CN110673480A - Robust control method of time-varying displacement constrained active suspension system - Google Patents

Robust control method of time-varying displacement constrained active suspension system Download PDF

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CN110673480A
CN110673480A CN201910948958.6A CN201910948958A CN110673480A CN 110673480 A CN110673480 A CN 110673480A CN 201910948958 A CN201910948958 A CN 201910948958A CN 110673480 A CN110673480 A CN 110673480A
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actuator
suspension system
active suspension
fault
follows
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CN110673480B (en
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刘艳军
曾强
刘磊
李大鹏
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Liaoning University of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Abstract

The invention discloses a robust control method of an active suspension system constrained by time-varying displacement, and belongs to the technical field of automobile stability control. According to the method, stress analysis is respectively carried out on a vehicle body and tires under a suspension according to a Newton second law and a Newton third law, a 1/4 vehicle active suspension system mathematical model containing an actuator fault mathematical model is established, a nonlinear active suspension system is identified based on a radial basis neural network, an actuator with fault compensation and a self-adaptation law thereof are designed, the stability of a closed-loop active suspension system is verified by adopting a barrier Lyapunov function, and finally parameters of the actuator and the self-adaptation law are adjusted to realize a final control target. The invention considers the idea of constraint control in the design of a fault compensation actuator of an active suspension system, thereby not only obviously improving the performance of the actuator when the actuator has a fault, but also ensuring the safety of the automobile.

Description

Robust control method of time-varying displacement constrained active suspension system
Technical Field
The invention relates to the technical field of automobile stability control, in particular to a robust control method of a time-varying displacement constrained active suspension system.
Background
With the increasing living standard and the continuous development of scientific technology, the active suspension system plays an important role in the automobile. Automotive suspension systems integrate electronic, sensing, signaling, power, and other important component systems. When the automobile runs and meets different road condition information, the automobile can utilize the active suspension system to adjust in real time, the overall safety of the automobile is guaranteed, and the riding comfort of passengers is improved.
During actual operation of the automotive suspension system, problems such as sensor failure, transmission signal errors and equipment aging can occur, and the problems can damage the suspension system. These faults, if not eliminated in a timely manner, can cause safety issues for the vehicle, such as failure of the motor in the active suspension system due to aging, sensor insensitivity resulting in deviation of the actuator input in the active suspension system, and so forth. Therefore, how to solve the control problem when a fault occurs in the active suspension system is a hot spot of current research.
An important research aspect for the development of active suspension systems is the assurance of safety, in particular for the driver and the passengers, that the vehicle can still be driven safely when the actuator fails. When the actuator fails, the excitation from the rough road surface received by the automobile is transmitted to the passengers, and meanwhile, the impact is caused to the integral structure of the automobile body and other electronic systems. Therefore, there is a need for an adaptive fault compensation controller with constraints to ensure the overall safety of the vehicle in the event of actuator failure, so that the controlled active suspension system becomes a closed loop system with adaptive and compensating faults.
At present, many achievements are achieved for self-adaptive control of an automobile suspension system at home and abroad, including sliding mode control, limited time control and H∞Control methods such as control and robust control are applied to control of a suspension system. However, these studies have rarely focused on the problem of fault-tolerant control of the suspension system, and particularly on the safety of the suspension system thereof. When an actuator of an automobile suspension system fails, attention is paid to how to improve the safety of the automobile suspension system. The controller is designed based on the constraint theory and the Lyapunov theorem, and finally, the control target of ensuring the safety of the automobile suspension system under the condition of actuator failure is realized.
