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CN111169247A - Vehicle active suspension coordinated anti-saturation control method based on command filtering - Google Patents

Vehicle active suspension coordinated anti-saturation control method based on command filtering Download PDF

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CN111169247A
CN111169247A CN202010056356.2A CN202010056356A CN111169247A CN 111169247 A CN111169247 A CN 111169247A CN 202010056356 A CN202010056356 A CN 202010056356A CN 111169247 A CN111169247 A CN 111169247A
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suspension
saturation
controller
formula
follows
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CN111169247B (en
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刘爽
郝若兰
赵丁选
巩明德
倪涛
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Yanshan University
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Yanshan University
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60G—VEHICLE SUSPENSION ARRANGEMENTS
    • B60G17/00—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load
    • B60G17/015—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements
    • B60G17/018—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements characterised by the use of a specific signal treatment or control method
    • B60G17/0182—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements characterised by the use of a specific signal treatment or control method involving parameter estimation, e.g. observer, Kalman filter

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  • Mechanical Engineering (AREA)
  • Vehicle Body Suspensions (AREA)

Abstract

The invention discloses a vehicle active suspension coordinated anti-saturation control method based on command filtering, belonging to the field of automobile control and comprising the following steps of: establishing a two-degree-of-freedom nonlinear active suspension model; step two, reasoning and coordinating a formula required by the anti-saturation controller according to the suspension mathematical model established in the step one, and performing stability certification; and step three, adjusting the parameters of the controller and comparing simulation results. The invention can solve the conflict between the vertical acceleration of the vehicle body and the dynamic stroke of the suspension, and effectively improves the riding comfort and the operation stability; the invention can also solve the problem of saturation of the driving force, effectively solves the influence of the output saturation of the actuator on a suspension system, and obviously improves the overall performance of the suspension; and the derivative of the virtual control is obtained by adopting a command filtering mode, so that the controller is more beneficial to practical application, obtains better control effect and can be applied to the field of suspension control.

Description

Vehicle active suspension coordinated anti-saturation control method based on command filtering
Technical Field
The invention relates to the technical field of automobile control, in particular to a vehicle active suspension coordinated anti-saturation control method based on command filtering.
Background
Because the active suspension can control the output active force through a control algorithm, the vertical acceleration of a vehicle body, the dynamic stroke of the suspension and the dynamic-static load ratio of a tire can be effectively reduced by designing the active force, and compared with a passive suspension and a semi-active suspension, the active suspension can effectively improve the smoothness, the driving safety and the like of vehicle driving, so that the passive suspension and the semi-active suspension are gradually replaced in the field of automobiles.
With the continuous popularization of the active suspension, the problems brought by the active suspension are worthy of further research, the active force output by the active suspension is considered, and due to the influences of a plurality of uncertain factors, uncertain disturbances and other factors existing in practice, the actuator needs to output larger active force to reduce the influence of external disturbances, but in practical application, the effect is not ideal because of the influence of amplitude saturation of the actuator, and if the influence of amplitude saturation of the actuator is not solved, the control effect is deteriorated. It is therefore necessary to take into account the output saturation problem of active suspensions. The active suspension is a complex nonlinear dynamic system, so that a proper nonlinear active suspension model is needed to be established. Since vehicle load is a variable, it is necessary to consider the problem of uncertain parameters in active suspension. In the active suspension system, a conflict exists between the vertical acceleration of a vehicle body and the dynamic stroke of a suspension, when the vertical acceleration of the vehicle body is reduced for obtaining better riding comfort, the value of the dynamic stroke of the suspension is increased, the service life of a vehicle is prolonged when the dynamic stroke of the suspension is increased, and the operation stability of the vehicle is also reduced, so that a method for coordinately controlling the vertical acceleration of the vehicle body and the dynamic stroke of the suspension is needed to be designed.
The existing research direction for active suspension vehicles should be biased to the following points:
establishing a suitable nonlinear model is necessary for further analyzing the performance of the active suspension and the design of the controller.
Considering the saturation problem of initiative suspension executor, if the executor produces the saturation, will seriously reduce system performance, can reduce and take comfortable performance, consequently designed auxiliary system in this patent, through designing anti saturation compensator, effectually improved vehicle riding comfort, operating stability and driving safety nature.
The vertical acceleration of the vehicle body and the dynamic stroke of the suspension are controlled in a coordinated mode, the operational stability and the riding comfort are related to the magnitude of the dynamic stroke of the suspension and the vertical acceleration of the vehicle body, but the conflict exists between the vertical acceleration of the vehicle body and the dynamic stroke of the suspension, and therefore the nonlinear filter can well switch and control the vertical acceleration of the vehicle body and the dynamic stroke of the suspension.
For the uncertainty estimation, the vehicle load is a variable during the vehicle travel. Therefore, it is necessary to consider the uncertainty of the parameters, and the traditional method cannot solve the influence caused by the uncertainty well.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a vehicle active suspension coordinated anti-saturation control method based on command filtering, which considers uncertain parameters in a suspension system, effectively solves the output saturation problem of an actuator in the active suspension system and the conflict between the vertical acceleration of a vehicle body and the dynamic stroke of the suspension by designing an anti-saturation compensation system and a controller, and solves the influence of the uncertain parameters on the system by adopting a self-adaptive method.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a vehicle active suspension coordinated anti-saturation control method based on command filtering is characterized in that: the method comprises the following steps:
the method comprises the following steps: establishing a two-degree-of-freedom nonlinear active suspension model;
step two: reasoning and coordinating a formula required by the anti-saturation controller according to the suspension mathematical model established in the step one, and carrying out stability certification;
step three: and (5) comparing the parameter adjustment of the controller with the simulation result.
