CN111898207B - Centroid slip angle estimation method considering dynamic load and road adhesion coefficient - Google Patents

Centroid slip angle estimation method considering dynamic load and road adhesion coefficient Download PDF

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CN111898207B
CN111898207B CN202010763226.2A CN202010763226A CN111898207B CN 111898207 B CN111898207 B CN 111898207B CN 202010763226 A CN202010763226 A CN 202010763226A CN 111898207 B CN111898207 B CN 111898207B
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CN111898207A (en
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张茜
周洪亮
刘志远
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Harbin Institute of Technology
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Abstract

A centroid slip angle estimation method considering dynamic load and road adhesion coefficient relates to a vehicle centroid slip angle estimation method. Determining the segmentation interval and the segmentation number of the lateral force linear segmentation model; establishing a PWA relational expression of the front and rear axle wheel lateral force and the wheel slip angle under the nominal load and the adhesion coefficient equal to 1; establishing a PWA relational expression of the front and rear axle wheel lateral force and the wheel slip angle under the nominal load and the adhesion coefficient of less than 1; establishing a PWA relational expression of the front and rear axle wheel lateral force and the wheel slip angle under the condition that the dynamic load is considered and the adhesion coefficient is less than 1; establishing a switching lateral dynamics model; and converting the switching lateral dynamics model into a switching T-S fuzzy model, estimating the slip angles of the front wheel and the rear wheel, and calculating the estimated value of the centroid slip angle. A method for establishing a piecewise affine lateral dynamics model by adopting a piecewise linear modeling thought is provided, and the change of the vertical load of a tire and the road adhesion coefficient can be reflected in real time.

Description

Centroid slip angle estimation method considering dynamic load and road adhesion coefficient
Technical Field
The invention relates to a vehicle mass center slip angle estimation method, in particular to a mass center slip angle estimation method considering dynamic load and road adhesion coefficient, and belongs to the technical field of vehicle state estimation.
Background
The vehicle mass center slip angle is an important parameter for representing the vehicle stability performance and is used for judging the stable boundary of vehicle running and yaw stability control. At present, a centroid slip angle sensor is expensive and cannot be used as a vehicle-mounted sensor only for research of analysis, test and evaluation. In an actual vehicle, the centroid slip angle information is obtained through an estimation technology, and the centroid slip angle estimation relates to an estimator modeling and design technology. The modeling and estimator design of the slip angle estimation method based on the kinematic model are simpler, but the requirements on the accuracy and the installation position of a lateral acceleration sensor and a yaw rate sensor used in estimation are higher, and larger estimation errors are easily caused by accumulated errors caused by zero drift and long-time integration of the sensors. The estimation method based on the dynamic model is complex in modeling and estimator design, reduces the requirements on the sensor, has higher estimation accuracy, and is the main method adopted at present.
The key problem of the dynamic model estimation method is how to establish a lateral dynamic model, and an estimator is designed according to the lateral dynamic model, and the difficult point is that when the lateral dynamic model is established, if a simpler linear tire lateral force model is adopted, the design of the estimator can be simplified, but the problem of low centroid slip angle estimation precision is brought, and the requirement of the centroid slip angle estimation precision under the full-driving working condition of a vehicle cannot be met; on the contrary, if a complex nonlinear tire lateral force model is adopted, the modeling precision is favorably improved, but the estimator is complex in design, the calculation cost is increased, the estimator is difficult to use in an actual vehicle-mounted controller, and the requirement of real-time calculation is difficult to meet.
The piecewise linear technology is adopted to describe the tire lateral force nonlinearity, and the tire lateral force nonlinear model has high model precision and a simple model expression, so that the estimator is relatively simple in design, high in estimation precision and easy to calculate in real time. However, piecewise linear modeling of tire lateral force is based on determined tire lateral force-slip angle data, and tire lateral force is related to tire vertical load and road adhesion coefficient in addition to slip angle. This means that the piecewise linear model is built based on the determined tire lateral force-slip angle data under the determined tire vertical load and road adhesion coefficient, and the tire load changes when the vehicle is turning, and the road adhesion coefficient is different under the full driving condition. Therefore, although the use of piecewise linear techniques to describe tire lateral forces has many advantages, piecewise linear models built at determined tire vertical loads and road adhesion coefficients are practically unusable.
