CN107791773B - Whole vehicle active suspension system vibration control method based on specified performance function - Google Patents

Whole vehicle active suspension system vibration control method based on specified performance function Download PDF

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CN107791773B
CN107791773B CN201710784924.9A CN201710784924A CN107791773B CN 107791773 B CN107791773 B CN 107791773B CN 201710784924 A CN201710784924 A CN 201710784924A CN 107791773 B CN107791773 B CN 107791773B
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suspension system
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CN107791773A (en
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那靖
裴倩倩
高贯斌
伍星
黄英博
伞红军
陈明方
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Kunming University of Science and Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60G—VEHICLE SUSPENSION ARRANGEMENTS
    • B60G17/00—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load
    • B60G17/015—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements
    • B60G17/018—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements characterised by the use of a specific signal treatment or control method
    • B60G17/0182—Resilient suspensions having means for adjusting the spring or vibration-damper characteristics, for regulating the distance between a supporting surface and a sprung part of vehicle or for locking suspension during use to meet varying vehicular or surface conditions, e.g. due to speed or load the regulating means comprising electric or electronic elements characterised by the use of a specific signal treatment or control method involving parameter estimation, e.g. observer, Kalman filter
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B60—VEHICLES IN GENERAL
    • B60G—VEHICLE SUSPENSION ARRANGEMENTS
    • B60G2600/00—Indexing codes relating to particular elements, systems or processes used on suspension systems or suspension control systems
    • B60G2600/18—Automatic control means
    • B60G2600/182—Active control means

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Abstract

The invention relates to a method for controlling vibration of a whole vehicle active suspension system based on a specified performance function, and belongs to the field of vehicle engineering. Firstly, establishing a dynamic model of a whole vehicle active suspension according to the automotive dynamics theory and Newton's second law; then designing a performance function to make the vertical displacement, the roll angle and the pitch angle converge in the boundary of the performance function; then, applying an inverse function to equivalently convert the vertical displacement, the roll angle and the pitch angle into conversion errors; and finally, designing control laws in the vertical direction, the side-rolling direction and the pitching direction through conversion errors, and performing active vibration control on the whole vehicle suspension. The invention is closer to the real vehicle condition; transient and steady-state performance of the suspension system is guaranteed, and robustness of the system is improved; for a complex nonlinear system such as a finished automobile suspension system, the control strategy based on the specified performance function avoids complex operations such as a system accurate modeling process and neural network on-line calculation, and is simple in design and small in calculated amount.

Description

Whole vehicle active suspension system vibration control method based on specified performance function
Technical Field
The invention relates to a method for controlling vibration of a whole vehicle active suspension system based on a specified performance function, and belongs to the field of vehicle engineering.
Background
With the rapid development of the vehicle field, people have higher and higher requirements on performance indexes such as the riding comfort and the operation stability of the automobile, and the performance of a suspension system as the most important damping part of the vehicle directly determines the overall performance of the vehicle. Therefore, the research on the vehicle suspension system is of great significance. Due to the fact that parameters of a whole vehicle model are more, most scholars adopt a quarter vehicle model and a half vehicle model when studying suspension vibration, the quarter vehicle model is not coupled, the half vehicle model does not consider the roll motion of a vehicle body, and the models cannot reflect the vibration conditions of the vehicle in the vertical direction, the roll direction and the pitch direction and have a certain difference with the actual conditions. Therefore, the patent establishes a seven-degree-of-freedom vehicle active suspension model and provides a method for controlling the vibration condition of the vehicle in the vertical, pitching and rolling directions based on a specified performance function, so that the vehicle always keeps a good running state.
For a nonlinear system with complex cascade and coupling, such as a finished automobile active suspension system, common control strategies are complex in design and large in calculation amount, and transient performance of the system is difficult to guarantee, so that a simple control strategy capable of planning performance is required to guarantee stability of the system.
Disclosure of Invention
The invention provides a vibration control method of a whole vehicle active suspension system based on a specified performance function, which designs controllers for the vertical direction, the lateral direction and the pitching direction of the suspension system, so that the vertical displacement, the acceleration, the roll angle and the pitching angle can be converged within a specified performance boundary within a limited time, and the stability of the system is improved.
The technical scheme of the invention is as follows: a vibration control method of a whole vehicle active suspension system based on a specified performance function is characterized by firstly establishing a dynamic model of the whole vehicle active suspension according to the automotive dynamics theory and Newton's second law; then designing a performance function to make the vertical displacement, the roll angle and the pitch angle converge in the boundary of the performance function; then, applying an inverse function to equivalently convert the vertical displacement, the roll angle and the pitch angle into conversion errors; and finally, designing control laws in the vertical direction, the side-rolling direction and the pitching direction through conversion errors, and performing active vibration control on the whole vehicle suspension.
