CN112526880B - Real-time estimation method for road surface height in vehicle driving process - Google Patents

Real-time estimation method for road surface height in vehicle driving process Download PDF

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CN112526880B
CN112526880B CN202011345674.7A CN202011345674A CN112526880B CN 112526880 B CN112526880 B CN 112526880B CN 202011345674 A CN202011345674 A CN 202011345674A CN 112526880 B CN112526880 B CN 112526880B
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suspension
observer
road surface
state
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赵林辉
高士金
刘志远
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Harbin Institute of Technology
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract

The invention discloses a real-time estimation method for road surface height in the running process of a vehicle, which comprises the following steps: firstly, establishing a quarter suspension model considering a suspension geometrical structure; secondly, converting the road surface height estimation problem into an unknown input reconstruction problem; establishing an estimation model considering the nonlinear characteristic of the suspension damper; fourthly, designing a state observer to estimate the state of the system; step five, calculating an error equation of the observer; designing an observer gain matrix to ensure that an observer error equation is stable; and seventhly, the estimation of the road surface height is realized through unknown input reconstruction. The method considers the influence of the geometrical structure of the suspension and the nonlinear characteristic of the damper, establishes a linear variable parameter model of the suspension system, designs a sliding mode observer, and realizes the real-time estimation of the road height under different road conditions. Meanwhile, the sensors required by the invention are all sensors existing on the vehicle, and the cost of the system can be reduced on the premise of ensuring the estimation precision of the road surface height.

Description

Real-time estimation method for road surface height in vehicle driving process
Technical Field
The invention belongs to the technical field of automobile control, relates to a real-time road height estimation method in the vehicle running process, and particularly relates to a real-time road height estimation method by utilizing suspension dynamics and considering the influence of a suspension geometrical structure and the nonlinear characteristic of a damper.
Background
With the rapid development of vehicle control technology, people increasingly demand vehicle handling stability and riding comfort. When a vehicle runs on an impact road or a continuously bumpy road, the impact caused by the height change of the road brings discomfort to passengers, influences the riding comfort of the vehicle, and even influences the operation stability and the running safety of the vehicle. Therefore, it is desirable for an automotive motion control system to be able to accurately estimate the height of the road surface during vehicle travel and use the information to improve the automotive motion control effect. For example: in the suspension control, if the road height can be accurately identified, the damping coefficient or the acting force of the suspension can be actively adjusted according to the road height, and the suspension control effect is optimized. Therefore, in order to improve the safety and comfort of the vehicle running, it is important to accurately estimate the road surface height during the vehicle running.
In the prior art, the method for acquiring the road surface height mainly comprises a direct measurement method, an indirect measurement method based on an image and an estimation method based on dynamic response. Among them, CN202511783U discloses a direct measurement method based on a road surface profile measuring instrument, which can measure longitudinal and transverse road surface profiles by using data collected by displacement sensors, but each component of the measuring instrument needs to be integrated on a cart, has a large volume, and cannot be installed in a vehicle for use. CN109564682A discloses a road surface shape estimation method based on images shot by a camera, and CN108955584A discloses a method and apparatus for estimating the undulation of a road surface according to the vertical height and horizontal distance between a laser radar and a scanned point, but the above method requires a camera or a laser radar mounted on a vehicle to acquire road surface information, and is relatively high in cost. CN110001335A proposes a road surface identification technology based on suspension dynamic stroke, and CN106985627A proposes a road surface identification technology based on suspension dynamic stroke and suspension sprung and unsprung mass acceleration signals, but all the above methods are based on statistical rules, and are only suitable for identifying the grade of a section of continuous road surface, and for discrete impact road surfaces and continuous long-wave road surfaces similar to deceleration strips, the accurate height of the road surface cannot be estimated in real time.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides the real-time road surface height estimation method in the vehicle running process, which has the advantages of mature theory, wide application range and high precision. The method considers the influence of the geometrical structure of the suspension and the nonlinear characteristic of the damper, establishes a linear variable parameter model of the suspension system, designs a sliding mode observer, and realizes the real-time estimation of the road height under different road conditions. Meanwhile, the sensors required by the invention are all sensors existing on the vehicle, and the cost of the system can be reduced on the premise of ensuring the estimation precision of the road surface height.
The purpose of the invention is realized by the following technical scheme:
a real-time estimation method for road surface height in the running process of a vehicle comprises the following steps:
step one, establishing a quarter suspension model considering the suspension geometry.
