CN110826143A - Fault-tolerant control method of automobile active suspension system based on switching control - Google Patents

Fault-tolerant control method of automobile active suspension system based on switching control Download PDF

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CN110826143A
CN110826143A CN201910661430.0A CN201910661430A CN110826143A CN 110826143 A CN110826143 A CN 110826143A CN 201910661430 A CN201910661430 A CN 201910661430A CN 110826143 A CN110826143 A CN 110826143A
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fault
active suspension
suspension system
equation
follows
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姚雪莲
杨艺
朱凯
王晨光
葛佳汪
王可贤
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Jiangsu Institute of 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
    • B60G17/0185—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 for failure detection
    • 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
    • B60G2600/08—Failure or malfunction detecting means

Abstract

The invention discloses a fault-tolerant control method of an automobile active suspension system based on switching control, which comprises the following steps: establishing a mathematical model of the automobile active suspension system under the condition of uncertain actuator faults, and expressing uncertain influence of actuator fault uncertainty on system control input in a mathematical model mode; designing a fault-tolerant controller based on a mathematical model of an active suspension under a fault, designing a basic feedback controller by combining inversion control to ensure the problem of a closed-loop system, designing a fault compensation controller aiming at each fault mode, and designing a controller capable of solving the corresponding fault mode based on switching control; and (3) adopting a Lyapunov function method to test the performance of the fault-tolerant controller. The invention mainly solves two key uncertain factors of the actuator failure mode and the actuator failure type, ensures that the automobile active suspension system realizes the expected control target under the condition of uncertain actuator failure and obtains ideal performance.

Description

Fault-tolerant control method of automobile active suspension system based on switching control
Technical Field
The invention relates to the technical field of automobile suspension control, in particular to a fault-tolerant control method of an automobile active suspension system based on switching control.
Background
Automotive suspension systems are fundamental to significantly improve passenger comfort and handling characteristics, and in general, vehicle suspensions can be divided into three types: passive, semi-active and active suspensions, active suspension systems have the best performance potential under different driving conditions compared to passive and semi-active suspension systems. Therefore, the control problem of the system is concerned widely, such as optimal control, predictive control, robust control, fuzzy control, adaptive control and the like, wherein the adaptive control method has strong capability of handling the uncertainty of the system and ensures that the system has better transient performance and steady-state performance under the uncertain condition. In practice, active suspension system actuators have a higher probability of failure than other components, which may lead to instability or even catastrophic failure of the control. Research shows that the traditional feedback control method cannot ensure that the system has expected performance under the condition of element failure, and serious actuator failure can cause the system to be unstable, so that a new control method needs to be proposed, thereby overcoming the influence of uncertain failure on the system performance, and ensuring that the system still has ideal stability and expected performance under normal or failure conditions.
Aiming at the problem of actuator faults of an automobile active suspension system, experts and scholars at home and abroad provide a series of effective methods, such as sliding mode control, reconstruction control, H-infinity control, inversion control and the like, most of the methods mainly solve the actuator faults of the types of jamming and gain failure in the automobile active suspension system and ensure the stability of a closed-loop system, the invention with the application number of 201611256758.7 in Chinese patent document provides a passive fault-tolerant control method of the automobile active suspension system, and the passive fault-tolerant control method is provided aiming at the problems of actuator gain failure faults and uncertain suspension parameters of the active suspension system, however, in actual situations, the automobile active suspension system can suffer from time-varying faults, the stabilization and tracking are two key performances of the suspension system, for the automobile active suspension system, the tracking control under the fault condition is more complex than the stability control problem, in actual operation, actuator faults have intrinsic uncertainty, namely the fault time, the fault type, the fault mode and the number of fault actuators are unknown, and a fault-tolerant control method designed for determining the fault type and the fault mode cannot be used for solving the uncertain fault condition, so that the problem of application limitation is caused. In multiple uncertainties of faults of the actuator, the uncertainty of the fault mode is the most key, and to eliminate the influence of the faults in the multiple uncertain fault modes on system performance, effective estimation needs to be carried out fundamentally aiming at fault values in all fault modes, then, an integrated control method is designed to effectively solve the fault problem under all fault conditions, and the uncertainties of the fault modes and fault parameters are solved substantially at the same time.
Disclosure of Invention
The invention aims to solve the technical problem of providing a fault-tolerant control method of an automobile active suspension system based on switching control, which mainly solves two key uncertain factors of an actuator fault mode and a fault type, ensures that the automobile active suspension system realizes an expected control target under the condition of not determining the actuator fault and obtains ideal performance.