Disclosure of Invention
In view of the above-mentioned deficiencies of the prior art, the present invention provides a robust control method for an active suspension system constrained by time-varying displacement.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a robust control method of an active suspension system constrained by time-varying displacement is disclosed as a flow chart in FIG. 1, and comprises the following steps:
step 1: establishing a mathematical model of the actuator fault of the active suspension system:
Figure BDA0002225126270000021
where u is the actuator output signal in the active suspension system and u is the actuator output signalcIs the actuator input signal, TfIs the time of occurrence of the fault, ρ is a failure factor, θ represents the departure fault, and there is a constantρAnd
Figure BDA0002225126270000022
such that the following inequality holds:
Figure BDA0002225126270000023
when the actuator has a deviation fault, ρ is 0, θ is not equal to 0, and u is equal tocNo longer functioning, deviating to the fault value θ;
when the actuator fails, determining rho belongs to (0,1), and theta is 0, and determining the percentage of the actuator losing the efficiency according to the specific numerical value of the failure factor rho;
step 2: respectively carrying out stress analysis on the automobile body and the tire under the suspension according to Newton's second law and Newton's third law, and establishing a mathematical model of the automobile active suspension system containing an actuator fault mathematical model, wherein the mathematical model comprises the following steps:
Figure BDA0002225126270000024
wherein, Fa、FsRespectively the spring force of the spring in the body and the damping force in the damper, FwAnd FrRespectively the spring force of the tire under suspension and the damping force of the tire under suspension, DsIs the vertical displacement of the vehicle body, DwIs the vertical displacement of the tire under the suspension, mcsIs the mass of the vehicle body, musIs the mass of the tire, and assumes that the upper and lower limits of the mass of the vehicle body are
Figure BDA0002225126270000025
The specific expressions of the elastic force and the damping force are as follows:
Figure BDA0002225126270000026
wherein k isaAnd caSpring coefficient and damping coefficient, k, of the vehicle body, respectivelytAnd ctRespectively the spring and damping coefficient of the tire under suspension, DrIs a road surface stimulus.
And step 3: designing an actuator with fault compensation and an adaptive law thereof based on a radial basis function neural network;
step 3.1: based on the mathematical model of the automobile active suspension system in the step 2, selecting the following state variables:
x1＝Ds,x3＝Dw,
Figure BDA0002225126270000028
step 3.2: establishing the following state space expression according to the mathematical model and the state variables of the automobile active suspension system:
Figure BDA0002225126270000031
where y is the output of the active suspension system;
step 3.3: based on the mathematical model of actuator failure in step 1, defining the following coordinate transformation for designing a failure compensation actuator:
e1＝x1-yd,e2＝x2-α1(4)
wherein, ydIs the desired trajectory, the first derivative of which
Figure BDA0002225126270000032
And second derivative
Figure BDA0002225126270000033
Are all bounded, α1Is a virtual actuator, e1To track errors, e2Is a transfer error;
step 3.4: respectively for error variable e1、e2Derivation:
Figure BDA0002225126270000034
step 3.5: in order to achieve the designed performance index, the virtual actuator is designed as follows:
wherein k is10 is a design parameter, and λ is defined as follows:
wherein beta is more than 0, ka(t) and kb(t) is respectively a time-varying upper bound and a time-varying lower bound of the tracking error, and the following conditions are met:
ka(t)＝yd(t)-k c(t) (8)
Figure BDA0002225126270000037
wherein the content of the first and second substances,andk c(t) is the asymmetric time-varying constraint bound for the active suspension system output y, namely:
Figure BDA0002225126270000039
Figure BDA00022251262700000310
step 3.6: according to the actuator fault model, the error variable e is calculated2The first derivative of (a) is further rewritten as follows:
Figure BDA0002225126270000041
wherein, Fz＝Fa+Fs，
Figure BDA0002225126270000042
Is an unknown continuous function of the time of day,
Figure BDA0002225126270000043
step 3.7: approximating the unknown function H (X) obtained in the step 3.6 in the system by adopting a radial basis function neural network to obtain the optimal weight W and approximation error of the neural network;