And step two, converting the road surface height estimation problem into an unknown input reconstruction problem.
(1) Defining a system state according to the suspension system dynamic model given in the step one
Figure GDA0003530646970000021
Wherein z issIn order to displace the sprung mass of the suspension,
Figure GDA0003530646970000031
is the velocity of the sprung mass displacement of the suspension, theta is the angular displacement of the stabilizer bar of the suspension relative to the equilibrium position,
Figure GDA0003530646970000032
is the angular velocity of the suspension stabilizer bar relative to the equilibrium position; selecting system outputs
Figure GDA0003530646970000033
Wherein
Figure GDA0003530646970000034
Is the suspension sprung mass acceleration, and Δ l is the relative displacement of the sprung and unsprung masses;
(2) based on the above definition, linearizing the model at the balance point in the first step to obtain:
Figure GDA0003530646970000035
wherein z isrIs the road surface height, faControl force applied for active suspension, the control force in semi-active suspension being taken to be 0, fdThe variable quantity of the vehicle body load is A, B, G, H, C, D, E and F are respectively corresponding coefficient matrixes;
in the above-described linearized model, the model,
Figure GDA0003530646970000036
the system measurement value can be obtained by the measurement of a sensor;
Figure GDA0003530646970000037
the system state quantity can be observed by a state observer; f. ofa，fdThe changes in the forces applied to the suspension and the body load, respectively, may be known quantities; z is a radical ofrAs road height, can be considered as an unknown input. Therefore, the problem of estimating the unknown road height can be converted into the unknown input z in the modelrThe reconstruction problem of (1).
Step three, establishing an estimation model considering the nonlinear characteristic of the suspension damper:
considering the linearized model in step two, the elements in the coefficient matrices a and C contain the suspension damping coefficient CpIn a real dynamic process cpIs a variable with speed, so that the coefficient matrices A and C are C-dependentpAlternatively, the system can be written as follows:
Figure GDA0003530646970000038
wherein, A (c)p)、C(cp) Representation matrix with parameter cpMay vary.
In order to deal with the problem of model variation due to the variation parameters, the model is rewritten into a form of a linear parametric system multicellular body. In a linear parametric system, a variable parameter c is selectedpFor scheduling variables, according to cpThe value range of (a) is selected as the vertex of the multicellular body (c)pmax,cpminWherein c ispmax,cpminRespectively is a variable parameter cpMaximum and minimum values of. C is topmax,cpminRespectively substituting the matrix A and the matrix C of the model to obtain a multicellular form of the linear variable parameter model:
Figure GDA0003530646970000041
wherein the content of the first and second substances,
Figure GDA0003530646970000042
is through a scheduling variable cpCalculated weight coefficient, AcpmaxIs cp＝cpmaxValue of the time matrix A, AcpminIs cp＝cpminThe value of the time matrix A, CcpmaxIs cp＝cpmaxValue of the time matrix C, CcpminIs cp＝cpminThe value of the time matrix C.
Step four, designing a state observer to estimate the state of the system:
the following form of state observer is designed:
Figure GDA0003530646970000043
wherein the content of the first and second substances,
Figure GDA0003530646970000044
is cp＝cpmaxThe time observer feeds back a gain matrix which,
Figure GDA0003530646970000045
is cp＝cpminThe time observer feeds back a gain matrix which,
Figure GDA0003530646970000046
is cp＝cpmaxA time observer sliding-mode gain matrix,
Figure GDA0003530646970000047
is cp＝cpminThe time observer sliding mode gain matrix.
To avoid the effect of buffeting on state estimation, use is made of
Figure GDA0003530646970000048
The sign function sign (e) in the observer is replaced, wherein e is the estimation error of the system output, eta is a small positive number, the slope of the function near the zero-value estimation error can be adjusted, and the reconstruction of the unknown input of the system is influencedAnd (4) precision.
Step five, calculating an error equation of the observer:
defining state estimation errors
Figure GDA0003530646970000051
The error equation is written in the form:
Figure GDA0003530646970000052
wherein:
Figure GDA0003530646970000053
Figure GDA0003530646970000054
designing an observer gain matrix to ensure that an error equation of the observer is stable, wherein the error equation is as follows:
Figure GDA0003530646970000055
wherein
Figure GDA0003530646970000056
Due to alpha in the above formula1,α2All values of are equal to cpIn relation, the above formula can be abbreviated as:
Figure GDA0003530646970000057
will be provided with
Figure GDA0003530646970000058
Viewed as a disturbance, the observer design problem can be converted to (A (c)p)-K(cp)C(cp) ) converges to 0. At the same time, for interference
Figure GDA0003530646970000059
Since it is related to the road height and the road height is bounded, the disturbance is bounded.