In order to achieve the aim, the control method provided by the invention comprises the steps of ① establishing a mathematical model of an automobile active suspension system under the condition of uncertain actuator faults, representing uncertain influence of actuator fault uncertainty on system control input in a mathematical model mode, ② designing a fault-tolerant controller based on the mathematical model of the active suspension under the faults, combining an inversion control design basis feedback controller to ensure the problem of a closed-loop system, designing a fault compensation controller aiming at each fault mode respectively, designing a controller capable of solving the corresponding fault mode based on switching control, and ③ checking the performance of the fault-tolerant controller by adopting a Lyapunov (Lyapunov) function method.
The invention provides the following specific technical scheme: a fault-tolerant control method of an automobile active suspension system based on switching control comprises the following steps:
establishing a mathematical model of an automobile active suspension system under the condition of uncertain faults;
a semi-vehicle active suspension system is adopted, and the system dynamic equation is as follows:
Figure BDA0002138673020000031
in the above formula (1), M and I are the mass and the moment of inertia of the vehicle body, respectively, and MfAnd mrFront and rear unsprung masses, respectively, Fdf，Fdr，FsfAnd FsrRespectively, force generated by spring damper, Ftf， Fbf，FtrAnd FbrRespectively the elastic and resistance forces, z, generated by the tyrecFor vertical displacement of the suspension, phi is the pitch angle, z1And z2For unsprung displacement, z01And z02For road excitation, a and b are the distance from the suspension to the center of gravity of the vehicle, u1And u2For the control input of the active suspension system, Ψ1(t)＝-Fdf- Fdr-Fsf-Fsr，Ψ2(t)＝-a(Fdf+Fsf)+b(Fdr+Fsr)，Fsf＝kf1Δyf， Fsr＝kr1Δyr，
Figure BDA0002138673020000032
Ftf＝kf2(z1-z01)， Ftr＝kr2(z2-z02) Wherein k isf1And kf2Denotes front and rear spring constants, bf1And br1Respectively front and rear damping coefficients, kf2And kr2The elastic coefficients of the front and rear tires, bf2And br2Damping coefficients, Δ y, of front and rear tires, respectivelyf＝zc+a sinφ-z1And Δ yr＝zc+b sinφ-z2Establishing a relation between the fault of the uncertain actuator and the active suspension for front and rear suspension spaces respectively, and representing the influence of the uncertainty of the fault of the actuator on an automobile active suspension system in a mathematical model mode;
the parameterized mathematical model of actuator failure is as follows:
Figure BDA0002138673020000034
in the above formula (2)
Figure BDA0002138673020000035
Respectively forming a fault vector for an unknown fault parameter vector and a known basis function
Figure BDA0002138673020000036
A set of failure modes that defines which actuator fails (i.e., the failure occurrence position) is defined as σ (t) ═ diag { σ (c) }1，σ2As an actuator
Figure BDA0002138673020000037
Then sigmaj(t) 1, otherwise σj(t)＝0；
The mathematical model of the control input to the system in the case of an indeterminate actuator failure is as follows:
Figure BDA0002138673020000041
selected state vector x1＝zc，
Figure BDA0002138673020000042
x3＝φ，
Figure BDA0002138673020000043
x5＝z1，
Figure BDA0002138673020000044
x7＝z2，
Figure BDA0002138673020000045
x13＝[x1，x3]T，x24＝[x2，x4]TAnd control output y ═ x1，x3]TSetting the desired control target to ym＝[rz，rφ]T；
Combining equation (1) and equation (3), the mathematical model of the automotive active suspension system under uncertain fault conditions can be obtained as follows:
Figure BDA0002138673020000046
designing a self-adaptive fault-tolerant controller based on a nonlinear model of the semi-vehicle active suspension system under the uncertain actuator faults;
and step three, adopting a Lyapunov function method to test the performance of the self-adaptive fault-tolerant controller.