According to the automobile dynamics theory and the Newton's second law, the dynamics model of the whole automobile active suspension is obtained as follows:
the kinetic equation of the vertical direction of the mass center of the vehicle body is as follows:
Figure BDA0001397792180000021
kinetic equation of vehicle body rolling direction:
Figure BDA0001397792180000022
the dynamic equation of the pitching direction of the vehicle body is as follows:
Figure BDA0001397792180000023
kinetic equations for the four wheel vertical directions:
Figure BDA0001397792180000024
in the formulae (1) to (4), M represents the vehicle body mass, and M i1,2,3,4 represents the unsprung mass of the four wheels; z is a radical ofsRepresenting the vertical displacement of the center of mass of the vehicle,
Figure BDA0001397792180000025
denotes zsA second derivative with respect to time; i isφRepresents the rolling moment of inertia of the vehicle body, phi is the roll angle,
Figure BDA0001397792180000026
represents the second derivative of phi with respect to time; i isθRepresenting the pitch moment of inertia of the vehicle body, theta is the pitch angle,
Figure BDA0001397792180000027
represents the second derivative of θ with respect to time; f si1,2,3,4 represents the spring force generated by the four-position spring; f di1,2,3,4 represents damping forces generated by the four-position damper; z is a radical ofuiI is 1,2,3,4 represents the vertical deformation of four wheels,
Figure BDA0001397792180000028
denotes zuiA second derivative with respect to time; y isiAnd i is 1,2,3 and 4, which represents the displacement input of the road surface excitation to the four wheels; k is a radical oftiAnd i is 1,2,3,4, which represents the stiffness coefficients of the four wheels; a and b represent the distances from the center of mass of the vehicle body to the front axle and the rear axle respectively; c and d represent the wheel track from the center of mass of the vehicle body to the front wheel and the rear wheel respectively; v represents the speed at which the vehicle is traveling; u. ofiAnd i is 1,2,3,4, which represents four active independent suspension system controllers output forces;
in formulae (1), (2) and (3), uz、uφAnd uθRepresenting the motion control forces in the vertical, roll and pitch directions, respectively, can be calculated as:
Figure BDA0001397792180000029
due to the designed output force u of the controller of the right rear active independent suspension system3And the output force u of the left rear active independent suspension system controller4The pitching motion of the vehicle body is not influenced, and the following expression can be obtained:
cu3-du4＝0(6)。
the dynamic model of the whole vehicle active suspension is x by defining a state variable1＝zs,
Figure BDA0001397792180000031
x3＝φ,
Figure BDA0001397792180000032
x5＝θ,
Figure BDA0001397792180000033
x7＝zu1,
Figure BDA0001397792180000034
x9＝zu2,
Figure BDA0001397792180000035
x11＝zu3,
Figure BDA0001397792180000036
x13＝zu4,
Figure BDA0001397792180000037
Can be rewritten as:
Figure BDA0001397792180000038
Figure BDA0001397792180000039
designing a performance function to make the vertical displacement, the roll angle and the pitch angle converge in the boundary of the performance function, and then applying an inverse function to make the vertical displacement, the roll angle and the pitch angle equivalently converted into conversion errors, specifically:
① vertical displacement of center of mass z for a vehicles＝x1Designing a performance function;
for z in the kinetic equation (1) of the vertical direction of the center of mass of the vehicle bodys＝x1Selecting a performance function rho1(t):R+→R-Comprises the following steps:
ρ1(t)＝δ1sech(τ1t)+ρ1∞(9)；
in formula (9), ρ1(t) in the positive real number interval R+Interval R to negative real number-Is a continuous slightly bounded decreasing function; delta1Is a normal number, ρ1∞For allowable steady state error, sech (τ)1t) is a hyperbolic secant function constant, τ 10 is the convergence speed of the function, t represents time, delta1And rho1∞The value is selected to satisfy delta1＞ρ1∞(ii) a The vertical displacement of the vehicle centroid should satisfy the following boundary conditions:
Figure BDA0001397792180000041
② error conversion operation is performed on the vertical displacement of the control target vehicle center of mass:
defining a control error s1The following were used:
Figure BDA0001397792180000042
in formula (11), Λ1> 0 is a normal quantity, T is a matrix transposition operator,
Figure BDA0001397792180000043
is x1A derivative with respect to time;
defining another smooth strictly monotonically increasing function
Figure BDA0001397792180000044
Function S (z)1) The following conditions should be satisfied:
Figure BDA0001397792180000045
in the formula (12), L∞Representing a bounded function;
to obtain a performance function rho1(t) and a strictly monotonically increasing function S (z)1) Based on the control error s1By function equivalent transformation, the following equation can be obtained:
Figure BDA0001397792180000046
in the formula (13), ζ1＝s1/ρ1(t) is an equivalent transformation variable;
③ design control force u of automobile movement in vertical directionzThe expression is as follows:
Figure BDA0001397792180000047
in formula (14), k1Control gain > 0;
④ repeating the above ① - ③, the whole vehicle initiative can be designed by the same methodMotion control force u of suspension system in roll directionφAnd a motion control force u in the pitch directionθComprises the following steps:
Figure BDA0001397792180000051
Figure BDA0001397792180000052
in equations (15) and (16), k2＞0,k3Control gain, > 0, ζ2And ζ3The angles x of the active suspension system of the whole vehicle in the roll direction and the pitch direction respectively3Phi and x5The equivalent transformation variable of θ.
