CN112356633A - Adaptive control method of vehicle active suspension system considering time lag interference - Google Patents

Adaptive control method of vehicle active suspension system considering time lag interference Download PDF

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CN112356633A
CN112356633A CN202010687289.4A CN202010687289A CN112356633A CN 112356633 A CN112356633 A CN 112356633A CN 202010687289 A CN202010687289 A CN 202010687289A CN 112356633 A CN112356633 A CN 112356633A
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time lag
control
formula
equation
suspension
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张旭
卢威
孟令建
曹洲
梁津
田栋
宋鹏成
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Shaanxi Automobile Group Co Ltd
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Shaanxi Automobile Group Co Ltd
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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
    • B60G17/0152—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 action on a particular type of suspension unit
    • B60G17/0157—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 action on a particular type of suspension unit non-fluid unit, e.g. electric motor
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

Abstract

The invention discloses a self-adaptive control method of a vehicle active suspension system considering time lag interference, which comprises the following steps: establishing a nonlinear active suspension system model with input time lag, and obtaining a dynamic equation of the active suspension according to a Newton second law; designing a self-adaptive back-pushing controller for resisting time-lag interference; analyzing the influence of the time lag on the system, calculating the critical time lag of the controlled suspension system, and obtaining the controllable time lag range of the self-adaptive back-pushing controller; selecting proper gain k1，k2And
Figure DDA0002588030670000011
and a feedback coefficient l1,l2,lsAnd lcTherefore, the nonlinear system can be controlled under the influence of a certain time lag range,ensuring that all constraints are limited within a reasonable range and meeting control indexes; the invention solves the problems of simple model, single control target and the like of the existing vehicle nonlinear suspension, and also solves the problems of time-lag interference of a controller, uncertainty of sprung mass and dynamic stability of the model under the condition of vehicle running.

Description

Adaptive control method of vehicle active suspension system considering time lag interference
Technical Field
The invention belongs to the technical field of anti-interference and self-adaptive control of suspension systems, and particularly relates to a self-adaptive control method of a vehicle active suspension system considering time lag interference.
Background
The suspension system is an important part of the vehicle bottom construction, and the main function of the suspension system is to isolate, absorb and dissipate the vibration caused by the uneven road, thereby effectively improving the comfort, stability and safety of the vehicle. Active suspension can generate active control force with different moments according to the motion state of a vehicle and road excitation at each moment, and the development key problem of an active suspension controller relates to the balance between the driving quality and the road handling stability, which is the key point of many researchers. In response to this key problem, researchers have applied a number of control strategies to them. E.g. H∞Control, neural network control, fuzzy control, robust control, sliding mode variable structure control and the like.
Although the above work has made great progress in improving vehicle performance, there are still some problems to be noted, especially, the time lag and uncertainty of the whole vehicle system during the running of the vehicle. In active suspension system design, time delays often occur throughout the control system because the controller performs some calculations associated with complex control laws. The existence of time lag can cause the performance of the controller to be reduced or even unstable, and the controller for resisting time lag interference is designed to improve the comprehensive performance of a vehicle suspension system. In addition, when a real active suspension system is modeled, model uncertainty generated by different vehicle body loads is ubiquitous, and therefore certain difficulty can be brought to design and implementation of a control scheme, and therefore certain practical engineering significance is achieved by considering the uncertainty of a suspension system model.
The self-adaptive reverse-thrust control is used as an effective control method of an uncertain nonlinear system, has the advantages of input saturation resistance, interference resistance, high control precision and the like, is widely researched and reported by many scholars, carries out effective self-adaptive adjustment aiming at the change of a control object and the interference of an external environment, belongs to a control strategy of real-time adjustment, is widely applied to a closed-loop system, gives out corresponding self-adaptive rhythm according to a control function, can estimate uncertain parameters in a model on line, adjusts the influence caused by the uncertain parameters, and realizes a final control target; meanwhile, the Lyapunov theory is combined to ensure the stability of the whole system.
This process was established in 1995, and many scholars have conducted intensive studies thereon after that. For example, the application of the self-adaptive reverse-pushing control method is introduced in details such as Dong Wen Han; in the development of the controller, the self-adaptive reverse-pushing controller capable of effectively improving the smoothness of the vehicle is developed by combining the filter principle; the Wangui incense and the like provide an adaptive robust control method based on a reverse thrust technology for a suspension system, so that the suspension performance is obviously improved. However, most of the existing research methods are based on 1/4 vehicle models with simple structures, the selectable range of the initial values of the controlled system is small, the control method has certain conservatism, and meanwhile, the situation that the time lag exists in the process controller is rare, and the design method of the controller is too ideal.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a self-adaptive backstepping control method of a vehicle active suspension system, which can resist time lag interference, system uncertainty and external excitation interference, and comprises the following steps of firstly, establishing a nonlinear vehicle active suspension system model containing time lag; secondly, designing a corresponding adaptive control law to realize online estimation of uncertain parameters of a suspension system model with time lag so as to adjust the influence caused by the uncertain parameters, and designing an active control force capable of tolerating time lag interference so as to realize the time lag interference resistance of the controller; then, analyzing the influence of the time lag on the system, and calculating the critical time lag of the controlled suspension system to further obtain the controllable time lag range of the self-adaptive back-pushing controller; finally, an integrated reverse-thrust controller capable of being adjusted in an adaptive mode is developed to restrain model uncertainty of a nonlinear suspension system and negative effects of the controller caused by time lag interference and road surface impact.
