CN110096750B - Self-adaptive dynamic surface control method considering nonlinear active suspension actuator - Google Patents

Self-adaptive dynamic surface control method considering nonlinear active suspension actuator Download PDF

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CN110096750B
CN110096750B CN201910261812.4A CN201910261812A CN110096750B CN 110096750 B CN110096750 B CN 110096750B CN 201910261812 A CN201910261812 A CN 201910261812A CN 110096750 B CN110096750 B CN 110096750B
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刘爽
郝若兰
赵丁选
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Yanshan University
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Abstract

The invention relates to a self-adaptive dynamic surface control method considering a nonlinear active suspension actuator, which comprises the steps of firstly establishing a two-degree-of-freedom nonlinear active suspension model through a step I; reasoning a formula required by the self-adaptive dynamic surface controller through the step two, and carrying out stability certification; and step three, adjusting the parameters of the controller and comparing simulation results. According to the invention, firstly, a nonlinear active suspension model is established, and the problem of differential explosion caused by nonlinear factors in a suspension system and multiple derivatives in a high-order system can be solved by adopting self-adaptive dynamic surface control, so that the controller is more beneficial to practical application, obtains a better control effect and can be applied to the field of suspension control.

Description

Self-adaptive dynamic surface control method considering nonlinear active suspension actuator
Technical Field
The invention belongs to the field of automobile dynamic control, and particularly relates to a self-adaptive dynamic surface control method considering a nonlinear active suspension actuator.
Background
The invention relates to a heavy vehicle, which is characterized in that the actual working environment of the heavy vehicle is relatively severe, the road condition is poor, the severe working environment aggravates the vibration of the vehicle, and a conventional passive oil-gas suspension cannot adjust different parameters according to different input of the road surface, so that the vehicle cannot adapt to different road surfaces. Three indicators that are considered to affect the performance of the suspension system are: the vertical acceleration of the vehicle body, the dynamic stroke and the dynamic and static load ratio of the suspension. The active suspension can reduce the influence caused by the vertical acceleration of the vehicle body and bump by a control algorithm, can also improve the running safety performance of the vehicle, and enables the suspension to move within the requirement of mechanical stroke limitation. Active suspensions are increasingly used in the automotive field, gradually replacing passive and semi-active suspensions.
With the increasing popularity of active suspensions. The problems brought by the method are worthy of further research, and considering that the rigidity and the damping in a suspension system are all nonlinear, the establishment of a proper nonlinear suspension system model is one of the directions in which the research needs to be focused, in addition, the action of a servo valve in a hydraulic active suspension controls the quantity of output oil, and further controls the output force, in order to solve the problems, some methods are subjected to linearization processing when the nonlinear suspension model is processed, or the established nonlinear model is too simple, and the actual suspension system is not fully considered; some existing methods do not fully consider servo valve modeling characteristics, and do not fully consider the influence of some uncertain parameters in the suspension system on the suspension system due to the influence of vehicle running.
The existing research direction for heavy vehicles is biased to the following points:
the establishment of a proper nonlinear model is very necessary for the analysis of control effect and system stability, a linear model is selected for a traditional suspension model, the linear model is convenient and simple in analysis and controller design, but the control precision cannot meet the requirement due to the fact that an actual suspension system is a nonlinear system and the linear suspension system model. Therefore, the establishment of a nonlinear suspension model is very necessary for the research of a suspension system.
For the application and improvement of the algorithm, based on the model of the nonlinear hydraulic active suspension taking the servo valve characteristic into consideration, the adaptive algorithm is adopted, the difficult problem of differential explosion is easily formed by multiple derivation in the design process of the controller, the solving becomes more difficult, the controller is more easily deteriorated, the controller becomes more complicated and is not beneficial to practical application, and therefore, it is necessary to design a proper algorithm to solve the differential explosion. The dynamic surface control algorithm is introduced on the basis of self-adaptive control, and the generation of differential explosion is well solved.
For the uncertainty estimation, the vehicle load is a variable during the vehicle travel. As the vehicle speed temperature changes, some parameters of the hydraulic device will change, so it is necessary to take into account the parameter uncertainty. The influence caused by uncertainty cannot be well solved by the traditional method, and the influence of uncertainty parameters on a system can be solved by the self-adaptive method.
Disclosure of Invention
The nonlinear active suspension model is established based on heavy-duty vehicles, considers the parameter uncertainty of a hydraulic system and the limitation of a self-adaptive backstepping algorithm on a high-order system, adopts a self-adaptive dynamic surface control method and provides a simulation control chart of the control algorithm.
