CN113602279B - Method for estimating mass center slip angle and tire lateral force of distributed driving electric automobile - Google Patents

Method for estimating mass center slip angle and tire lateral force of distributed driving electric automobile Download PDF

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CN113602279B
CN113602279B CN202110997824.0A CN202110997824A CN113602279B CN 113602279 B CN113602279 B CN 113602279B CN 202110997824 A CN202110997824 A CN 202110997824A CN 113602279 B CN113602279 B CN 113602279B
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CN113602279A (en
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任彦君
王凡勋
柏硕
张紫涵
沈童
冯斌
付琪
梁晋豪
危奕
华政硕
陈乐彬
项朋仑
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Nanjing Quake Electric Technology Co ltd
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Wujiazhibao Automobile Technology Jiangsu Co ltd
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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
    • B60W40/00—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models
    • 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
    • B60W40/00—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models
    • B60W40/10—Estimation or calculation of non-directly measurable driving parameters for road vehicle drive control systems not related to the control of a particular sub unit, e.g. by using mathematical models related to vehicle motion
    • 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
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Abstract

The invention belongs to the field of state estimation and safety control of electric vehicles, and discloses a method for estimating a mass center side deflection angle and a tire side force of a distributed driving electric vehicle, which estimates the mass center side deflection angle and the tire side force of the vehicle in real time based on an interactive multi-model algorithm-volume Kalman filtering, establishes an eight-degree-of-freedom vehicle model comprising longitudinal motion, transverse motion, yaw motion, roll motion and motion of four tires, and takes the influence of the roll motion and load transfer in the driving process of the vehicle into consideration by a nonlinear vehicle model; then establishing a linear tire model and a nonlinear Dugoff tire model as a model set of an interactive multi-model; estimating the mass center slip angle of the vehicle and the lateral force of the tire; the method provided by the invention aims at greatly reducing the problem of inaccurate estimation result caused by inaccurate establishment of the nonlinear dynamic model, and the volume Kalman filtering reaches a third order approximation, so that the estimation precision of the vehicle mass center slip angle and the tire lateral force is finally improved.

Description

Method for estimating mass center slip angle and tire lateral force of distributed driving electric automobile
Technical Field
The invention relates to a method for estimating a centroid slip angle and a tire lateral force of a distributed driving electric automobile, and belongs to the field of state estimation and safety control of electric automobiles.
Background
Compared with the traditional fuel oil type automobile, the distributed driving electric automobile has great advantages as one of the mainstream directions of the current automobile industry development, for example, the structure of the chassis is more simplified, and the chassis components are relatively independent and can be optimally designed; the torque response is quicker, and a redundant transmission mechanism is not needed for transmission; the control execution is more accurate, and the instruction input system can be executed efficiently and with extremely low error. In addition, the structural optimization provides convenience for the configuration and the use of the vehicle-mounted sensor, and various vehicle state parameters such as longitudinal vehicle speed and the like in the vehicle running process can be measured and fed back instantly.
In the field of vehicle stable running and safety control, vehicle state parameters which cannot be directly measured by standard vehicle-mounted sensors such as a vehicle mass center and a vehicle yaw angle are also very important and are limited by factors such as manufacturing cost, a vehicle body framework and the like, and the feasibility of a scheme for performing filtering calculation and estimation on the vehicle state parameters by using the parameters measured by the standard vehicle-mounted sensors and vehicle structure parameters such as vehicle mass and the like is high.
The current method for carrying out filtering calculation and estimation on vehicle state parameters is mostly designed based on a Kalman filtering technology, and noise in the estimation process is subjected to a series of processing by utilizing the statistical characteristics of prior noise, so that the measurement error can be effectively dealt with, and the more accurate estimation on the selected quantity is realized.
The vehicle state parameter estimation algorithm based on the Kalman filtering technology comprises a Kalman filtering algorithm, an extended Kalman filtering algorithm, an unscented Kalman filtering algorithm and the like. However, the conventional first-order linear kalman filter algorithm has a very high requirement on the modeling stability of noise in the estimation process, and cannot cope with the problem that the model is mismatched and then filtered and dispersed due to the change of tire state (such as skidding) in the vehicle running process, and the applicability is not wide. The extended Kalman filtering algorithm and the unscented Kalman filtering algorithm based on the nonlinear dynamical equation have certain applicability to a linear system and a nonlinear system, and the estimation precision is improved compared with the traditional first-order linear Kalman filtering algorithm, but the matrix dimension for calculation in the estimation process is generally higher, so that the method has extremely high requirements on the calculation capacity of a vehicle-mounted controller, and meanwhile, the high-order truncation error in the estimation process is more obvious, and the filtering process is unstable, so that the application of the technology in engineering is also hindered to a certain extent.
Disclosure of Invention
The invention provides a real-time estimation method of the mass center slip angle and the tire lateral force of a vehicle for a distributed driving electric vehicle, and the estimation result has great significance for an active safety control system of the electric vehicle.
The technical scheme adopted by the invention for solving the technical problems is as follows:
the method for estimating the centroid slip angle and the tire lateral force of the distributed drive electric automobile comprises the following steps of:
step one, considering the complexity of the running condition of the vehicle and the fact that the distributed driving electric vehicle has higher degree of freedom, an eight-degree-of-freedom vehicle dynamic equation is established, wherein the eight-degree-of-freedom vehicle dynamic equation comprises longitudinal motion, transverse motion, yaw motion, roll motion and motion of four tires;
selecting a linear tire model and a nonlinear Dugoff tire model as a model set of an interactive multi-model algorithm;
estimating the mass center and the side deflection angle of the vehicle and the tire side force based on an interactive multi-model algorithm-volume Kalman filtering, wherein the algorithm process comprises the following steps: input interaction, cubature Kalman filtering, model updating probability and output interaction.
Considering longitudinal motion, transverse motion, yaw motion, roll motion and motion of four tires of the vehicle under complex working conditions in the step one, and establishing a vehicle dynamic model;
the eight-degree-of-freedom vehicle dynamics equation is established as follows:
Figure GDA0004009224370000021
Figure GDA0004009224370000022
Figure GDA0004009224370000023
Figure GDA0004009224370000024
Figure GDA0004009224370000025
Figure GDA0004009224370000026
wherein, the expressions (1) and (2) are respectively longitudinal and transverse motion equations of the vehicle body of the vehicle, the expressions (3) and (4) are respectively longitudinal and transverse motion equations of the whole vehicle, and the expressions (5) and (6) are respectively transverse and side-rolling motion equations of the whole vehicle; m, m s Respectively representing the total mass of the vehicle and the sprung mass of the vehicle; i is zz 、I xz 、I xxs 、I xzs Respectively representing the yaw moment of the vehicle, the product of the moment of inertia of the mass of the vehicle around the x and z axes, the yaw moment of the sprung mass of the vehicle and the product of the moment of inertia of the sprung mass of the vehicle around the x and z axes; v x 、V y 、ω z 、ω x Respectively representing a vehicle longitudinal speed, a vehicle lateral speed, a vehicle yaw rate and a vehicle yaw rate; beta, delta and phi respectively represent a vehicle mass center slip angle, a front wheel rotating angle and a vehicle slip angle; f x 、F y Respectively representing the longitudinal force and the lateral force of four wheels of the vehicle; subscripts i = f, r respectively denote the vehicle front axle and the vehicle rear axle, subscripts j = q, p respectively denote the vehicle left wheel and the vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively denote the vehicle left front wheel, right front wheel, left rear wheelAnd a right rear wheel; h represents the vertical distance from the center of mass of the sprung part of the vehicle to the roll axis; m z 、M x Respectively representing yaw moment and roll moment; b is f 、B r Respectively showing the front and rear rail widths of the vehicle; l is f 、L r Respectively representing the front and rear wheel base of the vehicle; g represents the gravitational acceleration; the upper symbol "·" represents the differentiation of the indicated quantity.
