleration, side acceleration, inclination and pitching etc., the load of the vertical force of tire can be with
It is described as (herein for do not consider that the uneven influence to vertical force is seen on road):
Wherein, hcgVehicle centroid height is represented, g represents acceleration of gravity, axRepresent longitudinal acceleration, ayRepresent longitudinal acceleration.
Therefore comprehensive longitudinal, the influence of side acceleration and road excitation to vertical force can be obtained and be hung down suffered by wheel reality
Xiang Li:
In the case where ignoring air drag, by longitudinal movement and pitching movement, can must establish the following equation:
By the rotary motion of two wheels, following formula can be obtained:
Wherein, ωiFor front and rear wheel angular velocity of rotation, TeiFor front-wheel drive torque, TbiFor rear wheel drive torque, R has for wheel
Imitate radius, JiFor the rotary inertia of wheel.
According to the definition of slip rate, the calculation expression such as following formula (26) of straight skidding rate can be obtained, above formula is accelerator
In slip rate calculating formula, following formula be braking process in slip rate calculating formula.
Wherein, ε is the constant value set, for avoiding the null situation of denominator.If without ε, in vehicle start or system
The moment that speed is zero during dynamic, it just will appear the situation of slip rate infinity, i.e. λi→ ∞, this does not obviously meet reality,
Prevent above-mentioned phenomenon from occurring so needing to add the lesser constant value ε of a value.By comparative test, ε chooses 0.1m/s and is
Optimum value.
In order to facilitate controller design, by formula (26) both sides derivation, formula (24) (25) brings the formula after derivation into
:
When only considering driving situation, formula be can be expressed as:
Formula (1) (14), which is arranged to obtain system model, is
Controller will be designed based on formula (29) below.
2, the sideway stability controller based on Model Predictive Control
Model Predictive Control is multi-step prediction, and the open loop that basic thought can be described as in one finite time-domain of line solver is optimal
Control problem, while guaranteeing that system meets objective function, state and input constraint etc..PREDICTIVE CONTROL can be summarized simply as follows three
Step: according to the current measurement information of acquisition and the following dynamic of prediction model forecasting system；Under the conditions of guaranteeing objective function and constraining
Line solver optimization problem；First element interaction of solution is in system.Model Predictive Control be at every sampling moment repeat into
Capable, and the following dynamic starting point of forecasting system is current measured value, that is, uses the measured value of each sampling instant as prediction
Primary condition.The basic principle of Model Predictive Control is as shown in Figure 7.In current time t, measured value is obtained from controlled system
x0, according to metrical information and prediction model, forecasting system is in prediction time domain TpThe interior following dynamic behaviourOptimize open-loop performance
Target function (there are four parts for objective function in the present invention), searches out control time domain TcInterior optimal control list entries
So that the system output of prediction is with the output of desired system closer to better, i.e. in Fig. 8 hatched area minimum.
In view of the nonlinear characteristic of four-wheel wheel hub electric car, can be solved just using Model Predictive Control Algorithm such
Therefore nonlinear problem devises NMPC controller herein to calculate the driving moment of front wheel angle and four wheels, from
And the yaw velocity of vehicle and side slip angle is allowed to track the desired value that upper layer is set.
System model is to be arranged the state-space model for obtaining system shown in formula (29)
Using the slip rate of yaw velocity γ, side slip angle β and four wheels as system state variable x=[β, γ,
λfl,λfr,λrl,λrr]T, control amount is u=[δf,Tfl,Tfr,Trl,Trr]TRespectively front wheel steering angle, four wheel driving electricity
The torque command of machine, system export y=[beta, gamma]T。
Discretization is carried out using Euler's formula, obtained discrete-time system model is as follows:
Wherein, k indicates sampling instant, TsFor sampling time, matrix
According to the basic principle and correlation theory of Model Predictive Control, p step prediction is derived
Y (k+1 | k)=Cx (k) (32)
MPC control algorithm can be with effective solution multiple target multiple constraint problem, and can be denoted as having weighting square
The multiple target equation of battle array, and obtain including the multi-dimensional optimizations variables such as front wheel steering angle, four-wheel drive torque.
Consider that the sideway stability controller principle of uneven road surface is as shown in Figure 9 designed by the present invention.It can realize simultaneously pair
The accurate control of four wheels, while also contemplating the constraint of vehicle safety constraint and motor.Vehicle performance, driving comfort
Property, vertical load variation and energy hole target be all to be realized by constructing corresponding cost function.Passing through between them
Weighting coefficient adjusts mutual specific gravity, to realize the compromise optimization between vehicle different performance index.
Optimization aim:
(1) in order to keep vehicle stabilization and good maneuverability, it is required that expectational model on system output tracking, therefore, main
The optimization aim wanted is
Q in formula1,Q2It is the weighting coefficient in optimization aim.
(2) motor torque means that more greatly the energy consumed from battery is bigger, reduces consumption energy, and control amount is put down
It is square and small as far as possible,
R in formula1,R2It is the weighting coefficient in optimization aim.
(3) due to slip rate be it is related to vertical force, by control slip rate, guarantee longitudinal performance of vehicle, while
It is able to achieve the control to a certain extent to vertical load.
(4) in order to reduce the variation of control action, smooth steering and motor driven behavior is kept, the change of control amount is reduced
Change,
S in formula1,S2It is the weighting coefficient in optimization aim.