The invention discloses a self-adaptive dynamic surface control method considering a nonlinear active suspension actuator, which comprises the following steps of:
s1, establishing a two-degree-of-freedom nonlinear suspension model: establishing a dynamic model of the suspension according to Newton's second law, and abstracting the dynamic model into a mathematical model of the suspension;
s11, establishing a dynamic model of the active suspension according to Newton' S second law:
Figure BDA0002015526060000021
Figure BDA0002015526060000022
the suspension system is a highly complex nonlinear system which is susceptible to various factors in practical application, and the damping force F in the expression is usedcWith elastic force FkConsider the nonlinear form:
wherein
Figure BDA0002015526060000023
Fk＝k(zs-zu)+ξ*k(zs-zu)3
Ft＝kt(zu-z0)
Figure BDA0002015526060000024
Because the electro-hydraulic actuator has small volume and good effect, in the design of the active suspension, an electro-hydraulic system is adopted as the actuator to generate vibration isolation force, the hydraulic device generally has the characteristic of nonlinearity, and the following equation is established by comprehensively considering the nonlinearity dynamics of the hydraulic device:
Fu＝APL (3)
Figure BDA0002015526060000031
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 FuRepresenting the output force of the active suspension, k representing the suspension stiffness coefficient, ktRepresenting the coefficient of stiffness of the tire, bfExpressing the damping coefficient of the tyre, xi expressing the non-linear degree of the suspension rigidity, A expressing the effective area of the piston of the hydraulic cylinder, A2Denotes the area of the piston in the cylinder, AzIndicates the area of the damping hole of the check valve, CdDenotes the flow coefficient, ρ denotes the hydraulic oil density, zsIndicating the vertical displacement of the body, zuIndicating the vertical displacement of the tyre, z0Indicating road surface input, PLRepresenting the load pressure, psDenotes the supply pressure, β e denotes the elastic stiffness of the oil, u denotes the displacement of the servo valve, CtRepresenting the leakage coefficient in the hydraulic cylinder;
Figure BDA0002015526060000032
kvdenotes the servo valve operator, where ω is the servo valve area gradient, kaFor servo valve gain, vtRepresenting the total compression volume of the hydraulic cylinder; eta1，η2Is a damping force coefficient sign introduced for simplifying the expression mode;
s2, designing an adaptive dynamic surface controller: designing an adaptive dynamic surface controller according to the suspension mathematical model established in the step S1, wherein the control targets of the controller comprise: the vertical acceleration of the vehicle body is reduced to improve the riding comfort; the dynamic stroke of the suspension is reduced, so that the service life of the suspension is prolonged; the dynamic-static load ratio of the tire is reduced so as to improve the driving safety;
designing a self-adaptive dynamic surface controller to stabilize the motion condition of the vehicle body:
let x1＝zs,
Figure BDA0002015526060000033
x3＝zu,
Figure BDA0002015526060000034
x5＝PL
x1Representing a first state variable, x2Denotes a second state variable, x3Denotes a third state variable, x4Denotes a fourth state variable, x5Represents a fifth state variable;
Figure BDA0002015526060000035
θ1，θ2，θ3，θ4in order to not determine the parameters of the device,
Figure BDA0002015526060000036
are each theta1，θ2，θ3，θ4An estimated value of (d);
the spool displacement u expression of the servo valve is given below:
Figure BDA0002015526060000037
wherein S2Is a dynamic surface function, tau2Is the time constant, k3Is a controller design parameter, z2Is the state error, z3Is a state error;
s3, adjusting parameters of the self-adaptive dynamic surface controller, and performing simulation verification: because the three control targets of the vertical acceleration of the vehicle body, the dynamic stroke of the suspension and the dynamic and static load ratio of the tire conflict with each other, the parameters of the controller are adjusted to obtain a numerical value which enables the parameter value of the controller to be moderate, so that the designed controller can simultaneously reduce the vertical acceleration of the vehicle body, the dynamic stroke of the suspension and the dynamic and static load ratio of the tire, and further the overall performance of the suspension is improved.
Preferably, the step S1 further includes the following steps,
s12, abstracting the dynamic model of the suspension into a mathematical model of the suspension, firstly writing the dynamic model into a state space expression form:
due to x1＝zs,
Figure BDA0002015526060000041
x3＝zu,
Figure BDA0002015526060000042
x5＝PLDede type (5)
Figure BDA0002015526060000043
Using the system uncertainty parameter theta1，θ2，θ3，θ4Rewriting formula (5) to formula (6):
Fk＝k(x1-x3)+ξ*k(x1-x3)3
Ft＝kt(x3-z0)
Figure BDA0002015526060000045
Figure BDA0002015526060000046
equation (6) is a mathematical model of the two-degree-of-freedom active suspension, and the adaptive dynamic surface controller is designed according to the mathematical model of the active suspension.