(II) establishing an expression of each tire vertical load in the second step as follows:
Figure GDA0004009224370000031
/>
Figure GDA0004009224370000032
Figure GDA0004009224370000033
Figure GDA0004009224370000034
wherein, F z Representing vehicle vertical forces; subscripts i = f, r respectively denote a vehicle front axle and a vehicle rear axle, subscripts j = q, p respectively denote a vehicle left wheel and a vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively denote a vehicle left front wheel, a right front wheel, a left rear wheel, and a right rear wheel; m, m s 、m uf 、m ur Respectively representing the total mass of the vehicle, the sprung mass of the vehicle, and the front and rear unsprung masses of the vehicle; c φf 、C φr Respectively representing the front roll rigidity and the rear roll rigidity of the vehicle; k is φf 、K φr Respectively representing the front roll damping coefficient and the rear roll damping coefficient of the vehicle; v x 、V y 、ω z 、ω x Respectively representing a vehicle longitudinal speed, a vehicle lateral speed, a vehicle yaw rate and a vehicle yaw rate; g represents the gravitational acceleration; h is a total of cg 、h uf 、h ur Respectively representing vehiclesThe height of the center of mass and the offset centers of the front wheel and the rear wheel from the ground; respectively representing the front and rear roll center heights of the vehicle; b is f 、B r Respectively showing the front and rear rail widths of the vehicle; l is f 、L r Respectively representing the front and rear wheel base of the vehicle; phi represents a roll angle; the upper symbol "·" denotes the differentiation of the quantity indicated.
The tire slip ratio expression is:
Figure GDA0004009224370000041
wherein λ represents a tire slip ratio; v x 、ω ij Respectively representing the vehicle longitudinal speed and the tire yaw rate; subscripts i = f, r respectively denote a vehicle front axle and a vehicle rear axle, subscripts j = q, p respectively denote a vehicle left wheel and a vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively denote a vehicle left front wheel, a right front wheel, a left rear wheel, and a right rear wheel; r e Is the effective radius of the tire.
(III) selecting a linear tire model and a nonlinear Dugoff tire model as a model set of the interactive multi-model algorithm;
the linear tire model is as follows:
the linear tire model slip angle expression is:
Figure GDA0004009224370000042
wherein α and δ respectively represent a tire slip angle and a front wheel rotation angle; v x 、V y 、ω z Respectively representing a vehicle longitudinal speed, a vehicle transverse speed and a vehicle yaw rate; b is f 、B r Respectively showing the front and rear rail widths of the vehicle; l is f 、L r Respectively representing the front and rear wheel base of the vehicle; phi represents a roll angle; epsilon f 、ε r Respectively representing the tilting coefficients of the front shaft side and the rear shaft side; subscripts i = f, r respectively denote the vehicle front axle and the vehicle rear axle, subscripts j = q, p respectively denote the vehicle left wheel and the vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively are tabulatedShowing the left front wheel, the right front wheel, the left rear wheel and the right rear wheel of the vehicle.
The linear tire longitudinal and lateral force expressions are:
F yij ＝-C yij α ij
F xij ＝k μ λ ij F zij
wherein, F x 、F y Respectively representing the longitudinal force and the transverse force of four wheels of the vehicle; alpha and lambda respectively represent a tire slip angle and a slip ratio; c y 、k μ Indicating the cornering stiffness and the linear region mu-lambda of the tyre ij An image slope; subscripts i = f, r respectively denote a vehicle front axle and a vehicle rear axle, subscripts j = q, p respectively denote a vehicle left wheel and a vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively denote a vehicle left front wheel, a right front wheel, a left rear wheel, and a right rear wheel.
The nonlinear Dugoff tire model is as follows:
the nonlinear tire model slip angle expression is as follows:
Figure GDA0004009224370000051
wherein α and δ represent a tire slip angle and a front wheel rotation angle; v x 、V y 、ω z Respectively representing a vehicle longitudinal speed, a vehicle transverse speed and a vehicle yaw rate; b is f 、B r Respectively showing the width of the front and the rear vehicle rails of the vehicle; l is a radical of an alcohol f 、L r Respectively representing the front and rear wheel base of the vehicle; phi represents a roll angle; subscripts i = f, r respectively denote a vehicle front axle and a vehicle rear axle, subscripts j = q, p respectively denote a vehicle left wheel and a vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively denote a vehicle left front wheel, a right front wheel, a left rear wheel, and a right rear wheel.
The non-linear Dugoff tire longitudinal and lateral force expressions are:
Figure GDA0004009224370000061
Figure GDA0004009224370000062
Figure GDA0004009224370000063
Figure GDA0004009224370000064
wherein, F x 、F y Respectively representing the longitudinal force and the transverse force of four wheels of the vehicle; alpha and lambda represent the tire slip angle and the slip ratio; c y Representing the tire cornering stiffness; s is the substitution amount of the function; subscript i = f, r represents the vehicle front and rear axles, respectively, subscript j = q, p represents the vehicle left and right wheels, respectively, whereby subscripts fq, fp, rq, rp represent the vehicle left and right front, rear, and rear wheels, respectively.
(IV) in the third step, estimating the vehicle mass center slip angle and the tire lateral force based on an interactive multi-model algorithm-volume Kalman filtering, wherein the input interactive process comprises the following steps:
the model probability mu of the model j in the previous step j (k-1) and State estimation
Figure GDA0004009224370000065
Gets a mixed estimate->
Figure GDA0004009224370000066
Assuming the linear tire model and the Dugoff nonlinear tire model are models i, j =1,2, respectively, the transfer matrix is therefore:
Figure GDA0004009224370000067
wherein P is a transition matrix, P in the transition matrix ij Probability of motion transfer, transfer moment, from model i to model j with element as targetThe subscript r = j for the elements in the array P, r being the number of model set models.
The prediction model is derived from the expression of model j:
Figure GDA0004009224370000068
wherein, mu j (k-1) represents the model probability of model j at time k-1 of the previous step,
Figure GDA0004009224370000069
the prediction probability of the model j is represented,
Figure GDA00040092243700000610
the summation operation for model i from 1 to r.
The expression of the mixing probability from model i to model j is:
Figure GDA0004009224370000071
wherein, mu ij (k-1; k-1) denotes the probability of mixture from model i to model j.
The hybrid state estimate is derived from the expression of model j:
Figure GDA0004009224370000072
wherein,
Figure GDA0004009224370000073
is a state estimate of the target, based on the status of the target>
Figure GDA0004009224370000074
Is the hybrid state estimate for model j.
Model probability mu of all filters in the last step j (k-1) and State estimation
Figure GDA0004009224370000075
Get covariance >>
Figure GDA0004009224370000076
The hybrid covariance estimate is derived from model j as:
Figure GDA0004009224370000077
where T represents the transpose of the matrix,
Figure GDA0004009224370000078
representing the initial state of the covariance of model j, device for combining or screening>
Figure GDA0004009224370000079
Representing the covariance of model i.