The invention is realized by the following technical scheme:
the self-adaptive control method of the vehicle active suspension system considering time lag interference comprises the following steps:
step 1: establishing a nonlinear active suspension system model containing time lag, and obtaining a dynamic equation of the active suspension according to a Newton second law as follows:
Figure BDA0002588030650000021
m in formula (1)sIndicating the body mass (sprung mass), muRepresents the unsprung mass (unsprung mass); fs(zs,zuT) represents the nonlinear spring force of the suspension portion,
Figure BDA0002588030650000022
representing a segmental damping force of the suspension part; ftRepresenting the spring force of the tire; z is a radical ofsIndicating vertical displacement of the body, zsRepresents the unsprung mass displacement, and u (t- τ) represents the actuator input force; tau is a time-lag variable and is an unknown time-invariant parameter; wherein Fs(zs,zu,t)，
Figure BDA0002588030650000023
And Ft(zu,zrThe output force of t) follows the following dynamics:
Fs(zs,zu,t)＝ksΔy+knsΔy3 (2)
Figure BDA0002588030650000024
Ft(zu,zr,t)＝kt(zu-zr) (4)
k in formulae (2) to (4)sExpressing the spring rate, k, in the linear regionnsRepresents the spring rate coefficient, k, of the nonlinear sectiontRepresenting the coefficient of stiffness of the tire, cs1Denotes the damping coefficient of expansion, cs2Denotes a compression damping coefficient, Δ y ═ zs-zuExpressed as suspension stroke, zrRepresenting a road surface disturbance input;
the state variables that define the suspension system are as follows:
Figure BDA0002588030650000031
conversion of kinetic equation (1) to
Figure BDA0002588030650000032
X in formula (5)1Indicating vertical displacement of the body, x2Indicating the vertical speed, x, of the vehicle body3Representing the unsprung mass displacement of the suspension, x4Representing suspension unsprung mass velocity;
step 2: designing an adaptive back-pushing controller resisting time lag and system uncertainty interference:
step 21: for the active suspension system equation (6), assume the suspended mass msThere are known upper and lower bounds, i.e. ms∈{ms:msmin≤ms≤msmax}，msminWhen indicating the vehicle is in an unloaded state, msmaxIndicating a vehicle full load condition; taking into account uncertain parameters in suspension systemsSimultaneously, the vertical speed of the vehicle body is taken as virtual control, and the stability of the vehicle body in a certain area is ensured through the virtual control:
selecting the actual virtual control function as x2(t) designing the desired value α of the virtual control1(t) so that only vertical velocity x2(t)＝α1(t), the vehicle body can be vertically displaced by x1(t) tends to be stably satisfied, while defining e2(t) as the actual state value x2(t) and the desired value alpha1Error between (t), i.e.
Figure BDA0002588030650000033
Selecting
Figure BDA0002588030650000034
K in formula (7)1Is a constant greater than zero
Selecting a semi-positive bound Lyapunov function
Figure BDA0002588030650000035
Derivation of this can yield:
Figure BDA0002588030650000036
k in formulas (7) and (8)1To be a tunable parameter
Step 22: the actual control active control force u (t-tau) is designed such that the error e between the desired value and the actual value state of the virtual control2(t) approaches zero or is bounded:
sprung mass motion of the vehicle is represented by equation (9):
Figure BDA0002588030650000041
theta in formula (9)1＝1/ms∈[θ1min,θ1max],θ1min＝1/msmax,θ1max＝1/msmin；
To the vertical speed of the car body
Figure BDA0002588030650000042
Further transformation:
Figure BDA0002588030650000043
in the formula (10)
Figure BDA0002588030650000044
Can obtain the product
Figure BDA0002588030650000045
The design control force u (t- τ) is:
Figure BDA0002588030650000046
in equation (12): k is a radical of2Is a constant number of times, and is,
Figure BDA0002588030650000047
is theta1An estimated value of (d);
defining an adaptive control law:
Figure BDA0002588030650000048
in the formula (13)
Figure BDA00025880306500000412
Is a constant larger than zero, which is an adaptive control law adjustable parameter,
for vehicle body speed error e2(t) derivation to obtain
Figure BDA0002588030650000049
Then, a half positive definite limit lyapunov candidate function is selected:
Figure BDA00025880306500000410
taking the derivative of equation (15) and substituting equations (12) - (14) results in:
Figure BDA00025880306500000411
and step 3: solving the critical time lag tau according to the linearization principle and vibration theory of the nonlinear systemmax：
According to the linearization principle requirement of a nonlinear system, a nonlinear force is linearized, and as can be seen from the formula (2) and the formula (3), a nonlinear spring force and a damping force are related to the vertical displacement and the vertical velocity of a suspension, and the linearization processing of the nonlinear spring force and the damping force needs the following two steps:
step 31: solving the root mean square values of the nonlinear spring force and the damping force without considering the time lag influence and the vertical displacement and the velocity of the suspension, wherein the expression is shown as (20):
Figure BDA0002588030650000051
by the same token, Ft(zu,zr,t),Δy,
Figure BDA0002588030650000052
Root mean square value of (d).