According to the LPV (linear variable parameter) system stability theory: for a given positive tunable parameter γ ∈ R, if a symmetric positive definite matrix P (c) existsp) The matrix Y (c)p) And the identity matrix I and a positive definite factor epsilon R meet the following conditions:
P(cp)＝PT(cp)，ε＞0
Figure GDA0003530646970000061
wherein:
Π(cp)＝P(cp)A(cp)+AT(cp)P(cp)-Y(cp)C(cp)-CT(cp)Y(cp)+εγI；
the designed LPV observer is stable.
Simultaneously, an observer gain matrix is obtained:
K(cp)＝P-1(cp)Y(cp)；
according to the formula, the gain of the sliding mode observer can be obtained.
Step seven: and (3) realizing the estimation of the road height through unknown input reconstruction:
once the estimation error equation reaches the sliding mode surface and the estimated system state converges to the true state, the sliding mode term in the observer
Figure GDA0003530646970000062
The road surface height can be approximated, namely the road surface height can be reconstructed as:
Figure GDA0003530646970000063
compared with the prior art, the invention has the following advantages:
1. the road surface height estimation method adopts a quarter suspension model which is more in accordance with the real geometrical structure of the suspension, and further, the change of model parameters is considered and processed, so that the model is more accurate;
2. the stability of the road surface height estimation method is ensured by the LPV observer stability theory, and the observer estimation error designed by the method is bounded theoretically;
3. the road surface height estimation method can accurately estimate the specific numerical value of the road surface height;
4. the road surface height estimation method utilizes the measurement information of the relative displacement of the sprung mass and the unsprung mass and the sprung mass acceleration of the suspension system, and the used sensors are all common sensors on the vehicle body, so that the road surface height estimation method has the advantage of low cost;
5. the road surface height estimation method is high in calculation efficiency and can meet the real-time requirement of a suspension control system;
6. the road surface height estimation method can be suitable for different suspension systems such as a semi-active suspension, an active suspension and the like.
Drawings
FIG. 1 is a schematic diagram of a McPherson suspension geometry;
FIG. 2 is a block diagram of a method for estimating road surface height;
FIG. 3 is a schematic diagram of the comparison between the estimated value and the actual value of the road surface height on the deceleration strip road surface;
FIG. 4 is a schematic representation of estimated values of road surface height over a sinusoidally varying road surface compared to actual values;
fig. 5 is a schematic diagram showing the comparison between the estimated value and the actual value of the road surface height on the random road surface.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings, but not limited thereto, and any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.
The invention provides a real-time estimation method for road surface height in the running process of a vehicle, which comprises the following steps:
the method comprises the following steps: a quarter suspension model is built that takes into account suspension geometry.
In order to establish a more accurate quarter suspension model, the influence of the real geometrical structure of the suspension is considered, and the suspension model is established by taking the Macpherson suspension as an example. A suspension taking into account the real geometry is shown in fig. 1, ignoring the effect of wheel-ground coupled damping, and from the lagrangian equation, the suspension system dynamics model can be derived as follows:
Figure GDA0003530646970000081
Figure GDA0003530646970000082
wherein:
D1＝mslC+mulCsin2(θ-θ0)；
Figure GDA0003530646970000083
Figure GDA0003530646970000084
b＝2lAlB；
c＝a2-abcosα′；
d＝ab-b2cosα′；
α′＝α+θ0。
in the formula: z is a radical ofs、
Figure GDA0003530646970000085
Are respectively a suspensionMass displacement, velocity and acceleration on the frame spring; theta, theta,
Figure GDA0003530646970000086
Angular displacement, angular velocity, angular acceleration (positive counterclockwise) of OC relative to equilibrium position in fig. 1, respectively; theta0And alpha is the angle between OC and the horizontal line and the angle between OA and the horizontal line in the steady state in FIG. 1, respectively; z is a radical ofrIs the road surface height; m issIs a quarter of the sprung mass of the suspension, muIs a quarter of the suspension unsprung mass, ksIs the suspension stiffness coefficient, cpIs the damping coefficient, k, of the suspension dampertIs a wheel-ground coupling stiffness coefficient; lA、lB、lCRespectively OA, OB and OC lengths in FIG. 1; f. ofaThe control force applied for the active suspension of fig. 1, in a semi-active suspension, the value is taken to be 0; f. ofdIs the change in the body load of fig. 1.