Preferably, the design process of the adaptive dynamic surface controller in step S2 specifically includes the following steps:
s21, the control targets of the controller are as follows: on the basis of considering the electro-hydraulic actuator, the controller is designed to reduce the vertical acceleration of the vehicle body, reduce the dynamic stroke of the suspension, reduce the dynamic-static load ratio of the tire and consider the external uncertain disturbance;
let F be-Fc-FkAnd F denotes the inverse of the sum of the nonlinear damping force and the nonlinear elastic force:
z1＝x1-yd (7)
z2＝x2-α1 (8)
z3＝x5-α2 (9)
wherein z is1＝x1-ydFor tracking error, z2＝x2-α1Is a state error, z3＝x5-α2Is a state error, α1For a stable virtual control function, α2For a stable virtual control function, ydIs a reference trajectory;
s22, because the suspension system is a system with higher order, the controller is designed based on the backstepping control theory, and in order to reduce the phenomena of complex calculation and differential explosion caused by multiple derivatives of the virtual control function in the backstepping control theory, the adaptive algorithm is improved, the dynamic surface control is added, and a virtual filter function beta is introduced1And (3) enabling the stable virtual control function to pass through a first-order filter, and estimating the derivative of the virtual control quantity by using a dynamic surface function:
Figure BDA0002015526060000051
α1(0)＝β1(0)
wherein tau is1Is a time constant, α1(0) Denotes alpha1Initial value of (1), beta1(0) Is represented by beta1Defining a dynamic surface function S1＝α1-β1It is possible to obtain:
Figure BDA0002015526060000052
Figure BDA0002015526060000053
Figure BDA0002015526060000054
1continuously bounded, defining its maximum value as M1；
Get
Figure BDA0002015526060000055
S23、z2＝x2-α2Is the state error of the second step, where α2Is a stable virtual control function, and introduces a virtual filter function beta2Let the virtual control function α be stable2Through a first order filter of which τ2Is a time constant, α2(0) Denotes alpha2Initial value of (1), beta2(0) Is represented by beta2An initial value of (1);
Figure BDA0002015526060000056
α2(0)＝β2(0)
defining a dynamic surface function S2＝α2-β2It is possible to obtain:
Figure BDA0002015526060000061
Figure BDA0002015526060000062
wherein
Figure BDA0002015526060000063
Figure BDA0002015526060000064
2Continuously bounded, defining its maximum value as M2；
Get
Figure BDA0002015526060000065
z3＝x5-α2，z3And (3) designing a controller to give servo valve displacement control according to the state error:
Figure BDA0002015526060000066
wherein
Figure BDA0002015526060000067
Are each theta1～θ4Estimated value of k3Are controller parameters.
Preferably, the specific design process of the uncertain parameter in the adaptive dynamic surface controller in step S2 is as follows:
in the active suspension system, the sprung mass is an uncertain parameter and constantly changes along with the number of passengers and the number of vehicle-mounted cargos, so that the uncertainty of the sprung mass needs to be considered in the design process of the controller, and the parameters of an electro-hydraulic servo valve in an electro-hydraulic actuating mechanism are easy to change along with the change of the running environment and the difference of the running state of a vehicle, so the uncertain parameter in the electro-hydraulic actuating mechanism needs to be considered in the design process of the controller;
the specific expression of the self-adaptation law for designing four uncertain parameters is as follows (15):
Figure BDA0002015526060000068
wherein
Figure BDA0002015526060000069
Is thetaiAn estimated value of the parameter of riDesign parameters for the adaptive law, ri＞0，i＝1～4；
Projection mapping
Figure BDA00020155260600000610
The definition is as follows: theta denotes the adaptation law to be designed
Figure BDA00020155260600000611
The parameter estimation error is defined as
Figure BDA0002015526060000071
And satisfies the following properties:
(1)
Figure BDA0002015526060000072
(2)
Figure BDA0002015526060000073
i.e. thetaiIs bounded;
θimaxdenotes thetaiMaximum value of, thetaiminDenotes thetaiThe minimum value of (a) is determined,
Figure BDA0002015526060000074
the parameter estimation error i is 1-4.
Preferably, the adjusting process of the stability of the adaptive dynamic surface controller in step S2 is:
selecting a first Lyapunov function V1The following were used:
Figure BDA0002015526060000075
Figure BDA0002015526060000076
from the young inequality one can obtain:
Figure BDA0002015526060000077
Figure BDA0002015526060000078
wherein sigma1The expression (18) and (19) can be substituted for the expression (17) to obtain the following expression:
Figure BDA0002015526060000079
selecting a second Lyapunov function as:
Figure BDA00020155260600000710
Figure BDA00020155260600000711
Figure BDA00020155260600000712
obtained by applying the Yang inequality, sigma2Is an arbitrarily small number in the young inequality:
Figure BDA00020155260600000713
Figure BDA0002015526060000081
substituting equations (22) and (23) into equation (21) can yield:
Figure BDA0002015526060000082
θ1maxdenotes theta1Maximum value of (d);
selecting a third Lyapunov function:
Figure BDA0002015526060000083
Figure BDA0002015526060000084
Figure BDA0002015526060000085
adjustment parameter k1＝0.5，k2＝300，k3＝300，τ1＝0.01，τ20.01 to ensure
Figure BDA0002015526060000086
The system is semi-globally asymptotically stable.