Step 32: the feedback coefficients of the two forces are further calculated from the root mean square value, and equations (2) and (3) are rewritten into equations (21) and (22):
Fs(zs,zu,t)＝lsΔy (21)
Figure BDA0002588030650000053
wherein ls，lcIs a feedback coefficient;
meanwhile, the active control force u (t-tau) is also subjected to linearization processing, and the state variable related to the system can be selected according to a control strategy;
the active control force u (t-tau), the system-dependent motion state variable x thereof, can be determined by step 21(t),x2(t), and when the time lag τ is 0, determining the expression of u (t) as follows:
Figure BDA0002588030650000054
wherein l1，l2Is a feedback coefficient;
by substituting formulae (21) to (23) into formula (24), it is possible to obtain:
Figure BDA0002588030650000055
when the system is free to vibrate, the dynamic equation expressed by the formula (24) can be rewritten as:
Figure BDA0002588030650000056
according to vibration theory, the form of the solution in equation (25) can be expressed as:
Figure BDA0002588030650000057
where w ═ σ + j ωcIs the complex modal frequency of the system, where σ is the attenuation coefficient, ωcIs the system natural frequency; when σ is 0, the system is critically stable;
equation (26) is substituted into equation (25) and the matrix representation is applied as:
Figure BDA0002588030650000061
wherein
Figure BDA0002588030650000062
z12＝-ls-lc(σ+jωc),
Figure BDA0002588030650000063
z22＝(σ+jωc)2mu+(lc+ct)(σ+jωc)+ls+kt.
The condition that the formula (27) has a non-zero solution is z10And z20Is equal to 0, i.e.
Figure BDA0002588030650000064
The simplified expression (28) is merged by using euler's formula, and can be written into a form of a + bj being 0; meanwhile, the real part a and the imaginary part b are separated, and the Euler formula is used to obtain the condition that the formula (27) has pure virtual root, so that the real root omega can be solved when the real part a is equal to 0c(ii) a From the imaginary part b equal to 0, the critical time lag τ of the system can be obtainedmax；
And 4, step 4: selecting proper gain k1,k2And
Figure BDA0002588030650000065
and a feedback coefficient l1,l2,lsAnd lcEnsuring the system is at 0-taumaxUnder the interference of a time-lag range, all constraints are limited within a reasonable range, a control target is achieved, and the control requirement is met.
Preferably, the step 22 is to design the actual control active control force so that the error e2(t) between the expected value and the actual value of the virtual control approaches zero or is bounded, and then the method further comprises:
step 23: verifying zero dynamic stability of a system tire subsystem:
let the output variable x1(t) is 0 and e2(t) is 0, and the active control force of the suspension system with time lag is obtained as follows:
Figure BDA0002588030650000066
by substituting equation (17) into the zero-dynamics system, i.e., into system equation (4), we can obtain:
Figure BDA0002588030650000067
rewriting equation (18) into the state space equation form yields:
Figure BDA0002588030650000068
in the formula (19), X (t) [ < x > ]3(t)x4(t)]T，
Figure BDA0002588030650000069
Since matrix a satisfies the herville criterion, the zero dynamic system (19) is stable.
Preferably, under different vibration responses, the adaptive control strategy needs to find the corresponding feedback coefficient l1，l2。
Compared with the prior art, the invention has the following beneficial technical effects:
establishing a nonlinear active suspension system model containing time lag; designing an adaptive back-pushing controller capable of adjusting uncertain parameters of a system; adjusting control parameters of the adaptive reverse-thrust controller to obtain an active controller resisting time lag interference, inhibiting the influence of the time lag of the controller on the performance of a vehicle suspension system, and calculating and analyzing to obtain a controllable range of the tolerable time lag of the controller so as to realize good control on the suspension system; the invention considers the practical factors of nonlinearity, uncertainty and controller delay, is used for the anti-interference control of the vehicle active suspension system, solves the problems that the existing vehicle suspension system has simple model and is easy to be interfered by the outside world, and the like, and simultaneously solves the problems that the controller is influenced by time lag, the sprung mass uncertainty and the dynamic stability of the model under the actual vehicle driving condition, thereby realizing the effective control of the vehicle suspension system and effectively improving the vehicle operation stability and comfort.