Further, the specific process of designing the adaptive fault-tolerant controller in the step two is as follows: designing a closed-loop feedback control law based on a backstepping control algorithm according to an error value between a controlled output and a given command of the active suspension system, and ensuring the stability of the active suspension system and the asymptotically tracking of the output y on an expected command ym，
The following coordinate transformation is performed:
z13＝x13-ym(5)
z24＝x24-α1(6)
α in equation (6)1Is a virtual control quantity, (5) combining (4) to obtain an expression:
z in formula (7)13Indicating a tracking error, and setting a virtual control amount α1The following were used:
α1＝-c1z13+[γz&,γm&]T(8)
c in formula (8)1Is a design parameter that is a function of,
equation (6) combines equations (7) and (8), while based on the dynamic characteristics of the suspension system, yields:
Figure BDA0002138673020000053
the feedback control law is set as follows:
Figure BDA0002138673020000055
in equation (11)
Figure BDA0002138673020000056
ud is the ideal feedback control law,
Figure BDA0002138673020000057
the control target implemented by the invention is that the closed loop system can still be kept stable and asymptotic output tracking can be realized under the condition that the automobile active suspension system has uncertain actuator faults, namely an equality
Equation (12) holds true even in the case of an indeterminate actuator failure, and σ is found by combining equations (11) and (12) above assuming that the failure parameters are known1＝{0，0}，σ＝ σ 21,0 and σ3Ideal fault compensation controller for three fault conditions (0, 1)
Figure BDA0002138673020000059
Andrespectively as follows:
Figure BDA00021386730200000512
Figure BDA00021386730200000513
wherein
The adaptive controller structure is derived from equations (13), (14) and (15) above:
v(1)(t)＝K21ud(t) (16)
Figure BDA0002138673020000063
theta in equations (17) and (18)1And theta2Respectively as a fault parameter
Figure BDA0002138673020000064
Andan estimated value of (d);
for a fault-free case σ ═ σ1The failure observer is designed as follows:
Figure BDA0002138673020000066
Figure BDA0002138673020000067
for a fault-free case σ ═ σ2The failure observer is designed as follows:
Figure BDA0002138673020000068
Figure BDA0002138673020000069
for a fault-free case σ ═ σ3The failure observer is designed as follows:
Figure BDA00021386730200000610
Figure BDA00021386730200000611
defining variables
Figure BDA00021386730200000612
And
Figure BDA00021386730200000613
combining equations (19) - (21) yields the state observation errors for the three fault cases as follows:
Figure BDA00021386730200000614
in conjunction with equations (22) - (24), the parameter update law is set as follows:
Figure BDA0002138673020000071
Figure BDA0002138673020000072
in equation (25) fl1，fl2Being a standard parametric projection function, Γl1And Γl2Is the set control gain matrix.
Further, the step three of adopting a Lyapunov function method to test the fault-tolerant controller specifically comprises the following steps:
and (3) adopting a Lyapunov function to test the design method of the fault-tolerant controller:
firstly, listing the Lyapunov function equation of the semi-vehicle active suspension system under three fault modes, when sigma is sigma(1)When the value is set to diag {0,0},
Figure BDA0002138673020000073
derivation of the Lyapunov function combined with equation (25) yields:
wherein c is11And c12Are two positive design parameters that are used to design the circuit,
when sigma is sigma(2)When diag {1,0}, the Lyapunov function is constructed as follows:
Figure BDA0002138673020000075
Γ in equation (28)l1For the adaptive gain matrix, the Lyapunov function is derived by combining equation (25):
Figure BDA0002138673020000076
when sigma is sigma(3)When diag {0,1}, the Lyapunov function is constructed as follows:
Figure BDA0002138673020000077
Γ in equation (28)l1For adaptive gain matrix, p-LyapuThe derivative of the Novolv Lyapunov function is combined with equation (25) to obtain:
Figure BDA0002138673020000078
the combination of the equations (27), (29) and (31) can obtain a controller which can ensure that the first four equations in the mathematical model equation (4) of the automobile active suspension system are stable and the asymptotic output tracking is realized, and the last four equations in the equation (4) are zero dynamic parts of the automobile active suspension system, so that z is enabled13＝z24The inputs are obtained as follows:
Figure BDA0002138673020000081
Figure BDA0002138673020000082
let u1、u2Respectively replace
Figure BDA0002138673020000083
And
Figure BDA0002138673020000084
the zero dynamic property is obtained as follows:
Figure BDA0002138673020000085
wherein
Figure BDA0002138673020000086
Figure BDA0002138673020000087
List Lyapunov function V ═ xTPx, wherein P is a positive definite matrix, and the derivative of the Lyapunov function is obtained by:
Figure BDA0002138673020000088
in the above formula (34), P and Q are respectively selected matrices, η1And η2Selecting design parameters
Figure BDA0002138673020000091
Combined inequality
Figure BDA0002138673020000092
And
Figure BDA0002138673020000093
obtaining:
Figure BDA0002138673020000094
equations (25) and (35) demonstrate that the fault tolerant controller is used for system stability and asymptotic tracking in an automotive active suspension system.