The control law of vertical, side-tipping and pitching directions is designed by converting errors, and active vibration control is carried out on the whole vehicle suspension, specifically: the obtained motion control forces u in the vertical, roll and pitch directionsz,uφAnd uθThe force distribution principle is adopted to distribute the four independent suspension system controllers according to the force distribution principle of the whole vehicle active independent suspension system, and the output force u of the four independent suspension system controllers can be calculated through simultaneous formulas (5) and (6)iA mathematical expression of i 1.. 4:
Figure BDA0001397792180000053
the obtained four active independent suspension system controllers output force uiAnd (i is 1,2,3 and 4) is input into a dynamic model of the active suspension system of the whole automobile to control the running state of the whole automobile.
The invention has the beneficial effects that:
1. the invention adopts the whole vehicle active suspension system as a research object to design the controller, fully considers the motion conditions and the coupling action of the vehicle body in the vertical, lateral and pitching directions and is closer to the real vehicle condition.
2. The invention adopts a control strategy based on a specified performance function, so that the vertical displacement, the roll angle and the pitch angle of the suspension system are always converged in the specified performance, the transient and steady performance of the suspension system is ensured, and the robustness of the system is improved.
3. For a complex nonlinear system such as a finished automobile suspension system, the control strategy based on the specified performance function avoids complex operations such as a system accurate modeling process and neural network on-line calculation, and is simple in design and small in calculated amount.
Drawings
FIG. 1 is a schematic diagram of a system for constructing a dynamic model of an active suspension of a finished vehicle according to the present invention;
FIG. 2 is a schematic illustration of a random rough road surface input provided by the present invention;
FIG. 3 is a graph of the vehicle body acceleration response of the present invention;
FIG. 4 is a comparison of the vertical, roll and pitch directions of the vehicle body under the influence of different control methods in accordance with the present invention;
FIG. 5 is a graph of the RMS response of vertical acceleration, vertical displacement, roll angle, and pitch angle of the present invention.
Detailed Description
Example 1: as shown in fig. 1-5, a method for controlling vibration of a whole vehicle active suspension system based on a specified performance function first establishes a dynamic model of the whole vehicle active suspension according to the automotive dynamics theory and newton's second law; then designing a performance function to make the vertical displacement, the roll angle and the pitch angle converge in the boundary of the performance function; then, applying an inverse function to equivalently convert the vertical displacement, the roll angle and the pitch angle into conversion errors; and finally, designing control laws in the vertical direction, the side-rolling direction and the pitching direction through conversion errors, and performing active vibration control on the whole vehicle suspension.
Further, it may be arranged that the specific steps of the method may be performed according to the following steps:
step1, obtaining a dynamic model of the whole vehicle active suspension according to the automobile dynamic theory and Newton's second law as follows:
the kinetic equation of the vertical direction of the mass center of the vehicle body is as follows:
Figure BDA0001397792180000061
kinetic equation of vehicle body rolling direction:
Figure BDA0001397792180000062
the dynamic equation of the pitching direction of the vehicle body is as follows:
Figure BDA0001397792180000063
kinetic equations for the four wheel vertical directions:
Figure BDA0001397792180000064
in the formulae (1) to (4), M represents the vehicle body mass, and MiI-1, 2,3,4 denotes the unsprung mass of the four wheels, m1M represents the unsprung mass of the right front wheel2M represents unsprung mass of the left front wheel3M represents the unsprung mass of the right rear wheel4Representing the left rear wheel unsprung mass; z is a radical ofsRepresenting the vertical displacement of the center of mass of the vehicle,
Figure BDA0001397792180000065
denotes zsA second derivative with respect to time; i isφRepresents the rolling moment of inertia of the vehicle body, phi is the roll angle,
Figure BDA0001397792180000071
represents the second derivative of phi with respect to time; i isθRepresenting the pitch moment of inertia of the vehicle body, theta is the pitch angle,
Figure BDA0001397792180000072
represents the second derivative of θ with respect to time; fsiWhere i is 1,2,3,4 denotes the spring force generated by the four-position spring, Fs1Showing the spring force, F, generated by the right front springs2Showing the spring force, F, generated by the left front springs3Showing the spring force, F, generated by the right rear springs4Representing the spring force generated by the left rear spring; fdiWhere i is 1,2,3,4 denotes damping forces generated by the four-position damper, Fd1Showing the damping force F generated by the front right damperd2Showing the damping force F generated by the left front damperd3Showing the damping force F generated by the right rear damperd4Representing the damping force generated by the left rear damper; z is a radical ofuiI is 1,2,3,4 represents the vertical deformation of four wheels,