Disclosure of Invention
The invention aims to provide a centroid slip angle estimation method considering dynamic load and road adhesion coefficient, provides a method for establishing a piecewise affine lateral dynamics model by adopting a piecewise linear modeling thought, has concise expression, is convenient for estimator design, and can reflect the change of tire vertical load and road adhesion coefficient in real time.
In order to achieve the purpose, the invention adopts the following technical scheme: a centroid slip angle estimation method considering dynamic load and road adhesion coefficient comprises the following steps:
the method comprises the following steps: according to the coefficient of adhesion mu-1 and the nominal load Fzf,FzrDetermining the segmentation interval and the segmentation number of the lateral force linear segmentation model according to experimental data of the relationship between the lateral force and the slip angle or data obtained by a magic formula tire model, wherein the segmentation interval is Up,f(p ═ 0, ± (a +1), …, ± (a +1)) and Uq,r(q ═ 0, ± (a +1), …, ± (a +1)), b ═ f, r respectively represent front axle and rear axle wheels, the number of segments is c ═ 2(a +1) +1, a ≧ 1;
step two: establishing an adhesion coefficient mu of 1 and a nominal load Fzf,FzrLateral force of wheel with lower front and rear axles
Figure BDA0002613664840000022
Angle of slip with wheel alphaf,αrThe PWA relational expression of (a):
Figure BDA0002613664840000021
wherein the content of the first and second substances,
Figure BDA0002613664840000031
Figure BDA0002613664840000032
the side slip angle of the front shaft is alphaf,pLateral force of time CqrAnd dqrObtained by the same method;
step three: establishing the coefficient of adhesion mu<1 and nominal load Fzf,FzrLateral force of wheel with lower front and rear axles
Figure BDA0002613664840000033
Angle of slip with wheel alphaf,αrThe PWA relational expression of (a) introducing variables
Figure BDA0002613664840000034
Characterization of
Figure BDA0002613664840000035
And
Figure BDA0002613664840000036
the relationship of (1):
Figure BDA0002613664840000037
step four: establishing a coefficient of adhesion mu taking into account the dynamic load<Wheel side force of front and rear axle under 1 condition
Figure BDA0002613664840000038
Angle of slip with wheel alphaf,αrThe dynamic loads of the front axle and the rear axle during steering are respectively delta Fzf,△Fzr：
Figure BDA0002613664840000039
Wherein the content of the first and second substances,
Figure BDA00026136648400000310
Figure BDA00026136648400000311
step five: establishing a switching lateral dynamics model with front and rear wheel slip angles as state variables according to the effective subareas:
get to satisfy alphaf·αrNot less than 0 and alphaf∈Upf，αr∈UqrIs marked with p, q, and will<p,q>For mapping as a positive integer, let θ ═ i ═ 1,2pq}(npq2(a +2) (a +2) -1), constructing an effective partition set θ;
taking i belongs to theta, and the side deflection angle alpha of the front wheel and the rear wheelf,αrFor the state quantities, a switching lateral dynamics model is established:
Figure BDA00026136648400000312
wherein the content of the first and second substances,
Figure BDA0002613664840000041
Figure BDA0002613664840000042
Figure BDA0002613664840000043
Figure BDA0002613664840000044
Figure BDA0002613664840000045
wherein, m, IzRepresenting vehicle mass and moment of inertia about the z-axis, v, respectivelyxFor longitudinal vehicle speed, MzIs yaw moment, delta is wheel steering angle, lf,lrIs the distance from the anterior-posterior axis to the center of mass, L ═ Lf+lr；
Step six: selecting a nonlinear item in a switching lateral dynamics model as a front piece variable, converting the switching lateral dynamics model into a switching T-S fuzzy model, designing a switching fuzzy observer according to an equation (6), estimating front and rear wheel slip angles, and calculating to obtain an estimated value of a centroid slip angle according to a relational equation of the wheel slip angle and the centroid slip angle, wherein the specific method comprises the following steps:
1) definition eta1＝ζf(αf,μ)φf,η2＝ζr(αr,μ)φrWhen formula (6) is
Figure BDA0002613664840000046
Setting eta1min≤η1≤η1max，η2min≤η2≤η2maxEta is to1And η2Are respectively expressed as eta1＝M11η1max+M12η1min，η2＝M21η2max+M22η2minWherein M is11,M12M21,M22The definition is as follows:
Figure BDA0002613664840000047
the formula (7) is represented by
Figure BDA0002613664840000051