(V) establishing a distributed driving electric automobile model in the third step:
establishing a state equation and an observation equation of a mass center slip angle and a tire lateral force of the distributed driving electric automobile:
Figure GDA00040092243700000710
wherein,
Figure GDA00040092243700000711
is the first derivative of the state variable; f (-) is a vehicle model state equation; h (-) is the vehicle model observation equation; x (t) is a state variable; u (t) is an input variable; z (t) is an observed variable; w (t) and v (t) are zero-mean, uncorrelated white noise; />
x(t)＝(β,F yfq ,F yfp ,F yrq ,F yrp ) T
u(t)＝(δ,F xfq ,F xfp ,F xrq ,F xrp ,ω fq ,ω fp ,ω rq ,ω rp ) T
z(t)＝(a x ,a y ,ω z ,ω x ) T
Wherein, F x 、F y Respectively representing the longitudinal force and the transverse force of four wheels of the vehicle; alpha, delta and beta respectively represent a tire slip angle, a front wheel corner and a centroid slip angle; omega z 、ω x 、ω ij Respectively representing the yaw angular velocity, the vehicle roll angle velocity and the wheel rotating speed of the vehicle; a is x 、a y Respectively representing the longitudinal acceleration and the lateral acceleration of the vehicle; subscripts i = f, r respectively denote a vehicle front axle and a vehicle rear axle, subscripts j = q, p respectively denote a vehicle left wheel and a vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively denote a vehicle left front wheel, a right front wheel, a left rear wheel, and a right rear wheel.
Establishing a vehicle model state equation f (-) and an observation equation h (-) by:
the functional expression f (-) is:
Figure GDA0004009224370000081
the functional expression h (-) is
Figure GDA0004009224370000082
Wherein f is 1 -f 5 Respectively representing the state equations of the vehicle model; h is 1 -h 4 Respectively representing vehicle model observation equations; f x 、F y Respectively representing the longitudinal force and the transverse force of four wheels of the vehicle; alpha, delta and beta respectively represent a tire slip angle, a front wheel rotation angle and a mass center slip angle; λ represents a tire slip ratio; subscripts i = f, r respectively denote a vehicle front axle and a vehicle rear axle, subscripts j = q, p respectively denote a vehicle left wheel and a vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively denote a vehicle left front wheel, a right front wheel, a left rear wheel, and a right rear wheel; m, m s Respectively representing the total mass of the vehicle and the sprung mass of the vehicle; omega z 、ω x Respectively representing the vehicle yaw angular velocity and the vehicle side slip angular velocity; g represents the gravitational acceleration; phi represents a roll angle; h denotes a vehicleThe center of mass of the sprung portion is at a perpendicular distance from the roll axis.
(VI) estimating the centroid side deflection angle and the tire side force of the vehicle based on an interactive multi-model algorithm-volume Kalman filtering, wherein the volume Kalman filtering process comprises the following steps:
discretizing a state equation and an observation equation of a mass center slip angle and a tire lateral force of the distributed driving electric automobile:
Figure GDA0004009224370000091
wherein x is k ∈R n Is a state vector of the system, R n Is an n-dimensional real number set; u. of k ∈R m For known control inputs, R m Is a m-dimensional real number set; z is a radical of formula k ∈R p Is the observation vector of the system, R p Is a p-dimensional real number set; function f R n ×R m →R n And h is R n ×R m →R p Respectively known nonlinear functions, and the arrow is a nonlinear mapping relation; w is a k And v k Respectively, the process noise and the observed measurement noise of the system;
initialization:
Figure GDA0004009224370000092
Figure GDA0004009224370000093
Figure GDA0004009224370000094
wherein,
Figure GDA0004009224370000095
and P 0 Is the initial system state and error covariance; />
Figure GDA0004009224370000096
And &>
Figure GDA0004009224370000097
The mean and variance of the initial noise of the system process; />
Figure GDA0004009224370000098
And &>
Figure GDA0004009224370000099
Initially measuring a noise mean and variance for a system process;
updating time:
will be provided with
Figure GDA00040092243700000910
As an initial state of the covariance of model j, <' >>
Figure GDA00040092243700000911
Initial state as a mixture state estimate for model j, both as P for volumetric Kalman filtering k-1|k-1 And &>
Figure GDA00040092243700000912
Initial input, factorization of error covariance matrix P k-1|k-1 ：
P k-1|k-1 ＝S k-1|k-1 S T k-1|k-1
Wherein S is k-1|k-1 Is a lower triangular matrix;
calculating volume points
Figure GDA00040092243700000913
Figure GDA00040092243700000914
Wherein,
Figure GDA00040092243700000915
k =2n, n being the dimension of the state to be estimated;
propagation volume point
Figure GDA00040092243700000916
Figure GDA0004009224370000101
State estimation
Figure GDA0004009224370000102
Expression:
Figure GDA0004009224370000103
error covariance matrix P xx,k|k-1 Expressed as:
Figure GDA0004009224370000104
/>
wherein Q is the system process noise variance;
updating measurement:
error covariance matrix P after factorization update k | k-1 ：
Figure GDA0004009224370000105
Wherein S is k|k-1 Is a lower triangular matrix;
updated volume points
Figure GDA0004009224370000106
Figure GDA0004009224370000107
Volume point of propagation
Figure GDA0004009224370000108
Figure GDA0004009224370000109
Observation of predicted values
Figure GDA00040092243700001010
Estimated as:
Figure GDA00040092243700001011
innovation variance matrix P zz,k|k-1 The expression is as follows:
Figure GDA00040092243700001012
estimating a covariance matrix P xz,k|k-1 The expression is as follows:
Figure GDA00040092243700001013
kalman gain W k Is expressed as
Figure GDA00040092243700001014
Status update
Figure GDA00040092243700001015
The expression is as follows:
Figure GDA0004009224370000111
error covariance P xx,k|k The expression is as follows:
Figure GDA0004009224370000112
(VII) estimating the mass center slip angle and the tire lateral force of the vehicle based on an interactive multi-model algorithm-volume Kalman filtering, wherein the process of updating the model probability is as follows:
updating the model probability:
and updating the model probability by adopting a likelihood function, wherein the likelihood function of the model j is as follows:
Figure GDA0004009224370000113
wherein v is j (k) Expressed as an innovation matrix, S j (k) The covariance matrix of the innovation is represented,
Figure GDA0004009224370000114
the inverse of the innovation covariance matrix, <' >>
Figure GDA0004009224370000115
As a transpose of the innovation matrix, Λ j (k) Representing the likelihood function of model j. />
The probability update for model j is:
Figure GDA0004009224370000116
wherein c represents a normalization constant, and
Figure GDA0004009224370000117
Λ j (k) A likelihood function representing model j, <' >>
Figure GDA0004009224370000118
Represents the prediction probability, μ, of model j j (k) Probability of model j.
(VIII) estimating the centroid slip angle and the tire lateral force of the vehicle based on an interactive multi-model algorithm-volume Kalman filtering, wherein the output interactive process comprises the following steps:
and (4) outputting interaction:
based on the model probability, the estimation results of all the filters are weighted and summed, and finally, the state estimation is calculated
Figure GDA0004009224370000119
The following can be obtained:
Figure GDA00040092243700001110
wherein, mu j (k) The probability of the model j is determined,
Figure GDA00040092243700001111
based on the result of the state estimation of the volume Kalman>
Figure GDA00040092243700001112
Is the final state estimation result;
based on the model probabilities, the estimation results of all filters are weighted and summed, and finally the covariance estimation P (k | k) is calculated:
Figure GDA0004009224370000121
wherein, mu j (k) The probability of the model j is determined,
Figure GDA0004009224370000122
as a result of the state estimation of the volumetric Kalman, P j (k | k) is the volume Kalman like covariance estimate, P (k | k) is the final covariance estimate, and->
Figure GDA0004009224370000123
Is the final state estimation result.