Figure BDA0001397792180000073
denotes zuiSecond derivative with respect to time, zu1Represents the amount of vertical deformation, z, of the front right wheelu2Vertical deformation amount, z, of left front wheelu3Represents the amount of vertical deformation, z, of the right rear wheelu4Represents the amount of vertical deformation of the left rear wheel; y isiWhere i is 1,2,3,4 denotes the displacement input of the road excitation to the four wheels, y1Indicating the displacement input, y, of the road excitation to the front right wheel2Indicating the displacement input, y, of the road excitation to the left front wheel3Indicating the displacement input, y, of the road excitation to the right rear wheel4Representing a displacement input of the road excitation to the left rear wheel; k is a radical oftiAnd i is 1,2,3,4, which represents the stiffness coefficients of the four wheels; a and b represent the distances from the center of mass of the vehicle body to the front and rear axles, respectively, kt1Expressing the stiffness coefficient, k, of the front right wheelt2Representing the stiffness coefficient, k, of the left wheelt3Representing the stiffness coefficient, k, of the right rear wheelt4Representing the stiffness coefficient of the left rear wheel; c and d represent the wheel track from the center of mass of the vehicle body to the front wheel and the rear wheel respectively; v represents the speed at which the vehicle is traveling; u. ofiAnd i is 1,2,3,4, the four active independent suspension system controller output forces, u1Representing the output force u of the controller of the right front active independent suspension system2Shows the output force u of the left front active independent suspension system controller3Representing the output force u of the controller of the right rear active independent suspension system4Representing the output force of the left rear active independent suspension system controller;
in formulae (1), (2) and (3), uz、uφAnd uθRepresenting the motion control forces in the vertical, roll and pitch directions, respectively, can be calculated as:
Figure BDA0001397792180000074
due to the designed output force u of the controller of the right rear active independent suspension system3And the output force u of the left rear active independent suspension system controller4The pitching motion of the vehicle body is not influenced, and the following expression can be obtained:
cu3-du4＝0(6)。
further, it may be provided that:
step2, the dynamic model of the whole vehicle active suspension is defined as x by defining a state variable1＝zs,
Figure BDA0001397792180000081
x3＝φ,
Figure BDA0001397792180000082
x5＝θ,
Figure BDA0001397792180000083
x7＝zu1,
Figure BDA0001397792180000084
x9＝zu2,
Figure BDA0001397792180000085
x11＝zu3,
Figure BDA0001397792180000086
x13＝zu4,
Figure BDA0001397792180000087
Can be rewritten as:
Figure BDA0001397792180000088
Figure BDA0001397792180000089
further, it may be provided that:
step3, vertical displacement of center of mass z for vehicles＝x1Designing a performance function;
for z in the kinetic equation (1) of the vertical direction of the center of mass of the vehicle bodys＝x1Selecting a performance function rho1(t):R+→R-Comprises the following steps:
ρ1(t)＝δ1sech(τ1t)+ρ1∞(9)；
in formula (9), ρ1(t) in the positive real number interval R+Interval R to negative real number-Is a continuous slightly bounded decreasing function; delta1Is a normal number, ρ1∞For allowable steady state error, sech (τ)1t) is a hyperbolic secant function constant, τ 10 is the convergence speed of the function, t represents time, delta1And rho1∞The value is selected to satisfy delta1＞ρ1∞(ii) a The vertical displacement of the vehicle centroid should satisfy the following boundary conditions:
Figure BDA0001397792180000091
step4, carrying out error conversion operation on the vertical displacement of the center of mass of the control target vehicle:
step4.1, defining control error s1The following were used:
Figure BDA0001397792180000092
in formula (11), Λ1> 0 is a normal quantity, T is a matrix transposition operator,
Figure BDA0001397792180000093
is x1A derivative with respect to time;
step4.2, DefinitionsA smooth strictly monotonic increasing function
Figure BDA0001397792180000094
Function S (z)1) The following conditions should be satisfied:
Figure BDA0001397792180000095
in the formula (12), L∞Representing a bounded function;
step4.3, obtaining a performance function rho1(t) and a strictly monotonically increasing function S (z)1) Based on the control error s1By function equivalent transformation, the following equation can be obtained:
Figure BDA0001397792180000096
in the formula (13), ζ1＝s1/ρ1(t) is an equivalent transformation variable;
step5 designing motion control force u of automobile in vertical directionzThe expression is as follows:
Figure BDA0001397792180000097
in formula (14), k1Control gain > 0;
step6, repeating the steps 3-Step5, and designing the motion control force u of the active suspension system of the whole vehicle in the roll direction in the same wayφAnd a motion control force u in the pitch directionθComprises the following steps:
Figure BDA0001397792180000101
Figure BDA0001397792180000102
in equations (15) and (16), k2＞0,k3Control gain, > 0, ζ2And ζ3The angles x of the active suspension system of the whole vehicle in the roll direction and the pitch direction respectively3Phi and x5The equivalent transformation variable of θ.