step 3.7.1: selecting a central value iota of a radial basis functioniEnsuring that there is a proper input vector sample value;
step 3.7.2: calculating variables
Figure BDA0002225126270000044
A Gaussian function of;
Figure BDA0002225126270000045
Figure BDA0002225126270000046
wherein eta isiIs the width of the Gaussian function, iotaiIs the central value of the selected Gaussian function, dmaxTo select the maximum Euclidean distance in the center, K is the number of centers;
and composing the obtained Gaussian function into the following matrix:
step 3.7.3: the unknown function h (x) obtained in step 3.6 is rewritten as follows:
H(X)＝WTφ(X)+ε(X) (16)
wherein W ═ W1,…,wn]T∈RnIs the optimal weight for the neural network; ε (X) is the approximation error and is bounded:
Figure BDA0002225126270000048
is a constant;
step 3.7.4: selecting the number of nodes of a neural network as n, wherein n is more than 1, and initializing the weight of each node by adopting a random number;
step 3.7.5: approximating H (X) obtained in the step 3.7.3 by using a radial basis function neural network to obtain the optimal weight and approximation error of the neural network;
step 3.8: designing an actuator with fault compensation and a corresponding adaptive law;
Figure BDA0002225126270000049
Figure BDA00022251262700000410
wherein k is2More than 0 and v more than 0 are design parameters, gamma is positive definite symmetric parameter matrix,
Figure BDA0002225126270000051
is an estimate of the optimal weight W with an estimation error of
Figure BDA0002225126270000052
μ1Is defined as follows:
Figure BDA0002225126270000053
wherein the content of the first and second substances,
Figure BDA0002225126270000054
and 4, step 4: verifying the stability of the closed-loop active suspension system by adopting a barrier Lyapunov function;
step 4.1: and (3) verifying by adopting a barrier Lyapunov function, and writing the following stability equation according to coordinate transformation:
Figure BDA0002225126270000055
wherein the content of the first and second substances,
Figure BDA0002225126270000056
in the discussion that follows, q (e)1) Abbreviated q, ka(t) and kb(t) are each abbreviated as kaAnd kb(ii) a And a positive constant exists
Figure BDA0002225126270000057
k a，
Figure BDA0002225126270000058
k bSo that the following equation holds:
Figure BDA0002225126270000059
step 4.2: the following error transformation is performed:
Figure BDA00022251262700000510
ξ＝qξb+(1-q)ξa(13)
step 4.3: the Lyapunov function can be redefined according to the error transformation described in step 4.3, as follows:
Figure BDA00022251262700000511
step 4.4: an unknown function H (X) obtained according to claim 3, incorporating the error variable e of claim 32The first derivative of (a) is rewritten as follows:
step 4.5: the redefined Lyapunov function is derived in combination with step 4.4, with the following results:
Figure BDA00022251262700000513
step 4.6: the actuator with fault compensation and the corresponding adaptation law and Young inequality obtained according to claim 3 scale the first derivative obtained in step 4.5 to obtain the inequality:
Figure BDA0002225126270000061
wherein the content of the first and second substances,v is a selected Lyapunov function;
step 4.7: the output y of the active suspension system of claim 2 can be judged to be in a progressively stable state from the inequality obtained in step 4.6 according to the Lyapunov stability criterion.
And 5: and adjusting parameters of the actuator and the self-adaptive law to realize the final control target.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in:
1. the invention considers the idea of constraint control in the design of a fault compensation actuator of an active suspension system, thereby not only ensuring the safety of the automobile, but also obviously improving the performance of the actuator when the actuator has a fault by comparing with an unconstrained self-adaptive control scheme;
2. the invention adopts asymmetric time-varying output constraint to compensate the nonlinear effect of the actuator, thereby improving the riding comfort and the operation stability to a certain extent; when the actuator fails, the influence caused by the failure of the actuator can be effectively compensated, so that the performance of the whole vehicle is improved;
3. the method adopts the radial basis function neural network to identify the nonlinear active suspension system, thereby improving the approximation capability of unknown smooth functions;
4. the invention can effectively weaken the influence on the suspension system and even the vehicle body when the actuator fails, and can play a certain protection role on the suspension structure and prevent the mechanical structure in the suspension from being damaged when the actuator fails.