The invention also has the following advantages:
1) the suspension system model is introduced into a nonlinear factor, so that the model is closer to an actual vehicle suspension system, and a tamping basis is laid for verifying the effectiveness of the invention.
2) Aiming at the uncertainty of the sprung mass in a suspension system model, a corresponding adaptive rule is designed according to an adaptive back-stepping control method, and the uncertain parameters in the model can be estimated on line to adjust the influence of the uncertain parameters on the vehicle, so that the dynamic stroke, the dynamic-static load ratio of the tire and the amplitude constraint of the active control force of the suspension are all met, and the performance of the vehicle is effectively improved.
3) The influence of controller delay on a suspension system is considered, and corresponding controller input force is designed, so that the controller can still ensure the riding comfort and the driving smoothness of the vehicle suspension system under the interference of a certain time delay range.
4) The critical input time-lag method of the computing system is provided, the system ensures the control capability of the controller within the control range, and the method can be widely popularized and applied to the design of other controllers.
5) The method is easy to operate and implement, redundant hardware is not needed in the system, and the cost is low.
The method provided by the invention is used as a vehicle suspension self-adaptive backstepping control method capable of resisting time lag factor interference, has certain practical significance and is easy to realize; and the system can still ensure the running performance and safety of the suspension system and simultaneously ensure the stability of the suspension system under the condition of time-lag interference.
Drawings
FIG. 1 is an 1/4 non-linear active suspension model of a vehicle with time-lag disturbances.
Fig. 2 is a schematic diagram of the adaptive back-stepping control.
FIG. 3 is a body acceleration curve of an active suspension system of (a), ABC and (b) NABC subjected to time lag interference.
FIG. 4 is a vehicle body acceleration response curve.
Fig. 5 is a suspension dynamic stroke response curve.
FIG. 6 is a tire dynamic load response curve.
Fig. 7 is an active control force response curve.
FIG. 8 is a flow chart of a method for adaptive control of an active suspension system of a vehicle that accounts for time-lag disturbances.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, 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 some, but not all, embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. 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.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
In the description of the present invention, it should also be noted that, unless otherwise explicitly specified or limited, the terms "disposed," "mounted," "connected," and "connected" are to be construed broadly and may, for example, be fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
The technical solution of the present invention will be explained with reference to specific embodiments.
As shown in fig. 1 and 2, in consideration of model uncertainty, nonlinearity and controller time-lag interference existing in an active suspension of a vehicle, an adaptive control method capable of resisting time-lag interference is provided, and a system still maintains good performance under the conditions of time-lag interference in a certain range and model uncertainty, which specifically comprises the following steps:
step 1: establishing a nonlinear active suspension system model containing time lag, and obtaining a dynamic equation of the active suspension according to a Newton second law as follows:
Figure BDA0002588030650000091
m in formula (1)sIndicating the body mass (sprung mass), muRepresents the unsprung mass (unsprung mass); fs(zs,zuT) represents the nonlinear spring force of the suspension portion,
Figure BDA0002588030650000092
representing a segmental damping force of the suspension part; ftRepresenting the spring force of the tire; z is a radical ofsIndicating vertical displacement of the body, zsRepresents the unsprung mass displacement, and u (t- τ) represents the actuator input force; tau is a time-lag variable and is an unknown time-invariant parameter; wherein Fs(zs,zu,t)，
Figure BDA0002588030650000093
And Ft(zu,zrThe output force of t) follows the following dynamics:
Fs(zs,zu,t)＝ksΔy+knsΔy3 (2)
Figure BDA0002588030650000094
Ft(zu,zr,t)＝kt(zu-zr) (4)
k in formulae (2) to (4)sExpressing the spring rate, k, in the linear regionnsRepresents the spring rate coefficient, k, of the nonlinear sectiontRepresenting the coefficient of stiffness of the tire, cs1Denotes the damping coefficient of expansion, cs2Denotes a compression damping coefficient, Δ y ═ zs-zuExpressed as suspension stroke, zrRepresenting a road surface disturbance input;
the state variables that define the suspension system are as follows:
Figure BDA0002588030650000095
conversion of kinetic equation (1) to
Figure BDA0002588030650000096
X in formula (5)1Indicating vertical displacement of the body, x2Indicating the vertical speed, x, of the vehicle body3Representing the unsprung mass displacement of the suspension, x4Representing suspension unsprung mass velocity;
step 2: designing an adaptive back-pushing controller resisting time lag and system uncertainty interference, which specifically comprises the following steps:
1) due to mass m of the vehicle bodysThe suspended mass m varies with the load of the vehicle body or the number of passengerssIs an uncertain parameter in a closed-loop suspension system formula (6). For the active suspension system equation (6), assume the suspended mass msThere are known upper and lower bounds, i.e. ms∈{ms:msmin≤ms≤msmax}，msminWhen indicating the vehicle is in an unloaded state, msmaxIndicating full load of vehicleState; the uncertain parameters are considered in a suspension system, the vertical speed of the vehicle body is used as virtual control, and the stability of the vehicle body in a certain area is ensured through the virtual control:
it can be seen from equation (6)
Figure BDA0002588030650000101
Selecting the actual virtual control function as x2(t) designing the desired value α of the virtual control1(t) so that only vertical velocity x2(t)＝α1(t), the vehicle body can be vertically displaced by x1(t) tends to be stably satisfied, while defining e2(t) as the actual state value x2(t) and the desired value alpha1Error between (t), i.e.
