CN114571940A - Nonlinear suspension control system under uncertain conditions - Google Patents

Nonlinear suspension control system under uncertain conditions Download PDF

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CN114571940A
CN114571940A CN202210178035.9A CN202210178035A CN114571940A CN 114571940 A CN114571940 A CN 114571940A CN 202210178035 A CN202210178035 A CN 202210178035A CN 114571940 A CN114571940 A CN 114571940A
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control
suspension
vehicle
inversion
vehicle body
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CN114571940B (en
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徐涛
赵又群
吕文博
李田
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Nanjing University of Aeronautics and Astronautics
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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
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60G—VEHICLE SUSPENSION ARRANGEMENTS
    • B60G17/00—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load
    • B60G17/015—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements
    • B60G17/018—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements characterised by the use of a specific signal treatment or control method
    • 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
    • B60G17/019—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 type of sensor or the arrangement thereof
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

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  • Mechanical Engineering (AREA)
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Abstract

The invention discloses a nonlinear suspension control system under uncertain conditions, which comprises an information acquisition module, an inversion controller module, a sliding mode controller module based on inversion control law and an actuator module; the information acquisition module acquires physical quantities such as road surface input, vehicle body stress and the like through a vehicle-mounted sensor; based on information acquired by a sensor, establishing a linear vehicle suspension model with uncertainty omitted, applying inversion control to control the change of a tracking target, and inputting the obtained control rate to a sliding mode controller module; by combining an inversion control law and a vehicle model considering uncertainty, the sliding mode controller module can eliminate the influence of uncertainty and disturbance; the final control force is output by an actuator of the active suspension, so that the control on the vertical displacement and pitching motion of the vehicle body is realized, the posture of the vehicle body is stabilized, and the riding comfort is ensured.