Drawings
FIG. 1 is a flow chart of a robust control method for a time-varying displacement constrained active suspension system of the present invention;
FIG. 2 is a graph of the vertical displacement of the actuator from the failed body at 6 seconds in an embodiment of the present invention;
FIG. 3 is a spatial view of the suspension of the vehicle body with the actuator deflected for 6 seconds under a fault condition in accordance with an embodiment of the present invention;
FIG. 4 is a vertical displacement of a vehicle body with a 6 second failure of an actuator according to an embodiment of the present invention;
fig. 5 is a suspension space of a vehicle body under a failure of an actuator for 6 seconds according to an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
As shown in fig. 1, the method of the present embodiment is as follows.
Step 1: establishing a mathematical model of the actuator fault of the active suspension system:
Figure BDA0002225126270000063
where u is the actuator output signal in the active suspension system and u is the actuator output signalcIs the actuator input signal, TfIs the time of occurrence of the fault, ρ is a failure factor, θ represents the departure fault, and there is a constantρAnd
Figure BDA0002225126270000071
such that the following inequality holds:
Figure BDA0002225126270000072
when the actuator has a deviation fault, ρ is 0, θ is not equal to 0, and u is equal tocNo longer functioning, deviating to the fault value θ;
when the actuator fails, determining rho belongs to (0,1), and theta is 0, and determining the percentage of the actuator losing the efficiency according to the specific numerical value of the failure factor rho;
the embodiment simulates the deviation fault and the failure fault of the actuator at 6 seconds respectively, wherein when the deviation fault occurs, rho is 0, theta is 50, and the deviation angle is 50 degrees; when the actual fault occurs, ρ is 0.5, θ is 0, and the actuator loses 50% of the efficiency.
Step 2: respectively carrying out stress analysis on the automobile body and the tire under the suspension according to Newton's second law and Newton's third law, and establishing a mathematical model of the automobile active suspension system containing an actuator fault mathematical model, wherein the mathematical model comprises the following steps:
Figure BDA0002225126270000073
wherein, Fa、FsRespectively the spring force of the spring in the body and the damping force in the damper, FwAnd FrRespectively the spring force of the tire under suspension and the damping force of the tire under suspension, DsIs the vertical displacement of the vehicle body, DwIs the vertical displacement of the tire under the suspension, mcsIs the mass of the vehicle body, musIs the mass of the tire, and assumes that the upper and lower limits of the mass of the vehicle body are
The specific expressions of the elastic force and the damping force are as follows:
wherein k isaAnd caSpring coefficient and damping coefficient, k, of the vehicle body, respectivelytAnd ctRespectively the spring and damping coefficient of the tire under suspension, DrIs a road surface stimulus.