Figure BDA0002588030650000102
Selecting
Figure BDA0002588030650000103
K in formula (7)1Is a constant greater than zero
Selecting a semi-positive bound Lyapunov function
Figure BDA0002588030650000104
Derivation of this can yield:
Figure BDA0002588030650000105
k in formulas (7) and (8)1To be a tunable parameter
2) The actual control active control force u (t-tau) is designed such that the error e between the desired value and the actual value state of the virtual control2(t) approaches zero or is bounded; sprung mass motion of the vehicle is represented by equation (9):
Figure BDA0002588030650000106
theta in formula (9)1＝1/ms∈[θ1min,θ1max],θ1min＝1/msmax,θ1max＝1/msmin；
To the vertical speed of the car body
Figure BDA0002588030650000107
Further transformation:
Figure BDA0002588030650000108
in the formula (10)
Figure BDA0002588030650000109
Can obtain the product
Figure BDA00025880306500001010
The design control force u (t- τ) is:
Figure BDA00025880306500001011
in equation (12): k is a radical of2Is a constant number of times, and is,
Figure BDA0002588030650000111
is theta1An estimated value of (d);
defining an adaptive control law:
Figure BDA0002588030650000112
in the formula (13)
Figure BDA0002588030650000113
Is a constant larger than zero, which is an adaptive control law adjustable parameter,
for vehicle body speed error e2(t) taking the derivative of the signal,can obtain the product
Figure BDA0002588030650000114
Then, a half positive definite limit lyapunov candidate function is selected:
Figure BDA0002588030650000115
taking the derivative of equation (15) and substituting equations (12) - (14) results in:
Figure BDA0002588030650000116
3) verifying zero dynamic stability of a system tire subsystem:
in 1) and 2), stabilization of the vehicle's vertical motion system has been demonstrated, so this step considers the stabilization of the tire subsystem, letting the output variable x1(t) is 0 and e2When t is 0, the active control force of the suspension system with time lag can be obtained as follows:
Figure BDA0002588030650000117
by substituting equation (17) into the zero-dynamics system, i.e., into system equation (4), we can obtain:
Figure BDA0002588030650000118
rewriting equation (18) into the state space equation form yields:
Figure BDA0002588030650000121
in the formula (19), X (t) [ < x > ]3(t)x4(t)]T，
Figure BDA0002588030650000122
Since matrix a satisfies the herville criterion, the zero dynamic system (19) is stable.
And step 3: in order to further research the influence of the time lag tau on a nonlinear active suspension system, solving the critical time lag tau according to the linearization principle and the vibration theory of the nonlinear systemmax：
Firstly, according to the linearization principle requirement of a nonlinear system, a nonlinear force is linearized, and as can be seen from the formula (2) and the formula (3), a nonlinear spring force and a damping force are related to the vertical displacement and the vertical velocity of a suspension, and the linearization processing of the two forces needs the following two steps:
31. solving the root mean square values of two forces without considering the time lag influence, and the vertical displacement and the speed of the suspension, and the expression is shown as (20):
Figure BDA0002588030650000123
by the same token, Ft(zu,zr,t),Δy,
Figure BDA0002588030650000124
Root mean square value of (d).
32. The feedback coefficients of the two forces are further calculated from the root mean square value, and equations (2) and (3) are rewritten into equations (21) and (22):
Fs(zs,zu,t)＝lsΔy (21)
Figure BDA0002588030650000125
wherein ls，lcIs a feedback coefficient.
Meanwhile, the active control force u (t-tau) is also subjected to linearization processing, and the state variable related to the system can be selected according to the control strategy through stepsStep 2 may determine an active control force u (t- τ), the system-dependent motion state variable x of which1(t),x2(t), and when the time lag τ is 0, determining the expression of u (t) as follows:
Figure BDA0002588030650000126
wherein l1，l2Is a feedback coefficient; meanwhile, in order to obtain an ideal control effect, under different vibration responses, the adaptive control strategy should find a corresponding feedback coefficient l1,l2I.e. different vibration responses, different feedback coefficients.
By substituting formulae (21) to (23) into formula (24), it is possible to obtain:
Figure BDA0002588030650000131
when the system is free to vibrate, the dynamic equation expressed by the formula (24) can be rewritten as:
Figure BDA0002588030650000132
according to vibration theory, the form of the solution in equation (25) can be expressed as:
Figure BDA0002588030650000133
where w ═ σ + j ωcIs the complex modal frequency of the system, where σ is the attenuation coefficient, ωcIs the system natural frequency; when σ is 0, the system is critically stable.