Compared with the prior art, the invention has the following beneficial effects:
1. the parameterized actuator fault model and the parameterized fault mode model are introduced, so that typical dead locking and gain failure faults can be represented, and other types of time-varying faults can be represented, so that the faults of the various types of actuators can be solved, and compared with other fault-tolerant control methods of an automobile active suspension system, the fault-tolerant control method provided by the invention has stronger applicability;
2. the invention establishes the relation between the uncertainty of the actuator fault and the control input of the system, and directly adjusts the parameters of the controller by updating the fault parameters on line, compared with other error-tolerant control methods, the control algorithm provided by the invention does not need to set a fault diagnosis unit, the controller structure is simpler, and the parameter adjustment is more direct;
3. the method effectively compensates the actuator faults in each fault mode, and a fault-tolerant controller matched with the actuator fault condition actually occurring at present of the automobile active suspension system is selected by designing a switching function to achieve an accurate control target.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the invention without limiting the invention.
FIG. 1 is a schematic view of an active suspension system for a vehicle according to the present invention;
FIG. 2 is a response graph of the desired command zero for vertical displacement tracking of an automotive active suspension in the event of an actuator failure;
FIG. 3 is a response plot of the pitch angle tracking expected command zero for an automotive active suspension in the event of an actuator failure;
FIG. 4 is a graph of control input signals for an active suspension of a vehicle in the event of an actuator failure;
fig. 5 is a diagram of switching command signals for a controller of an active suspension of a vehicle in the event of an actuator failure.
Detailed Description
The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, and it should be understood that the preferred embodiments described herein are merely for purposes of illustration and explanation and are not intended to limit the invention.
Example (b):
as shown in fig. 1, an embodiment of the present invention provides a fault-tolerant control method for an active suspension system of an automobile based on switching control, where the fault-tolerant control method includes the following steps:
establishing a mathematical model of an automobile active suspension system under the condition of uncertain faults;
a semi-vehicle active suspension system is adopted, and the system dynamic equation is as follows:
Figure BDA0002138673020000101
in the above formula (1), M and I are the mass and the moment of inertia of the vehicle body, respectively, and MfAnd mrRespectively front and rear non-springCarrier mass, Fdf，Fdr，FsfAnd FsrRespectively, force generated by spring damper, Ftf， Fbf，FtrAnd FbrRespectively the elastic and resistance forces, z, generated by the tyrecFor vertical displacement of the suspension, phi is the pitch angle, z1And z2For unsprung displacement, z01And z02For road excitation, a and b are the distance from the suspension to the center of gravity of the vehicle, u1And u2For the control input of the active suspension system, Ψ1(t)＝-Fdf- Fdr-Fsf-Fsr，Ψ2(t)＝-a(Fdf+Fsf)+b(Fdr+Fsr)，Fsf＝kf1Δyf， Fsr＝kr1Δyr，
Figure BDA0002138673020000111
Ftf＝kf2(z1-z01)， Ftr＝kr2(z2-z02) Wherein k isf1And kf2Denotes front and rear spring constants, bf1And br1Respectively front and rear damping coefficients, kf2And kr2The elastic coefficients of the front and rear tires, bf2And br2Damping coefficients, Δ y, of front and rear tires, respectivelyf＝zc+a sinφ-z1And Δ yr＝zc+b sinφ-z2Establishing a relation between the fault of the uncertain actuator and the active suspension for front and rear suspension spaces respectively, and representing the influence of the uncertainty of the fault of the actuator on an automobile active suspension system in a mathematical model manner;
the parameterized mathematical model of actuator failure is as follows:
Figure BDA0002138673020000112
in the above formula (2)
Figure BDA0002138673020000113
Respectively unknown fault parametersVector and known basis functions to form a fault vector
Figure BDA0002138673020000114
A set of failure modes that defines which actuator fails (i.e., the failure occurrence position) is defined as σ (t) ═ diag { σ (c) }1，σ2As an actuator
Figure BDA0002138673020000115
Then sigmaj(t) 1, otherwise σj(t)＝0；
The mathematical model of the control input to the system in the case of an indeterminate actuator failure is as follows:
Figure BDA0002138673020000116
selected state vector x1＝zc，
Figure BDA0002138673020000117
x3＝φ，
Figure BDA0002138673020000118
x5＝z1，x7＝z2，
Figure BDA00021386730200001110
x13＝[x1，x3]T，x24＝[x2，x4]TAnd control output y ═ x1，x3]TSetting the desired control target to ym＝[rz，rφ]T；
Combining equation (1) and equation (3), the mathematical model of the automotive active suspension system under uncertain fault conditions can be obtained as follows:
Figure BDA0002138673020000121
designing a self-adaptive fault-tolerant controller based on a nonlinear model of the semi-vehicle active suspension system under the uncertain actuator faults;
and step three, adopting a Lyapunov function method to test the performance of the self-adaptive fault-tolerant controller.