Compared with the prior art, the invention has the following technical advantages:
the method estimates the vehicle centroid side deviation angle and the tire side force in real time based on the interactive multi-model algorithm-volume Kalman filtering, aims at the uncertainty of nonlinear and non-established dynamic models, and leads to vehicle state parameter estimation errors due to inaccurate modeling, can perform weighted calculation on the estimation results of two different vehicle road system models, and fully utilizes the estimation results of the different vehicle road system models under different working conditions, so that the problem of inaccurate estimation results due to inaccurate non-linear dynamic model establishment is greatly reduced, the Kalman filtering reaches three-order approximation, and the estimation accuracy of the vehicle centroid side deviation angle and the tire side force is improved.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention for estimating the vehicle center of mass cornering angle and tire cornering power;
FIG. 2 is a diagram of a dynamic model of an embodiment of the present invention in view of chassis roll;
FIG. 3 is a diagram of a dynamic model of the overall structure of a vehicle according to an embodiment of the present invention;
FIG. 4 is a diagram of a dynamic model that considers the occurrence of yaw during vehicle travel according to an embodiment of the present invention;
FIG. 5 is a diagram of an interactive multi-model-volumetric Kalman algorithm filtering process employed by an embodiment of the present invention.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic views illustrating only the basic structure of the present invention in a schematic manner, and thus show only the constitution related to the present invention.
The method for estimating the centroid slip angle and the tire lateral force of the distributed driving electric automobile comprises the following steps as shown in the figure:
step one, establishing an eight-degree-of-freedom whole vehicle dynamics model of a vehicle, as shown in figures 2-4;
considering longitudinal motion, transverse motion, yaw motion, roll motion and motion of four tires of a vehicle under a complex working condition, and establishing a vehicle dynamic model;
the eight-degree-of-freedom vehicle dynamics equation is established as follows:
Figure GDA0004009224370000124
Figure GDA0004009224370000125
Figure GDA0004009224370000131
Figure GDA0004009224370000132
Figure GDA0004009224370000133
Figure GDA0004009224370000134
wherein, the expressions (1) and (2) are respectively longitudinal and transverse motion equations of the vehicle body of the vehicle, the expressions (3) and (4) are respectively longitudinal and transverse motion equations of the whole vehicle, and the expressions (5) and (6) are respectively transverse and side-rolling motion equations of the whole vehicle; m, m s Respectively representing the total mass of the vehicle and the sprung mass of the vehicle; i is zz 、I xz 、I xxs 、I xzs Respectively representing the yaw moment of the vehicle, the product of the moment of inertia of the vehicle mass around the x and z axes, the yaw moment of the vehicle sprung mass and the product of the moment of inertia of the vehicle sprung mass around the x and z axes; v x 、V y 、ω z 、ω x Respectively representing a vehicle longitudinal speed, a vehicle lateral speed, a vehicle yaw rate and a vehicle yaw rate; beta, delta and phi respectively represent a vehicle mass center slip angle, a front wheel rotating angle and a vehicle slip angle; f x 、F y Respectively represent longitudinal force and lateral force of four wheels of the vehicle(ii) a Subscripts i = f, r respectively denote a vehicle front axle and a vehicle rear axle, subscripts j = q, p respectively denote a vehicle left wheel and a vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively denote a vehicle left front wheel, a right front wheel, a left rear wheel, and a right rear wheel; h represents the vertical distance from the center of mass of the sprung part of the vehicle to the roll axis; m z 、M x Respectively showing yaw moment and roll moment; b f 、B r Respectively showing the width of the front and the rear vehicle rails of the vehicle; l is f 、L r Respectively representing the front and rear wheel base of the vehicle; g represents the acceleration of gravity; the upper symbol "·" represents the differentiation of the indicated quantity.
Step two, selecting a linear tire model and a nonlinear Dugoff tire model as a model set of an interactive multi-model algorithm
Establishing an expression of vertical load of each tire as follows:
Figure GDA0004009224370000141
Figure GDA0004009224370000142
Figure GDA0004009224370000143
Figure GDA0004009224370000144
wherein, F z Representing vehicle vertical forces; subscript i = f, r represents the vehicle front and rear axles, respectively, subscript j = q, p represents the vehicle left and right wheels, respectively, whereby subscripts fq, fp, rq, rp represent the vehicle left and right front wheels, respectively; m, m s 、m uf 、m ur Respectively representing the total mass of the vehicle, the sprung mass of the vehicle, and the front and rear unsprung masses of the vehicle; c φf 、C φr Respectively representing the front roll rigidity and the rear roll rigidity of the vehicle; k φf 、K φr Respectively representing the front roll damping coefficient and the rear roll damping coefficient of the vehicle; v x 、V y 、ω z 、ω x Respectively representing a vehicle longitudinal speed, a vehicle lateral speed, a vehicle yaw rate and a vehicle yaw rate; g represents the gravitational acceleration; h is cg 、h uf 、h ur Respectively representing the mass center of the vehicle and the heights of the front and rear wheel side eccentric centers from the ground; respectively representing the front and rear roll center heights of the vehicle; b is f 、B r Respectively showing the front and rear rail widths of the vehicle; l is f 、L r Respectively representing the front and rear wheel base of the vehicle; phi represents a roll angle; the upper symbol "·" denotes the differentiation of the quantity indicated.
The tire slip ratio expression is:
Figure GDA0004009224370000145
wherein λ represents a tire slip ratio; v x 、ω ij Respectively representing the vehicle longitudinal speed and the tire yaw rate; subscripts i = f, r respectively denote a vehicle front axle and a vehicle rear axle, subscripts j = q, p respectively denote a vehicle left wheel and a vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively denote a vehicle left front wheel, a right front wheel, a left rear wheel, and a right rear wheel; r e Is the effective radius of the tire.
(II) selecting a linear tire model and a nonlinear Dugoff tire model as a model set of an interactive multi-model algorithm;
the linear tire model is as follows:
the linear tire model slip angle expression is:
Figure GDA0004009224370000151
/>
wherein α and δ respectively represent a tire slip angle and a front wheel rotation angle; v x 、V y 、ω z Respectively representing a vehicle longitudinal speed, a vehicle lateral speed and a vehicle yaw rate; b is f 、B r Respectively showing the front and rear rail widths of the vehicle; l is f 、L r Respectively representing the front and rear wheel base of the vehicle; phi represents a roll angle; epsilon f 、ε r Respectively representing the side tilting rotation coefficients of the front shaft and the rear shaft; subscripts i = f, r respectively denote a vehicle front axle and a vehicle rear axle, subscripts j = q, p respectively denote a vehicle left wheel and a vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively denote a vehicle left front wheel, a right front wheel, a left rear wheel, and a right rear wheel.