The technical scheme of the invention is further improved as follows: the first step comprises the following steps:
i, establishing a dynamic model of the active suspension according to Newton's second law:
Figure BDA0002373010170000031
in formula (1), Fc,Fk,Ft,FbThe expression of (a) is as follows:
Figure BDA0002373010170000032
Fk＝kk(zs-zu)+kkn(zs-zu)
Ft＝kt(zu-z0)
Figure BDA0002373010170000033
wherein m is m in the suspension dynamics modelsRepresenting the sprung mass of the suspension, muRepresenting unsprung mass of the suspension, FcRepresenting the non-linear damping force of the suspension, FkRepresenting the non-linear stiffness of the suspension, FtRepresenting the stiffness of the tyre, FbIndicating the damping of the tyre, uzRepresenting the output force, k, of the active suspensionkExpressing the linear stiffness coefficient, k, of the suspensionknNonlinear wash, k, representing suspension stiffnesstRepresenting the coefficient of stiffness of the tire, bfRepresenting the damping coefficient, z, of the tyresIndicating the vertical displacement of the body, zuIndicating the vertical displacement of the tyre, z0Representing a road surface input;
II: abstracting the dynamics model into a mathematical model of the suspension:
the kinetic model is first written in the form of a state space expression:
establishing a space state expression of the active suspension of the vehicle, and defining state variables as follows:
Figure BDA0002373010170000034
the kinetic equation of equation (1) is rewritten as:
Figure BDA0002373010170000035
definition of theta1＝1/msIs an uncertain parameter of the system;
to facilitate the design of the controller, the following arguments are introduced:
Lemma1
presence of gammac> 0 and a controller parameter k > 0, satisfies the following equation, the state error z1Satisfy H∞The performance, d, represents the external disturbance,
Figure BDA0002373010170000041
Lemma2
the command filtering is defined as follows:
Figure BDA0002373010170000042
Figure BDA0002373010170000043
wherein phi1(0)＝β1(0)，φ2(0)＝0，φ1，φ2is the output of the command filter, β1is the input of a command filter, if the input signal beta is greater than 01satisfies | beta1|≤η1，
Figure BDA0002373010170000044
η21Is a normal number, there is 0 < ζn＜1，ωnGreater than 0, may be such that phi1-β1|≤κ1，
Figure BDA0002373010170000045
Is bounded;
Lemma3
for any positive number λiWhen | vi|＜λiThen, the following inequality is satisfied:
Figure BDA0002373010170000046
the formula (2) is a mathematical model of the two-degree-of-freedom active suspension, and a coordinated anti-saturation controller is designed according to the mathematical model of the active suspension.
The technical scheme of the invention is further improved as follows: the second step comprises the following steps:
designing a coordinated anti-saturation controller according to the suspension mathematical model established in the first step, wherein the control target of the controller comprises the steps of coordinating and controlling the vertical acceleration of the vehicle body and the dynamic stroke of the suspension, wherein the coordination and control of the vertical acceleration of the vehicle body and the dynamic stroke of the suspension are required to improve the riding comfort and the operation stability because the vertical acceleration of the vehicle body and the dynamic stroke of the suspension in the suspension conflict with each other;
s1: designing a coordinated anti-saturation controller to stabilize the motion state of the vehicle body:
let x1＝zs,
Figure BDA0002373010170000051
x3＝zu,
Figure BDA0002373010170000052
x1Representing a first state variable, x2Denotes a second state variable, x3Denotes a third state variable, x4Represents a fourth state variable;
the anti-saturation output force of the active suspension is designed as follows:
Figure BDA0002373010170000053
in the formula Fm＝-Fc-Fk,k2＞0,g1＞0k2,g1Are all the design parameters of the controller,
Figure BDA0002373010170000054
is the derivative of the virtual control variable solved by command filtering; z is a radical of2Is a defined state variable, v1Is a defined error compensation, e2Is a defined auxiliary error variable that is,
Figure BDA0002373010170000055
is theta1Estimated value of theta1＝1/ms，ysmIs the maximum value allowed by the set suspension dynamic stroke;
s2: the stability of the coordinated anti-saturation controller was demonstrated.
The technical scheme of the invention is further improved as follows: the design process of the coordinated anti-saturation controller in the step S1 specifically includes the following steps:
s11, coordinating and controlling the relationship between the vertical acceleration of the vehicle body and the dynamic stroke of the suspension:
defining the dynamic stroke of the suspension as
Y1＝zs-zu＝x1-x3
Due to the limitation of physical and mechanical structures, the service life of the suspension, therefore, the dynamic stroke of the suspension should be limited within a reasonable range:
Y1≤ysm＜Δysmax
in the formula ysmThe maximum range of the suspension dynamic stroke set for the patent is smaller than the maximum allowable value of the suspension dynamic stroke, so that the suspension dynamic stroke can be effectively improved, and the running smoothness of a vehicle is improved;
in order to coordinately control the relationship between the vertical acceleration of the vehicle body and the dynamic stroke of the suspension, the following nonlinear filter is designed:
Figure BDA0002373010170000061
in the formula of1Is a small positive number, k3For the design parameter of the nonlinear filter, state x3After filtering, obtaining
Figure BDA0002373010170000062
ψ1(Y1) Is a suspension dynamic travel function and is defined as follows:
Figure BDA0002373010170000063
in the formula of1For design parameters, the ratios in equation (3)
Figure BDA0002373010170000064
ψ1(Y1) Change slowly, so in the filter equation, will ψ1(Y1) As a constant process, we can obtain:
Figure BDA0002373010170000065
when the suspension stroke is within a given range, i.e. Y1≤ysmAvailable psi1(Y1) When 0, there is:
Figure BDA0002373010170000066
in this case a low-pass filter, x3Will fail to pass, the main function of the controller is to adjust the vertical acceleration of the vehicle body; when the suspension stroke exceeds the range specified by the patent, the following conditions are adopted:
Figure BDA0002373010170000067
the high-pass filter is adopted, and the controller is mainly used for adjusting the dynamic stroke of the front wheel and the rear wheel of the suspension;
s12, designing a coordinated anti-saturation controller, and defining the state error as follows:
Figure BDA0002373010170000068
z2＝x2-α1
designing a command filtering mode to obtain a derivative of the virtual control signal; design command filtering is shown as lemma 2:
Figure BDA0002373010170000071
in the formula beta1is the input of a command filter, α1＝φ1,1,
Figure BDA0002373010170000072
respectively, of the command filter, but the command filter may cause a filtering error, and therefore, in order to reduce the command filtering error (α)1-β1) Define error compensation as:
Figure BDA0002373010170000074
xi in the formula1,ξ2The error compensation signal can compensate the filtering error and improve the control effect, and the following error compensation signals are designed:
Figure BDA0002373010170000073
in the formula k2,μ1Designing parameters for the controller;
the virtual control function is defined as follows:
Figure BDA0002373010170000075
in the formula L1＝ε1+k3ψ1(Y1)，k1Designing parameters for the controller;
s13: because various uncertain disturbances exist in an actual suspension physical system, a larger main force needs to be output in an active suspension to counteract the potential disturbances, but the actual vehicle suspension system has physical limitation, and the force output by the active suspension cannot be increased without limit, so that an anti-saturation compensation link is designed to solve the saturation phenomenon of the output main force to obtain better smoothness, and a saturation function is defined as:
uz＝sat(vz) (9)
the saturation error is defined as:
Δuz＝sat(vz)-vz
sat(vz) Is defined as:
Figure BDA0002373010170000081
the auxiliary error variables are defined as follows:
e2＝z2-η2
variable η in the formula2The design is as follows:
Figure BDA0002373010170000082
the anti-saturation output force of the active suspension is as follows:
Figure BDA0002373010170000083
in the formula Fm＝-Fc-Fk,k2＞0,g1＞0；
Design uncertainty parameters are as follows:
Figure BDA0002373010170000084
in the formula tau1＝(Fm+uz)e2,r1The parameter of the design is more than 0,
Figure BDA0002373010170000085
θ1in order to not determine the parameters of the device,
Figure BDA0002373010170000086
are each theta1An estimated value of (d); theta1maxIs theta1Maximum value of, theta1minIs theta1Minimum value of (1), Fm＝-Fc-FkIs a defined intermediate quantity, e2Are defined variables.