Further, in this embodiment, the specific process of designing the adaptive fault-tolerant controller in the step two is as follows: in fig. 1, a closed-loop feedback control law is designed based on Backstepping control algorithm according to an error value between a controlled output and a given command of an active suspension system, so that the stability of the active suspension system and the output y of the active suspension system are ensured to gradually track an expected command ym，
The following coordinate transformation is performed:
z13＝x13-ym(5)
z24＝x24-α1(6)
α in equation (6)1Is a virtual control quantity, (5) combining (4) to obtain an expression:
Figure BDA0002138673020000122
z in formula (7)13Indicating a tracking error, and setting a virtual control amount α1The following were used:
α1＝-c1z13+[γz&,γm&]T(8)
c in formula (8)1Is a design parameter that is a function of,
equation (6) combines equations (7) and (8), while based on the dynamic characteristics of the suspension system, yields:
Figure BDA0002138673020000131
Figure BDA0002138673020000132
the feedback control law is set as follows:
Figure BDA0002138673020000133
in equation (11)
Figure BDA0002138673020000134
ud is the ideal feedback control law,
Figure BDA0002138673020000135
the control target implemented by the invention is that the closed loop system can still be kept stable and asymptotic output tracking can be realized under the condition that the automobile active suspension system has uncertain actuator faults, namely an equality
Figure BDA0002138673020000136
Equation (12) holds true even in the case of an indeterminate actuator failure, and σ is found by combining equations (11) and (12) above assuming that the failure parameters are known1＝{0，0}，σ＝ σ 21,0 and σ3Ideal fault compensation controller for three fault conditions (0, 1)
Figure BDA0002138673020000137
And
Figure BDA0002138673020000138
respectively as follows:
Figure BDA0002138673020000139
Figure BDA00021386730200001310
Figure BDA00021386730200001311
wherein
Figure BDA00021386730200001316
The adaptive controller structure is derived from equations (13), (14) and (15) above:
v(1)(t)＝K21ud(t) (16)
Figure BDA00021386730200001312
theta in equations (17) and (18)1And theta2Respectively as a fault parameter
Figure BDA00021386730200001314
And
Figure BDA00021386730200001315
an estimated value of (d);
for a fault-free case σ ═ σ1The failure observer is designed as follows:
Figure BDA0002138673020000141
Figure BDA0002138673020000142
for a fault-free case σ ═ σ2The failure observer is designed as follows:
Figure BDA0002138673020000144
for a fault-free case σ ═ σ3＝{0，1 design fault observer as follows:
Figure BDA0002138673020000145
Figure BDA0002138673020000146
defining variables
Figure BDA0002138673020000147
And
Figure BDA0002138673020000148
combining equations (19) - (21) yields the state observation errors for the three fault cases as follows:
Figure BDA0002138673020000149
in conjunction with equations (22) - (24), the parameter update law is set as follows:
Figure BDA00021386730200001410
Figure BDA00021386730200001411
in equation (25) fl1，fl2Being a standard parametric projection function, Γl1And Γl2Is the set control gain matrix.