Step7, and the motion control forces u in the vertical, roll and pitch directions obtained in Step3-Step6z,uφAnd uθThe force distribution principle is adopted to distribute the four independent suspension system controllers according to the force distribution principle of the whole vehicle active independent suspension system, and the output force u of the four independent suspension system controllers can be calculated through simultaneous formulas (5) and (6)iA mathematical expression of i 1.. 4:
Figure BDA0001397792180000103
the obtained four active independent suspension system controllers output force uiAnd (i is 1,2,3 and 4) is input into a dynamic model of the active suspension system of the whole automobile to control the running state of the whole automobile.
Example 2: a method for jointly controlling an active suspension system of a whole vehicle based on a specified performance function comprises the following specific steps:
the method is characterized in that the motion control of a specified performance function is carried out on an E-type SUV according to the process of the invention, a nonlinear simplified diagram of a whole vehicle active suspension is shown in figure 1, and numerical simulation is carried out through combined simulation of Matlab/Simulink and Carsim software.
Step1, establishing a dynamic model of the active suspension of the whole vehicle: according to the automobile dynamics theory and Newton's second law, the dynamic model of the whole automobile active suspension system is obtained as follows:
the kinetic equation of the vertical direction of the mass center of the vehicle body is as follows:
Figure BDA0001397792180000104
kinetic equation of vehicle body rolling direction:
Figure BDA0001397792180000111
the dynamic equation of the pitching direction of the vehicle body is as follows:
Figure BDA0001397792180000112
kinetic equations for the four wheel vertical directions:
Figure BDA0001397792180000113
equations (1) to (4), M1590 kg represents the vehicle body mass, Mi(i ═ 1,2,3,4) denotes unsprung mass, where m is160kg represents the unsprung mass of the right front wheel, m260kg represents the unsprung mass of the left front wheel, m375kg represents the unsprung mass of the right rear wheel, m475kg represents the left rear wheel unsprung mass. z is a radical ofsRepresenting a vertical displacement of a center of mass of the vehicle; i isφ＝894.4kgm2Representing the roll moment of inertia of the vehicle body, wherein phi is a roll angle; i isθ＝2687.1kgm2Representing the pitch moment of inertia of the vehicle body, wherein theta is a pitch angle; fsi(i ═ 1,2,3,4) denotes the spring force generated by the spring, where Fs1Showing the spring force, F, generated by the right front springs2Showing the spring force, F, generated by the left front springs3Showing the spring force, F, generated by the right rear springs4Representing the spring force generated by the left rear spring; fdi(i ═ 1,2,3,4) denotes the damping force generated by the damper, where Fd1Showing the damping force F generated by the front right damperd2Showing the damping force F generated by the left front damperd3Showing the damping force F generated by the right rear damperd4Representing the damping force generated by the left rear damper; z is a radical ofui(i ═ 1,2,3,4) represents the amount of vertical deformation of the wheel, where z representsu1Represents the amount of vertical deformation, z, of the front right wheelu2Vertical deformation amount, z, of left front wheelu3Represents the amount of vertical deformation, z, of the right rear wheelu4Represents the amount of vertical deformation of the left rear wheel; y isi(i ═ 1,2,3,4) represents the displacement input of the road surface excitation, where y is1Indicating the displacement input, y, of the road excitation to the front right wheel2Indicating road surface excitation pairDisplacement input, y, of the left front wheel3Indicating the displacement input, y, of the road excitation to the right rear wheel4Representing a displacement input of the road excitation to the left rear wheel; k is a radical ofti(i ═ 1,2,3,4) represents the stiffness coefficients of the four wheels, where k ist1502000N/m represents the stiffness coefficient of the right front wheel, kt2502000N/m represents the stiffness coefficient of the left wheel, kt3502000N/m represents the stiffness coefficient of the right rear wheel, kt4502000N/m represents the stiffness coefficient of the left rear wheel; a 1.18m and b 1.77m respectively represent the distances from the center of mass of the vehicle body to the front axle and the rear axle; c-0.7875 m and d-0.7875 m respectively represent the wheel distances from the center of mass of the vehicle body to the front wheels and the rear wheels; v ═ 60km/h represents the speed at which the vehicle is traveling; u. ofi(i ═ 1,2,3,4) represents four active independent suspension system controller output forces, where u is1Representing the output force u of the controller of the right front active independent suspension system2Shows the output force u of the left front active independent suspension system controller3Representing the output force u of the controller of the right rear active independent suspension system4Representing the left rear active independent suspension system controller output force.