In this embodiment, the selected vehicle body mass of the active suspension system is mcs600kg, wheel mass mus60kg, spring constant ka18000N/m, damping coefficient ca2400Ns/m, coefficient of elasticity k of the tire under active suspensiont150000N/m, its damping coefficient ct1000 Ns/m. And a periodic interference signal with the amplitude of 0.02cm and the frequency of 5HZ is given as a road surface excitation Dr(t)＝0.02sin(10πt)。
And step 3: designing an actuator with fault compensation and an adaptive law thereof based on a radial basis function neural network;
step 3.1: based on the mathematical model of the automobile active suspension system in the step 2, selecting the following state variables:
x1＝Ds,
Figure BDA0002225126270000081
x3＝Dw,
Figure BDA0002225126270000082
in this embodiment, the initial value is x1(0)＝0.03，x2(0)＝x3(0)＝x4(0)＝0；
Step 3.2: establishing the following state space expression according to the mathematical model and the state variables of the automobile active suspension system:
Figure BDA0002225126270000083
where y is the output of the active suspension system;
step 3.3: based on the mathematical model of actuator failure in step 1, defining the following coordinate transformation for designing a failure compensation actuator:
e1＝x1-yd,e2＝x2-α1(18)
wherein the desired trajectory y d0, first derivative thereof
Figure BDA0002225126270000084
And second derivative
Figure BDA0002225126270000085
Are all bounded, α1Is a virtual actuator, e1To track errors, e2Is a transfer error;
step 3.4: respectively for error variable e1、e2Derivation:
Figure BDA0002225126270000086
step 3.5: in order to achieve the designed performance index, the virtual actuator is designed as follows:
Figure BDA0002225126270000087
wherein k is1800 is a design parameter, and λ is defined as follows:
Figure BDA0002225126270000088
wherein, beta >0，ka(t) and kb(t) is respectively a time-varying upper bound and a time-varying lower bound of the tracking error, and the following conditions are met:
ka(t)＝yd(t)-k c(t) (22)
Figure BDA0002225126270000091
wherein the content of the first and second substances,
Figure BDA0002225126270000092
andk c(t) is the asymmetric time-varying constraint bound for the active suspension system output y, namely:
Figure BDA0002225126270000093
Figure BDA0002225126270000094
the time-varying constraint boundaries selected in this embodiment are respectively:
ka(t)＝(0.12-0.007)e-0.3t+0.007
kb(t)＝(0.1-0.008)e-0.5t+0.008
step 3.6: according to the actuator fault model, the error variable e is calculated2The first derivative of (a) is further rewritten as follows:
Figure BDA0002225126270000095
wherein, Fz＝Fa+Fs，Is an unknown continuous function of the time of day,
Figure BDA0002225126270000097
step 3.7: approximating the unknown function H (X) obtained in the step 3.6 in the system by adopting a radial basis function neural network to obtain the optimal weight W and approximation error of the neural network;
step 3.7.1: selecting a central value iota of a radial basis functioniEnsuring that there is a proper input vector sample value;
step 3.7.2: calculating variables
Figure BDA0002225126270000098
A Gaussian function of;
Figure BDA00022251262700000910
wherein eta isiIs the width of the Gaussian function, iotaiIs the central value of the selected Gaussian function, dmaxTo select the maximum Euclidean distance in the center, K is the number of centers;
and composing the obtained Gaussian function into the following matrix:
Figure BDA00022251262700000911
step 3.7.3: the unknown function h (x) obtained in step 3.6 is rewritten as follows:
H(X)＝WTφ(X)+ε(X)(16)
wherein W ═ W1,…,wn]T∈RnIs the optimal weight for the neural network; ε (X) is the approximation error and is bounded:
Figure BDA0002225126270000101
is a constant;
step 3.7.4: selecting 20 nodes of a neural network, and initializing the weight of each node by adopting a random number;
step 3.7.5: approximating H (X) obtained in the step 3.7.3 by using a radial basis function neural network to obtain the optimal weight and approximation error of the neural network;
step 3.8: designing an actuator with fault compensation and a corresponding adaptive law;
Figure BDA0002225126270000102
wherein k is2800 and v > 0 are design parameters, gamma is a positive definite symmetric parameter matrix,
Figure BDA0002225126270000104
is an estimate of the optimal weight W with an estimation error ofIn this embodiment, the adaptive law initial value is selected as
In the formula (17) < mu >1Is defined as follows:
Figure BDA0002225126270000107
wherein the content of the first and second substances,
Figure BDA0002225126270000108
and 4, step 4: verifying the stability of the closed-loop active suspension system by adopting a barrier Lyapunov function;
step 4.1: and (3) verifying by adopting a barrier Lyapunov function, and writing the following stability equation according to coordinate transformation:
Figure BDA0002225126270000109
wherein the content of the first and second substances,
Figure BDA00022251262700001010