Description

Nonlinear suspension control system under uncertain conditions
Technical Field
The invention belongs to the technical field of automobile intellectualization, and particularly relates to a nonlinear suspension system under an uncertain condition.
Background
In order to solve the problems of smoothness and riding comfort of the vehicle, a suspension system is indispensable. With the continuous development of automobile intelligent technology, the active suspension technology gradually becomes the mainstream. At present, the control difficulty of the active suspension is the uncertainty research of the nonlinearity of suspension parameters, the precision error of a sensor and external random disturbance. The accuracy and real-time of the suspension vehicle model are challenged by the existence of the factors. Therefore, the control strategy provided by the invention can make up for the defects of the common suspension control strategy, and realize the control of the nonlinear suspension system under the uncertain condition, thereby improving the driving smoothness of the vehicle.
Disclosure of Invention
In order to solve the technical problems mentioned in the background art, the present invention proposes a nonlinear suspension control system that does not depend on the accuracy of the established suspension vehicle model.
In order to achieve the technical purpose, the technical scheme of the invention is as follows:
as shown in fig. 1, the present invention relates to a nonlinear suspension control system under uncertain conditions, comprising: the system comprises an information acquisition module, an inversion controller module, a sliding mode controller module based on an inversion control law and an actuator module; the information acquisition module is used for acquiring input information; the inversion controller module establishes a linear vehicle suspension model with uncertainty omitted based on the heat input information, controls the change of a tracking target by applying inversion control, and inputs the obtained control rate to the sliding mode controller module; the sliding mode controller module based on the inversion control law can eliminate the influence of uncertainty and disturbance by combining the inversion control law and a vehicle model considering uncertainty; the actuator module is an active suspension actuator and is used for outputting final control force, controlling vertical displacement and pitching motion of the vehicle body and stabilizing the posture of the vehicle body, so that the riding comfort is ensured.
Furthermore, the information acquisition module acquires road surface input, vehicle body stress and vehicle motion state variables through a vehicle-mounted sensor.
Further, for an ideal linear model, the method for providing an inversion control law is as follows:
3.1, establishing a half-car model of the active suspension, wherein a kinetic equation is as follows:
Figure BDA0003521136800000021
in the above formula, v is the vehicle speed; i isyIs the moment of inertia; m is the suspension mass; m is1,m2Front and rear wheel masses; a and b are distances between the mass center and the front and rear suspension frames; theta is a pitch angle; z is the vertical displacement of the vehicle body; z is a radical of1,z2The front wheel and the rear wheel are vertically displaced; fs1,Fs2Front and rear suspension spring forces; fd1,Fd2Damping forces for front and rear suspensions, Ft1,Ft2Front and rear wheel tire force, ks1,ks2The front and rear suspension elastic coefficients; k is a radical ofd1,kd2Is the damping coefficient of the front and rear suspension, kt1,kt2Is the radial stiffness coefficient of the front and rear wheels, u1,u2A force generated for the controller; q. q of1,q2Is a road surface;
3.2, solving a state space equation:
defining the state variables and the control variables as
Figure BDA0003521136800000022
In the formula, xi(i ═ 1,2,3,4,5,6) are vehicle state variables;
simplifying a state space equation and expressing the equation by a matrix;
3.3, introducing a Lyapunov function to prove the stability of the system and obtaining an inversion controller:
Figure BDA0003521136800000023
in the formula u1rAnd u2rRepresenting the inverse control force of the actuator output,
Figure BDA0003521136800000024
and
Figure BDA0003521136800000025
second derivative representing a reference state quantity of the vehicle body, e1And e3A tracking error indicating the state of the vehicle body,
Figure BDA0003521136800000026
and
Figure BDA0003521136800000027
representing the first derivative of the tracking error.
Further, based on an inverse control law, the proposed sliding mode control strategy is as follows:
4.1, considering that the parameters are disturbed, the uncertainty exists to rewrite the state space equation:
Figure BDA0003521136800000031
wherein, the delta A, the delta B and the delta D are used for representing the difference between the linear model and the actual model, and the A, the B and the D represent a corresponding matrix of a state space equation obtained by the linear relation; this difference is mainly caused by non-linearities in the suspension spring and damping parameters, accuracy errors of the sensor and external random disturbances.