The linear tire longitudinal and lateral force expressions are:
F yij ＝-C yij α ij
F xij ＝k μ λ ij F zij
wherein, F x 、F y Respectively representing the longitudinal force and the transverse force of four wheels of the vehicle; alpha and lambda respectively represent a tire slip angle and a slip ratio; c y 、k μ Indicating the cornering stiffness and the linear region mu-lambda of the tyre ij An image slope; subscripts i = f, r respectively denote a vehicle front axle and a vehicle rear axle, subscripts j = q, p respectively denote a vehicle left wheel and a vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively denote a vehicle left front wheel, a right front wheel, a left rear wheel, and a right rear wheel.
The non-linear Dugoff tire model is as follows:
the nonlinear tire model slip angle expression is as follows:
Figure GDA0004009224370000161
wherein, alpha and delta represent a tire slip angle and a front wheel rotation angle; v x 、V y 、ω z Respectively representing a vehicle longitudinal speed, a vehicle transverse speed and a vehicle yaw rate; b is f 、B r Respectively showing the width of the front and the rear vehicle rails of the vehicle; l is f 、L r Respectively representing the front and rear wheel base of the vehicle; phi represents a roll angle; subscripts i = f, r respectively denote a vehicle front axle and a vehicle rear axle, subscripts j = q, p respectively denote a vehicle left wheel and a vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively denote a vehicle left front wheel, a right front wheel, a left rear wheel, and a right rear wheel.
The non-linear Dugoff tire longitudinal and lateral force expressions are:
Figure GDA0004009224370000162
Figure GDA0004009224370000163
Figure GDA0004009224370000164
Figure GDA0004009224370000165
wherein, F x 、F y Respectively representing the longitudinal force and the transverse force of four wheels of the vehicle; alpha and lambda represent the slip angle and slip ratio of the tire; c y Representing the tire cornering stiffness; s is the substitution amount of the function; subscript i = f, r represents the vehicle front and rear axles, respectively, subscript j = q, p represents the vehicle left and right wheels, respectively, whereby subscripts fq, fp, rq, rp represent the vehicle left and right front, rear, and rear wheels, respectively.
Estimating the mass center and the side deflection angle of the vehicle and the tire side force based on an interactive multi-model algorithm-volume Kalman filtering, wherein the algorithm process comprises the following steps: input interaction, volumetric kalman filtering, update model probability, and output interaction, as shown in fig. 5;
the input interaction process is as follows:
the model probability mu of the model j in the previous step j (k-1) and State estimation
Figure GDA0004009224370000171
Gets a mixed estimate->
Figure GDA0004009224370000172
Assuming that the linear tire model and the Dugoff nonlinear tire model are models i, j =1,2, respectively, the transfer matrix is therefore:
Figure GDA0004009224370000173
wherein P is a transition matrix, P in the transition matrix ij The element is the motion transition probability of the target from the ith model to the jth model, the subscript r = j of the element in the transition matrix P, and r is the number of model set models.
The prediction model is derived from the expression of model j:
Figure GDA0004009224370000174
wherein, mu j (k-1) represents the model probability of model j at time k-1 of the previous step,
Figure GDA0004009224370000175
the prediction probability of the model j is represented,
Figure GDA0004009224370000176
the summation operation for model i from 1 to r.
The expression of the mixing probability from model i to model j is:
Figure GDA0004009224370000177
wherein, mu ij (k-1; k-1) represents the mixing probability from model i to model j.
The hybrid state estimate is derived from the expression of model j:
Figure GDA0004009224370000178
wherein,
Figure GDA0004009224370000179
is a state estimate of the target, based on the status of the target>
Figure GDA00040092243700001710
Is a hybrid state estimate of model j.
Model probability mu of all filters in the last step j (k-1) and State estimation
Figure GDA00040092243700001711
Get the covariance->
Figure GDA00040092243700001712
The hybrid covariance estimate is derived from model j as:
Figure GDA00040092243700001713
where T represents the transpose of the matrix,
Figure GDA0004009224370000181
representing the initial state of the covariance of model j, device for combining or screening>
Figure GDA0004009224370000182
Representing the covariance of model i.
(II) establishing distributed driving electric automobile model
Establishing a state equation and an observation equation of a mass center slip angle and a tire lateral force of the distributed driving electric automobile:
Figure GDA0004009224370000183
wherein,
Figure GDA0004009224370000184
is the first derivative of the state variable; f (-) is the vehicle model equation of state; h (-) is the vehicle model observation equation; x (t) is a state variable; u (t) is an input variable; z (t) isMeasuring a variable; w (t) and v (t) are zero-mean, uncorrelated white noise;
x(t)＝(β,F yfq ,F yfp ,F yrq ,F yrp ) T
u(t)＝(δ,F xfq ,F xfp ,F xrq ,F xrp ,ω fq ,ω fp ,ω rq ,ω rp ) T
z(t)＝(a x ,a y ,ω z ,ω x ) T
wherein, F x 、F y Respectively representing the longitudinal force and the transverse force of four wheels of the vehicle; alpha, delta and beta respectively represent a tire slip angle, a front wheel corner and a centroid slip angle; omega z 、ω x 、ω ij Respectively representing the yaw angular velocity, the vehicle roll angle velocity and the wheel rotating speed of the vehicle; a is x 、a y Respectively representing the longitudinal acceleration and the lateral acceleration of the vehicle; subscripts i = f, r respectively denote a vehicle front axle and a vehicle rear axle, subscripts j = q, p respectively denote a vehicle left wheel and a vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively denote a vehicle left front wheel, a right front wheel, a left rear wheel, and a right rear wheel.
Establishing a vehicle model state equation f (-) and an observation equation h (-) by:
the functional expression f (-) is:
Figure GDA0004009224370000185
the functional expression h (-) is:
Figure GDA0004009224370000191
wherein, f 1 -f 5 Respectively representing the state equations of the vehicle model; h is 1 -h 4 Respectively representing vehicle model observation equations; f x 、F y Respectively representing the longitudinal force and the transverse force of four wheels of the vehicle; alpha, delta and beta respectively represent a tire slip angle, a front wheel corner and a centroid slip angle; λ represents a tire slip ratio; lower partThe index i = f, r denotes the vehicle front axle and the vehicle rear axle, respectively, the index j = q, p denotes the vehicle left wheel and the vehicle right wheel, respectively, whereby the indices fq, fp, rq, rp denote the vehicle left front wheel, right front wheel, left rear wheel and right rear wheel, respectively; m, m s Respectively representing the total mass of the vehicle and the sprung mass of the vehicle; omega z 、ω x Respectively representing the vehicle yaw angular velocity and the vehicle side slip angular velocity; g represents the gravitational acceleration; phi represents a roll angle; h represents the vertical distance from the center of mass of the sprung portion of the vehicle to the roll axis.