in the discussion that follows，q(e1) Abbreviated q, ka(t) and kb(t) are each abbreviated as kaAnd kb(ii) a And a positive constant exists
Figure BDA00022251262700001011
k a，
Figure BDA00022251262700001012
k bSo that the following equation holds:
step 4.2: the following error transformation is performed:
Figure BDA00022251262700001014
ξ＝qξb+(1-q)ξa(27)
step 4.3: the Lyapunov function can be redefined according to the error transformation described in step 4.3, as follows:
Figure BDA00022251262700001015
step 4.4: an unknown function H (X) obtained according to claim 3, incorporating the error variable e of claim 32The first derivative of (a) is rewritten as follows:
Figure BDA0002225126270000111
step 4.5: the redefined Lyapunov function is derived in combination with step 4.4, with the following results:
Figure BDA0002225126270000112
step 4.6: the actuator with fault compensation and the corresponding adaptation law and Young inequality obtained according to claim 3 scale the first derivative obtained in step 4.5 to obtain the inequality:
Figure BDA0002225126270000113
wherein the content of the first and second substances,
Figure BDA0002225126270000114
v is a selected Lyapunov function;
step 4.7: the output y of the active suspension system of claim 2 can be judged to be in a progressively stable state from the inequality obtained in step 4.6 according to the Lyapunov stability criterion.
And 5: and adjusting parameters of the actuator and the self-adaptive law to realize the final control target.
In a simulation experiment, compared with an unconstrained adaptive control method, the scheme of the adaptive fault compensation actuator with the output constraint can find that when the actuator generates a deviation fault, the vertical displacement of a vehicle body is shown in figure 2 and the suspension space is shown in figure 3, and when the fault occurs in 6 seconds, the front-back fluctuation of the vertical displacement fault of the vehicle body is smaller and better than that of the unconstrained scheme. When the actuator fails, the vertical displacement of the vehicle body is shown in fig. 4 and the suspension space is shown in fig. 5, and when the actuator fails in 6 seconds, the adaptive control scheme with the output constraint can be found to have better control performance.

Claims (4)

1. A robust control method of an active suspension system constrained by time-varying displacement is characterized by comprising the following steps:
step 1: establishing a mathematical model of the actuator fault of the active suspension system:
Figure FDA0002225126260000011
where u is the actuator output signal in the active suspension system and u is the actuator output signalcIs the actuator input signal, TfTime of occurrence of failure, ρIs a failure factor, theta represents a deviation fault, and is constantρAnd
Figure FDA0002225126260000012
such that the following inequality holds:
Figure FDA0002225126260000013
when the actuator has a deviation fault, ρ is 0, θ is not equal to 0, and u is equal tocNo longer functioning, deviating to the fault value θ;
when the actuator fails, determining rho belongs to (0,1), and theta is 0, and determining the percentage of the actuator losing the efficiency according to the specific numerical value of the failure factor rho;
step 2: respectively carrying out stress analysis on the automobile body and the tire under the suspension according to Newton's second law and Newton's third law, and establishing a mathematical model of the automobile active suspension system containing an actuator fault mathematical model;
and step 3: designing an actuator with fault compensation and an adaptive law thereof based on a radial basis function neural network;
and 4, step 4: verifying the stability of the closed-loop active suspension system by adopting a barrier Lyapunov function;
and 5: and adjusting parameters of the actuator and the self-adaptive law to realize the final control target.
2. The robust control method of a time-varying displacement constrained active suspension system as claimed in claim 1, wherein the mathematical model of the automotive active suspension system in step 2 is as follows:
Figure FDA0002225126260000014
wherein, Fa、FsRespectively the spring force of the spring in the body and the damping force in the damper, FwAnd FrRespectively the spring force of the tire under suspension and the damping force of the tire under suspension, DsIs the vertical displacement of the vehicle body, DwIs the vertical displacement of the tire under the suspension, mcsIs the mass of the vehicle body, musIs the mass of the tire, and assumes that the upper and lower limits of the mass of the vehicle body are
Figure FDA0002225126260000015
The specific expressions of the elastic force and the damping force are as follows:
Figure FDA0002225126260000016
wherein k isaAnd caSpring coefficient and damping coefficient, k, of the vehicle body, respectivelytAnd ctRespectively the spring and damping coefficient of the tire under suspension, DrIs a road surface stimulus.