4.2, design integral slip plane:
defining the integral slip plane as s ═ s1 s2]TThe integral slip plane is designed as follows:
s＝Hx-∫H[(A+BΨ)x+BΘxd+D]dt
Figure BDA0003521136800000032
Figure BDA0003521136800000033
in the formula, xi1，ξ2，ξ3And xi4Representing a given constant, matrix xdΨ and Θ satisfy ur＝[u1r u2r]T＝Ψx+Θxd；
The sliding mode control law based on the inverse control law is
u＝ur-T(x)sgn(s)
T(x)＝(HB)-1Υ
Figure BDA0003521136800000034
Where σ is a given positive number; | HB | represents the Frobenius norm of HB; | x | | represents the Euclidean norm of x;
and a Lyapunov function is introduced later to prove the stability of the control system, so that
Figure BDA0003521136800000035
In the formula (I), the compound is shown in the specification,
Figure BDA0003521136800000036
the derivative of the Lyapunov function is expressed.
Adopt the beneficial effect that above-mentioned technical scheme brought:
the invention considers the nonlinearity of the suspension parameters and the uncertainty of disturbance, and the proposed control strategy does not depend on the accuracy of the established suspension vehicle model. Therefore, the system has strong applicability and is convenient to realize and popularize. The feasibility and convergence of the inversion sliding mode controller are good.
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FIG. 1 is a diagram of the control system of the present invention;
FIG. 2 is an active suspension model half car for use with the present invention;
FIG. 3 is a schematic diagram of a nonlinear suspension control strategy methodology of the present invention;
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
As shown in fig. 1-3, the invention designs a nonlinear suspension control system and a control method under uncertain conditions, which mainly comprise an information acquisition module, an inversion controller module, a sliding mode controller module based on inversion control law and an actuator module; the information acquisition module acquires physical quantities such as road surface input, vehicle body stress and the like through a vehicle-mounted sensor; the inversion controller module establishes a linear vehicle suspension model with uncertainty omitted based on information obtained by a sensor, controls the change of a tracking target by applying inversion control, and inputs the obtained control rate to the sliding mode controller module; the sliding mode controller module based on the inversion control law can eliminate the influence of uncertainty and disturbance by combining the inversion control law and a vehicle model considering uncertainty; the actuator module is an active suspension actuator and is used for outputting final control force, controlling vertical displacement and pitching motion of the vehicle body and stabilizing the posture of the vehicle body, so that the riding comfort is ensured.
Before a control strategy is given, a suitable model needs to be established. The invention adopts a classic semi-vehicle model to describe the characteristics of an active suspension, as shown in figure 2
From the model, the following kinetic equations can be given:
Figure BDA0003521136800000051
selecting u according to kinetic equation1And u2As a control command. The state variables and control variables may be defined as follows:
Figure BDA0003521136800000052
in the formula, xi(i ═ 1,2,3,4,5,6) are vehicle state variables;
thus, the state space equation can be expressed in a matrix form. The simplified form is as follows:
Figure BDA0003521136800000053
Ft＝f(x,q)
wherein:
Figure BDA0003521136800000054
Figure BDA0003521136800000061
in fact, for suspension systems, uncertainty is primarily derived from the non-linear parametric behavior. Due to the parametric non-linear characteristics, the spring and the damping force are not purely linear. In addition, tire forces are complex non-linear functions with respect to road surface input and state space variables that can be acquired by onboard sensors.
In view of the above uncertainties, the state space equation can be rewritten as follows:
Figure BDA0003521136800000062
where Δ a, Δ B, and Δ D are used to characterize the difference between the linear model and the actual model, which is mainly caused by the non-linearity of the suspension spring and damping parameters, the accuracy error of the sensor, and external random disturbances.
Ideal body movement zdAnd thetadTaking the value as zero. In other words, the riding comfort can be ensured by controlling the vertical displacement and the pitching motion. If the tracking error approaches zero, the goal is achieved. According to the concept of the scheme, x of the ideal motion is introduced1dAnd x3d. The tracking error is defined as follows:
Figure BDA0003521136800000063
a Lyapunov function based on the above error is given below to demonstrate the stability of the system. It is clear that the function is positive.
Figure BDA0003521136800000064
Its time derivative can be written as follows:
Figure BDA0003521136800000071
to further demonstrate stability, two additional ideal states were introduced and defined as follows:
Figure BDA0003521136800000072
in the above formula, k1And k3Is a known positive constant. x is the number of2dAnd x4dIs a new ideal state. Their error from the actual state variable can also be represented.
Figure BDA0003521136800000073
It is apparent that when the new ideal state is the same as the actual state variable, e2And e4Will approach zero. Therefore, a new Lyapunov function is proposed that contains four errors.
Figure BDA0003521136800000074
The derivative of the above equation is obtained, and the result is:
Figure BDA0003521136800000075
on this basis, the added equation is as follows:
Figure BDA0003521136800000076
a designed inversion controller is obtained.
Figure BDA0003521136800000077
In the formula u1rAnd u2rRepresenting the inverse control force of the actuator output,
Figure BDA0003521136800000078
and
Figure BDA0003521136800000079
second derivative representing a reference state quantity of the vehicle body, e1And e3A tracking error indicating the state of the vehicle body,
Figure BDA00035211368000000710
and
Figure BDA00035211368000000711
representing the first derivative of the tracking error.
The derivative of the Lyapunov function becomes of the form:
Figure BDA00035211368000000712
according to the Lyapunov-like lemma, the following conclusions can be drawn.
Figure BDA0003521136800000081
This means that the control system is asymptotically stable and the proposed control strategy has proven to be feasible.
By working up the above equations, a simplified form of the inversion control law can be expressed as follows.
ur＝Ψx+Θxd
Wherein: u. ur＝[u1r u2r]T,
Figure BDA0003521136800000082
Figure BDA0003521136800000083
Figure BDA0003521136800000084
Substituting the inversion control law into the control system state equation, the closed-loop system state space equation can be expressed as follows:
Figure BDA0003521136800000085
wherein, the delta A, the delta B and the delta D are used for representing the difference between the linear model and the actual model, and the A, the B and the D represent a corresponding matrix of a state space equation obtained by the linear relation; this difference is mainly caused by non-linearities in the suspension spring and damping parameters, accuracy errors of the sensor and external random disturbances.
The integrated slip plane is designed as follows, taking into account the uncertainty effects.
s＝Hx-∫H[(A+BΨ)x+BΘxd+D]dt
Figure BDA0003521136800000086
Where H is a specified constant matrix, ξ1，ξ2，ξ3And xi4Representing a given constant, matrix xdΨ and Θ satisfy ur＝[u1r u2r]T＝Ψx+Θxd；
In addition, matrix elements satisfying the following conditions are also designed:
Figure BDA0003521136800000091
the expression of the invertible matrix HB is
Figure BDA0003521136800000092
Under practical conditions, the uncertainty is bounded. The vehicle type and road conditions determine the upper bound of uncertainty. Based on the theory, an unknown function matrix is introduced
Figure BDA0003521136800000093
And
Figure BDA0003521136800000094
to represent uncertainty.
Figure BDA0003521136800000095
Defining a total combined uncertainty as δ ═ δ1 δ2]T。
Figure BDA0003521136800000096
For each portion that is bounded, the following condition is satisfied:
Figure BDA0003521136800000097
wherein sigma0And σ1Are given constants and are all positive. | | · | | represents the Euclidean norm.
The sliding mode surface derivative.
Figure BDA0003521136800000098
To obtain an equivalent control law ueqLet a
Figure BDA0003521136800000099
Equivalent control law ueqIs composed of
ueq＝-[H(B+ΔB)]-1[HΔAx+HΔD-HBΨx-HBΘxd]
Will be equivalent to control law ueqSubstituted to obtain
Figure BDA0003521136800000101
By comparison, the state space equation of an uncertain system is the same as that of a linear system. Therefore, the conclusion can be drawn that the influence of uncertainty can be eliminated by combining the sliding mode control strategy of the inversion control law.
Defining the control law as u ═ u1 u2]T. The designed inverse sliding mode controller is specifically expressed as follows:
u＝ur-T(x)sgn(s)
T(x)＝(HB)-1Υ
Figure BDA0003521136800000102
where σ is a known positive constant. | HB | represents the Frobenius norm of HB. | x | | represents the Euclidean norm of x.
Choosing Lyapunov function as
Figure BDA0003521136800000103
The time derivative of the Lyapunov function is obtained as
Figure BDA0003521136800000104
The stability and convergence of the control system are demonstrated.
Finally, the calculated control force is output by the actuator of the active suspension.
The nonlinear suspension control system considers the nonlinearity of suspension parameters and disturbance uncertainty, and the proposed control strategy does not depend on the accuracy of an established suspension vehicle model. Therefore, the system has strong applicability, is convenient to realize and popularize, and has good feasibility and convergence of the inversion sliding mode controller.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.