In formulae (1), (2) and (3), uz、uφAnd uθRepresenting the motion control forces in the vertical, roll and pitch directions, respectively, can be calculated as:
Figure BDA0001397792180000121
due to the designed output force u of the controller of the right rear active independent suspension system3And the output force u of the left rear active independent suspension system controller4The pitching motion of the vehicle body is not influenced, and the following expression can be obtained:
cu3-du4＝0(6)；
step2, defining the state variable as x1＝zs,
Figure BDA0001397792180000122
x3＝φ,
Figure BDA0001397792180000123
x5＝θ,
Figure BDA0001397792180000124
x7＝zu1,
Figure BDA0001397792180000125
x9＝zu2,
Figure BDA0001397792180000126
x11＝zu3,
Figure BDA0001397792180000127
x13＝zu4,
Figure BDA0001397792180000128
The dynamic model of the whole vehicle active suspension system can be rewritten as:
Figure BDA0001397792180000129
Figure BDA0001397792180000131
step3, vertical displacement of center of mass z for vehicles＝x1Designing a performance function;
z in equation (1) for dynamics in the vertical direction of the center of mass of the vehicle bodys＝x1Selecting a performance function rho1(t):R+→R-Is composed of
ρ1(t)＝δ1sech(τ1t)+ρ1∞(9)；
In formula (9), ρ1(t) in the positive real number interval R+Interval R to negative real number-Is a continuous slightly bounded decreasing function; delta1Is a normal number, ρ1∞For allowable steady state error, sech (τ)1t) is a hyperbolic secant function constant, τ 10 is the convergence speed of the function, t represents time, delta1And rho1∞The value is selected to satisfy delta1＞ρ1∞(ii) a The vertical displacement of the vehicle centroid should satisfy the following boundary conditions:
Figure BDA0001397792180000132
step4, vertical displacement z of center of mass of control target vehicles＝x1Carrying out error conversion operation:
step4.1, defining control error s1The following were used:
Figure BDA0001397792180000133
in formula (11), Λ1> 0 is a normal quantity, T is a matrix transposition operator,
Figure BDA0001397792180000134
is x1A derivative with respect to time;
step4.2, another smooth strictly monotonic increasing function is defined
Figure BDA0001397792180000135
Function S (z)1) The following conditions should be satisfied:
Figure BDA0001397792180000136
in the formula (12), L∞Representing a bounded function;
step4.3, obtaining a performance function rho1(t) and a strictly monotonically increasing function S (z)1) Based on the control error s1By inverse function operation transformation, the following equation can be obtained:
Figure BDA0001397792180000141
in the formula (13), ζ1＝s1/ρ1(t) is an equivalent transformation variable;
step5 designing motion control force u of automobile in vertical directionzThe expression is as follows:
Figure BDA0001397792180000142
in formula (14), k1Control gain > 0;
step6, repeating Step3-Step5, and designing the motion control force u of the active suspension system of the whole vehicle in the roll direction in the same wayφAnd a motion control force u in the pitch directionθComprises the following steps:
Figure BDA0001397792180000144
Figure BDA0001397792180000143
in equations (15) and (16), k2＞0,k3Control gain, > 0, ζ2And ζ3The angles x of the active suspension system of the whole vehicle in the roll direction and the pitch direction respectively3Phi and x5An equivalent transformation variable of θ;
step7, and the motion control forces u in the vertical, roll and pitch directions obtained in Step3-Step6z,uφAnd uθThe force distribution principle is adopted to distribute the four independent suspension system controllers according to the force distribution principle of the whole vehicle active independent suspension system, and the output force u of the four independent suspension system controllers can be calculated through simultaneous formulas (5) and (6)iA mathematical expression of i 1.. 4:
Figure BDA0001397792180000151
the obtained four active independent suspension system controllers output force uiAnd (i is 1,2,3 and 4) is input into a dynamic model of the active suspension system of the whole automobile to control the running state of the whole automobile.
In order to verify the effectiveness of the whole vehicle active suspension controller, the invention establishes a 1200m long random rough road surface as the road surface displacement input in the Carsim software, and the road surface response curve is shown in figure 2, and the vehicle runs on the road surface at the speed of 60 km/h.