The technical scheme of the invention is further improved as follows: the specific method in S2 is as follows:
the lyapunov function of the first step is first chosen as follows:
Figure BDA0002373010170000087
the derivation of equation (13) can be:
Figure BDA0002373010170000091
from equation (6), the definition of the error compensation and the state error definition of the system can be derived:
Figure BDA0002373010170000092
for v1The derivation can be:
Figure BDA0002373010170000093
due to x2＝z2+α1X is to be2＝z2+α1And formula (3) into the above formula:
Figure BDA0002373010170000094
in the formula L1＝ε1+k3ψ1(Y1)；
Herein, design is made
Figure BDA0002373010170000095
Will be provided with
Figure BDA0002373010170000096
Is substituted into
Figure BDA0002373010170000097
The method can be obtained by the following steps:
Figure BDA0002373010170000098
because of the fact that
Figure BDA0002373010170000099
Substitution of equation (15) into equation (14) yields:
Figure BDA00023730101700000910
herein, design is made
Figure BDA00023730101700000911
will beta1Substitution into equation (16) can give:
Figure BDA00023730101700000912
the second step of the Lyapunov function is selected as follows:
Figure BDA00023730101700000913
to V2The derivation can be:
Figure BDA00023730101700000914
from z1,z2The definition can be given as follows:
v2＝z2-ξ2＝x2-α1-ξ2
for v2The derivation can be:
Figure BDA0002373010170000101
will be provided with
Figure BDA0002373010170000102
Substitution into
Figure BDA0002373010170000103
The following can be obtained:
Figure BDA0002373010170000104
designed here
Figure BDA0002373010170000105
And will be
Figure BDA0002373010170000106
Is substituted into
Figure BDA0002373010170000107
The method can be obtained by the following steps:
Figure BDA0002373010170000108
by e2The definition can be given as follows:
Figure BDA0002373010170000109
substituting equation (10) into equation (18) yields:
Figure BDA00023730101700001010
substitution of formula (19) into
Figure BDA00023730101700001011
The following can be obtained:
Figure BDA00023730101700001012
design vzAs follows:
Figure BDA00023730101700001013
design uncertainty parameter
Figure BDA00023730101700001014
As follows:
Figure BDA0002373010170000111
v is to bezSubstitution into equation (19) yields:
Figure BDA0002373010170000112
the above formula and formula (22) are substituted into formula (20):
Figure BDA0002373010170000113
available according to Lemma 3:
Figure BDA0002373010170000114
therefore, the following can be obtained:
Figure BDA0002373010170000115
by the inequality 2ab ≦ a2+b2The following can be obtained:
Figure BDA0002373010170000116
and because of
Figure BDA0002373010170000117
Is bounded by order
Figure BDA0002373010170000118
Further, it is possible to obtain:
Figure BDA0002373010170000119
let C1＝min{μ1,k2Is obtained by the formula (24):
Figure BDA00023730101700001110
namely, it is
Figure BDA00023730101700001111
At t → ∞, z1,z2,v1,v2,η2The system is stable due to the fact that the system is bounded;
the design and stability of the suspension system to be researched are considered to be formed by two subsystems, namely a sprung mass subsystem, an unsprung mass subsystem and a controller, and are proved to mainly aim at the sprung mass subsystem, so that the stability of the unsprung mass subsystem is required to be met, and the stability of the whole suspension system can be proved; therefore, the zero dynamic stability of the system is demonstrated below:
let z1＝z2＝0,v1＝v2＝0,e2When the external disturbance d is 0, the actuator will not be saturated because the saturation force of the suspension is caused by the external disturbance, so we can obtain:
uz＝-Fm(25)
substituting equation (25) into the unsprung mass subsystem may result in:
X＝A1X+BZ (26)
writing equation (26) in the form of a matrix:
wherein
Figure BDA0002373010170000121
Because A is1Is Hurwitz, so the zero dynamics of the system is asymptotically stable, attested to completion.
The technical scheme of the invention is further improved as follows: the concrete method in the third step is as follows:
a: the values of the suspension system parameters and the controller parameters are used for adjusting the controller parameters, so that the controller parameters obtain a certain numerical value, the vertical acceleration of a vehicle body, the dynamic stroke of the suspension and the dynamic and static load ratio of tires are further reduced, the safety performance and the operation stability of vehicle running are improved, and better riding comfort is obtained;
b: and the adjusting controller analyzes the effect of the coordinated anti-saturation controller applied to the suspension system.