The invention has the following beneficial effects:
(1) the invention firstly establishes an accurate nonlinear suspension system model, considers the nonlinearity of suspension damping and the nonlinearity of rigidity, and simultaneously considers the damping and the rigidity of the tire. The problem that a suspension mathematical model is simple is solved.
(2) On the basis of the model, nonlinear modeling of the actuator is considered, differential explosion generated by application of a self-adaptive backstepping control algorithm in a high-order system is solved on the basis of uncertainty, and the controller is more beneficial to practical application.
Drawings
FIG. 1 is a flow chart of an adaptive dynamic surface control method of the present invention considering a nonlinear active suspension actuator;
FIG. 2 is a diagram of a suspension system model of the present invention;
FIG. 3 is a schematic view of a road surface input according to the present invention;
FIG. 4 is a graph of the vertical acceleration of the vehicle body of the present invention;
FIG. 5 is a graph of the dynamic travel of the suspension of the present invention; and
FIG. 6 is a dynamic-static load ratio curve diagram of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The technical scheme adopted by the invention for solving the technical problems is as follows:
step one, establishing a two-degree-of-freedom nonlinear active suspension model;
secondly, reasoning a formula required by the controller of the patent and carrying out stability certification;
and step three, adjusting the parameters of the controller and comparing simulation results.
The technical scheme is explained in detail as follows:
step 1, establishing a two-degree-of-freedom nonlinear active suspension model, wherein the two-degree-of-freedom nonlinear active suspension model comprises establishing a dynamic model of a suspension and abstracting the dynamic model into a mathematical model of the suspension according to a Newton's second law;
step 1.1, 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 suspension modelsRepresenting the sprung mass of the suspension, muRepresenting unsprung mass of the suspension, FcExpressing the nonlinear damping force of the suspension, FkRepresenting the non-linear stiffness of the suspension, FtRepresenting the stiffness of the tyre, FbIndicating damping of the tyre, zsIndicating the vertical displacement of the body, zuIndicating the vertical displacement of the tyre, z0Representing the road surface input, according to the procedure shown in fig. 1, a dynamic model is first established according to newton's second law as follows:
Figure BDA0002015526060000091
Figure BDA0002015526060000092
wherein
Figure BDA0002015526060000093
Fk＝k(zs-zu)+ξ*k(zs-zu)3
Ft＝kt(zu-z0)
Figure BDA0002015526060000094
Consider the force of a hydraulic device providing an active suspension system:
Fu＝APL (3)
Figure BDA0002015526060000101
wherein k istRepresenting the coefficient of stiffness of the tire, bfRepresents the tire damping coefficient, k represents the suspension stiffness coefficient, and ξ represents the degree of non-linearity of the suspension stiffness. A. the2Denotes the area of the piston in the cylinder, AzIndicates the area of the damping hole of the check valve, CdDenotes the flow coefficient, PLRepresenting load pressure,. beta.e representing the elastic stiffness of the oil, psThe supply pressure is indicated, u the displacement of the servo valve and a the effective area of the cylinder piston. CtThe coefficient of leakage in the hydraulic cylinder is represented,
Figure BDA0002015526060000102
kvis a servo valve operator, where ω is the servo valve area gradient, ρ represents the hydraulic oil density, kaFor servo valve gain, vtRepresenting the total compression volume of the cylinder, FuRepresenting the output force, η, of the active suspension1，η2Is the sign of the damping force coefficient introduced to simplify the expression.
Step 1.2, converting a suspension dynamic model into a suspension mathematical model;
let x1＝zs,
Figure BDA0002015526060000103
x3＝zu,
Figure BDA0002015526060000104
x5＝PL，
x1Representing a first state variable, x2Denotes a second state variable, x3Denotes a third state variable, x4Denotes a fourth state variable, x5A fifth state variable is represented which is,
Figure BDA0002015526060000105
using a system uncertainty parameter of
Figure BDA0002015526060000106
Rewriting formula (5) to formula (6):
Figure BDA0002015526060000111
Fk＝k(x1-x3)+ξ*k(x1-x3)3
Ft＝kt(x3-z0)
Figure BDA0002015526060000112
Figure BDA0002015526060000113
the formula (6) is a two-degree-of-freedom active suspension mathematical model, and the adaptive dynamic surface controller is designed according to the active suspension mathematical model.
Step 2: reasoning a formula required by the self-adaptive dynamic surface controller of the patent and carrying out stability certification;
and 2.1, designing a self-adaptive dynamic surface controller to stabilize the motion condition of the vehicle body.
