CN114253133A - Sliding mode fault-tolerant control method and device based on dynamic event trigger mechanism - Google Patents

Sliding mode fault-tolerant control method and device based on dynamic event trigger mechanism Download PDF

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CN114253133A
CN114253133A CN202111488737.9A CN202111488737A CN114253133A CN 114253133 A CN114253133 A CN 114253133A CN 202111488737 A CN202111488737 A CN 202111488737A CN 114253133 A CN114253133 A CN 114253133A
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胡艳艳
关馨郁
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University of Science and Technology Beijing USTB
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Abstract

The invention discloses a sliding mode fault-tolerant control method and device based on a dynamic event trigger mechanism, and relates to the technical field of sliding mode control. The method comprises the following steps: establishing a dynamic model of a discrete networked control system; designing a state sliding mode observer of a discrete networked control system based on the condition that the system has sensor faults; designing a sliding mode surface based on an observer estimation result; designing a dynamic event trigger mechanism; and designing a sliding mode fault-tolerant controller based on an observer method. The invention provides a sliding mode fault-tolerant control scheme considering sensor faults under a dynamic event trigger mechanism aiming at a networked control system.

Description

Sliding mode fault-tolerant control method and device based on dynamic event trigger mechanism
Technical Field
The invention relates to the technical field of sliding mode control, in particular to a sliding mode fault-tolerant control method and a sliding mode fault-tolerant control device based on a dynamic event trigger mechanism.
Background
Sliding mode control has gained wide attention in engineering applications as an effective robust control strategy, and mainly drives a state trajectory from an initial state to a certain preset sliding mode surface and keeps stable through a special control method. Compared with the traditional control method, the sliding mode control technology has the advantages of strong robustness, system order reduction, quick response and the like, thereby receiving attention and research of people.
In a network environment, the limited bandwidth is not sufficient to guarantee a complete transmission of data. It is desirable to provide an event triggering scheme to determine whether a sampling signal can be transmitted, thereby reducing the data transmission frequency and reducing the occurrence of network induced phenomena. In practical systems, sensors are prone to failure, which if handled improperly can cause instability of the system and even catastrophic failure. The fault-tolerant control can ensure the stability of a closed-loop system and keep the function of a fault system within an acceptable range, thereby improving the safety and reliability of the system. The controller is designed by combining sliding mode control and fault-tolerant control, so that the state track can effectively reach the sliding mode surface and keep a stable state. The sliding mode control method has stronger robustness and anti-interference performance, and the method has very important practical significance in processing a networked system with event triggering and sensor faults by using the sliding mode fault-tolerant control method.
The existing sliding mode fault-tolerant control problem is mainly researched and developed around actuator faults, but in a practical engineering system, the sensor faults are inevitable. In addition, under a network environment, data transmission is often influenced by network bandwidth, and compared with time triggering, a dynamic event triggering mechanism is adopted to reduce the transmission quantity of data, so that the pressure of the network bandwidth can be relieved better, and the calculation quantity is reduced. In contrast, currently, a sliding-mode fault-tolerant control scheme which considers both dynamic event triggering and sensor faults does not exist for a networked control system.
Disclosure of Invention
The invention provides a method for controlling a network control system by using a sliding mode fault-tolerant control scheme, which aims at solving the problem that the network control system does not have the sliding mode fault-tolerant control scheme considering sensor faults under a dynamic event trigger mechanism.
In order to solve the technical problems, the invention provides the following technical scheme:
in one aspect, the present invention provides a sliding mode fault-tolerant control method based on a dynamic event trigger mechanism, where the method is implemented by an electronic device, and the method includes:
and S1, establishing a dynamic model of the discrete networked control system.
And S2, designing a state sliding mode observer of the discrete networked control system based on the condition that the system has sensor faults.
And S3, designing a sliding mode surface based on observer estimation information.
And S4, designing a dynamic event trigger mechanism.
And S5, designing a sliding-mode fault-tolerant controller based on an observer method.