Due to the adoption of the technical scheme, the invention has the technical progress that:
1. according to the invention, uncertain parameters in a suspension system are considered, through designing an anti-saturation compensation system and a controller, the output saturation problem of an actuator in an active suspension system and the conflict between the vertical acceleration of a vehicle body and the dynamic stroke of the suspension are effectively solved, the influence of the uncertain parameters on the system is solved by adopting a self-adaptive method, and the overall performance of the suspension system is improved.
2. In order to coordinate and control the vertical acceleration of the vehicle body and the dynamic stroke of the suspension, the nonlinear filter is designed, and the derivative of virtual control is obtained in a command filtering mode, so that the controller is more beneficial to practical application, a better control effect is obtained, the nonlinear filter can be applied to the field of suspension control, and the riding comfort, the operation stability and the like of the vehicle are effectively improved.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram of a model suspension system of the present invention;
FIG. 3 is a schematic of the road surface input of the present invention;
FIG. 4 is an active force diagram of the present invention;
FIG. 5 is a graph of the vertical acceleration of the vehicle body of the present invention;
FIG. 6 is a graph of the dynamic travel of the suspension of the present invention;
FIG. 7 is a dynamic-static load ratio curve diagram of the present invention.
Detailed Description
The present invention will be described in further detail with reference to FIGS. 1 to 7 and examples:
step one, establishing a two-degree-of-freedom nonlinear active suspension model: establishing a dynamic model of the suspension and abstracting the dynamic model into a mathematical model of the suspension according to Newton's second law;
i: establishing a two-degree-of-freedom nonlinear active suspension dynamic model;
FIG. 2 is a model diagram of a suspension system, in which m is a dynamic model of the suspensionsRepresenting the sprung mass of the suspension, muRepresenting unsprung mass of the suspension, FcRepresenting the non-linear damping force of the suspension, FkRepresenting the non-linear stiffness of the suspension, FtRepresenting the stiffness of the tyre, FbIndicating the damping of the tyre, uzRepresenting the output force, k, of the active suspensionkExpressing the linear stiffness coefficient, k, of the suspensionknNonlinear wash, k, representing suspension stiffnesstRepresenting the coefficient of stiffness of the tire, bfRepresenting the damping coefficient, z, of the tyresIndicating the vertical displacement of the body, zuIndicating the vertical displacement of the tyre, z0Representing road surface input.
According to the procedure shown in fig. 1, a kinetic model is first established according to newton's second law as follows:
establishing a dynamic model of the active suspension according to Newton's second law:
Figure BDA0002373010170000141
in formula (1), Fc,Fk,Ft,FbThe expression of (a) is as follows:
Figure BDA0002373010170000142
Fk＝kk(zs-zu)+kkn(zs-zu)
Ft＝kt(zu-z0)
Figure BDA0002373010170000143
II: converting the suspension dynamics model into a suspension mathematical model;
let x1＝zs,
Figure BDA0002373010170000144
x3＝zu,
Figure BDA0002373010170000145
x1Representing a first state variable, x2Denotes a second state variable, x3Denotes a third state variable, x4Represents a fourth state variable
The kinetic equation of equation (1) is rewritten as:
Figure BDA0002373010170000146
the parameter m is easily caused by different loads of vehiclessChanges occur, thus defining theta1＝1/msIs an uncertain parameter of the system.
To facilitate the design of the controller, the following arguments are introduced:
Lemma1
presence of gammac> 0 and the controller parameter k > 0, satisfies the following equation, we call the state error z1Satisfy H∞And (4) performance. d represents an external disturbance.
Figure BDA0002373010170000147
Lemma2
The command filtering is defined as follows:
Figure BDA0002373010170000151
Figure BDA0002373010170000152
wherein phi1(0)＝β1(0)，φ2(0)＝0，φ1，φ2is the output of the command filter, β1for t > 0, if the input signal β is1satisfies | beta1|≤η1，
Figure BDA0002373010170000153
η21Is a normal number, there is 0 < ζn＜1，ωn> 0, can be such that | φ1-β1|≤κ1，
Figure BDA0002373010170000154
Is bounded.
Lemma3
For any positive number λiWhen | vi|＜λiThen, the following inequality is satisfied:
Figure BDA0002373010170000155
the formula (2) is a mathematical model of the two-degree-of-freedom active suspension, and a coordinated anti-saturation controller is designed according to the mathematical model of the active suspension.
Step two: reasoning and coordinating a formula required by the anti-saturation controller according to the suspension mathematical model established in the step one, and carrying out stability certification;
s1: and designing a coordinated anti-saturation controller to stabilize the motion condition of the vehicle body.
The control targets of the controller are: and the relationship between the vertical acceleration of the vehicle body and the dynamic stroke of the suspension is coordinately controlled. Because of the conflict between vertical acceleration on the vehicle and the suspension stroke.
Defining the dynamic stroke of the suspension as follows:
Y1＝zs-zu＝x1-x3
due to the limitation of physical and mechanical structures, the service life of the suspension, therefore, the dynamic stroke of the suspension should be limited within a reasonable range:
Y1≤ysm＜Δysmax
in the formula ysmThe maximum range of the suspension dynamic stroke set by the patent is smaller than the maximum allowable value of the suspension dynamic stroke, so that the suspension dynamic stroke can be effectively improved, and the running smoothness of a vehicle is improved.
In order to coordinately control the relationship between the vertical acceleration of the vehicle body and the dynamic stroke of the suspension, the following nonlinear filter is designed:
Figure BDA0002373010170000161
in the formula of1Is a small positive number, k3For the design parameter of the nonlinear filter, state x3After filtering, obtaining
Figure BDA0002373010170000162
ψ1(Y1) Is a suspension dynamic travel function and is defined as follows:
Figure BDA0002373010170000163
in the formula of1For design parameters, the ratios in equation (3)
Figure BDA0002373010170000164
ψ1(Y1) Change slowly, so in the filter equation, will ψ1(Y1) As a constant process, we can obtain:
Figure BDA0002373010170000165
when the suspension stroke is within a given range, i.e. Y1≤ysmAvailable psi1(Y1) When 0, there is:
Figure BDA0002373010170000166
in this case a low-pass filter, x3Will not pass through, the main function of the controller is to adjust the vertical acceleration of the body. When the suspension stroke exceeds the range specified by the patent, the following conditions are adopted:
Figure BDA0002373010170000167
in this case a high pass filter, and the main function of the controller will be to adjust the travel of the front and rear wheels of the suspension.