Equation (26) is substituted into equation (25) and the matrix representation is applied as:
Figure BDA0002588030650000134
wherein
Figure BDA0002588030650000135
z12＝-ls-lc(σ+jωc),
Figure BDA0002588030650000136
z22＝(σ+jωc)2mu+(lc+ct)(σ+jωc)+ls+kt.
The condition that the formula (27) has a non-zero solution is z10And z20Is equal to 0, i.e.
Figure BDA0002588030650000137
The simplified equation (28) is merged by using the euler equation, and can be written in a form of a + bj being 0, and the real a and the imaginary b are separated and the euler equation is used to obtain the condition that the equation (27) has a pure virtual root. So from the real part a being equal to 0, the real root ω can be solvedc(ii) a From the imaginary part b equal to 0, the critical time lag τ of the system can be obtainedmax。
The large input time lag causes instability divergence of an active suspension system of the designed controller, and along with the continuous increase of the time lag time, the instability phenomenon of the suspension system can occur, so that the riding comfort is seriously affected, and therefore the control capability of the controller can be obtained through the calculation of the critical time lag; however, different road surface excitation inputs and different control methods can obtain different feedback coefficients, and different critical time lags can be calculated.
And 4, step 4: selecting proper gain k1,k2And
Figure BDA0002588030650000141
and a feedback coefficient l1,l2,lsAnd lcSo as to ensure that a certain time lag range (0-tau) exists in the systemmax) Under the interference of (3), all constraints are limited within a reasonable range, a control target is achieved, and the control requirements are met.
This implementationIn the example, 2) in step 2), the conclusion can be drawn according to equation (16):
Figure BDA0002588030650000142
further obtain
Figure BDA0002588030650000143
Therefore, it is possible to obtain:
Figure BDA0002588030650000144
it can be seen that the vertical displacement of the vehicle body is bounded, and that C is the boundary1And C2The value of (c) may be infinitely small.
The effectiveness of the implementation is demonstrated in an example simulation.
The following description of the suspension system mass uncertainty is: mass m of vehicle bodys＝330.75-404.25(kg)。
In order to verify the effectiveness of the invention, a rough road surface is considered to be selected as road surface excitation input, the rough road surface aims at the road surface under the bad road condition, generally, in the suspension research, the sine periodic disturbance is adopted to simulate the rough road surface, and the expression is as follows:
zr(t)＝0.0254sin(2πt)+0.005sin(10.5πt)+0.001sin(21.5πt) (30)
it should be noted that the rough road surface of the present study simulates road disturbance by combining low frequency vibration response close to the resonance frequency (1Hz) of the vehicle body with high frequency vibration response. Through the continuous periodic disturbance, the vehicle body is strongly impacted, so that when the controller is designed, if the interference of the road surface on a suspension system can be met, the performance of the suspension system is greatly improved.
Some actual vehicle suspension system parameters: the parameters of the automobile active suspension system are as follows: m iss367.5 kg; suspension unsprung mass: m isu139.5 kg; spring linear stiffness coefficient: k is a radical ofs102000N/m; spring nonlinear stiffness coefficient: k is a radical ofns6800N/m; suspension damping extension coefficient: c. Cs13463 Ns/m; suspension damping compression coefficient: c. Cs2866 Ns/m; tire modulus of elasticity: k is a radical oft736176N/m; tire damping coefficient: c. Ct＝1600Ns/m；
Selecting control law parameters: k is a radical of1＝k2＝10；
Figure BDA0002588030650000145
Initial system value condition xi(0)＝0cm(i＝1,2,3,4)。
A nonlinear suspension system dynamic model with time lag is built in Simulink, an adaptive back-pushing controller resisting time lag interference is built at the same time, time domain simulation is carried out on a controlled system by combining control parameters, and discussion and analysis are carried out in the following three modes:
(1) PS: an uncontrolled passive suspension;
(2) ABC: an active suspension under the traditional self-adaptive reverse thrust control;
(3) NABC: an active suspension under adaptive backward thrust control for resisting time lag interference;
FIG. 3 is a body acceleration curve for a time-lapse disturbed (a) ABC, (b) NABC active suspension system; from fig. 3, it can be seen that vehicle body acceleration simulation curves of ABC and NABC active suspension systems affected by different input time lags under excitation of a rough road surface increase the vehicle body acceleration continuously with increasing time delay, which shows that the time lag seriously affects the performance of the suspension system, and for an ABC controller, when the time lag increases to 22ms, the controller cannot control the suspension system, but rather, the performance of the system becomes worse; and when the time lag of the NABC controller is increased to 80ms, the acceleration curve of the vehicle body is still stable, and the controller still has a good control effect.