The controller is designed according to the mathematical model, so that the acceleration of the vehicle body is reduced, the dynamic stroke of the suspension is reduced, and the dynamic-static load ratio is reduced on the basis of meeting the conditions.
Let F be-Fc-FkF represents the opposite number of the sum of the nonlinear damping force and the nonlinear elastic force,
z1＝x1-yd (7)
z2＝x2-α1 (8)
z3＝x5-α2 (9)
z1＝x1-ydis the tracking error, z2＝x2-α1，z3＝x5-α2Is the state error, where α1Is a stable virtual control function, ydThe method is a reference track, and considering that multiple derivation of a high-order system can cause differential explosion, so that a controller becomes more complicated and is not beneficial to practical application, therefore, the adaptive algorithm is improved, dynamic surface control is added, and a virtual filter function beta is introduced1Passing the stabilized virtual control function through a first order filter, where1Is a time constant, α1(0) Denotes alpha1Initial value of (1), beta1(0) Is represented by beta1An initial value of (1);
Figure BDA0002015526060000114
defining a dynamic surface function S1＝α1-β1It is possible to obtain:
Figure BDA0002015526060000121
Figure BDA0002015526060000122
Figure BDA0002015526060000123
1continuously bounded, defining its maximum value as M1；
Get
Figure BDA0002015526060000124
z2＝x2-α2Is the state error of the second step, where α2Is a stable virtual control function, and introduces a virtual filter function beta2Let the virtual control function α be stable2Through a first order filter of which τ2Is a time constant, α2(0) Denotes alpha2Initial value of (1), beta2(0) Is represented by beta2An initial value of (1);
Figure BDA0002015526060000125
defining a dynamic surface function S2＝α2-β2It is possible to obtain:
Figure BDA0002015526060000126
Figure BDA0002015526060000127
wherein
Figure BDA0002015526060000128
Figure BDA0002015526060000129
2Continuously bounded, defining its maximum value as M2；
Get
Figure BDA00020155260600001210
Figure BDA00020155260600001211
z3＝x5-α2Wherein
Figure BDA00020155260600001212
Is thetaiAn estimated value of the parameter of, z3Is a state error, a controller is designed to give servo valve displacement control,
Figure BDA0002015526060000131
Figure BDA0002015526060000132
the adaptive law expression for the four uncertain parameters is as follows:
Figure BDA0002015526060000133
wherein
Figure BDA0002015526060000134
Is thetaiAn estimated value of the parameter of riIs an adaptive law design parameter, ri＞0，i＝1～4；
Projection mapping
Figure BDA0002015526060000135
The definition is as follows: theta denotes the adaptation law to be designed
Figure BDA0002015526060000136
Theorem1 according to parameter thetaiIs defined as the parameter estimation error
Figure BDA0002015526060000137
And satisfies the following properties:
(1)
Figure BDA0002015526060000138
is that the material is bounded by the surface,
Figure BDA0002015526060000139
(2)
Figure BDA00020155260600001310
θimaxdenotes thetaiMaximum value of, thetaiminDenotes thetaiThe minimum value of (a) is determined,
Figure BDA00020155260600001311
the parameter estimation error i is 1-4.
And (3) proving that:
item I uncertain parameter
Figure BDA00020155260600001312
Is bounded;
item II if thetaiWhen the value is equal to 0, then
Figure BDA00020155260600001313
The current value will remain unchanged because
Figure BDA00020155260600001314
Item III ifiIf greater than 0, then
Figure BDA00020155260600001315
Increase monotone to thetaimaxBecause of
Figure BDA00020155260600001316
When in use
Figure BDA00020155260600001317
Increase to thetaimaxTime, force design
Figure BDA00020155260600001318
Item IV is the same, if ΘiIf less than 0, then
Figure BDA00020155260600001319
Reduce monotone to thetaiminWherein
Figure BDA00020155260600001320
Will remain until
Figure BDA00020155260600001321
From 0 to a positive number, and thus
Figure BDA00020155260600001322
Is bounded at [ theta ]imin,θimax]Internal;
the V-th strip
Figure BDA0002015526060000141
Item VI is in formula (19) if
Figure BDA0002015526060000142
And thetaiIf greater than 0, then
Figure BDA0002015526060000143
Therefore, the temperature of the molten metal is controlled,
Figure BDA0002015526060000144
3) if it is not
Figure BDA0002015526060000145
And thetai< 0 then
Figure BDA0002015526060000146
Therefore, the temperature of the molten metal is controlled,
Figure BDA0002015526060000147
4) in addition to the others, it is possible to provide,
Figure BDA0002015526060000148
then there is
Figure BDA0002015526060000149
Thus, it is possible to provide
Figure BDA00020155260600001410
The above is the design process of the adaptive dynamic surface controller, and the stability of the controller is demonstrated below.