Optionally, the method further comprises: substituting the equivalent control law into the observer to obtain a closed-loop system, and obtaining the equivalent control law which satisfies the asymptotic stability and H of the closed-loop system based on the Lyapunov function theory and the linear matrix inequality method∞And (4) sufficient criterion of performance index.
Optionally, the state space form of the dynamic model of the discrete networked control system in S1 is shown as the following formula (1):
Figure BDA00033976256600000210
wherein ,
Figure BDA0003397625660000021
is an n-dimensional state vector of the system;
Figure BDA0003397625660000022
representing a set of real numbers;
Figure BDA0003397625660000023
is the m-dimensional control input of the system;
Figure BDA0003397625660000024
is the p-dimensional measurement output of the system;
Figure BDA0003397625660000025
is q-dimension controlled output of the system; a. the1Is a system matrix; b is an input matrix of the system; c is a measurement matrix of the system; d1 and D2Is an external disturbance matrix of the system, A2Is the output matrix of the system; a. the1,A2,B,C,D1 and D2A known matrix with appropriate dimensions;
Figure BDA0003397625660000026
and
Figure BDA0003397625660000027
respectively w and v dimensions belonging to2External perturbation of [0, ∞) where l2[0, ∞) is the square multiplicative function of Hilbert space; Δ a represents the parameter uncertainty, satisfying Δ a ═ MFN, where F is an unknown matrix, satisfying FTF ≦ I, M and N being known matrices with appropriate dimensions; g (x)k) Non-linear disturbance, satisfies | g (x)k)‖≤r‖xkII, wherein i g (x)k) II is g (x)k) Norm of | xkII is xkR > 0 represents a known constant.
Alternatively, the sensor failure model in S2 is as shown in the following equation (2):
Figure BDA0003397625660000031
wherein ,
Figure BDA0003397625660000032
Figure BDA0003397625660000033
Figure BDA0003397625660000034
wherein ,Fs＝diag{f1,f2,…,fqPreag, diag is a diagonal matrix;
Figure BDA0003397625660000035
i＝1,2,…,q， ifis fiThe lower bound of (a) is,
Figure BDA0003397625660000037
is fiUpper bound of, satisfy
Figure BDA0003397625660000038
When f isiWhen 1, i is 1,2, …, q, the sensor is in normal operation.
When f isiAt 0, i 1,2, …, q, the sensor is completely inoperable.
When f isiE (0,1), i is 1,2, …, q, the sensor fails.
The measurement output with sensor failure is denoted as yF＝Fsyk。
Alternatively, the sliding mode observer in S2 is represented by the following formula (3):
Figure BDA0003397625660000039
wherein,
Figure BDA00033976256600000310
which represents the state of the observer,
Figure BDA00033976256600000311
representing the controlled output zkL represents the observer gain matrix.
Alternatively, the sliding mode surface function in S3 is represented by the following formula (4):
Figure BDA00033976256600000312
wherein S iskA sliding mode function representing the time k,
Figure BDA00033976256600000313
is a parameter matrix of a sliding mode surface to be designed, G is BTP1，P1> 0 is the positive definite matrix to be solved.
Alternatively, the dynamic event triggering mechanism model in S4 is shown as the following equation (5):
Figure BDA00033976256600000314
wherein,
Figure BDA00033976256600000315
represents a set of positive integers; { l0,l1… is the time sequence from the observer to the current state of the controller; definition of l00; sigma and theta are given positive scalars;
Figure BDA00033976256600000316
wherein
Figure BDA00033976256600000317
For the state estimation at the time instant k,
Figure BDA0003397625660000041
is the latest released state; etakRepresents internal dynamic variables, satisfies
Figure BDA0003397625660000042
Where T is the transpose of the matrix, λ ∈ (0,1) is a given constant, η0The initial conditions are given as ≧ 0.
Optionally, designing the sliding-mode fault-tolerant controller based on the observer method in S5 includes:
according to Sk+1＝SkThe equivalent control law is represented by the following formula (6) when 0:
Figure BDA0003397625660000043
wherein,-1is an inverse matrix.
Based on the dynamic event triggering mechanism, the equivalent control law is rewritten into the following formula (7):
Figure BDA0003397625660000044
when the difference of the sliding mode surface functions satisfies the following equations (8) and (9),
ΔSk≤-ωe-μksgn(Sk)-κSkif S isk＞0 (8)
ΔSk≥-ωe-μksgn(Sk)-κSkIf S isk＜0 (9)
Wherein, kappa is more than 0 and less than 1, omega is more than 0, and mu is more than or equal to 0.
Designing a sliding-mode fault-tolerant controller as shown in the following formula (10):
Figure BDA0003397625660000045
wherein,
Figure BDA0003397625660000046
on the other hand, the invention provides a sliding mode fault-tolerant control device based on a dynamic event trigger mechanism, which is applied to realize a sliding mode fault-tolerant control method based on the dynamic event trigger mechanism, and comprises the following steps:
and the dynamic model establishing module is used for establishing a dynamic model of the discrete networked control system.
And the observer design module is used for designing a state sliding mode observer of the discrete networked control system based on the condition that the system has sensor faults.