Claims (4)

1. A non-linear suspension control system under uncertain conditions comprising: the system comprises an information acquisition module, an inversion controller module, a sliding mode controller module based on an inversion control law and an actuator module; the information acquisition module is used for acquiring input information; the inversion controller module establishes a linear vehicle suspension model with uncertainty omitted based on the input information, controls the change of a tracking target by applying inversion control, and inputs the obtained control rate to the sliding mode controller module; the sliding mode controller module based on the inversion control law combines the inversion control law and a vehicle model considering uncertainty; the actuator module is an active suspension actuator and is used for outputting final control force, realizing control over vertical displacement and pitching motion of the vehicle body and stabilizing the posture of the vehicle body.
2. The nonlinear suspension control system under indeterminate conditions as set forth in claim 1, wherein: the information acquisition module acquires road surface input, vehicle body stress and vehicle motion state variables through a vehicle-mounted sensor.
3. The nonlinear suspension control system under indeterminate conditions as set forth in claim 1, wherein: for an ideal linear model, the method for inverting the control law is as follows:
3.1, establishing a half-car model of the active suspension, wherein a dynamic equation is as follows:
Figure FDA0003521136790000011
in the above formula, v is the vehicle speed; i isyIs the moment of inertia; m is the suspension mass; m is1,m2Front and rear wheel masses; a and b are distances between the mass center and the front and rear suspension frames; theta is a pitch angle; z is the vertical displacement of the vehicle body; z is a radical of1,z2The front wheel and the rear wheel are vertically displaced; fs1,Fs2Front and rear suspension spring forces; fd1,Fd2Damping forces for front and rear suspensions, Ft1,Ft2Front and rear wheel tire force, ks1,ks2The front and rear suspension elastic coefficients; k is a radical ofd1,kd2Is the damping coefficient of the front and rear suspension, kt1,kt2Is the radial stiffness coefficient of the front and rear wheels, u1,u2A force generated for the controller; q. q.s1,q2Exciting the road surface;
3.2, solving a state space equation:
defining the state variables and the control variables as
Figure FDA0003521136790000021
In the formula, xi(i ═ 1,2,3,4,5,6) are vehicle state variables;
simplifying a state space equation and expressing the equation by a matrix;
3.3, introducing a Lyapunov function to prove the stability of the system and obtaining an inversion controller:
Figure FDA0003521136790000022
in the formula u1rAnd u2rRepresenting the inverse control force of the actuator output,
Figure FDA0003521136790000023
and
Figure FDA0003521136790000024
second derivative representing a reference state quantity of the vehicle body, e1And e3A tracking error indicating the state of the vehicle body,
Figure FDA0003521136790000025
and
Figure FDA0003521136790000026
representing the first derivative of the tracking error.
4. The nonlinear suspension control system under indeterminate conditions as set forth in claim 1, wherein: based on an inversion control law, the sliding mode control strategy is as follows:
4.1, considering that the parameters are disturbed, the uncertainty exists to rewrite the state space equation:
Figure FDA0003521136790000027
wherein, the delta A, the delta B and the delta D are used for representing the difference between the linear model and the actual model, and the A, the B and the D represent a corresponding matrix of a state space equation obtained by the linear relation;
4.2, design integral slip plane:
defining the integral sliding surface as s ═ s1 s2]TThe integral slip plane is as follows:
s＝Hx-∫H[(A+BΨ)x+BΘxd+D]dt
Figure FDA0003521136790000028
Figure FDA0003521136790000029
in the formula, xi1，ξ2，ξ3And xi4Representing a given constant, matrix xdΨ and Θ satisfy ur＝[u1r u2r]T＝Ψx+Θxd；
The sliding mode control law based on the inverse control law is
u＝ur-T(x)sgn(s)
T(x)＝(HB)-1Υ
Figure FDA0003521136790000031
Where σ is a given positive number; | HB | represents the Frobenius norm of HB; | x | | represents the Euclidean norm of x;
finally, a Lyapunov function is introduced to obtain
Figure FDA0003521136790000032
In the formula (I), the compound is shown in the specification,
Figure FDA0003521136790000033
the derivative of the Lyapunov function is expressed.
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CN108995495A (en) * 2018-08-09 2018-12-14 燕山大学 A kind of the anti-saturation self-adaptation control method and system of non-linear Active suspension
CN111487870A (en) * 2020-04-26 2020-08-04 贵州理工学院 Design method of adaptive inversion controller in flexible active suspension system
CN113147307A (en) * 2021-06-03 2021-07-23 山东理工大学 Active suspension inversion control method based on reference model
CN113400883A (en) * 2021-07-29 2021-09-17 安徽工业大学 Dissipation performance control method and device for vehicle active suspension system
CN113427961A (en) * 2021-06-28 2021-09-24 齐齐哈尔大学 H-infinity switching control method for automobile active suspension based on T-S fuzzy model
CN113879062A (en) * 2021-11-03 2022-01-04 南阳师范学院 Self-adaptive control method for automobile active suspension

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20060293817A1 (en) * 2005-06-23 2006-12-28 Takahide Hagiwara Intelligent electronically-controlled suspension system based on soft computing optimizer
CN107444056A (en) * 2017-06-23 2017-12-08 南京农业大学 Nonlinear spring suspension Active Control Method based on passive
CN108995495A (en) * 2018-08-09 2018-12-14 燕山大学 A kind of the anti-saturation self-adaptation control method and system of non-linear Active suspension
CN111487870A (en) * 2020-04-26 2020-08-04 贵州理工学院 Design method of adaptive inversion controller in flexible active suspension system
CN113147307A (en) * 2021-06-03 2021-07-23 山东理工大学 Active suspension inversion control method based on reference model
CN113427961A (en) * 2021-06-28 2021-09-24 齐齐哈尔大学 H-infinity switching control method for automobile active suspension based on T-S fuzzy model
CN113400883A (en) * 2021-07-29 2021-09-17 安徽工业大学 Dissipation performance control method and device for vehicle active suspension system
CN113879062A (en) * 2021-11-03 2022-01-04 南阳师范学院 Self-adaptive control method for automobile active suspension

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