Step 2.2 demonstrates the stability of the adaptive dynamic surface controller.
Selecting a first Lyapunov function V1：
Figure BDA00020155260600001411
Figure BDA00020155260600001412
Figure BDA00020155260600001413
By substituting formula (13) into formula (22):
Figure BDA00020155260600001414
from the young inequality one can obtain:
Figure BDA00020155260600001415
wherein sigma1Represents an arbitrarily small number in the young inequality:
Figure BDA00020155260600001416
by substituting formula (24) or formula (25) for formula (23), it is possible to obtain:
Figure BDA0002015526060000151
selecting a second Lyapunov function as:
Figure BDA0002015526060000152
Figure BDA0002015526060000153
Figure BDA0002015526060000154
will z3＝x5-α2，S2＝α2-β2Substitution into equation (32) can result:
Figure BDA0002015526060000155
Figure BDA0002015526060000156
the application of the Yang inequality can obtain:
Figure BDA0002015526060000157
wherein sigma2Represents any small number in the young inequality;
Figure BDA0002015526060000158
substituting equations (31) and (30) into equation (29) can yield:
Figure BDA0002015526060000159
selecting a third Lyapunov function:
Figure BDA00020155260600001510
Figure BDA00020155260600001511
Figure BDA0002015526060000161
when formula (18) is substituted into formula (33):
Figure BDA0002015526060000162
by substituting formula (18) into formula (34):
Figure BDA0002015526060000163
adjusting the parameters appropriately so that k1,k2,k3Large value, τ1,τ2Take a smaller value, σ1,σ2When the value is smaller, the method can lead to
Figure BDA0002015526060000164
The system is semi-globally asymptotically stable.
And 3, adjusting the parameters of the controller and comparing simulation results.
And 3.1, dereferencing the suspension system parameters and the controller parameters.
Simulation verification
Suspension system parameters are shown in Table 1
TABLE 1
Figure BDA0002015526060000165
Figure BDA0002015526060000171
In consideration of the general generality of the sinusoidal road surface, the sinusoidal road surface is mainly selected in the simulation verification of the text.
The selected controller parameters are:
k1＝0.5,k2＝300,k3＝300,τ1＝0.01,τ2＝0.02,r1＝0.01,r2＝0.1,r3＝0.1,r4＝0.01；
and adjusting the controller according to the controller parameters, and verifying the effectiveness of the self-adaptive dynamic surface controller.
And 3.2, adjusting the controller, and analyzing the effect of the adaptive dynamic surface controller applied to the suspension system.
Road surface input is z0＝0.02·sin(6πt)。
The control effect of the controller is further explained by a graphical comparison, selecting a sinusoidal road surface input as shown in fig. 3. The control effect of the vertical acceleration of the vehicle body is shown in fig. 4, the control effect is obviously smaller than the acceleration of the passive suspension, the root mean square value of the acceleration of the active suspension is 0.12 through simulation calculation, the root mean square value of the acceleration of the passive suspension is 1.2, and compared with the performance of the acceleration, the performance of the acceleration is improved by 90%, so that the running smoothness of the vehicle can be improved to a great extent, the riding comfort is improved, and the control target of the vehicle is achieved. The control effect diagram of the dynamic stroke of the suspension is shown in fig. 5, the root mean square value of the dynamic stroke of the active suspension is 0.017, the root mean square value of the dynamic stroke of the passive suspension is 0.021, and compared with the performance of the dynamic stroke of the suspension, the control effect of the dynamic-static load ratio is shown in fig. 6, the dynamic-static load ratio of the active suspension is 0.0799, the dynamic-static load ratio of the passive suspension is 0.1141, compared with the performance of the dynamic-static load ratio, the control effect of the dynamic-static load ratio is 30%, and compared with the passive suspension, the safety performance of the vehicle can be further improved.
The comparison of the simulation results of fig. 3-6 shows that the control algorithm of the present invention can further improve the riding comfort, smoothness and operation safety of the vehicle when applied to the active suspension.
The foregoing is a preferred embodiment of the present application and is not intended to limit the scope of the invention, it should be understood that various modifications may be made by those skilled in the art without departing from the principles of the present application and that such modifications are also considered to be within the scope of the present application.