Further, in this embodiment, the step three of adopting the Lyapunov function method to test the fault-tolerant controller specifically includes:
and (3) adopting a Lyapunov function to test the design method of the fault-tolerant controller:
firstly, listing the Lyapunov function equation of the semi-vehicle active suspension system under three fault modes, when sigma is sigma(1)When the value is set to diag {0,0},
Figure BDA0002138673020000151
derivation of the Lyapunov function combined with equation (25) yields:
Figure BDA0002138673020000152
wherein c is11And c12Are two positive design parameters that are used to design the circuit,
when sigma is sigma(2)When diag {1,0}, the Lyapunov function is constructed as follows:
Figure BDA0002138673020000153
Γ in equation (28)l1For the adaptive gain matrix, the Lyapunov function is derived by combining equation (25):
Figure BDA0002138673020000154
when sigma is sigma(3)When diag {0,1}, the Lyapunov function is constructed as follows:
Figure BDA0002138673020000155
Γ in equation (28)l1For the adaptive gain matrix, the Lyapunov function is derived by combining equation (25):
Figure BDA0002138673020000156
the combination of the equations (27), (29) and (31) can obtain a controller which can ensure that the first four equations in the mathematical model equation (4) of the automobile active suspension system are stable and the asymptotic output tracking is realized, and the last four equations in the equation (4) are zero dynamic parts of the automobile active suspension system, so that z is enabled13＝z24The inputs are obtained as follows:
Figure BDA0002138673020000157
Figure BDA0002138673020000158
let u1、u2Respectively replaceAnd
Figure BDA0002138673020000162
the zero dynamic property is obtained as follows:
Figure BDA0002138673020000163
wherein
Figure BDA00021386730200001610
Figure BDA0002138673020000164
List Lyapunov function V ═ xTPx, wherein P is a positive definite matrix, and the derivative of the Lyapunov function is obtained by:
Figure BDA0002138673020000165
in the above formula (34), P and Q are respectively selected matrices, η1And η2Selecting design parameters
Figure BDA0002138673020000166
Combined inequality
Figure BDA0002138673020000167
And
Figure BDA0002138673020000168
obtaining:
equations (25) and (35) demonstrate that the fault tolerant controller is used for system stability and asymptotic tracking in an automotive active suspension system.
Further, in this embodiment, in order to explain that the fault-tolerant control method of the vehicle active suspension system based on the switching control can effectively solve the fault of the uncertain multi-type and multi-mode actuators, and can implement the asymptotic output tracking, the following simulation conditions are given:
semi-vehicle active suspension system, M1200 kg, Mf＝mr＝100kg，I＝600kgm2， kf1＝kf2＝15000N/m，br1＝br2＝2500Ns/m；kf2＝kr2＝200000N/m， bf2＝br21000Ns/m, 1.2m of a, 1.5m of b, 20m/s of forward speed V of the vehicle, and 1s ≦ t ≦ 1.25s of road surface input signal
Figure BDA0002138673020000171
Otherwise z o10, wherein the slope height h of the roadside inputb＝2cm；
Actuator failure condition one: when t is more than or equal to 0s and less than 3s, no actuator fault occurs; when t is more than or equal to 3s, the first actuator has a fault u1(t) 10N; when t is more than or equal to 3s and less than 7s, the first actuator is recovered to be normal without failure; when t is more than or equal to 7s and less than 9s, the second actuator has a fault u2(t) ═ 5sin (5t) N; when t is more than or equal to 9s, the second actuator is recovered to be normal, and the system has no fault.
Simulation parameters: x is the number of1(0)＝1cm，x3(0) 0.01rad, initial value of the remaining states 0, c11＝c21＝c31＝12，c12＝c22＝c32＝10，Γ1l＝100I2×2，Γ2l＝100I2×2Fault basis function
Figure BDA0002138673020000172
As shown in fig. 2 and 3, it can be seen from fig. 2 and 3 that, regardless of the type of the constant-value fault or the time-varying fault, the fault-tolerant control method provided in this embodiment can ensure the stable and asymptotic output tracking of the closed-loop system in the uncertain alternating fault mode.
As shown in fig. 4 and 5, it can be seen from fig. 4 and 5 that when the fault condition changes, the switching command of the controller can be quickly switched to the fault compensation controller matched with the current fault condition, so as to improve the rate of tracking error convergence.
In summary, in this embodiment, according to the fault-tolerant control method for an automotive active suspension system based on switching control of this embodiment, a mathematical model of the semi-automotive active suspension system under the condition of an uncertain actuator fault is established, a fault compensation controller is respectively designed for each fault mode, an integrated controller capable of handling all fault conditions is designed based on switching control, the performance of the controller is analyzed based on the Lyapunov function, and the design designs an effective controller for each fault mode, so that the effect and the rapidity of fault-tolerant control are greatly improved.
The invention is improved in that the fault-tolerant control method of the automobile active suspension system based on switching control comprises ①, designing a mathematical model of the automobile active suspension system under the condition of uncertain actuator faults, representing uncertain influence of actuator fault uncertainty on system control input in the mode of the mathematical model, ②, designing a fault-tolerant controller based on the mathematical model of the active suspension under the faults, ensuring the problem of a closed-loop system by combining an inversion control design basic feedback controller, designing a fault compensation controller aiming at each fault mode respectively, designing a controller capable of solving the corresponding fault mode based on the switching control, and ③, testing the performance of the fault-tolerant controller by adopting a Lyapunov function method.
Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art will understand that various changes, modifications and substitutions can be made without departing from the spirit and scope of the invention as defined by the appended claims. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (3)

1. A fault-tolerant control method of an automobile active suspension system based on switching control is characterized by comprising the following steps:
establishing a mathematical model of an automobile active suspension system under the condition of uncertain faults;
a semi-vehicle active suspension system is adopted, and the system dynamic equation is as follows:
in the above formula (1), M and I are the mass and the moment of inertia of the vehicle body, respectively, and MfAnd mrFront and rear unsprung masses, respectively, Fdr，Fdr，FsfAnd FsrRespectively, force generated by spring damper, Ftf，Fbf，FtrAnd FbrRespectively the elastic and resistance forces, z, generated by the tyrecFor vertical displacement of the suspension, phi is the pitch angle, z1And z2For unsprung displacement, z01And z02For road excitation, a and b are the distance between the suspension and the center of gravity of the vehicle body, u1And u2For the control input of the active suspension system, Ψ1(t)＝-Fdf-Fdr-Fsf-Fsr，Ψ2(t)＝-a(Fdf+Fsf)+b(Fdr+Fsr)，Fsf＝kf1Δyf，Fsr＝kr1Δyr，
Figure FDA0002138673010000012
Ftf＝kf2(z1-z01)，Ftr＝kr2(z2-z02) Wherein k isf1And kf2Denotes front and rear spring constants, bf1And br1Respectively front and rear damping coefficients, kf2And kr2The elastic coefficients of the front and rear tires, bf2And br2Damping coefficient, Δ y, of front and rear tires, respectivelyf＝zc+asinφ-z1And Δ yr＝zc+b sinφ-z2Establishing a relation between the fault of the uncertain actuator and the active suspension for front and rear suspension spaces respectively, and representing the influence of the uncertainty of the fault of the actuator on an automobile active suspension system in a mathematical model manner;
the parameterized mathematical model of actuator failure is as follows:
in the above formula (2)
Figure FDA0002138673010000014
Respectively forming a fault vector for an unknown fault parameter vector and a known basis function
Figure FDA0002138673010000015
A set of failure modes that defines which actuator fails (i.e., the failure occurrence position) is defined as σ (t) ═ diag { σ (c) }1，σ2As an actuatorThen sigmaj(t) 1, otherwise σj(t)＝0；
The mathematical model of the control input to the system in the case of an indeterminate actuator failure is as follows:
selected state vector x1＝zc，x3＝φ，x5＝z1，
Figure FDA0002138673010000025
x7＝z2，x13＝[x1，x3]T，x24＝[x2，x4]TAnd control output y ═ x1，x3]TSetting the desired control target to ym＝[rz，rφ]T；
Combining equation (1) and equation (3), a mathematical model of the active suspension system of the automobile under uncertain fault conditions can be obtained as follows:
Figure FDA0002138673010000027
designing a self-adaptive fault-tolerant controller based on a nonlinear model of the semi-vehicle active suspension system under the uncertain actuator faults;
and step three, adopting a Lyapunov function method to test the performance of the self-adaptive fault-tolerant controller.