(III) the process of the volume Kalman filtering is as follows:
discretizing a state equation and an observation equation of a mass center slip angle and a tire lateral force of the distributed driving electric automobile:
Figure GDA0004009224370000192
wherein x is k ∈R n Is a state vector of the system, R n Is an n-dimensional real number set; u. u k ∈R m For known control inputs, R m Is a m-dimensional real number set; z is a radical of k ∈R p Is the observation vector of the system, R p Is a p-dimensional real number set; function f R n ×R m →R n And h is R n ×R m →R p Respectively known nonlinear functions, and the arrow is a nonlinear mapping relation; w is a k And v k Respectively, the process noise and the observed measurement noise of the system;
initialization:
Figure GDA0004009224370000193
Figure GDA0004009224370000194
Figure GDA0004009224370000195
wherein,
Figure GDA0004009224370000196
and P 0 Is the initial system state and error covariance; />
Figure GDA0004009224370000197
And &>
Figure GDA0004009224370000198
The mean and variance of the initial noise of the system process; />
Figure GDA0004009224370000199
And &>
Figure GDA00040092243700001910
Initially measuring a noise mean and variance for a system process;
updating time:
will be provided with
Figure GDA0004009224370000201
As an initial state of the covariance of model j, <' >>
Figure GDA0004009224370000202
Initial state as a mixture state estimate for model j, both as P for volumetric Kalman filtering k-1|k-1 And &>
Figure GDA0004009224370000203
Initial input, factorized error covariance matrix P k-1|k-1 ：
P k-1|k-1 ＝S k-1|k-1 S T k-1|k-1
Wherein S is k-1k-1 Is a lower triangular matrix;
calculating volume points
Figure GDA0004009224370000204
Figure GDA0004009224370000205
Wherein,
Figure GDA0004009224370000206
k =2n, n being the dimension of the state to be estimated;
propagation volume point
Figure GDA0004009224370000207
Figure GDA0004009224370000208
State estimation
Figure GDA0004009224370000209
Expression: />
Figure GDA00040092243700002010
Error covariance matrix P xx,k|k-1 Expressed as:
Figure GDA00040092243700002011
wherein Q is the system process noise variance;
updating measurement:
error covariance matrix P after factorization update k|k-1 ：
Figure GDA00040092243700002012
Wherein S is k|k-1 Is a lower triangular matrix;
updated volume points
Figure GDA00040092243700002013
Figure GDA00040092243700002014
Volume point of propagation
Figure GDA00040092243700002015
Figure GDA00040092243700002016
Observation of predicted values
Figure GDA00040092243700002017
Estimated as:
Figure GDA0004009224370000211
innovation variance matrix P zz,k|k-1 The expression is as follows:
Figure GDA0004009224370000212
estimating a covariance matrix P xz,kk-1 The expression is as follows:
Figure GDA0004009224370000213
kalman gain W k Is expressed as
Figure GDA0004009224370000214
Status update
Figure GDA0004009224370000215
The expression is as follows:
Figure GDA0004009224370000216
error covariance P xx,k|k The expression is as follows:
Figure GDA0004009224370000217
(IV) the process of updating the model probabilities is as follows:
updating the model probability:
and updating the model probability by adopting a likelihood function, wherein the likelihood function of the model j is as follows:
Figure GDA0004009224370000218
wherein v is j (k) Expressed as an innovation matrix, S j (k) The covariance matrix of the innovation is represented,
Figure GDA0004009224370000219
the inverse of the innovation covariance matrix, <' >>
Figure GDA00040092243700002110
As a transpose of the innovation matrix, Λ j (k) Representing the likelihood function of model j.
The probability update for model j is:
Figure GDA00040092243700002111
wherein c represents a normalization constant, and
Figure GDA00040092243700002112
Λ j (k) A likelihood function representing model j, <' >>
Figure GDA00040092243700002113
Represents the prediction probability, μ, of model j j (k) Probability of model j.
(V) the process of output interaction is as follows:
and (4) outputting interaction:
based on the model probability, the estimation results of all the filters are weighted and summed, and finally, the state estimation is calculated
Figure GDA0004009224370000221
The following can be obtained:
Figure GDA0004009224370000222
wherein, mu j (k) The probability of the model j is determined,
Figure GDA0004009224370000223
based on the result of the state estimation of the volume Kalman>
Figure GDA0004009224370000224
Is the final state estimation result;
based on the model probabilities, the estimation results of all filters are weighted and summed, and finally the covariance estimation P (k | k) is calculated:
Figure GDA0004009224370000225
wherein, mu j (k) The probability of the model j is determined,
Figure GDA0004009224370000226
as a result of the state estimation of the volumetric Kalman, P j (k | k) is the volume Kalman like covariance estimate, and P (k | k) is the final covariance estimate, based on>
Figure GDA0004009224370000227
Is the final state estimation result. />

Claims (7)

1. The method for estimating the centroid slip angle and the tire lateral force of the distributed driving electric automobile is characterized by comprising the following steps of:
establishing an eight-degree-of-freedom vehicle dynamic equation, which comprises longitudinal motion, transverse motion, yaw motion, roll motion and motion of four tires;
selecting a linear tire model and a nonlinear Dugoff tire model as a model set of an interactive multi-model algorithm;
estimating the mass center slip angle of the vehicle and the tire lateral force based on an interactive multi-model algorithm-volume Kalman filtering;
establishing an eight-degree-of-freedom vehicle dynamics equation comprising longitudinal motion, transverse motion, yaw motion, side-tipping motion and motion of four tires to obtain a vehicle dynamics model;
the eight-degree-of-freedom vehicle dynamics equation is established as follows:
Figure FDA0004009224360000011
Figure FDA0004009224360000012
Figure FDA0004009224360000013
Figure FDA0004009224360000014
Figure FDA0004009224360000015
Figure FDA0004009224360000016
wherein, the expressions (1) and (2) are respectively longitudinal and transverse motion equations of the vehicle body of the vehicle, the expressions (3) and (4) are respectively longitudinal and transverse motion equations of the whole vehicle, and the expressions (5) and (6) are respectively transverse and side-rolling motion equations of the whole vehicle; m, m s Respectively representing the total mass of the vehicle and the sprung mass of the vehicle; i is zz 、I xz 、I xxs 、I xzs Respectively representing the yaw moment of the vehicle, the product of the moment of inertia of the mass of the vehicle around the x and z axes, the yaw moment of the sprung mass of the vehicle and the product of the moment of inertia of the sprung mass of the vehicle around the x and z axes; v x 、V y 、ω z 、ω x Respectively representing a vehicle longitudinal speed, a vehicle lateral speed, a vehicle yaw rate and a vehicle yaw rate; beta, delta and phi respectively represent a vehicle mass center slip angle, a front wheel rotating angle and a vehicle slip angle; f x 、F y Respectively representing longitudinal force and lateral force of four wheels of the vehicle; subscripts i = f, r respectively denote a vehicle front axle and a vehicle rear axle, subscripts j = q, p respectively denote a vehicle left wheel and a vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively denote a vehicle left front wheel, a right front wheel, a left rear wheel, and a right rear wheel; h represents the vertical distance from the center of mass of the sprung part of the vehicle to the roll axis; m z 、M x Respectively showing yaw moment and roll moment; b is f 、B r Respectively showing the front and rear rail widths of the vehicle; l is f 、L r Respectively representing the front and rear wheel base of the vehicle; g represents the gravitational acceleration; the upper symbol "·" denotes the differentiation of the quantity indicated;
establishing an expression of each tire vertical load as follows:
Figure FDA0004009224360000021
Figure FDA0004009224360000022
Figure FDA0004009224360000023
Figure FDA0004009224360000024
wherein, F z Representing vehicle vertical forces; subscripts i = f, r respectively denote a vehicle front axle and a vehicle rear axle, subscripts j = q, p respectively denote a vehicle left wheel and a vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively denote a vehicle left front wheel, a right front wheel, a left rear wheel, and a right rear wheel; m, m s 、m uf 、m ur Respectively representing the total mass of the vehicle, the sprung mass of the vehicle, and the front and rear unsprung masses of the vehicle; c φf 、C φr Respectively representing the front and rear roll stiffness of the vehicle; k φf 、K φr Respectively representing the front roll damping coefficient and the rear roll damping coefficient of the vehicle; v x 、V y 、ω z 、ω x Respectively representing a vehicle longitudinal speed, a vehicle lateral speed, a vehicle yaw rate and a vehicle yaw rate; g represents the gravitational acceleration; h is cg 、h uf 、h ur Respectively representing the mass center of the vehicle and the heights of the front and rear wheel side eccentric centers from the ground; respectively representing the front and rear roll center heights of the vehicle; b is f 、B r Respectively showing the width of the front and the rear vehicle rails of the vehicle; l is a radical of an alcohol f 、L r Respectively representing the front and rear wheel base of the vehicle; phi represents a roll angle; the upper mark "·" represents the differentiation of the quantity indicated;
the tire slip ratio expression is:
Figure FDA0004009224360000031
wherein λ represents a tire slip ratio; v x 、ω ij Respectively representing the vehicle longitudinal speed and the tire yaw rate; the subscripts i = f, r respectively denote the vehicle front axle and the vehicle rear axle, the subscripts j = q, p respectively denote the vehicle left wheel and the vehicle right wheel, whereby the subscripts fq, fp, rq, rp respectively denote the vehicleA left front wheel, a right front wheel, a left rear wheel and a right rear wheel; r e Is the effective radius of the tire.