FIG. 4 is a vehicle body acceleration response curve for the suspension system; it can be seen from fig. 4 that the active suspension system under the NABC controller can still improve the riding comfort well when the time lag is 22ms, but the ABC controller has an almost ineffective control effect, and the acceleration curve has a slower convergence speed than the PS system, which seriously affects the running smoothness of the vehicle.
5-7 are response curves of the performance index of the NABC active suspension system under different time lags; by analyzing the simulation curves of various performance index parameters of the NABC active suspension system shown in the figures 5-7, the dynamic stroke of the suspension is smaller than the maximum suspension stroke of 0.15m under the influence of different time-lag states. Meanwhile, the dynamic-static load ratio is less than 1, which indicates that the dynamic load of the tire is less than the static load, and the tire can not be separated from the ground when the vehicle runs on a severe road surface; the active control force is also smaller than the allowed maximum control force amplitude 10000N; therefore, the NABC can still keep the suspension system stable under the influence of time-lag factors, and the driving safety of the active suspension system is effectively ensured. The controller has time lag, which provides greater challenges for the development of the controller, so that the adaptive controller for resisting time lag interference provided by the invention can greatly improve the anti-interference performance of a suspension system. When a vehicle passes through a rough and severe road surface, a general controller may not provide real-time control and may cause continuous impact on a suspension system.
The embodiments given above are preferable examples for implementing the present invention, and the present invention is not limited to the above-described embodiments. Any non-essential addition and replacement made by the technical characteristics of the technical scheme of the invention by a person skilled in the art belong to the protection scope of the invention.

Claims (3)

1. An adaptive control method for an active suspension system of a vehicle taking into account time lag disturbances, comprising the steps of:
step 1: establishing a nonlinear active suspension system model containing time lag, and obtaining a dynamic equation of the active suspension according to a Newton second law as follows:
Figure FDA0002588030640000011
m in formula (1)sRepresenting sprung mass, muIndicating unsprung loadQuality; fs(zs,zuT) represents the nonlinear spring force of the suspension portion,
Figure FDA0002588030640000012
representing a segmental damping force of the suspension part; ftRepresenting the spring force of the tire; z is a radical ofsIndicating vertical displacement of the body, zsRepresents the unsprung mass displacement, and u (t- τ) represents the actuator input force; tau is a time-lag variable and is an unknown time-invariant parameter; wherein Fs(zs,zu,t)，
Figure FDA0002588030640000013
And Ft(zu,zrThe output force of t) follows the following dynamics:
Fs(zs,zu,t)＝ksΔy+knsΔy3 (2)
Figure FDA0002588030640000014
Ft(zu,zr,t)＝kt(zu-zr) (4)
k in formulae (2) to (4)sExpressing the spring rate, k, in the linear regionnsRepresents the spring rate coefficient, k, of the nonlinear sectiontRepresenting the coefficient of stiffness of the tire, cs1Denotes the damping coefficient of expansion, cs2Denotes a compression damping coefficient, Δ y ═ zs-zuExpressed as suspension stroke, zrRepresenting a road surface disturbance input;
the state variables that define the suspension system are as follows:
Figure FDA0002588030640000015
conversion of kinetic equation (1) to
Figure FDA0002588030640000016
X in formula (5)1Indicating vertical displacement of the body, x2Indicating the vertical speed, x, of the vehicle body3Representing the unsprung mass displacement of the suspension, x4Representing suspension unsprung mass velocity;
step 2: designing an adaptive back-pushing controller resisting time lag and system uncertainty interference:
step 21: for the active suspension system equation (6), assume the suspended mass msThere are known upper and lower bounds, i.e. ms∈{ms:msmin≤ms≤msmax}，msminWhen indicating the vehicle is in an unloaded state, msmaxIndicating a vehicle full load condition; the uncertain parameters are considered in a suspension system, the vertical speed of the vehicle body is used as virtual control, and the stability of the vehicle body in a certain area is ensured through the virtual control:
selecting the actual virtual control function as x2(t) designing the desired value α of the virtual control1(t) so that only vertical velocity x2(t)＝α1(t), the vehicle body can be vertically displaced by x1(t) tends to be stably satisfied, while defining e2(t) as the actual state value x2(t) and the desired value alpha1Error between (t), i.e.