Wherein A isij,bijFrom η1min,η1max,η2min,η2maxA in alternative formula (6)i(η1,η2),bi(η1,η2) Inner η1,η2So as to obtain the compound with the characteristics of,
Figure BDA0002613664840000052
2) selecting yaw rate gamma and lateral acceleration ayAs a measurement output y
Figure BDA0002613664840000053
Wherein the content of the first and second substances,
Figure BDA0002613664840000054
3) discretizing the formulae (9) and (10) are
Figure BDA0002613664840000055
Wherein, TsIn order to be the sampling period of time,
Figure BDA0002613664840000056
4) let the observer take the form of
Figure BDA0002613664840000057
Wherein the content of the first and second substances,
Figure BDA0002613664840000058
estimator gain Lil＝P-1WilObtained by solving the following optimization problem:
Figure BDA0002613664840000059
5) the estimated value obtained according to the step 4)
Figure BDA00026136648400000510
Calculating an estimate of the centroid slip angle
Figure BDA00026136648400000511
Figure BDA0002613664840000061
Compared with the prior art, the invention has the beneficial effects that: the invention provides a method for establishing a piecewise affine (PWA) lateral dynamics model by adopting a piecewise linear modeling thought, which overcomes the problem that a linear piecewise model cannot represent the vertical load change of a tire and the road surface adhesion coefficient change, so that the established lateral dynamics model has the advantages of simple piecewise linear model expression and convenience for estimator design, and can reflect the change of the vertical load of the tire and the road surface adhesion coefficient in real time, and in addition, the invention only needs the tire lateral force-lateral deflection angle data under the working condition that the nominal load of the tire and the road surface adhesion coefficient are 1, does not need experimental data under other working conditions, and has small dependence on the experimental data.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic illustration of a front wheel side force segment interval;
FIG. 3 is a rear wheel side force segment interval schematic;
FIG. 4 is a piecewise linear approximation of the front wheel lateral force with the number of segments c-7;
fig. 5 is a piecewise linear approximation curve of the rear wheel lateral force with the number of segments c being 7.
Detailed Description
The technical solutions in the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the invention, rather than all embodiments, and all other embodiments obtained by those skilled in the art without any creative work based on the embodiments of the present invention belong to the protection scope of the present invention.
Referring to fig. 1, the invention discloses a centroid slip angle estimation method considering dynamic load and road adhesion coefficient, comprising the following steps:
the method comprises the following steps: according to the coefficient of adhesion mu-1 and the nominal load Fzf,FzrDetermining the segmentation interval and the segmentation number of the lateral force linear segmentation model according to experimental data of the relationship between the lateral force and the slip angle or data obtained by a magic formula tire model, wherein the segmentation interval is Up,f(p ═ 0, ± (a +1), …, ± (a +1)) and Uq,r(q ═ 0, ± (1, …, ± (a +1)) (where b ═ f, r denote front axle and rear axle wheels, respectively), the number of segments is c ═ 2(a +1) +1, a ≧ 1, a is an intermediate parameter selected according to the accuracy requirement, see fig. 2-2And 5, as follows:
a) estimated slip angle alphabAt + -alphab,maxIn the range, i.e. alphab∈[-αb,max,αb,max](αb,maxMaximum wheel slip angle, may take alphab,maxNot less than 10 degree, p-alphab∈[-αb,max,αb,max]Segmenting with the number of segments c being 2(a +1) +1 (a being more than or equal to 1), and obtaining a segmented interval by utilizing the symmetrical property of lateral force:
Figure BDA0002613664840000071
Figure BDA0002613664840000072
Figure BDA0002613664840000073
b) segment interval U0,bAlpha in (A)b,0Of the through type
Figure BDA0002613664840000074
To obtain wherein CybRepresenting the tire cornering stiffness;
c) segment interval Ua,b,U-a,bAlpha in (A)b,aSo that the coefficient of adhesion mu is 1 and the nominal load Fzf,FzrExperimental data of the relation between the lower lateral force and the lateral deflection angle or the lateral deflection angle corresponding to the maximum lateral force in data obtained by other tire models;
d) segment interval U1，b～Ua-1，bAnd U-1，b～U-(a-1)，bAlpha in (A)b,d(d-1, …, a-1), using
Figure BDA0002613664840000075
Or any other non-uniform segmentation method.