2. The method for estimating the centroid slip angle and the tire lateral force of the distributed drive electric vehicle according to claim 1, wherein in the second step, a linear tire model and a nonlinear Dugoff tire model are selected as a model set of an interactive multi-model algorithm, and the method comprises the following steps:
the linear tire model is:
the linear tire model slip angle expression is:
Figure FDA0004009224360000032
wherein, alpha and delta respectively represent a tire slip angle and a front wheel rotation angle; v x 、V y 、ω z Respectively representing a vehicle longitudinal speed, a vehicle transverse speed and a vehicle yaw rate; b f 、B r Respectively showing the front and rear rail widths of the vehicle; l is f 、L r Respectively representing the front and rear wheel base of the vehicle; phi represents a roll angle; epsilon f 、ε r Respectively representing the side tilting rotation coefficients of the front shaft and the rear shaft; subscript i = f, r represents the vehicle front and rear axles, respectively, subscript j = q, p represents the vehicle left and right wheels, respectively, whereby subscripts fq, fp, rq, rp represent the vehicle left and right front wheels, respectively;
the linear tire longitudinal and lateral force expressions are:
F yij ＝-C yij α ij
F xij ＝k μ λ ij F zij
wherein, F x 、F y Respectively representing the longitudinal force and the transverse force of four wheels of the vehicle; alpha and lambda respectively represent a tire slip angle and a slip ratio; c y 、k μ Indicating the cornering stiffness and the linear region mu-lambda of the tyre ij An image slope; subscripts i = f, r respectively denote the vehicle front axle and the vehicle rear axle, and subscripts j = q, p respectively denote the vehicle left wheel and the vehicleA right vehicle wheel whereby the subscripts fq, fp, rq, rp denote the vehicle's left front wheel, right front wheel, left rear wheel, and right rear wheel, respectively;
the nonlinear Dugoff tire model is:
the nonlinear tire model slip angle expression is as follows:
Figure FDA0004009224360000041
wherein α and δ represent a tire slip angle and a front wheel rotation angle; v x 、V y 、ω z Respectively representing a vehicle longitudinal speed, a vehicle lateral speed and a vehicle yaw rate; b is f 、B r Respectively showing the front and rear rail widths of the vehicle; l is a radical of an alcohol f 、L r Respectively representing the front and rear wheel base of the vehicle; phi represents a roll angle; subscripts i = f, r respectively denote a vehicle front axle and a vehicle rear axle, subscripts j = q, p respectively denote a vehicle left wheel and a vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively denote a vehicle left front wheel, a right front wheel, a left rear wheel, and a right rear wheel;
the non-linear Dugoff tire longitudinal and lateral force expressions are:
Figure FDA0004009224360000042
/>
Figure FDA0004009224360000043
Figure FDA0004009224360000044
Figure FDA0004009224360000045
wherein, F x 、F y Respectively showing the longitudinal direction of four wheels of the vehicleA lateral force, a transverse force; alpha and lambda represent the slip angle and slip ratio of the tire; c y Representing the tire cornering stiffness; s is the substitution amount of the function; subscripts i = f, r respectively denote a vehicle front axle and a vehicle rear axle, subscripts j = q, p respectively denote a vehicle left wheel and a vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively denote a vehicle left front wheel, a right front wheel, a left rear wheel, and a right rear wheel.
3. The method for estimating the centroid slip angle and the tire lateral force of the distributed-drive electric vehicle according to claim 1, wherein in the third step, the centroid slip angle and the tire lateral force of the vehicle are estimated based on an interactive multi-model algorithm-volumetric Kalman filtering, and the input interaction process is as follows:
inputting interaction, and comparing the model probability mu of the model j in the previous step j (k-1) and State estimation
Figure FDA0004009224360000051
Obtaining a mixture estimate
Figure FDA0004009224360000052
Assuming that the linear tire model and the Dugoff nonlinear tire model are models i, j =1,2, respectively, the transfer matrix is therefore:
Figure FDA0004009224360000053
wherein P is a transition matrix, and P in the transition matrix ij The element is the motion transfer probability of the target from the ith model to the jth model, the subscript r = j of the element in the transfer matrix P, and r is the number of model set models;
the prediction model is derived from the expression of model j:
Figure FDA0004009224360000054
wherein, mu j (k-1) tableShowing the model probability of model j at time k-1 of the previous step,
Figure FDA0004009224360000055
represents the predicted probability of model j, <' > is>
Figure FDA0004009224360000056
Summing operation from 1 to r for model i;
the expression of the mixing probability from model i to model j is:
Figure FDA0004009224360000057
wherein, mu ij (k-1; k-1) represents the probability of mixture from model i to model j;
the hybrid state estimate is derived from the expression of model j:
Figure FDA0004009224360000061
wherein,
Figure FDA0004009224360000062
is a state estimate of the target, based on the status of the target>
Figure FDA0004009224360000063
A hybrid state estimate for model j; />
Model probability mu of all filters in the last step j (k-1) and state estimation
Figure FDA0004009224360000064
Get covariance >>
Figure FDA0004009224360000065
The hybrid covariance estimate is derived from model j as:
Figure FDA0004009224360000066
where T represents the transpose of the matrix,
Figure FDA0004009224360000067
represents an initial state of covariance of model j, <' >>
Figure FDA0004009224360000068
Representing the covariance of model i.