The state error is defined as follows:
Figure BDA0002373010170000171
z2＝x2-α1
since in practice there are difficulties in obtaining the derivative, the patent envisages that the derivative of the virtual control signal is obtained by means of filtering. Design command filtering is shown as lemma 2:
Figure BDA0002373010170000172
in the formula beta1is the input of a command filter, α1＝φ1,1,
Figure BDA0002373010170000173
but the command filter may cause a filtering error, and therefore, in order to reduce the command filtering error (α)1-β1) The influence of (c).
Error compensation is defined as:
Figure BDA0002373010170000175
xi in the formula1,ξ2The error compensation signal can compensate the filtering error and improve the control effect, and the following error compensation signals are designed:
Figure BDA0002373010170000174
in the formula k2,μ1Parameters are designed for the controller.
The virtual control function is defined as follows:
Figure BDA0002373010170000176
in the formula L1＝ε1+k3ψ1(Y1)，k1Parameters are designed for the controller.
There are various uncertain disturbances in the actual suspension physical system, these potential disturbances act in the vehicle suspension system, and the active suspension is required to output larger active force to counteract these potential disturbances, but the actual vehicle suspension system is physically limited, and the force output by the active suspension cannot be increased without limit. An anti-saturation compensation link is introduced in the part to solve the saturation phenomenon of the output driving force so as to obtain better smoothness.
The saturation function is defined as:
uz＝sat(vz) (9)
the saturation error is defined as:
Δuz＝sat(vz)-vz
sat(vz) Is defined as:
Figure BDA0002373010170000181
the auxiliary error variables are defined as follows:
e2＝z2-η2
variable η in the formula2The design is as follows:
Figure BDA0002373010170000182
the anti-saturation output force of the active suspension is as follows:
Figure BDA0002373010170000183
in the formula Fm＝-Fc-Fk,k2＞0,g1＞0。
Design uncertainty parameters are as follows:
Figure BDA0002373010170000184
in the formula tau1＝(Fm+uz)e2,r1The parameter of the design is more than 0,
Figure BDA0002373010170000185
θ1in order to not determine the parameters of the device,
Figure BDA0002373010170000186
are each theta1An estimated value of (d); theta1maxIs theta1Maximum value of, theta1minIs theta1Minimum value of (1), Fm＝-Fc-FkIs a defined intermediate quantity, e2Are defined variables.
In order to coordinate the design process of the anti-saturation controller, the stability of the controller is demonstrated below.
S2: the stability of the coordinated anti-saturation controller was demonstrated.
The lyapunov function of the first step is first chosen as follows:
Figure BDA0002373010170000191
the derivation of equation (13) can be:
Figure BDA0002373010170000192
from equation (6), the definition of the error compensation and the state error definition of the system can be derived:
Figure BDA0002373010170000193
for v1The derivation can be:
Figure BDA0002373010170000194
due to x2＝z2+α1X is to be2＝z2+α1And formula (3) into the above formula:
Figure BDA0002373010170000195
in the formula L1＝ε1+k3ψ1(Y1)。
Herein, design is made
Figure BDA0002373010170000196
Will be provided with
Figure BDA0002373010170000197
Is substituted into
Figure BDA0002373010170000198
The method can be obtained by the following steps:
Figure BDA0002373010170000199
because of the fact that
Figure BDA00023730101700001910
Substitution of equation (15) into equation (14) yields:
Figure BDA00023730101700001911
herein, design is made
Figure BDA00023730101700001912
will beta1Substitution into equation (16) can give:
Figure BDA0002373010170000201
the second step of the Lyapunov function is selected as follows:
Figure BDA0002373010170000202
to V2The derivation can be:
Figure BDA0002373010170000203
from z1,z2The definition can be given as follows:
v2＝z2-ξ2＝x2-α1-ξ2
for v2The derivation can be:
Figure BDA0002373010170000204
will be provided with
Figure BDA0002373010170000205
Substitution into
Figure BDA0002373010170000206
The following can be obtained:
Figure BDA0002373010170000207
designed here
Figure BDA0002373010170000208
And will be
Figure BDA0002373010170000209
Is substituted into
Figure BDA00023730101700002010
The method can be obtained by the following steps:
Figure BDA00023730101700002011
by e2The definition can be given as follows:
Figure BDA00023730101700002012
substituting equation (10) into equation (18) yields:
Figure BDA00023730101700002013
substitution of formula (19) into
Figure BDA00023730101700002014
The following can be obtained:
Figure BDA0002373010170000211
design vzAs follows:
Figure BDA0002373010170000212
design uncertainty parameter
Figure BDA0002373010170000213
As follows:
Figure BDA0002373010170000214
v is to bezSubstitution into equation (19) yields:
Figure BDA0002373010170000215
the above formula and formula (22) are substituted into formula (20):
Figure BDA0002373010170000216
available according to Lemma 3:
Figure BDA0002373010170000217
therefore, the following can be obtained:
Figure BDA0002373010170000218
by the inequality 2ab ≦ a2+b2The following can be obtained:
Figure BDA0002373010170000219
and because of
Figure BDA00023730101700002110
Is bounded by order
Figure BDA00023730101700002111
Further, it is possible to obtain:
Figure BDA00023730101700002112
let C1＝min{μ1,k2Is obtained by the formula (24):
Figure BDA0002373010170000221
namely, it is
Figure BDA0002373010170000222
At t → ∞, z1,z2,v1,v2,η2The system is stable and the certification is finished.
In addition, the invention also proves the zero dynamic stability:
the invention considers the researched suspension system to be composed of two subsystems, namely a sprung mass subsystem, an unsprung mass subsystem and a controller, and the design and stability of the controller prove that the system mainly aims at the sprung mass subsystem, so that the stability of the unsprung mass subsystem is required to be met, and the whole suspension system can be proved to be stable; therefore, zero dynamic stability of the system is demonstrated in this section.