Claims (3)

1. A method of adaptive dynamic surface control considering a nonlinear active suspension actuator, the method comprising the steps of:
s1, establishing a two-degree-of-freedom nonlinear suspension model: establishing a dynamic model of the suspension according to Newton's second law, and abstracting the dynamic model into a mathematical model of the suspension;
s11, establishing a dynamic model of the active suspension according to Newton' S second law:
Figure FDA0002555761150000011
Figure FDA0002555761150000012
the suspension system is a highly complex nonlinear system which is susceptible to various factors in practical application, and the damping force F in the expression is usedcWith elastic force FkConsider the nonlinear form:
wherein
Figure FDA0002555761150000013
Fk＝k(zs-zu)+ξ*k(zs-zu)3
Ft＝kt(zu-z0)
Figure FDA0002555761150000014
Because the electro-hydraulic actuator has small volume and good effect, in the design of the active suspension, an electro-hydraulic system is adopted as the actuator to generate vibration isolation force, the hydraulic device generally has the characteristic of nonlinearity, and the following equation is established by comprehensively considering the nonlinearity dynamics of the hydraulic device:
Fu＝APL (3)
Figure FDA0002555761150000015
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 FuRepresenting the output force of the active suspension, k representing the suspension stiffness coefficient, ktRepresenting the coefficient of stiffness of the tire, bfExpressing the damping coefficient of the tyre, xi expressing the non-linear degree of the suspension rigidity, A expressing the effective area of the piston of the hydraulic cylinder, A2Denotes the area of the piston in the cylinder, AzIndicates the area of the damping hole of the check valve, CdDenotes the flow coefficient, ρ denotes the hydraulic oil density, zsIndicating the vertical displacement of the body, zuIndicating the vertical displacement of the tyre, z0Indicating road surface input, PLRepresenting the load pressure, psDenotes the supply pressure, β e denotes the elastic stiffness of the oil, u denotes the displacement of the servo valve, CtRepresenting the leakage coefficient in the hydraulic cylinder;
Figure FDA0002555761150000016
kvdenotes the servo valve operator, where ω is the servo valve area gradient, kaFor servo valve gain, vtRepresenting the total compression volume of the hydraulic cylinder; eta1，η2Is a damping force coefficient sign introduced for simplifying the expression mode;
s12, abstracting the dynamic model of the suspension into a mathematical model of the suspension, firstly writing the dynamic model into a state space expression form:
due to the fact that
Figure FDA0002555761150000021
Obtaining the formula (5):
Figure FDA0002555761150000022
using the system uncertainty parameter theta1，θ2，θ3，θ4Rewriting formula (5) to formula (6):
Figure FDA0002555761150000023
Fk＝k(x1-x3)+ξ*k(x1-x3)3
Ft＝kt(x3-z0)
Figure FDA0002555761150000024
Figure FDA0002555761150000025
the formula (6) is a mathematical model of the two-degree-of-freedom active suspension, and a self-adaptive dynamic surface controller is designed aiming at the mathematical model of the active suspension;
s2, designing an adaptive dynamic surface controller: designing an adaptive dynamic surface controller according to the suspension mathematical model established in the step S1, wherein the control targets of the controller comprise: the vertical acceleration of the vehicle body is reduced to improve the riding comfort; the dynamic stroke of the suspension is reduced, so that the service life of the suspension is prolonged; the dynamic-static load ratio of the tire is reduced so as to improve the driving safety;
designing a self-adaptive dynamic surface controller to stabilize the motion condition of the vehicle body:
order to
Figure FDA0002555761150000031
x1Representing a first state variable, x2Denotes a second state variable, x3Denotes a third state variable, x4Denotes a fourth state variable, x5Represents a fifth state variable;
Figure FDA0002555761150000032
θ1，θ2，θ3，θ4in order to not determine the parameters of the device,
Figure FDA0002555761150000033
are each theta1，θ2，θ3，θ4An estimated value of (d);
the spool displacement u expression of the servo valve is given below:
Figure FDA0002555761150000034
wherein S2Is a dynamic surface function, tau2Is the time constant, k3Is a controller design parameter, z2Is the state error, z3Is a state error;
the design process of the self-adaptive dynamic surface controller specifically comprises the following steps:
s21, the control targets of the controller are as follows: on the basis of considering the electro-hydraulic actuator, the controller is designed to reduce the vertical acceleration of the vehicle body, reduce the dynamic stroke of the suspension, reduce the dynamic-static load ratio of the tire, consider the external uncertain disturbance,
let F be-Fc-FkF represents the opposite number of the sum of the nonlinear damping force and the nonlinear elastic force,
z1＝x1-yd (7)
z2＝x2-α1 (8)
z3＝x5-α2 (9)
wherein z is1＝x1-ydFor tracking error, z2＝x2-α1Is a state error, z3＝x5-α2Is a state error, α1For a stable virtual control function, α2For a stable virtual control function, ydIs a reference trajectory;