3. The robust control method of a time varying displacement constrained active suspension system as claimed in claim 1, wherein the procedure of step 3 is as follows:
step 3.1: based on the mathematical model of the active suspension system of a vehicle as claimed in claim 2, the following state variables are selected:
Figure FDA0002225126260000021
step 3.2: establishing the following state space expression according to the mathematical model and the state variables of the automobile active suspension system:
Figure FDA0002225126260000022
where y is the output of the active suspension system;
step 3.3: based on the mathematical model of actuator failure of claim 1, the following coordinate transformation is defined for designing a failure-compensated actuator:
e1＝x1-yd,e2＝x2-α1(4)
wherein, ydIs the desired trajectory, the first derivative of whichAnd second derivative
Figure FDA0002225126260000024
Are all bounded, α1Is a virtual actuator, e1To track errors, e2Is a transfer error;
step 3.4: respectively for error variable e1、e2Derivation:
Figure FDA0002225126260000025
step 3.5: in order to achieve the designed performance index, the virtual actuator is designed as follows:
Figure FDA0002225126260000026
wherein k is10 is a design parameter, and λ is defined as follows:
Figure FDA0002225126260000027
wherein beta is more than 0, ka(t) and kb(t) is respectively a time-varying upper bound and a time-varying lower bound of the tracking error, and the following conditions are met:
ka(t)＝yd(t)-k c(t) (8)
wherein the content of the first and second substances,
Figure FDA0002225126260000032
andk c(t) is the asymmetric time-varying constraint bound for the active suspension system output y, i.e.：
Figure FDA0002225126260000034
Step 3.6: according to the actuator fault model, the error variable e is calculated2The first derivative of (a) is further rewritten as follows:
Figure FDA0002225126260000035
wherein, Fz＝Fa+Fs，
Figure FDA0002225126260000036
Is an unknown continuous function of the time of day,
Figure FDA0002225126260000037
step 3.7: approximating the unknown function H (X) obtained in the step 3.6 in the system by adopting a radial basis function neural network to obtain the optimal weight W and approximation error of the neural network;
step 3.7.1: selecting a central value iota of a radial basis functioniEnsuring that there is a proper input vector sample value;
step 3.7.2: calculating variables
Figure FDA0002225126260000038
A Gaussian function of;
Figure FDA0002225126260000039
Figure FDA00022251262600000310
wherein eta isiIs the width of the Gaussian function, iotaiIs selectedCentral value of Gaussian function, dmaxTo select the maximum Euclidean distance in the center, K is the number of centers;
and composing the obtained Gaussian function into the following matrix:
Figure FDA00022251262600000311
step 3.7.3: the unknown function h (x) obtained in step 3.6 is rewritten as follows:
H(X)＝WTφ(X)+ε(X) (16)
wherein W ═ W1,…,wn]T∈RnIs the optimal weight for the neural network; ε (X) is the approximation error and is bounded:
Figure FDA00022251262600000312
Figure FDA00022251262600000313
is a constant;
step 3.7.4: selecting the number of nodes of a neural network as n, wherein n is more than 1, and initializing the weight of each node by adopting a random number;
step 3.7.5: approximating H (X) obtained in the step 3.7.3 by using a radial basis function neural network to obtain the optimal weight and approximation error of the neural network;
step 3.8: designing an actuator with fault compensation and a corresponding adaptive law;
Figure FDA0002225126260000041
wherein k is2More than 0 and v more than 0 are design parameters, gamma is positive definite symmetric parameter matrix,
Figure FDA0002225126260000043
is an estimate of the optimal weight W with an estimation error of
Figure FDA0002225126260000044
μ1Is defined as follows:
Figure FDA0002225126260000045
wherein the content of the first and second substances,
Figure FDA0002225126260000046