To sum up, total objective function is obtained, i.e.,
Constraint:
Motor constraint of saturation:
The torque of four motors and it should be equal to total driving torque T from driving pedalt,
With constrained optimization problem required for thus establishing, and the solution in the application tool box Matlab is non-thread
Property planning equation fmincon function line solver optimization method, obtain control amount.
Claims (2)
1. a kind of intact stability model predictive control method, it is characterised in that: the steps include:
One, consider that the electric car mechanics of road roughness and kinetic model are built
(1) consider the mechanics of vehicles model buildings of road roughness
Formula (1) (2) are obtained according to the force analysis at vehicle body and wheel:
Vehicle body, suspension and wheel force analysis obtain:
Vehicle can generate pitching movement in uneven road surface traveling, can be obtained according to equalising torque at vehicle body:
Force analysis obtains tire force at tire:
Fti=kti(xwi-xoi) (6)
To progress mechanical analysis at suspension:
Wherein, i=f, r respectively represent the front wheels and rear wheels of vehicle, mwiFor wheel mass, m is car body mass, xwiIt is vertical for wheel
Displacement, xbiFor car body front and back end vertical deviation, xoiFor road excitation, ksiFor suspension flexibility coefficient, csiFor suspension damping coefficient,
ktiFor tire spring rate, ctiFor tire damped coefficient, FtiFor tire force, FsiFor suspension power, IhbIt is rotated for body car body around y-axis
Inertia, θ are the pitch angle of pitching movement, and a, b are respectively wheel base；
Equation (3)-equation (6) is arranged available:
Wherein,
By above-mentioned equation, tire pressure in model of vibration can be obtained are as follows:
(2) vehicle dynamic model is built
Controller model
Wherein, β is side slip angle yaw angle, represents the angle between the vehicle longitudinal axis and speed direction vector, and γ is vehicle body
Yaw-rate；β and γ represents two freedom degrees for simplifying two degrees of freedom vehicle dynamic model；Fyf,FyrRespectively represent two degrees of freedom
Auto model front-wheel lateral force and rear-wheel lateral force, m represent complete vehicle quality, and V represents longitudinal speed, Lf,LrRespectively represent vehicle matter
The heart to front axle distance and mass center to rear axle distance；MzIt is vehicle yaw moment, is expressed as follows
Wherein, d represents uniaxial left and right sides wheelspan, Fxfl Fxfr Fxrl FxrrRepresent the near front wheel, left rear wheel, off-front wheel and off hind wheel
Longitudinal force；
The magic formula model of side force of tire:
Fyi=Dsin (Carctan (B αi-E(Bαi-arctanBαi))) (13)
Wherein, i=f, r represent front wheels and rear wheels, and B, C, D and E have vertical load decision, so side force of tire FyiIt is one
With side drift angle αiWith vertical load FzRelevant function；
Lateral force is changed to obtain the cubic term expression formula of side force of tire:
Wherein, Cf,CrFor front-and rear-wheel steer rigidity, Ka,KbFor fitting coefficient, front and rear wheel side drift angle is as follows:
Wherein, δfFor front wheel angle；
The vertical force load simultaneous of tire is
Wherein, hcgVehicle centroid height is represented, g represents acceleration of gravity, axRepresent longitudinal acceleration, ayRepresent longitudinal acceleration；?
Vertical force suffered by wheel reality:
By longitudinal movement and pitching movement, establish the following equation:
By the rotary motion of two wheels, following formula is obtained:
Wherein, ωiFor front and rear wheel angular velocity of rotation, TeiFor front-wheel drive torque, TbiFor rear wheel drive torque, R is that wheel is effective
Radius, JiFor the rotary inertia of wheel；
According to the definition of slip rate, the calculation expression such as following formula (26) of straight skidding rate is obtained, above formula is the cunning in accelerator
Shifting rate calculating formula, following formula are the slip rate calculating formula in braking process
Wherein, ε is the constant value set,
By formula (26) both sides derivation, the formula that formula (24) (25) is brought into after derivation is obtained:
When only considering driving situation, formula is expressed are as follows:
Formula (1) (14), which is arranged to obtain system model, is
Two, sideway stability controller
System model is to be arranged the state-space model for obtaining system shown in formula (29)
N=3,4,5,6, s=fl, fr, rl, rr
Using the slip rate of yaw velocity γ, side slip angle β and four wheels as system state variable x=[β, γ,
λfl,λfr,λrl,λrr]T, control amount is u=[δf,Tfl,Tfr,Trl,Trr]TRespectively front wheel steering angle, four wheel drive motors
Torque command, system export y=[beta, gamma]T；
Discretization is carried out using Euler's formula, obtained discrete-time system model is as follows:
Wherein, k indicates sampling instant, TsFor sampling time, matrix
Derive p step predicted state and prediction output:
Mutual specific gravity is adjusted by weighting coefficient, to realize the compromise optimization between vehicle different performance index.
2. intact stability model predictive control method according to claim 1, it is characterised in that: optimization aim:
(1) main optimization aim is
Q in formula1,Q2It is the weighting coefficient in optimization aim；
(2) quadratic sum of control amount is small as far as possible,
R in formula1,R2It is the weighting coefficient in optimization aim；
(3) by control slip rate, guarantee longitudinal performance of vehicle, while realizing the control to vertical load
(4) reduce the variation of control amount
S in formula1,S2It is the weighting coefficient in optimization aim；
Obtain total objective function
Constraint:
Motor constraint of saturation:
The torque of four motors and it should be equal to total driving torque T from driving pedalt,
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