In the simulation, a prescribed performance function in the vertical direction of the vehicle body is set to ρ1(t) 0.1sech (12t) +0.002, and a predetermined performance function in the roll direction ρ2(t) 0.3sech (7t) +0.03, and a predetermined performance function in the pitch direction ρ3(t) ═ 0.4sech (6t) + 0.13. Other parameters are set to be lambda in the simulation process of the whole vehicle active suspension system1＝15，Λ2＝9.43，Λ3＝11.33,k1＝1230,k2＝2790,k35970. Fig. 3 shows the vehicle body acceleration, i.e., sprung mass acceleration response curves under different control methods. As can be seen from FIG. 3, the method proposed by the present invention can significantly reduce the magnitude of the sprung mass acceleration, thereby improving driving comfort. Fig. 4 shows the comparison results of the vertical, roll and pitch directions of the vehicle body under the action of different control methods. Compared with the traditional Backstepping control method, the active suspension system adopting the preset performance function control method can simultaneously ensure that the transient state and the steady state motion attitude of the vehicle are both restrained within the preset error boundary range, namely the vertical displacement zsThe roll angle phi and the pitch angle theta can be converged within a preset boundary, so that the vehicle body jolt is effectively reduced, and the running stability of the vehicle is ensured; these requirements are not met by active suspension systems using the conventional Backstepping control method.
Root Mean Square (RMS) values of various variables (acceleration, displacement, roll angle and pitch angle) of an automobile are closely related to ride comfort, so the RMS value can be generally used as an index to measure ride comfort and operation safety. The root mean square value of the n-dimensional vector x may be calculated as:
Figure BDA0001397792180000161
vertical acceleration
Figure BDA0001397792180000162
Is perpendicular toDisplacement zsSide-tipping moment of inertia IφAnd pitch moment of inertia IθThe root mean square value of (a) is shown in fig. 5, which makes it possible to observe the percentage of reduction of each comparison method more intuitively. It can be seen from fig. 5 that, compared with the active suspension system adopting the traditional Backstepping control method, the active suspension system adopting the preset performance function control method can realize the sprung mass acceleration of the whole vehicle
Figure BDA0001397792180000163
Vertical displacement of center of mass zsSide-tipping moment of inertia IφAnd pitch and roll inertia IθThe magnitude was reduced by 61.8%, 86.3%, 11.8%, 47.9%, respectively. Therefore, the controller provided by the invention can realize better inhibition effect of the active suspension system on road excitation.
While the present invention has been described in detail with reference to the embodiments, the present invention is not limited to the embodiments and various changes can be made without departing from the spirit and scope of the present invention by those skilled in the art.

Claims (1)

1. A vibration control method of a whole vehicle active suspension system based on a specified performance function is characterized in that: firstly, establishing a dynamic model of a whole vehicle active suspension according to the automotive dynamics theory and Newton's second law; then designing a performance function to make the vertical displacement, the roll angle and the pitch angle converge in the boundary of the performance function; then, applying an inverse function to equivalently convert the vertical displacement, the roll angle and the pitch angle into conversion errors; finally, designing control laws in the vertical direction, the side-tipping direction and the pitching direction through conversion errors, and carrying out active vibration control on the whole vehicle suspension;
according to the automobile dynamics theory and the Newton's second law, the dynamics model of the whole automobile active suspension is obtained as follows:
the kinetic equation of the vertical direction of the mass center of the vehicle body is as follows:
Figure FDA0002188300580000018
kinetic equation of vehicle body rolling direction:
Figure FDA0002188300580000011
the dynamic equation of the pitching direction of the vehicle body is as follows:
Figure FDA0002188300580000012
kinetic equations for the four wheel vertical directions:
Figure FDA0002188300580000013
in the formulae (1) to (4), M represents the vehicle body mass, and Mi1,2,3,4 represents the unsprung mass of the four wheels; z is a radical ofsRepresenting the vertical displacement of the center of mass of the vehicle,
Figure FDA0002188300580000014
denotes zsA second derivative with respect to time; i isφRepresents the rolling moment of inertia of the vehicle body, phi is the roll angle,
Figure FDA0002188300580000015
represents the second derivative of phi with respect to time; i isθRepresenting the pitch moment of inertia of the vehicle body, theta is the pitch angle,
Figure FDA0002188300580000016
represents the second derivative of θ with respect to time; fsi1,2,3,4 represents the spring force generated by the four-position spring; fdi1,2,3,4 represents damping forces generated by the four-position damper; z is a radical ofuiI is 1,2,3,4 represents the vertical deformation of four wheels,