Step two: and converting the road height estimation problem into an unknown input reconstruction problem.
In the quarter suspension model established in the first step, the road height is coupled with the suspension state and cannot be directly used for estimating the road height. For this purpose, the model in step one is linearized.
Defining the system state as the suspension system dynamic model given in the step one
Figure GDA0003530646970000091
Output is as
Figure GDA0003530646970000092
Wherein:
Figure GDA0003530646970000093
to suspension sprung mass acceleration, Δ l is the amount of change in the length of AB in FIG. 1, i.e., the relative displacement of the sprung and unsprung masses. As can be seen from the geometrical relationship in fig. 1:
Figure GDA0003530646970000094
in the formula: l and l' are the lengths of the sprung and unsprung masses, respectively.
As can be seen from equations (1) and (2), in the suspension model derived from the lagrange equation, the state variable and the road height zrCoupled together, make it difficult to estimate road height using the model, so it is considered to linearize the model at the equilibrium point.
At the equilibrium point
Figure GDA0003530646970000095
And (5) carrying out linearization processing on the model in the step one. Wherein z issIn order to displace the sprung mass of the suspension,
Figure GDA0003530646970000096
theta is the angular displacement relative to the equilibrium position, i.e., the amount of angular change relative to the equilibrium position,
Figure GDA0003530646970000097
is the corresponding angular velocity. f. ofaControl force applied for active suspension, in semi-active suspension this value takes the value 0, fdIs the amount of change in body load, zrIs the road surface height. In a steady state condition at the equilibrium point, the above variables are all apparently 0.
Obtaining a linearized equation of state:
Figure GDA0003530646970000101
wherein:
Figure GDA0003530646970000102
Figure GDA0003530646970000103
W1＝(mslC+mulCsin2(-θ0))2；
Figure GDA0003530646970000104
Figure GDA0003530646970000105
Figure GDA0003530646970000111
Figure GDA0003530646970000112
Figure GDA0003530646970000113
Figure GDA0003530646970000114
Figure GDA0003530646970000115
Figure GDA0003530646970000116
Figure GDA0003530646970000117
Figure GDA0003530646970000118
Figure GDA0003530646970000119
obtaining a linearized measurement equation:
Figure GDA00035306469700001110
wherein:
Figure GDA0003530646970000121
in expressions (3) and (4), the control force f exerted by the active suspension is taken into accountaAnd change of vehicle body load fdAre all known inputs, and the road surface excitation zrIs an unknown input. In particular, when using semi-active dynamic suspensions, f a0; when the vehicle body load is not changed, fd＝0。
For the systems described in the expressions (3) and (4), the system output is selected by comprehensively considering the cost and the road height estimation effect
Figure GDA0003530646970000122
And Δ l, the sprung mass acceleration of the suspension system and the relative displacement of the sprung and unsprung masses, are measured quantities. The invention designs an observer to estimate the state of the system and linearizes the model by reconstructing the unknown input zrAnd the estimation of the road surface height is realized. Thereby converting the road height estimation problem into the state estimation of the system described by expressions (3) and (4) and as an unknown input zrThe reconstruction problem of (1).
Step three: and establishing an estimation model considering the nonlinear characteristic of the suspension damper.
Consider the linearized model in step two, where parameter cpIs the damping coefficient of the suspension damper, which is a variable with speed in the practical process, and the parameter c is noticedpOnly at a24、a44Then the system can be written as follows:
Figure GDA0003530646970000123
wherein the content of the first and second substances,
Figure GDA0003530646970000124
is a state variable selected by the system;
Figure GDA0003530646970000125
is a system measurement; z is a radical ofrIs the road surface height; f. ofa,fdThe amount of change in the control force and body load, respectively, applied to the active suspension is a known input. A (c)p)、C(cp) Is dependent on the parameter cpThe changed matrix, B, G, H, D, E, F, is the corresponding coefficient matrix, namely:
Figure GDA0003530646970000131
Figure GDA0003530646970000132
to deal with this variation, the model is rewritten to the form of a linear parametric system multicellular body. In a linear parametric system, a variable parameter c is selectedpFor scheduling variables, according to cpThe value range of (a) is selected as the vertex of the multicellular body (c)pmax,cpminWherein c ispmax,cpminRespectively is a variable parameter cpMaximum and minimum values of. C is topmax,cpminRespectively substituting the A matrix and the C matrix of the model to obtain the form of the multicellular body of the linear variable parameter model:
Figure GDA0003530646970000133
wherein the content of the first and second substances,
Figure GDA0003530646970000134
is through a scheduling variable cpCalculated weight coefficient, zrIs the road surface height, fa,fdThe control force and body load, respectively, applied to the active suspension are known inputs.