Let z1＝z2＝0,v1＝v2＝0,e2When the external disturbance d is 0, the actuator will not be saturated because the saturation force of the suspension is caused by the external disturbance, so we can obtain:
uz＝-Fm(25)
substituting equation (25) into the unsprung mass subsystem may result in:
X＝A1X+BZ (26)
writing equation (26) in the form of a matrix:
wherein
Figure BDA0002373010170000223
Because A is1Is Hurwitz, so that the zero dynamics of the system is asymptoticAnd (4) the product is stable.
Step three: and (5) comparing the parameter adjustment of the controller with the simulation result.
A: and (4) values of suspension system parameters and controller parameters.
The invention provides a coordinated anti-saturation control strategy, which effectively solves the saturation phenomenon of an actuator in a suspension system, also coordinately controls the relationship between the vertical acceleration of a vehicle body and the dynamic stroke of the suspension, integrally improves the smoothness in the driving process of the vehicle, and carries out simulation comparison verification in the step in order to prove the effectiveness of the method provided by the invention, and the coordinated anti-saturation control method provided by the invention is respectively compared with a self-adaptive backstepping method and a passive suspension without a control method. The root mean square values of the suspension performance indicators under different conditions were calculated. The suspension system parameters were:
ms＝600kg,mu＝60kg,kt＝2×105N/m,bf＝1000Ns/m,
kk＝18000N/m,kkn＝1000Ns/m,be＝2500Ns/m
the controller parameters take the values as:
r1＝0.01,ysm＝0.04,λ3＝0.07,k1＝10,μ1＝200,k2＝200,g1＝0.3,ε1＝0.01
and adjusting the controller according to the controller parameters, and verifying the effectiveness of the coordinated anti-saturation controller.
B: and the adjusting controller analyzes the effect of the coordinated anti-saturation controller applied to the suspension system.
The control effect of the controller is further explained by the comparison of the figures.
Road surface input using z0A 0.04sin (6 tt) sinusoidal road surface input, such as the road surface input shown in fig. 3. In practical application, the actuator needs to provide larger main force to eliminate the influence of external disturbance, however, due to the limitation of physical factors of the actuator, the main force output by the actuator cannot be increased after reaching a certain value, and therefore execution is performedThe device can be saturated, if the saturation problem of the actuator is not considered at the moment, the simulation effect can be deviated, fig. 4 is a comparison graph when the main power is saturated or not, and it can be seen from the graph that the main power in the simulation result at a certain moment reaches 5500N, which is difficult to reach in practice, so that the saturation problem of the actuator is considered, and in order to verify the effectiveness of anti-saturation control, u is setzmax＝2300Nuzmin＝-2300N
As shown in fig. 5: the vertical acceleration of the vehicle body is compared, as shown in FIG. 6: the dynamic stroke of the suspension is shown as a comparison graph in FIG. 7: for a comparison graph of the dynamic-static load ratio of the tire, the vertical acceleration of a vehicle body, the dynamic stroke of a suspension and the dynamic-static load ratio of the tire under three different conditions can be seen from the graphs in FIGS. 5, 6 and 7, the root mean square values of different properties of the suspension are calculated by MATLAB and are shown in Table 1:
TABLE 1 root mean square value of suspension Performance index
Figure BDA0002373010170000241
From fig. 5, it can be seen that when the actuator is saturated, the value of the vertical acceleration of the vehicle body is stabilized to fluctuate around 0 by the coordinated anti-saturation control method proposed by the present invention, whereas the value of the vertical acceleration of the vehicle body by the general conventional adaptive backstepping control method reaches 2m/s2A trend of (a); compared with the self-adaptive backstepping control method, the coordinated anti-saturation control method provided by the invention has the advantage that the vertical acceleration of the vehicle body is reduced by 88%. Compared with a passive suspension, the vertical acceleration of the vehicle body is reduced by 97%, so that the vertical acceleration of the vehicle body can be obviously reduced when the actuator is saturated, and the riding comfort of the vehicle is obviously improved.
Compared with a passive suspension, the method of the invention reduces the dynamic stroke of the suspension by 10 percent, and the method of the invention coordinates and controls the relationship between the vertical acceleration of the vehicle body and the dynamic stroke of the suspension as shown in FIG. 6. From fig. 6, it can be seen that the suspension stroke of the controller designed by the invention is setRange ysmCompared with a passive suspension, the dynamic-static load ratio of the tire based on the method provided by the invention is reduced by 18%, and the driving safety performance of the vehicle is improved.
By combining the comparison and analysis of the simulation result graphs, the coordinated anti-saturation control method provided by the invention can effectively compensate the influence of saturation on the vehicle performance when the actuator is saturated, and can coordinate and control the vertical acceleration of the vehicle body and the dynamic stroke of the suspension, thereby obviously improving the running smoothness of the vehicle.
In summary, the invention considers the uncertain parameters in the suspension system, designs the anti-saturation compensation system and the controller, designs the nonlinear filter, obtains the derivative of the virtual control by adopting the command filtering mode, solves the influence of the uncertain parameters on the system by adopting the self-adaptive method, improves the overall performance of the suspension system, effectively improves the riding comfort and the operation stability of the vehicle, and has practical applicability.

Claims (6)

1. A vehicle active suspension coordinated anti-saturation control method based on command filtering is characterized in that: the method comprises the following steps:
the method comprises the following steps: establishing a two-degree-of-freedom nonlinear active suspension model;
step two: reasoning and coordinating a formula required by the anti-saturation controller according to the suspension mathematical model established in the step one, and carrying out stability certification;
step three: and (5) comparing the parameter adjustment of the controller with the simulation result.