Figure FDA0002188300580000017
i-1, 2,3,4 denotes zuiA second derivative with respect to time; y isiAnd i is 1,2,3 and 4, which represents the displacement input of the road surface excitation to the four wheels; k is a radical oftiAnd i is 1,2,3,4, which represents the stiffness coefficients of the four wheels; a and b represent the distances from the center of mass of the vehicle body to the front axle and the rear axle respectively; c and d represent the wheel track from the center of mass of the vehicle body to the front wheel and the rear wheel respectively; v represents the speed at which the vehicle is traveling; u. ofiAnd i is 1,2,3,4, which represents four active independent suspension system controllers output forces;
in formulae (1), (2) and (3), uz、uφAnd uθRepresenting the motion control forces in the vertical, roll and pitch directions, respectively, can be calculated as:
Figure FDA0002188300580000021
due to the designed output force u of the controller of the right rear active independent suspension system3And the output force u of the left rear active independent suspension system controller4The pitching motion of the vehicle body is not influenced, and the following expression can be obtained:
cu3-du4＝0(6)；
the dynamic model of the whole vehicle active suspension is x by defining a state variable1＝zs,
Figure FDA0002188300580000022
x3＝φ,
Figure FDA0002188300580000023
x5＝θ,
Figure FDA0002188300580000024
x7＝zu1,
Figure FDA0002188300580000025
x9＝zu2,
Figure FDA0002188300580000026
x11＝zu3,
Figure FDA0002188300580000027
x13＝zu4,
Figure FDA0002188300580000028
Can be rewritten as:
Figure FDA0002188300580000029
Figure FDA00021883005800000210
designing a performance function to make the vertical displacement, the roll angle and the pitch angle converge in the boundary of the performance function, and then applying an inverse function to make the vertical displacement, the roll angle and the pitch angle equivalently converted into conversion errors, specifically:
① vertical displacement of center of mass z for a vehicles＝x1Designing a performance function;
for z in the kinetic equation (1) of the vertical direction of the center of mass of the vehicle bodys＝x1Selecting a performance function rho1(t):R+→R-Comprises the following steps:
ρ1(t)＝δ1sech(τ1t)+ρ1∞(9)；
in formula (9), ρ1(t) in the positive real number interval R+Interval R to negative real number-Is a continuous slightly bounded decreasing function; delta1Is a normal number, ρ1∞For allowable steady state error, sech (τ)1t) is a hyperbolic secant function constant, τ10 is the convergence speed of the function, t represents time, delta1And rho1∞The value is selected to satisfy delta1＞ρ1∞(ii) a The vertical displacement of the vehicle centroid should satisfy the following boundary conditions:
Figure FDA0002188300580000031
② error conversion operation is performed on the vertical displacement of the control target vehicle center of mass:
defining a control error s1The following were used:
Figure FDA0002188300580000032
in formula (11), Λ1> 0 is a normal quantity, T is a matrix transposition operator,
Figure FDA0002188300580000033
is x1A derivative with respect to time;
defining another smooth strictly monotonically increasing function
Figure FDA0002188300580000034
Function S (z)1) The following conditions should be satisfied:
Figure FDA0002188300580000035
in the formula (12), L∞Representing a bounded function;
to obtain a performance function rho1(t) and a strictly monotonically increasing function S (z)1) Based on the control error s1By function equivalent transformation, the following equation can be obtained:
Figure FDA0002188300580000036
in the formula (13), ζ1＝s1/ρ1(t) is an equivalent transformation variable;
③ design control force u of automobile movement in vertical directionzThe expression is as follows:
Figure FDA0002188300580000037
in formula (14), k1Control gain > 0;
④ repeating above ① - ③, the motion control force u of the active suspension system in the roll direction of the whole vehicle can be designed by the same methodφAnd a motion control force u in the pitch directionθComprises the following steps:
Figure FDA0002188300580000041
Figure FDA0002188300580000042
in equations (15) and (16), k2＞0,k3Control gain, > 0, ζ2And ζ3The angles x of the active suspension system of the whole vehicle in the roll direction and the pitch direction respectively3Phi and x5An equivalent transformation variable of θ;
the control law of vertical, side-tipping and pitching directions is designed by converting errors, and active vibration control is carried out on the whole vehicle suspension, specifically: the obtained motion control forces u in the vertical, roll and pitch directionsz,uφAnd uθThe force distribution principle is adopted to distribute the four independent suspension system controllers according to the force distribution principle of the whole vehicle active independent suspension system, and the output force u of the four independent suspension system controllers can be calculated through simultaneous formulas (5) and (6)iAnd i is a mathematical expression of 1 … 4:
Figure FDA0002188300580000043
the obtained four active independent suspension system controllers output force uiAnd (i is 1,2,3 and 4) is input into a dynamic model of the active suspension system of the whole automobile to control the running state of the whole automobile.
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