Figure GDA0003530646970000135
To change the parameter cpTaking the coefficient matrix at the boundary value, namely:
Figure GDA0003530646970000136
Figure GDA0003530646970000137
b, G, H, D, E and F are corresponding coefficient matrixes respectively.
Step four: a state observer is designed to estimate the system state.
For the linear parametric system described in expression (6), measurable system output is utilized
Figure GDA0003530646970000141
As the observed quantity, a state observer is designed. Wherein
Figure GDA0003530646970000142
To determine the suspension sprung mass acceleration, Δ l is the relative displacement of the sprung and unsprung masses.
Consider faAnd fdFor known amount, respectively for cp＝cpmaxAnd cp＝cpminTwo cases design the state observer.
When c is going top＝cpmaxThe time design state observer is as follows:
Figure GDA0003530646970000143
wherein:
Figure GDA0003530646970000144
in order to feed back the gain to the observer,
Figure GDA0003530646970000145
in order to obtain the sliding-mode gain of the observer,
Figure GDA0003530646970000146
respectively represent the state x1、x2、x3、x4Is determined by the estimated value of (c),
Figure GDA0003530646970000147
respectively represent outputs y1、y2An estimate of (d).
Similarly, when cp＝cpminThe time design state observer is as follows:
Figure GDA0003530646970000148
wherein:
Figure GDA0003530646970000149
in order to feed back the gain to the observer,
Figure GDA00035306469700001410
in order to obtain the sliding-mode gain of the observer,
Figure GDA00035306469700001411
respectively represent the state x1、x2、x3、x4Is determined by the estimated value of (c),
Figure GDA00035306469700001412
respectively represent outputs y1、y2An estimate of (d).
The state observer is written in the form of a multicellular body as follows:
Figure GDA0003530646970000151
wherein:
Figure GDA0003530646970000152
respectively as feedback gain matrixes of the observer at the top of the multicellular body;
Figure GDA0003530646970000153
respectively, observer sliding mode gain matrixes at the top of the multicellular body.
In order to avoid the influence of buffeting on state estimation, the invention adopts the following equivalent symbolic functions to replace the symbolic function sign (e) in the observer designed by the expression (9):
Figure GDA0003530646970000154
in the formula:
Figure GDA0003530646970000155
an estimation error that is an output; η is a small positive number that can adjust the slope of the function around the zero-valued estimation error, affecting the reconstruction accuracy for unknown inputs to the system.
Step five: an observer error equation is calculated.
Defining the state estimation error:
Figure GDA0003530646970000156
are respectively paired with cp＝cpmaxAnd cp＝cpminThe estimation error equation of the observer is calculated for both cases. When c is going top＝cpmaxThe observer error equation is then as follows:
Figure GDA0003530646970000161
wherein:
Figure GDA0003530646970000162
Figure GDA0003530646970000163
Figure GDA0003530646970000164
Figure GDA0003530646970000165
similarly, when cp＝cpminThe observer error equation is then as follows:
Figure GDA0003530646970000166
wherein:
Figure GDA0003530646970000167
Figure GDA0003530646970000168
Figure GDA0003530646970000169
Figure GDA00035306469700001610
writing the error equation to the form of a multicellular body is as follows:
Figure GDA0003530646970000171
wherein:
Figure GDA0003530646970000172
Figure GDA0003530646970000173
step six: and designing an observer gain matrix to ensure that an observer error equation is stable.
The error equation is as follows:
Figure GDA0003530646970000174
in the formula (I), the compound is shown in the specification,
Figure GDA0003530646970000175
indicating the road height estimation error.