4. the robust control method of a time varying displacement constrained active suspension system as claimed in claim 1, wherein the procedure of step 4 is as follows:
step 4.1: and (3) verifying by adopting a barrier Lyapunov function, and writing the following stability equation according to coordinate transformation:
Figure FDA0002225126260000047
wherein the content of the first and second substances,
Figure FDA0002225126260000048
in the discussion that follows, q (e)1) Abbreviated q, ka(t) and kb(t) are each abbreviated as kaAnd kb(ii) a And a positive constant exists
Figure FDA0002225126260000049
k a，
Figure FDA00022251262600000410
k bSo that the following equation holds:
step 4.2: the following error transformation is performed:
Figure FDA00022251262600000412
step 4.3: the Lyapunov function can be redefined according to the error transformation described in step 4.3, as follows:
Figure FDA00022251262600000413
step 4.4: an unknown function H (X) obtained according to claim 3, incorporating the error variable e of claim 32The first derivative of (a) is rewritten as follows:
Figure FDA0002225126260000051
step 4.5: the redefined Lyapunov function is derived in combination with step 4.4, with the following results:
Figure FDA0002225126260000052
step 4.6: the actuator with fault compensation and the corresponding adaptation law and Young inequality obtained according to claim 3 scale the first derivative obtained in step 4.5 to obtain the inequality:
Figure FDA0002225126260000053
wherein the content of the first and second substances,
Figure FDA0002225126260000054
v is a selected Lyapunov function;
step 4.7: the output y of the active suspension system of claim 2 can be judged to be in a progressively stable state from the inequality obtained in step 4.6 according to the Lyapunov stability criterion.
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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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
CN113022247A (en) * 2021-03-09 2021-06-25 渤海大学 Adaptive fixed time event trigger fuzzy control method for active vehicle suspension system
CN115107605A (en) * 2022-07-07 2022-09-27 辽宁工业大学 Automobile seat active suspension system containing actuator fault and control method
US11938776B1 (en) 2022-02-14 2024-03-26 Zoox, Inc. Multiple model active suspension control
CN115107605B (en) * 2022-07-07 2024-05-10 辽宁工业大学 Active suspension system of automobile seat containing actuator faults and control method

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104267595A (en) * 2014-10-21 2015-01-07 南京理工大学 Adaptive robust position control method for motor servo system with time-varying output constraint function
CN109188906A (en) * 2018-09-13 2019-01-11 辽宁工业大学 A kind of automobile active seat suspension system control method with time-varying displacement constraint

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104267595A (en) * 2014-10-21 2015-01-07 南京理工大学 Adaptive robust position control method for motor servo system with time-varying output constraint function
CN109188906A (en) * 2018-09-13 2019-01-11 辽宁工业大学 A kind of automobile active seat suspension system control method with time-varying displacement constraint

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
曾强: "汽车悬架系统的自适应控制及其动态性能分析", 《中国优秀硕士学位论文全文数据库（电子期刊）工程科技Ⅱ辑》 *

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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
CN111487870B (en) * 2020-04-26 2022-09-16 贵州理工学院 Design method of adaptive inversion controller in flexible active suspension system
CN113022247A (en) * 2021-03-09 2021-06-25 渤海大学 Adaptive fixed time event trigger fuzzy control method for active vehicle suspension system
US11938776B1 (en) 2022-02-14 2024-03-26 Zoox, Inc. Multiple model active suspension control
CN115107605A (en) * 2022-07-07 2022-09-27 辽宁工业大学 Automobile seat active suspension system containing actuator fault and control method
CN115107605B (en) * 2022-07-07 2024-05-10 辽宁工业大学 Active suspension system of automobile seat containing actuator faults and control method

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