2. The switching control-based fault-tolerant control method for the active suspension system of the automobile according to claim 1, wherein the specific process of designing the adaptive fault-tolerant controller in the second step is as follows: based on the error value between the controlled output and the given command of the active suspension systemDesigning a closed-loop feedback control law in a Backstepping control algorithm to ensure the stability of an active suspension system and output a y asymptotic tracking expected command ym，
The following coordinate transformation is performed:
z13＝x13-ym(5)
z24＝x24-α1(6)
α in equation (6)1Is a virtual control quantity, (5) combining (4) to obtain an expression:
Figure RE-FDA0002330365490000031
z in formula (7)13Indicating a tracking error, and setting a virtual control amount α1The following were used:
α1＝-c1z13+[γz&，γm&]T(8)
c in formula (8)1Is a design parameter that is a function of,
equation (6) combines equations (7) and (8), while based on the dynamic characteristics of the suspension system, yields:
Figure RE-FDA0002330365490000032
Figure RE-FDA0002330365490000033
the feedback control law is set as follows:
Figure RE-FDA0002330365490000034
in equation (11)
Figure RE-FDA0002330365490000035
udIs an ideal feedback control law and is characterized in that,
Figure RE-FDA0002330365490000036
Figure RE-FDA0002330365490000037
equation (12) holds true even in the case of an indeterminate actuator failure, and σ is found by combining equations (11) and (12) above assuming that the failure parameters are known1＝{0，0}，σ＝σ21,0 and σ3Ideal fault compensation controller for three fault conditions (0, 1)
Figure RE-FDA0002330365490000038
Andrespectively as follows:
Figure RE-FDA00023303654900000310
Figure RE-FDA00023303654900000311
Figure RE-FDA00023303654900000312
wherein
Figure RE-FDA0002330365490000041
The adaptive controller structure is derived from equations (13), (14) and (15) above:
v(1)(t)＝K21ud(t) (16)
Figure RE-FDA0002330365490000042
Figure RE-FDA0002330365490000043
theta in equations (17) and (18)1And theta2Respectively as a fault parameter
Figure RE-FDA0002330365490000044
And
Figure RE-FDA0002330365490000045
an estimated value of (d);
for a fault-free case σ ═ σ1The failure observer is designed as follows:
Figure RE-FDA0002330365490000046
for a fault-free case σ ═ σ2The failure observer is designed as follows:
Figure RE-FDA0002330365490000048
Figure RE-FDA0002330365490000049
for a fault-free case σ ═ σ3The failure observer is designed as follows:
Figure RE-FDA00023303654900000410
Figure RE-FDA00023303654900000411
defining variables
Figure RE-FDA00023303654900000412
Andcombining equations (19) - (21) yields the state observation errors for the three fault cases as follows:
Figure RE-FDA00023303654900000414
Figure RE-FDA00023303654900000416
Figure RE-FDA00023303654900000417
Figure RE-FDA00023303654900000418
Figure RE-FDA00023303654900000419
in conjunction with equations (22) - (24), the parameter update law is set as follows:
Figure RE-FDA0002330365490000051
Figure RE-FDA0002330365490000052
in equation (25) fl1，fl2Being a standard parametric projection function, Γl1And Γl2Is the set control gain matrix.
3. The switching control-based fault-tolerant control method for the active suspension system of the automobile according to claim 2, wherein the step three of adopting a Lyapunov function method to test the fault-tolerant controller specifically comprises the following steps:
and (3) adopting a Lyapunov function to test the design method of the fault-tolerant controller:
firstly, listing the Lyapunov function equation of the semi-vehicle active suspension system under three fault modes, when sigma is sigma(1)When the value is set to diag {0,0},
Figure FDA0002138673010000053
derivation of the Lyapunov function combined with equation (25) yields:
Figure FDA0002138673010000054
wherein c is11And c12Are two positive design parameters that are used to design the circuit,
when sigma is sigma(2)When diag {1,0}, the Lyapunov function is constructed as follows:
Figure FDA0002138673010000055
Γ in equation (28)l1For the adaptive gain matrix, the Lyapunov function is derived by combining equation (25):
Figure FDA0002138673010000056
when sigma is sigma(3)When diag {0,1}, the Lyapunov function is constructed as follows:
Γ in equation (28)l1For the adaptive gain matrix, the Lyapunov function is derived by combining equation (25):
Figure FDA0002138673010000061
the combination of the equations (27), (29) and (31) can obtain a controller which can ensure that the first four equations in the mathematical model equation (4) of the automobile active suspension system are stable and the asymptotic output tracking is realized, and the last four equations in the equation (4) are zero dynamic parts of the automobile active suspension system, so that z is enabled13＝z24The inputs are obtained as follows:
Figure FDA0002138673010000062
Figure FDA0002138673010000063
let u1、u2Respectively replace
Figure FDA0002138673010000064
And
Figure FDA0002138673010000065
the zero dynamic property is obtained as follows:
Figure FDA0002138673010000066
wherein
Figure FDA0002138673010000067
List Lyapunov function V ═ xTPx, wherein P is a positive definite matrix, and the derivative of the Lyapunov function is obtained by:
Figure FDA0002138673010000069
Figure FDA0002138673010000071
in the above formula (34), P and Q are respectively selected matrices, η1And η2Selecting design parameters
Figure FDA0002138673010000072
Combined inequalityAnd
Figure FDA0002138673010000074
obtaining:
Figure FDA0002138673010000075
equations (25) and (35) demonstrate that the fault tolerant controller is used for system stability and asymptotic tracking in an automotive active suspension system.
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