Step two: establishing an adhesion coefficient mu of 1 and a nominal load Fzf,FzrLateral force of wheel with lower front and rear axles
Figure BDA0002613664840000076
Angle of slip with wheel alphaf,αrThe PWA relational expression of (a):
Figure BDA0002613664840000077
wherein the content of the first and second substances,
Figure BDA0002613664840000081
Figure BDA0002613664840000082
the side slip angle of the front shaft is alphaf,pLateral force in time, according to the coefficient of adhesion mu 1 and the nominal load Fzf,FzrExperimental data on the relationship between the lateral force and the slip angle was obtained, CqrAnd dqrObtained by the same method.
Step three: establishing the coefficient of adhesion mu<1 and nominal load Fzf,FzrThe PWA relational expression of the wheel side force and the wheel slip angle of the lower front axle and the lower rear axle is used
Figure BDA0002613664840000083
Respectively represents the road surface adhesion coefficient mu<1, front and rear axle wheel side force under nominal load, introducing variable
Figure BDA0002613664840000084
Characterization of
Figure BDA0002613664840000085
And
Figure BDA0002613664840000086
the formula for calculating the lateral force of the front and rear axle wheels is:
Figure BDA0002613664840000087
zeta of different side force zonesf(αfμ) and ζr(αrμ) the calculation method is as follows:
Figure BDA0002613664840000088
wherein the content of the first and second substances,
Figure BDA0002613664840000089
step four: establishing a coefficient of adhesion mu taking into account the dynamic load<Under the condition of 1, the relation expression of the PWA of the wheel side force of the front axle and the rear axle and the wheel side slip angle is that if the dynamic loads of the front axle and the rear axle and the inner side and the outer side wheels are respectively delta F during steeringzf,△FzrThen, the road surface adhesion coefficient μ<1, dynamic load Δ Fzf,△FzrWhen the lateral force of the front and rear axle wheels
Figure BDA0002613664840000091
The calculation formula of (A) is as follows:
Figure BDA0002613664840000092
wherein the content of the first and second substances,
Figure BDA0002613664840000093
Figure BDA0002613664840000094
step five: establishing a switching lateral dynamics model with front and rear wheel slip angles as state variables according to the effective subareas:
get to satisfy alphaf·αrNot less than 0 and alphaf∈Upf，αr∈UqrIs marked with p, q, and will<p,q>To mapping as positive integers, i.e.<p,q>→ i (i is a positive integer), and θ ═ i ═ 1,2pq}(npq2(a +2) (a +2) -1), constructing an effective partition set θ;
take i ∈ theta, front and rear wheelsSlip angle alphaf,αrFor the state quantities, a switching lateral dynamics model is established:
Figure BDA0002613664840000095
wherein the content of the first and second substances,
Figure BDA0002613664840000096
Figure BDA0002613664840000097
Figure BDA0002613664840000098
Figure BDA0002613664840000101
Figure BDA0002613664840000102
wherein, m, IzRepresenting vehicle mass and moment of inertia about the z-axis, v, respectivelyxFor longitudinal vehicle speed, MzIs yaw moment, delta is wheel steering angle, lf,lrIs the distance from the anterior-posterior axis to the center of mass, L ═ Lf+lr。
Step six: selecting a nonlinear item in a switching lateral dynamics model as a front piece variable, converting the switching lateral dynamics model into a switching T-S fuzzy model, designing a switching fuzzy observer, estimating front and rear wheel slip angles, and calculating to obtain an estimated value of the centroid slip angle according to a relation between the wheel slip angles and the centroid slip angle:
designing a switching fuzzy observer according to the formula (6) to estimate the wheel slip angle alphaf,αrCalculating the centroid sideThe deflection angle estimation value specifically includes:
1) definition eta1＝ζf(αf,μ)φf,η2＝ζr(αr,μ)φrWhen formula (6) is
Figure BDA0002613664840000103