Due to alpha in the above formula1,α2All values of are equal to cpIn relation, the above formula can be abbreviated as:
Figure GDA0003530646970000176
will be provided with
Figure GDA0003530646970000177
As a disturbance, the observer gain design can be converted to (A (c)p)-K(cp)C(cp) ) convergence on 0. At the same time, for interference
Figure GDA0003530646970000178
Due to the fact that
Figure GDA0003530646970000179
In relation to road height, and road height is bounded, then the disturbance is known to be bounded, then (A (c)p)-K(cp)C(cp) The estimated error of the road surface height is also bounded at convergence.
According to the LPV (linear variable parameter) system stability theorem: for a given positive tunable parameter γ ∈ R, if a symmetric positive definite matrix P (c) existsp) The matrix Y (c)p) And the identity matrix I and a positive definite factor epsilon R meet the following conditions:
Figure GDA0003530646970000181
wherein:
Π(cp)＝P(cp)A(cp)+AT(cp)P(cp)-Y(cp)C(cp)-CT(cp)Y(cp)+εγI；
the designed LPV observer is stable.
Simultaneously, an observer gain matrix is obtained:
K(cp)＝P-1(cp)Y(cp) (17)；
and proper sliding mode gain can be obtained through the stability theorem of the LPV observer.
Step seven: and the estimation of the road surface height is realized through unknown input reconstruction.
Once the estimation error equation reaches the sliding mode surface and the estimated system state converges to the true state, the sliding mode term in the observer
Figure GDA0003530646970000182
The road surface height can be approximated, namely the road surface height can be reconstructed as:
Figure GDA0003530646970000183
it can be seen that the deviation between the measured output and the estimated output is used to reconstruct the road height.
According to the invention, the measurement information of two sensors, namely the measurement information of the relative displacement of the sprung mass and the unsprung mass of the suspension system and the measurement information of the sprung mass acceleration are utilized, and when the error of an observer converges to zero, the estimation of the road surface height can be realized; the suspension model used by the road surface height estimation method of the invention is more in line with the actual suspension structure, and the change of model parameters is considered. Therefore, the road surface height estimation method has the advantages of low cost, high precision and real-time performance.
Example (b):
and designing simulation operation parameters and the feedback gain and sliding mode gain of the observer according to the design requirements of the vehicle suspension and the expected simulation operation result.
The designed simulation operation related parameters and observer gains are as follows:
ms＝283.7kg,mu＝37.6kg,ks＝18500N/m,kt＝180000N/m,
cpmin＝1500N/m,cpmin＝3000N/m,α′＝70.5°,θ0＝2°,
lA＝0.6257m,lB＝0.3232m,lC＝0.3742m,η＝0.001。
Figure GDA0003530646970000191
Figure GDA0003530646970000192
the embodiment verifies the estimation effect of the method on deceleration strip road surfaces, sinusoidally-varying road surfaces and random road surfaces respectively.
Fig. 3 is a schematic diagram of comparison between the estimated road surface height and the actual road surface height on the road surface of the speed bump in the embodiment. The road surface is a trapezoidal bulge road surface with an upper bottom of 10cm, a lower bottom of 30cm and a height of 5cm on a flat road surface, and is used for simulating the situation that a vehicle passes through a speed bump; fig. 4 is a schematic diagram of the comparison of the estimated road surface height with the actual road surface height on a sinusoidally varying road surface as mentioned in the example. The road surface is a road surface with sine variation in height, the amplitude is 0.05m, the frequency is 1rad/s, and the road surface is used for simulating the situation that a vehicle passes through the road with sine variation; fig. 5 is a schematic diagram showing the comparison between the estimated road surface height and the actual road surface height on the random road surface mentioned in the example. The road surface is used for simulating the situation that vehicles pass through a random road surface.
As can be seen from fig. 3, 4, and 5: the road surface height estimation method can obtain better estimation effect under different road surface conditions.