Figure FDA0002588030640000021
Selecting
Figure FDA0002588030640000022
K in formula (7)1Is a constant greater than zero
Selecting a semi-positive bound Lyapunov function
Figure FDA0002588030640000023
Derivation of this can yield:
Figure FDA0002588030640000024
k in formulas (7) and (8)1To be a tunable parameter
Step 22: the actual control active control force u (t-tau) is designed such that the error e between the desired value and the actual value state of the virtual control2(t) approaches zero or is bounded:
sprung mass motion of the vehicle is represented by equation (9):
Figure FDA0002588030640000025
theta in formula (9)1＝1/ms∈[θ1min,θ1max],θ1min＝1/msmax,θ1max＝1/msmin；
To the vertical speed of the car body
Figure FDA0002588030640000026
Further transformation:
Figure FDA0002588030640000027
in the formula (10)
Figure FDA0002588030640000028
Can obtain the product
Figure FDA0002588030640000029
The design control force u (t- τ) is:
Figure FDA00025880306400000210
in the formula (12)：k2Is a constant number of times, and is,
Figure FDA00025880306400000211
is theta1An estimated value of (d);
defining an adaptive control law:
Figure FDA00025880306400000212
in the formula (13)
Figure FDA00025880306400000213
Is a constant larger than zero, which is an adaptive control law adjustable parameter,
for vehicle body speed error e2(t) derivation to obtain
Figure FDA0002588030640000031
Then, a half positive definite limit lyapunov candidate function is selected:
Figure FDA0002588030640000032
taking the derivative of equation (15) and substituting equations (12) - (14) results in:
Figure FDA0002588030640000033
and step 3: solving the critical time lag tau according to the linearization principle and vibration theory of the nonlinear systemmax：
According to the linearization principle requirement of a nonlinear system, a nonlinear force is linearized, and as can be seen from the formula (2) and the formula (3), a nonlinear spring force and a damping force are related to the vertical displacement and the vertical velocity of a suspension, and the linearization processing of the nonlinear spring force and the damping force needs the following two steps:
step 31: solving the root mean square values of the nonlinear spring force and the damping force without considering the time lag influence and the vertical displacement and the velocity of the suspension, wherein the expression is shown as (20):
Figure FDA0002588030640000034
by the same token, Ft(zu,zr,t),Δy,
Figure FDA0002588030640000035
Root mean square value of (d).
Step 32: the feedback coefficients of the two forces are further calculated from the root mean square value, and equations (2) and (3) are rewritten into equations (21) and (22):
Fs(zs,zu,t)＝lsΔy (21)
Figure FDA0002588030640000036
wherein ls，lcIs a feedback coefficient;
meanwhile, the active control force u (t-tau) is also subjected to linearization processing, and the state variable related to the system can be selected according to a control strategy;
the active control force u (t-tau), the system-dependent motion state variable x thereof, can be determined by step 21(t),x2(t), and when the time lag τ is 0, determining the expression of u (t) as follows:
Figure FDA0002588030640000037
wherein l1，l2Is a feedback coefficient;
by substituting formulae (21) to (23) into formula (24), it is possible to obtain:
Figure FDA0002588030640000041
when the system is free to vibrate, the dynamic equation expressed by the formula (24) can be rewritten as:
Figure FDA0002588030640000042
according to vibration theory, the form of the solution in equation (25) can be expressed as:
Figure FDA0002588030640000043
where w ═ σ + j ωcIs the complex modal frequency of the system, where σ is the attenuation coefficient, ωcIs the system natural frequency; when σ is 0, the system is critically stable;
equation (26) is substituted into equation (25) and the matrix representation is applied as:
Figure FDA0002588030640000044
wherein
Figure FDA0002588030640000045
z12＝-ls-lc(σ+jωc),
Figure FDA0002588030640000046
z22＝(σ+jωc)2mu+(lc+ct)(σ+jωc)+ls+kt.
The condition that the formula (27) has a non-zero solution is z10And z20Is equal to 0, i.e.
Figure FDA0002588030640000047
The simplified expression (28) is merged by using euler's formula, and can be written into a form of a + bj being 0; meanwhile, the real part a and the imaginary part b are separated, and the Euler formula is used to obtain the condition that the formula (27) has pure virtual root, so that the real root omega can be solved when the real part a is equal to 0c(ii) a From the imaginary part b equal to 0, the critical time lag τ of the system can be obtainedmax；
And 4, step 4: selecting proper gain k1,k2And
Figure FDA0002588030640000048
and a feedback coefficient l1,l2,lsAnd lcEnsuring the system is at 0-taumaxUnder the interference of a time-lag range, all constraints are limited within a reasonable range, a control target is achieved, and the control requirement is met.
2. The adaptive control method for an active suspension system of a vehicle taking into account time lag disturbance according to claim 1, wherein the step 22 of designing the actual control active control force such that the error e2(t) between the desired value and the actual value of the virtual control approaches zero or is bounded further comprises:
step 23: verifying zero dynamic stability of a system tire subsystem:
let the output variable x1(t) is 0 and e2(t) is 0, and the active control force of the suspension system with time lag is obtained as follows:
Figure FDA0002588030640000049
by substituting equation (17) into the zero-dynamics system, i.e., into system equation (4), we can obtain:
Figure FDA0002588030640000051
rewriting equation (18) into the state space equation form yields:
Figure FDA0002588030640000052
in the formula (19), X (t) [ < x > ]3(t) x4(t)]T，
Figure FDA0002588030640000053
Since matrix a satisfies the herville criterion, the zero dynamic system (19) is stable.
3. The adaptive control method for an active suspension system of a vehicle considering time lag interference of claim 1, wherein the adaptive control strategy needs to find a corresponding feedback coefficient l under different vibration responses1，l2。
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