Setting eta1min≤η1≤η1max，η2min≤η2≤η2maxEta is to1And η2Are respectively expressed as eta1＝M11η1max+M12η1min，η2＝M21η2max+M22η2minWherein M is11,M12M21,M22The definition is as follows:
Figure BDA0002613664840000104
the formula (7) is represented by
Figure BDA0002613664840000105
Wherein A isij,bijFrom η1min,η1max,η2min,η2maxA in alternative formula (6)i(η1,η2),bi(η1,η2) Inner η1,η2So as to obtain the compound with the characteristics of,
Figure BDA0002613664840000106
2) selecting yaw rate gamma and lateral acceleration ayAs a measurement output y
Figure BDA0002613664840000111
Wherein the content of the first and second substances,
Figure BDA0002613664840000112
3) discretizing the formulae (9) and (10) are
Figure BDA0002613664840000113
Wherein, TsIn order to be the sampling period of time,
Figure BDA0002613664840000114
4) let the observer take the form of
Figure BDA0002613664840000115
Wherein the content of the first and second substances,
Figure BDA0002613664840000116
estimator gain Lil＝P-1WilObtained by solving the following optimization problem:
Figure BDA0002613664840000117
5) the estimated value obtained according to the step 4)
Figure BDA0002613664840000118
Calculating an estimate of the centroid slip angle
Figure BDA0002613664840000119
Figure BDA00026136648400001110
The invention provides a lateral force PWA description method reflecting load and attachment coefficient changes and a mass center slip angle estimation method based on a lateral force PWA model under a piecewise affine (PWA) model framework. The technical route is as follows: the method comprises the steps of providing a PWA model for building tire lateral force under determined adhesion coefficient and load, providing the PWA model suitable for road surfaces with different adhesion coefficients and dynamic load change by introducing parameters and dynamic load change quantities representing the adhesion coefficients, providing a vehicle lateral dynamic model taking vehicle front and rear wheel side deflection angles as state variables on the basis of the PWA model, aiming at the non-linear problem caused by introduction of parameters related to the adhesion coefficients, adopting a switching fuzzy model, providing a wheel deflection angle observer design method, and calculating a mass center deflection angle according to the relation between the mass center deflection angle and the wheel deflection angle.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.

Claims (2)

1. A centroid slip angle estimation method considering dynamic load and road adhesion coefficient is characterized in that: the estimation method comprises the following steps:
the method comprises the following steps: according to the coefficient of adhesion mu-1 and the nominal load Fzf,FzrLateral force and slip angle of the lower partDetermining the sectional interval and the sectional number of the lateral force linear sectional model according to experimental data of the system or data obtained by a magic formula tire model, wherein the sectional interval is Up,f(p ═ 0, ± (a +1), …, ± (a +1)) and Uq,r(q ═ 0, ± (a +1), …, ± (a +1)), b ═ f, r respectively represent front axle and rear axle wheels, the number of segments is c ═ 2(a +1) +1, a ≧ 1;
step two: establishing an adhesion coefficient mu of 1 and a nominal load Fzf,FzrLateral force of wheel with lower front and rear axles
Figure FDA0002613664830000011
Angle of slip with wheel alphaf,αrThe PWA relational expression of (a):
Figure FDA0002613664830000012
wherein the content of the first and second substances,
Figure FDA0002613664830000013
Figure FDA0002613664830000014
the side slip angle of the front shaft is alphaf,pLateral force of time CqrAnd dqrObtained by the same method;
step three: establishing the coefficient of adhesion mu<1 and nominal load Fzf,FzrLateral force of wheel with lower front and rear axles
Figure FDA0002613664830000015
Angle of slip with wheel alphaf,αrThe PWA relational expression of (a) introducing variables
Figure FDA0002613664830000016
And
Figure FDA0002613664830000017
characterization of