4. The method for estimating the centroid slip angle and the tire side force of the distributed-drive electric vehicle as claimed in claim 1, wherein the vehicle model of the distributed-drive electric vehicle is established as follows:
establishing a state equation and an observation equation of a mass center slip angle and a tire lateral force of the distributed driving electric automobile:
Figure FDA0004009224360000069
wherein,
Figure FDA00040092243600000610
is the first derivative of the state variable; f (-) is a vehicle model state equation; h (-) is the vehicle model observation equation; x (t) is a state variable; u (t) is an input variable; z (t) is an observed variable; w (t) and v (t) are zero-mean, uncorrelated white noise;
x(t)＝(β,F yfq ,F yfp ,F yrq ,F yrp ) T
u(t)＝(δ,F xfq ,F xfp ,F xrq ,F xrp ,ω fq ,ω fp ,ω rq ,ω rp ) T
z(t)＝(a x ,a y ,ω z ,ω x ) T
wherein, F x 、F y Respectively representing the longitudinal force and the transverse force of four wheels of the vehicle; alpha, delta and beta respectively represent a tire slip angle, a front wheel corner and a centroid slip angle; omega z 、ω x 、ω ij Respectively representing the yaw angular velocity, the vehicle roll angle velocity and the wheel rotating speed of the vehicle; a is x 、a y Respectively representing the longitudinal acceleration and the lateral acceleration of the vehicle; subscripts i = f, r respectively denote a vehicle front axle and a vehicle rear axle, subscripts j = q, p respectively denote a vehicle left wheel and a vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively denote a vehicle left front wheel, a right front wheel, a left rear wheel, and a right rear wheel;
establishing a vehicle model state equation f (-) and an observation equation h (-) by:
the functional expression f (-) is
Figure FDA0004009224360000071
The functional expression h (-) is
Figure FDA0004009224360000072
Wherein f is 1 -f 5 Respectively representing the state equations of the vehicle model; h is 1 -h 4 Respectively representing vehicle model observation equations; f x 、F y Respectively representing the longitudinal force and the transverse force of four wheels of the vehicle; alpha, delta and beta respectively represent a tire slip angle, a front wheel corner and a centroid slip angle; λ represents a tire slip ratio; subscripts i = f, r respectively denote a vehicle front axle and a vehicle rear axle, subscripts j = q, p respectively denote a vehicle left wheel and a vehicle right wheel, whereby subscripts fq, fp, rq, rp respectively denote a vehicle left front wheel, a right front wheel, a left rear wheel, and a right rear wheel; m, m s Respectively representing the total mass of the vehicle and the sprung mass of the vehicle; omega z 、ω x Respectively representing the vehicle yaw angular velocity and the vehicle side slip angular velocity; g represents the gravitational acceleration; phi represents a roll angle; h represents the vertical distance from the center of mass of the sprung portion of the vehicle to the roll axis.
5. The method for estimating the centroid slip angle and the tire lateral force of the distributed-drive electric vehicle according to claim 4, wherein in the third step, the centroid slip angle and the tire lateral force of the vehicle are estimated based on an interactive multi-model algorithm-volume Kalman filtering, and the volume Kalman filtering comprises the following processes:
discretizing the established state equation and observation equation:
Figure FDA0004009224360000073
wherein x is k ∈R n Is a state vector of the system, R n Is an n-dimensional real number set; u. of k ∈R m For known control inputs, R m Is an m-dimensional real number set; z is a radical of formula k ∈R p Is the observation vector of the system, R p Is a p-dimensional real number set; function f R n ×R m →R n And h is R n ×R m →R p Respectively known nonlinear functions, and the arrow is a nonlinear mapping relation; w is a k And v k Respectively, process noise and observed measurement noise of the system;
initialization, and enabling:
Figure FDA0004009224360000081
Figure FDA0004009224360000082
Figure FDA0004009224360000083
wherein,
Figure FDA0004009224360000084
and P 0 Is the initial system state and error covariance; />
Figure FDA0004009224360000085
And &>
Figure FDA0004009224360000086
The mean and variance of the initial noise of the system process;
Figure FDA0004009224360000087
and &>
Figure FDA0004009224360000088
Initially measuring a noise mean and variance for a system process;
updating time:
will be provided with
Figure FDA0004009224360000089
As an initial state of the covariance of model j, <' >>
Figure FDA00040092243600000810
Initial state as a mixture state estimate for model j, both as P for volumetric Kalman filtering k-1|k-1 And &>
Figure FDA00040092243600000811
Initial input, factorized error covariance matrix P k-1|k-1 ：
P k-1|k-1 ＝S k-1|k-1 S T k-1|k-1
Wherein S is k-1|k-1 Is a lower triangular matrix;
calculating volume points
Figure FDA00040092243600000812
/>
Figure FDA00040092243600000813
Wherein,
Figure FDA00040092243600000814
k =2n, n being the dimension of the state to be estimated;
propagation volume point
Figure FDA00040092243600000815
Figure FDA00040092243600000816
State estimation
Figure FDA00040092243600000817
Expression:
Figure FDA00040092243600000818
error covariance matrix P xx,k|k-1 Expressed as:
Figure FDA0004009224360000091
wherein Q is the system process noise variance;
updating measurement:
error covariance matrix P after factorization update k|k-1 ：
Figure FDA0004009224360000092
Wherein S is k|k-1 Is a lower triangular matrix;
updated volume points
Figure FDA0004009224360000093
Figure FDA0004009224360000094
Volume point of propagation
Figure FDA0004009224360000095
Figure FDA0004009224360000096
Observation of predicted values
Figure FDA0004009224360000097
Estimated as:
Figure FDA0004009224360000098
innovation variance matrix P zz,k|k-1 The expression is as follows:
Figure FDA0004009224360000099
estimating a covariance matrix P xz,k|k-1 The expression is as follows:
Figure FDA00040092243600000910
kalman gain W k Is expressed as
Figure FDA00040092243600000911
/>
Status update
Figure FDA00040092243600000912
The expression is as follows:
Figure FDA00040092243600000913
error covariance P xx,k|k The expression is as follows:
Figure FDA00040092243600000914
6. the method for estimating the centroid slip angle and the tire lateral force of the distributed-drive electric vehicle according to claim 1, wherein in the third step, the centroid slip angle and the tire lateral force of the vehicle are estimated based on an interactive multi-model algorithm-volumetric kalman filter, and the process of updating the model probability is as follows:
updating the model probability:
updating the model probability by using a likelihood function, wherein the likelihood function of the model j is as follows:
Figure FDA0004009224360000101
wherein v is j (k) Expressed as an innovation matrix, S j (k) The covariance matrix of the innovation is represented,
Figure FDA0004009224360000102
the inverse of the innovation covariance matrix, <' >>
Figure FDA0004009224360000103
As a transpose of the innovation matrix, Λ j (k) A likelihood function representing model j;
the probability update for model j is:
Figure FDA0004009224360000104
wherein c represents a normalization constant, and
Figure FDA0004009224360000105
Λ j (k) A likelihood function representing model j, <' >>
Figure FDA0004009224360000106
Represents the prediction probability, μ, of model j j (k) Probability of model j.
7. The method for estimating the centroid slip angle and the tire lateral force of the distributed drive electric vehicle as claimed in claim 1, wherein in the third step, the centroid slip angle and the tire lateral force of the vehicle are estimated based on an interactive multi-model algorithm-volumetric kalman filter, and the output interaction process is as follows:
and (4) outputting interaction:
based on the model probability, the estimation results of all the filters are weighted and summed, and finally, the state estimation is calculated
Figure FDA0004009224360000107
The following can be obtained:
Figure FDA0004009224360000108
wherein, mu j (k) The probability of the model j is determined,
Figure FDA0004009224360000109
for the result of a state estimation of the volume Kalman>
Figure FDA00040092243600001010
Is the final state estimation result;
based on the model probabilities, the estimation results of all filters are weighted and summed, and finally the covariance estimation P (k | k) is calculated:
Figure FDA00040092243600001011
/>
wherein, mu j (k) The probability of the model j is determined,
Figure FDA0004009224360000111
as a result of the state estimation of the volumetric Kalman, P j (k | k) is the volume Kalman like covariance estimate, and P (k | k) is the final covariance estimate, based on>
Figure FDA0004009224360000112
Is the final state estimation result. />
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