s22, because the suspension system is a system with higher order, the controller is designed based on the backstepping control theory, and in order to reduce the phenomena of complex calculation and differential explosion caused by multiple derivatives of the virtual control function in the backstepping control theory, the adaptive algorithm is improved, the dynamic surface control is added, and a virtual filter function beta is introduced1And (3) enabling the stable virtual control function to pass through a first-order filter, and estimating the derivative of the virtual control quantity by using a dynamic surface function:
Figure FDA0002555761150000035
α1(0)＝β1(0)
wherein tau is1Is a time constant, α1(0) Denotes alpha1Initial value of (1), beta1(0) Is represented by beta1Defining a dynamic surface function S1＝α1-β1It is possible to obtain:
Figure FDA0002555761150000041
Figure FDA0002555761150000042
Figure FDA0002555761150000043
1continuously bounded, defining its maximum value as M1，
Get
Figure FDA0002555761150000044
S23、z2＝x2-α2Is the state error of the second step, where α2Is a stable virtual control function, and introduces a virtual filter function beta2Let the virtual control function α be stable2Through a first order filter of which τ2Is a time constant, α2(0) Denotes alpha2Initial value of (1), beta2(0) Is represented by beta2An initial value of (1);
Figure FDA0002555761150000045
α2(0)＝β2(0)
defining a dynamic surface function S2＝α2-β2It is possible to obtain:
Figure FDA0002555761150000046
Figure FDA0002555761150000047
wherein
Figure FDA0002555761150000048
Figure FDA0002555761150000049
2Continuously bounded, defining its maximum value as M2；
Get
Figure FDA00025557611500000410
z3＝x5-α2，z3And (3) designing a controller to give servo valve displacement control according to the state error:
Figure FDA00025557611500000411
wherein
Figure FDA00025557611500000412
Are each theta1～θ4Estimated value of k3Is a controller parameter;
s3, adjusting parameters of the self-adaptive dynamic surface controller, and performing simulation verification: because the three control targets of the vertical acceleration of the vehicle body, the dynamic stroke of the suspension and the dynamic and static load ratio of the tire conflict with each other, the parameters of the controller are adjusted to obtain a numerical value which enables the parameter value of the controller to be moderate, so that the designed controller can simultaneously reduce the vertical acceleration of the vehicle body, the dynamic stroke of the suspension and the dynamic and static load ratio of the tire, and further the overall performance of the suspension is improved.
2. The adaptive dynamic surface control method considering nonlinear active suspension actuators as claimed in claim 1, wherein the specific design process of the uncertain parameters in the adaptive dynamic surface controller in the step S2 is as follows:
in the active suspension system, the sprung mass is an uncertain parameter and constantly changes along with the number of passengers and the number of vehicle-mounted cargos, so that the uncertainty of the sprung mass needs to be considered in the design process of the controller, and the parameters of an electro-hydraulic servo valve in an electro-hydraulic actuating mechanism are easy to change along with the change of the running environment and the difference of the running state of a vehicle, so the uncertain parameter in the electro-hydraulic actuating mechanism needs to be considered in the design process of the controller;
the specific expression of the self-adaptation law for designing four uncertain parameters is as follows (15):
Figure FDA0002555761150000051
wherein
Figure FDA0002555761150000052
Is thetaiAn estimated value of the parameter of riDesign parameters for the adaptive law, ri＞0，i＝1～4；
Projection mapping
Figure FDA0002555761150000053
The definition is as follows: theta denotes the adaptation law to be designed
Figure FDA0002555761150000054
The parameter estimation error is defined as
Figure FDA0002555761150000055
And satisfies the following properties:
(1)
Figure FDA0002555761150000056
(2)
Figure FDA0002555761150000057
i.e. thetaiIs bounded;
θimaxdenotes thetaiMaximum value of, thetaiminDenotes thetaiThe minimum value of (a) is determined,
Figure FDA0002555761150000058
the parameter estimation error i is 1-4.
3. The adaptive dynamic surface control method considering nonlinear active suspension actuators as claimed in claim 2, wherein the adjusting process of the adaptive dynamic surface controller stability in step S2 is:
selecting a first Lyapunov function V1The following were used:
Figure FDA0002555761150000059
Figure FDA0002555761150000061
from the young inequality one can obtain:
Figure FDA0002555761150000062
Figure FDA0002555761150000063
wherein sigma1The expression (18) and (19) can be substituted for the expression (17) to obtain the following expression:
Figure FDA0002555761150000064
selecting a second Lyapunov function as:
Figure FDA0002555761150000065
Figure FDA0002555761150000066
Figure FDA0002555761150000067
obtained by applying the Yang inequality, sigma2Is an arbitrarily small number in the young inequality:
Figure FDA0002555761150000068
Figure FDA0002555761150000069
substituting equations (22) and (23) into equation (21) can yield:
Figure FDA00025557611500000610
θ1maxdenotes theta1Maximum value of (d);
selecting a third Lyapunov function:
Figure FDA0002555761150000071
Figure FDA0002555761150000072
Figure FDA0002555761150000073
adjustment parameter k1＝0.5，k2＝300，k3＝300，τ1＝0.01，τ20.01 to ensure
Figure FDA0002555761150000074
The system is semi-globally asymptotically stable.
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