Claims (3)

1. A real-time estimation method for road surface height in the running process of a vehicle is characterized by comprising the following steps:
step one, establishing a quarter suspension model considering a suspension geometrical structure:
in order to establish a more accurate quarter suspension model, the invention considers the influence of the real geometrical structure of the suspension, establishes the suspension model by taking the Macpherson suspension as an example, ignores the influence of wheel-ground coupling damping, and can obtain a suspension system dynamic model as follows according to a Lagrange equation:
Figure FDA0003530646960000011
Figure FDA0003530646960000012
wherein:
D1＝mslC+mulCsin2(θ-θ0)；
Figure FDA0003530646960000013
Figure FDA0003530646960000014
b＝2lAlB；
c＝a2-abcosα′；
d＝ab-b2cosα′；
α′＝α+θ0；
in the formula: z is a radical ofs、
Figure FDA0003530646960000021
Respectively suspension sprung mass displacement, velocity and acceleration; theta, theta,
Figure FDA0003530646960000022
Angular displacement, angular velocity, angular acceleration of OC relative to a equilibrium position, respectively; theta0And alpha is respectively an included angle between OC and the horizontal line and an included angle between OA and the horizontal line in a steady state; z is a radical ofrIs the road surface height; m issIs a quarter of the sprung mass of the suspension, muIs a quarter of the suspension unsprung mass, ksIs the suspension stiffness coefficient, cpIs the damping coefficient, k, of the suspension dampertIs a wheel-ground coupling stiffness coefficient; lA、lB、lCOA, OB, OC length, respectively; f. ofaControl force applied for active suspension, in semi-active suspension, the value is taken as 0; f. ofdIs the change in body load;
step two, converting the road surface height estimation problem into an unknown input reconstruction problem:
defining the system state as the suspension system dynamic model given in the step one
Figure FDA0003530646960000023
Output is as
Figure FDA0003530646960000024
Wherein:
Figure FDA0003530646960000025
for suspension sprung mass acceleration, Δ l is the amount of change in the length of AB, i.e., the relative displacement of the sprung and unsprung masses, as can be seen from the geometric relationship:
Figure FDA0003530646960000026
in the formula: l and l' are the lengths of the sprung and unsprung masses, respectively;
as can be seen from equations (1) and (2), in the suspension model derived from the lagrange equation, the state variable and the road height zrCoupled together, making it difficult to estimate road height using the model, so considering that the model is linearized at the balance point;
at the equilibrium point
Figure FDA0003530646960000027
Carrying out linearization processing on the model in the step one, wherein zsIn order to displace the sprung mass of the suspension,
Figure FDA0003530646960000028
theta is the angular displacement relative to the equilibrium position, i.e., the amount of angular change relative to the equilibrium position,
Figure FDA0003530646960000029
to corresponding angular velocity, faControl force applied for active suspension, in semi-active suspension this value takes the value 0, fdIs the amount of change in body load, zrIs the road surface height; in a steady state condition at the equilibrium point, the above variables are all apparently 0;
obtaining a linearized equation of state:
Figure FDA0003530646960000031
wherein:
Figure FDA0003530646960000032
Figure FDA0003530646960000033
W1＝(mslC+mulCsin2(-θ0))2；
Figure FDA0003530646960000034
Figure FDA0003530646960000035
Figure FDA0003530646960000041
Figure FDA0003530646960000042
Figure FDA0003530646960000043
Figure FDA0003530646960000044
Figure FDA0003530646960000045
Figure FDA0003530646960000046
Figure FDA0003530646960000047
Figure FDA0003530646960000048
Figure FDA0003530646960000049
obtaining a linearized measurement equation:
Figure FDA00035306469600000410
wherein:
Figure FDA0003530646960000051
in expressions (3) and (4), the control force f exerted by the active suspension is taken into accountaAnd change of load of vehicle body fdAre all known inputs, and the road surface excitation zrFor unknown inputs, in particular when using semi-active dynamic suspensions, fa0; when the load of the vehicle body is not changed, fd＝0；
Step three, establishing an estimation model considering the nonlinear characteristic of the suspension damper:
consider the linearized model in step two, where parameter cpIs the damping coefficient of the suspension damper, which is a variable with speed in the practical process, and the parameter c is noticedpOnly at a24、a44When it appears, the systemThe following can be written:
Figure FDA0003530646960000052
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003530646960000053
is a state variable selected by the system;
Figure FDA0003530646960000054
is a system measurement; z is a radical ofrIs the road surface height; f. ofa,fdThe amount of change in the control force and body load applied to the active suspension, respectively, is a known input; a (c)p)、C(cp) Is dependent on the parameter cpThe changed matrix, B, G, H, D, E, F, is the corresponding coefficient matrix, namely:
Figure FDA0003530646960000055
Figure FDA0003530646960000056
in order to process the variable parameters, the model is rewritten into a form of a multicellular body of a linear parametric system; in a linear parametric system, a variable parameter c is selectedpFor scheduling variables, according to cpThe value range of (a) is selected as the vertex of the multicellular body (c)pmax,cpminWherein c ispmax,cpminRespectively is a variable parameter cpMaximum and minimum values of; c is topmax,cpminRespectively substituting the A matrix and the C matrix of the model to obtain the form of the multicellular body of the linear variable parameter model:
Figure FDA0003530646960000061
wherein the content of the first and second substances,
Figure FDA0003530646960000062
is by scheduling variable cpCalculated weight coefficient, zrIs the road surface height, fa,fdThe control force and the vehicle body load respectively applied to the active suspension are known inputs;
Figure FDA0003530646960000063
is a variable parameter cpTaking the coefficient matrix at the boundary value, namely:
Figure FDA0003530646960000064
Figure FDA0003530646960000065
b, G, H, D, E and F are corresponding coefficient matrixes respectively;
step four, designing a state observer to estimate the state of the system:
for the linear parametric system described in expression (6), measurable system output is utilized
Figure FDA0003530646960000066
As an observed quantity, a state observer is designed, wherein
Figure FDA0003530646960000067
Is the suspension sprung mass acceleration, and Δ l is the relative displacement of the sprung and unsprung masses;
consider faAnd fdFor known amount, respectively for cp＝cpmaxAnd cp＝cpminDesigning a state observer under two conditions;
when c is going top＝cpmaxThe time design state observer is as follows:
Figure FDA0003530646960000071
wherein:
Figure FDA0003530646960000072
in order to feed back the gain to the observer,
Figure FDA0003530646960000073
in order to obtain the sliding-mode gain of the observer,
Figure FDA0003530646960000074
respectively represent the state x1、x2、x3、x4Is determined by the estimated value of (c),
Figure FDA0003530646960000075
respectively represent outputs y1、y2An estimated value of (d);
similarly, when cp＝cpminThe time design state observer is as follows:
Figure FDA0003530646960000076
wherein:
Figure FDA0003530646960000077
in order to feed back the gain to the observer,
Figure FDA0003530646960000078
in order to obtain the sliding-mode gain of the observer,
Figure FDA0003530646960000079
respectively represent the state x1、x2、x3、x4Is determined by the estimated value of (c),
Figure FDA00035306469600000710
respectively represent outputs y1、y2An estimated value of (d);
the state observer is written in the form of a multicellular body as follows:
Figure FDA00035306469600000711
wherein:
Figure FDA00035306469600000712
respectively as feedback gain matrixes of the observer at the top of the multicellular body;
Figure FDA0003530646960000081
respectively are observer sliding mode gain matrixes at the top of the multicellular body;
in order to avoid the influence of buffeting on state estimation, the following equivalent sign functions are adopted to replace the sign function sign (e) in the observer designed by expression (9):
Figure FDA0003530646960000082
in the formula:
Figure FDA0003530646960000083
is the estimated error of the output; eta is a small positive number, and can adjust the slope of the function near a zero-value estimation error to influence the reconstruction precision of unknown input to the system;
step five, calculating an error equation of the observer:
defining the state estimation error:
Figure FDA0003530646960000084
are respectively paired with cp＝cpmaxAnd cp＝cpminCalculating an estimation error equation of the observer under two conditions;
when c is going top＝cpmaxThe observer error equation is then as follows:
Figure FDA0003530646960000085
wherein:
Figure FDA0003530646960000091
Figure FDA0003530646960000092
Figure FDA0003530646960000093
Figure FDA0003530646960000094
similarly, when cp＝cpminThe observer error equation is then as follows:
Figure FDA0003530646960000095
wherein:
Figure FDA0003530646960000096
Figure FDA0003530646960000097
Figure FDA0003530646960000098
Figure FDA0003530646960000099
writing the error equation to the form of a multicellular body is as follows:
Figure FDA00035306469600000910
wherein:
Figure FDA0003530646960000101
Figure FDA0003530646960000102
designing an observer gain matrix to ensure the stability of an observer error equation, wherein the observer gain matrix is as follows:
K(cp)＝P-1(cp)Y(cp)；
the error equation is:
Figure FDA0003530646960000103
seventhly, the estimation of the road height is realized through unknown input reconstruction, wherein the road height reconstruction is as follows:
Figure FDA0003530646960000104
2. the method according to claim 1, wherein in the fifth step,
Figure FDA0003530646960000105
Figure FDA0003530646960000106
3. the method according to claim 1, wherein in the sixth step,
Figure FDA0003530646960000107
in the formula (I), the compound is shown in the specification,
Figure FDA0003530646960000108
representing the road height estimation error.
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