2. The vehicle active suspension coordinated anti-saturation control method based on command filtering is characterized in that: the first step comprises the following steps:
i, establishing a dynamic model of the active suspension according to Newton's second law:
Figure FDA0002373010160000011
in formula (1), Fc,Fk,Ft,FbThe expression of (a) is as follows:
Figure FDA0002373010160000012
Fk＝kk(zs-zu)+kkn(zs-zu)
Ft＝kt(zu-z0)
Figure FDA0002373010160000013
wherein m is m in the suspension dynamics modelsRepresenting the sprung mass of the suspension, muRepresenting unsprung mass of the suspension, FcRepresenting the non-linear damping force of the suspension, FkRepresenting the non-linear stiffness of the suspension, FtRepresenting the stiffness of the tyre, FbIndicating the damping of the tyre, uzRepresenting the output force, k, of the active suspensionkExpressing the linear stiffness coefficient, k, of the suspensionknNonlinear wash, k, representing suspension stiffnesstRepresenting the coefficient of stiffness of the tire, bfRepresenting the damping coefficient, z, of the tyresIndicating the vertical displacement of the body, zuIndicating the vertical displacement of the tyre, z0Representing a road surface input;
II: abstracting the dynamics model into a mathematical model of the suspension:
the kinetic model is first written in the form of a state space expression:
establishing a space state expression of the active suspension of the vehicle, and defining state variables as follows:
Figure FDA0002373010160000021
the kinetic equation of equation (1) is rewritten as:
Figure FDA0002373010160000022
definition of theta1＝1/msIs an uncertain parameter of the system;
to facilitate the design of the controller, the following arguments are introduced:
Lemma1
presence of gammac> 0 and a controller parameter k > 0, satisfies the following equation, the state error z1Satisfy H∞Performance, d represents an external disturbance;
Figure FDA0002373010160000023
Lemma2
the command filtering is defined as follows:
Figure FDA0002373010160000024
Figure FDA0002373010160000025
wherein phi1(0)＝β1(0)，φ2(0)＝0，φ1，φ2is the output of the command filter, β1is the input of a command filter, if the input signal beta is greater than 01satisfies | beta1|≤η1，
Figure FDA0002373010160000026
η1，η21Is a normal number, there is 0 < ζn＜1，ωn> 0, can be such that | φ1-β1|≤κ1，
Figure FDA0002373010160000027
Is bounded;
Lemma3
for any positive number λiWhen | vi|＜λiThen, the following inequality is satisfied:
Figure FDA0002373010160000028
the formula (2) is a mathematical model of the two-degree-of-freedom active suspension, and a coordinated anti-saturation controller is designed according to the mathematical model of the active suspension.
3. The vehicle active suspension coordinated anti-saturation control method based on command filtering is characterized in that: the second step comprises the following steps:
designing a coordinated anti-saturation controller according to the suspension mathematical model established in the first step, wherein the control target of the controller comprises the steps of coordinating and controlling the vertical acceleration of the vehicle body and the dynamic stroke of the suspension, and the riding comfort and the operation stability are improved by coordinating and controlling the vertical acceleration of the vehicle body and the dynamic stroke of the suspension because the vertical acceleration of the vehicle body and the dynamic stroke of the suspension in the suspension conflict with each other;
s1: designing a coordinated anti-saturation controller to stabilize the motion state of the vehicle body:
let x1＝zs,
Figure FDA0002373010160000031
x3＝zu,
Figure FDA0002373010160000032
x1Representing a first state variable, x2Denotes a second state variable, x3Denotes a third state variable, x4Represents a fourth state variable;
the anti-saturation output force of the active suspension is designed as follows:
Figure FDA0002373010160000033
in the formula Fm＝-Fc-Fk,k2＞0,g1＞0k2,g1Are all the design parameters of the controller,
Figure FDA0002373010160000034
is the derivative of the virtual control variable solved by command filtering; z is a radical of2Is a defined state variable, v1Is a defined error compensation, e2Is a defined auxiliary error variable that is,
Figure FDA0002373010160000035
is theta1Estimated value of theta1＝1/ms，ysmIs the maximum value allowed by the set suspension dynamic stroke;
s2: the stability of the coordinated anti-saturation controller was demonstrated.
4. The vehicle active suspension coordinated anti-saturation control method based on command filtering is characterized in that: the design process of the coordinated anti-saturation controller in the step S1 specifically includes the following steps:
s11, coordinating and controlling the relationship between the vertical acceleration of the vehicle body and the dynamic stroke of the suspension:
defining the dynamic stroke of the suspension as follows:
Y1＝zs-zu＝x1-x3
due to the limitation of physical and mechanical structures, the service life of the suspension, therefore, the dynamic stroke of the suspension should be limited within a reasonable range:
Y1≤ysm＜Δysmax
in the formula ysmThe maximum range of the suspension dynamic stroke set for the patent is smaller than the maximum allowable value of the suspension dynamic stroke, so that the suspension dynamic stroke can be effectively improved, and the running smoothness of a vehicle is improved;
in order to coordinately control the relationship between the vertical acceleration of the vehicle body and the dynamic stroke of the suspension, the following nonlinear filter is designed:
Figure FDA0002373010160000041
in the formula of1Is a small positive number, k3For the design parameter of the nonlinear filter, state x3After filtering, obtaining
Figure FDA0002373010160000042
ψ1(Y1) Is a suspension dynamic travel function and is defined as follows:
Figure FDA0002373010160000043
in the formula of1For design parameters, the ratios in equation (3)
Figure FDA0002373010160000044
ψ1(Y1) Change slowly, so in the filter equation, will ψ1(Y1) As a constant process, we can obtain:
Figure FDA0002373010160000045
when the suspension stroke is within a given range, i.e. Y1≤ysmAvailable psi1(Y1) When 0, there is:
Figure FDA0002373010160000046
in this case a low-pass filter, x3Will fail to pass, the main function of the controller is to adjust the vertical acceleration of the vehicle body; when the suspension stroke exceeds the range specified by the patent, the following conditions are adopted:
Figure FDA0002373010160000051
the high-pass filter is adopted, and the controller is mainly used for adjusting the dynamic stroke of the front wheel and the rear wheel of the suspension;
s12, designing a coordinated anti-saturation controller, and defining the state error as follows:
Figure FDA0002373010160000052
z2＝x2-α1
designing a command filtering mode to obtain a derivative of the virtual control signal; design command filtering is shown as lemma 2:
Figure FDA0002373010160000053
in the formula beta1is the input of a command filter, α1＝φ1,1,
Figure FDA0002373010160000054
respectively, of the command filter, but the command filter may cause a filtering error, and therefore, in order to reduce the command filtering error (α)1-β1) Define error compensation as:
Figure FDA0002373010160000055
xi in the formula1,ξ2The error compensation signal can compensate the filtering error and improve the control effect, and the following error compensation signals are designed:
Figure FDA0002373010160000056
in the formula k2,μ1Designing parameters for the controller;
the virtual control function is defined as follows:
Figure FDA0002373010160000057
in the formula L1＝ε1+k3ψ1(Y1)，k1Designing parameters for the controller;
s13: because various uncertain disturbances exist in an actual suspension physical system, a larger main force needs to be output in an active suspension to counteract the potential disturbances, but the actual vehicle suspension system has physical limitation, and the force output by the active suspension cannot be increased without limit, so that an anti-saturation compensation link is designed to solve the saturation phenomenon of the output main force to obtain better smoothness, and a saturation function is defined as:
uz＝sat(vz) (9)
the saturation error is defined as:
Δuz＝sat(vz)-vz
sat(vz) Is defined as:
Figure FDA0002373010160000061
the auxiliary error variables are defined as follows:
e2＝z2-η2
variable η in the formula2The design is as follows:
Figure FDA0002373010160000062
the anti-saturation output force of the active suspension is as follows:
Figure FDA0002373010160000063
in the formula Fm＝-Fc-Fk,k2＞0,g1＞0；
Design uncertainty parameters are as follows:
Figure FDA0002373010160000064
in the formula tau1＝(Fm+uz)e2,r1The parameter of the design is more than 0,
Figure FDA0002373010160000071
θ1in order to not determine the parameters of the device,
Figure FDA0002373010160000072
are each theta1An estimated value of (d); theta1maxIs theta1Maximum value of, theta1minIs theta1Minimum value of (1), Fm＝-Fc-FkIs a defined intermediate quantity, e2Are defined variables.