Figure FDA0002613664830000018
And
Figure FDA0002613664830000019
and
Figure FDA00026136648300000110
and
Figure FDA00026136648300000111
the relationship of (1):
Figure FDA00026136648300000112
step four: establishing a coefficient of adhesion mu taking into account the dynamic load<Wheel side force of front and rear axle under 1 condition
Figure FDA00026136648300000113
Angle of slip with wheel alphaf,αrThe dynamic loads of the front axle and the rear axle during steering are respectively delta Fzf,△Fzr：
Figure FDA00026136648300000114
Wherein the content of the first and second substances,
Figure FDA0002613664830000021
Figure FDA0002613664830000022
step five: establishing a switching lateral dynamics model with front and rear wheel slip angles as state variables according to the effective subareas:
get to satisfy alphaf·αrNot less than 0 and alphaf∈Up,f，αr∈Uq,rMarks p, q and maps pairs < p, q > to positive integers, θ ═ { i | i ═ 1,2pq}(npq2(a +2) (a +2) -1), constructing an effective partition set θ;
taking i belongs to theta, and the side deflection angle alpha of the front wheel and the rear wheelf,αrFor the state quantities, a switching lateral dynamics model is established:
Figure FDA0002613664830000023
wherein the content of the first and second substances,
Figure FDA0002613664830000024
Figure FDA0002613664830000025
Figure FDA0002613664830000026
Figure FDA0002613664830000027
Figure FDA0002613664830000028
wherein, m, IzRepresenting vehicle mass and moment of inertia about the z-axis, v, respectivelyxFor longitudinal vehicle speed, MzIs yaw moment, delta is wheel steering angle, lf,lrIs the distance from the anterior-posterior axis to the center of mass, L ═ Lf+lr；
Step six: selecting a nonlinear item in a switching lateral dynamics model as a front piece variable, converting the switching lateral dynamics model into a switching T-S fuzzy model, designing a switching fuzzy observer according to an equation (6), estimating front and rear wheel slip angles, and calculating to obtain an estimated value of a centroid slip angle according to a relational equation of the wheel slip angle and the centroid slip angle, wherein the specific method comprises the following steps:
1) definition eta1＝ζf(αf,μ)φf,η2＝ζr(αr,μ)φrWhen formula (6) is
Figure FDA0002613664830000031
Setting eta1min≤η1≤η1max，η2min≤η2≤η2maxEta is to1And η2Are respectively expressed as eta1＝M11η1max+M12η1min，η2＝M21η2max+M22η2minWherein M is11,M12M21,M22The definition is as follows:
Figure FDA0002613664830000032
the formula (7) is represented by
Figure FDA0002613664830000033
Wherein A isij,bijFrom η1min,η1max,η2min,η2maxA in alternative formula (6)i(η1,η2),bi(η1,η2) Inner η1,η2So as to obtain the compound with the characteristics of,
Figure FDA0002613664830000034
2)selecting yaw rate gamma and lateral acceleration ayAs a measurement output y
Figure FDA0002613664830000035
Wherein the content of the first and second substances,
Figure FDA0002613664830000036
3) discretizing the formulae (9) and (10) are
Figure FDA0002613664830000041
Wherein, TsIn order to be the sampling period of time,
Figure FDA0002613664830000042
4) let the observer take the form of
Figure FDA0002613664830000043
Wherein the content of the first and second substances,
Figure FDA0002613664830000044
estimator gain Lil＝P-1WilObtained by solving the following optimization problem:
Figure FDA0002613664830000045
5) the estimated value obtained according to the step 4)
Figure FDA0002613664830000046
Calculating an estimate of the centroid slip angle
Figure FDA0002613664830000047
Figure FDA0002613664830000048
2. The method of estimating the centroid slip angle taking into account the dynamic load and the road adhesion coefficient as set forth in claim 1, wherein: zeta of the different side force zones in the third stepf(αfμ) and ζr(αrμ) the calculation method is as follows:
Figure FDA0002613664830000049
wherein the content of the first and second substances,
Figure FDA0002613664830000051
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