5. The vehicle active suspension coordinated anti-saturation control method based on command filtering is characterized in that: the specific method in S2 is as follows:
the lyapunov function of the first step is first chosen as follows:
Figure FDA0002373010160000073
the derivation of equation (13) can be:
Figure FDA0002373010160000074
from equation (6), the definition of the error compensation and the state error definition of the system can be derived:
Figure FDA0002373010160000075
for v1The derivation can be:
Figure FDA0002373010160000076
due to x2＝z2+α1X is to be2＝z2+α1And formula (3) into the above formula:
Figure FDA0002373010160000077
in the formula L1＝ε1+k3ψ1(Y1)；
Herein, design is made
Figure FDA0002373010160000078
Will be provided with
Figure FDA0002373010160000079
Is substituted into
Figure FDA00023730101600000710
The method can be obtained by the following steps:
Figure FDA00023730101600000711
because of the fact that
Figure FDA00023730101600000712
Substitution of equation (15) into equation (14) yields:
Figure FDA00023730101600000713
herein, design is made
Figure FDA0002373010160000081
will beta1Substitution into equation (16) can give:
Figure FDA0002373010160000082
the second step of the Lyapunov function is selected as follows:
Figure FDA0002373010160000083
to V2The derivation can be:
Figure FDA0002373010160000084
from z1,z2The definition can be given as follows:
v2＝z2-ξ2＝x2-α1-ξ2
for v2The derivation can be:
Figure FDA0002373010160000085
will be provided with
Figure FDA0002373010160000086
Substitution into
Figure FDA0002373010160000087
The following can be obtained:
Figure FDA0002373010160000088
designed here
Figure FDA0002373010160000089
And will be
Figure FDA00023730101600000810
Is substituted into
Figure FDA00023730101600000811
The method can be obtained by the following steps:
Figure FDA00023730101600000812
by e2The definition can be given as follows:
Figure FDA00023730101600000813
substituting equation (10) into equation (18) yields:
Figure FDA00023730101600000814
substitution of formula (19) into
Figure FDA00023730101600000815
The following can be obtained:
Figure FDA00023730101600000816
design vzAs follows:
Figure FDA0002373010160000091
design uncertainty parameter
Figure FDA0002373010160000092
As follows:
Figure FDA0002373010160000093
v is to bezSubstitution into equation (19) yields:
Figure FDA0002373010160000094
the above formula and formula (22) are substituted into formula (20):
Figure FDA0002373010160000095
available according to Lemma 3:
Figure FDA0002373010160000096
therefore, the following can be obtained:
Figure FDA0002373010160000097
by the inequality 2ab ≦ a2+b2The following can be obtained:
Figure FDA0002373010160000098
and because of
Figure FDA0002373010160000099
Is bounded by order
Figure FDA00023730101600000910
Further, it is possible to obtain:
Figure FDA00023730101600000911
let C1＝min{μ1,k2Is obtained by the formula (24):
Figure FDA0002373010160000101
namely, it is
Figure FDA0002373010160000102
At t → ∞, z1,z2,v1,v2,η2The system is stable due to the fact that the system is bounded;
the design and stability of the suspension system to be researched are considered to be formed by two subsystems, namely a sprung mass subsystem, an unsprung mass subsystem and a controller, and are proved to mainly aim at the sprung mass subsystem, so that the stability of the unsprung mass subsystem is required to be met, and the stability of the whole suspension system can be proved; therefore, the zero dynamic stability of the system is demonstrated below:
let z1＝z2＝0,v1＝v2＝0,e2When the external disturbance d is 0, the actuator will not be saturated because the saturation force of the suspension is caused by the external disturbance, so we can obtain:
uz＝-Fm(25)
substituting equation (25) into the unsprung mass subsystem may result in:
X＝A1X+BZ (26)
writing equation (26) in the form of a matrix:
wherein
Figure FDA0002373010160000103
Because A is1Is Hurwitz, so the zero dynamics of the system is asymptotically stable, attested to completion.
6. The vehicle active suspension coordinated anti-saturation control method based on command filtering is characterized in that: the specific method in the third step is as follows:
a: the values of the suspension system parameters and the controller parameters are used for adjusting the controller parameters, so that the controller parameters obtain a certain numerical value, the vertical acceleration of a vehicle body, the dynamic stroke of the suspension and the dynamic and static load ratio of tires are further reduced, the safety performance and the operation stability of vehicle running are improved, and better riding comfort is obtained;
b: and the adjusting controller analyzes the effect of the coordinated anti-saturation controller applied to the suspension system.
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CN118428178A (en) * 2024-07-02 2024-08-02 中国人民解放军海军工程大学 Overload simulation analysis method and system based on double-degree-of-freedom model

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