And the sliding mode surface design module is used for designing the sliding mode surface based on the observer estimation information.
And the dynamic event trigger mechanism design module is used for designing a dynamic event trigger mechanism.
And the sliding mode fault-tolerant controller design module is used for designing the sliding mode fault-tolerant controller based on the observer method.
Optionally, the method further comprises: substituting the equivalent control law into the observer to obtain a closed-loop system, and obtaining the equivalent control law which satisfies the asymptotic stability and H of the closed-loop system based on the Lyapunov function theory and the linear matrix inequality method∞And (4) sufficient criterion of performance index.
Optionally, the state space form of the dynamic model of the discrete networked control system is as shown in the following equation (1):
Figure BDA00033976256600000515
wherein,
Figure BDA0003397625660000051
is an n-dimensional state vector of the system;
Figure BDA0003397625660000052
representing a set of real numbers;
Figure BDA0003397625660000053
is the m-dimensional control input of the system;
Figure BDA0003397625660000054
is the p-dimensional measurement output of the system;
Figure BDA0003397625660000055
is q-dimension controlled output of the system; a. the1Is a system matrix; b is an input matrix of the system; c is a measurement matrix of the system; d1And D2Is an external disturbance matrix of the system, A2Is the output matrix of the system; a. the1,A2,B,C,D1And D2A known matrix with appropriate dimensions;
Figure BDA0003397625660000056
and
Figure BDA0003397625660000057
respectively w and v dimensions belonging to2External perturbation of [0, ∞) where l2[0, ∞) is the square multiplicative function of Hilbert space; Δ a represents the parameter uncertainty, satisfying Δ a ═ MFN, where F is an unknown matrix, satisfying FTF ≦ I, M and N being known matrices with appropriate dimensions; g (x)k) Non-linear disturbance, satisfies | g (x)k)‖≤r‖xk‖，Wherein, | g (x)k) II is g (x)k) Norm of | xkII is xkR > 0 represents a known constant.
Alternatively, the sensor failure model is as shown in equation (2) below:
Figure BDA0003397625660000058
wherein,
Figure BDA0003397625660000059
Figure BDA00033976256600000510
Figure BDA00033976256600000511
wherein, Fs＝diag{f1,f2,…,fqPreag, diag is a diagonal matrix;
Figure BDA00033976256600000512
i＝1,2,…,q， ifis fiThe lower bound of (a) is,
Figure BDA00033976256600000513
is fiUpper bound of, satisfy
Figure BDA00033976256600000514
When f isiWhen 1, i is 1,2, …, q, the sensor is in normal operation.
When f isiAt 0, i 1,2, …, q, the sensor is completely inoperable.
When f isiE (0,1), i is 1,2, …, q, the sensor fails.
Will have sensor failureThe measurement output is denoted yF＝Fsyk。
Alternatively, the sliding-mode observer is represented by the following formula (3):
Figure BDA0003397625660000061
wherein,
Figure BDA0003397625660000062
which represents the state of the observer,
Figure BDA0003397625660000063
representing the controlled output zkL represents the observer gain matrix.
Alternatively, the sliding mode surface function is represented by the following formula (4):
Figure BDA0003397625660000064
wherein S iskA sliding mode function representing the time k,
Figure BDA0003397625660000065
is a parameter matrix of a sliding mode surface to be designed, G is BTP1，P1> 0 is the positive definite matrix to be solved.
Alternatively, the dynamic event trigger mechanism model is shown as the following equation (5):
Figure BDA0003397625660000066
wherein,
Figure BDA0003397625660000067
represents a set of positive integers; { l0,l1… is the time sequence from the observer to the current state of the controller; definition of l00; sigma and theta are given positive scalars;
Figure BDA0003397625660000068
wherein
Figure BDA0003397625660000069
For the state estimation at the time instant k,
Figure BDA00033976256600000610
is the latest released state; etakRepresents internal dynamic variables, satisfies
Figure BDA00033976256600000611
Wherein,Tfor the transpose of the matrix, λ ∈ (0,1) is given constant, η0The initial conditions are given as ≧ 0.
Optionally, the sliding-mode fault-tolerant controller design module is further configured to:
according to Sk+1＝SkThe equivalent control law is represented by the following formula (6) when 0:
Figure BDA00033976256600000612
wherein,-1is an inverse matrix.
Based on the dynamic event triggering mechanism, the equivalent control law is rewritten into the following formula (7):
Figure BDA00033976256600000613
when the difference of the sliding mode surface functions satisfies the following equations (8) and (9),
ΔSk≤-ωe-μksgn(Sk)-κSkif S isk＞0 (8)
ΔSk≥-ωe-μksgn(Sk)-κSkIf S isk＜0 (9)
Wherein, kappa is more than 0 and less than 1, omega is more than 0, and mu is more than or equal to 0.
Designing a sliding-mode fault-tolerant controller as shown in the following formula (10):
Figure BDA00033976256600000614
wherein,
Figure BDA00033976256600000615
in one aspect, an electronic device is provided, where the electronic device includes a processor and a memory, where the memory stores at least one instruction, and the at least one instruction is loaded and executed by the processor to implement the sliding-mode fault-tolerant control method based on a dynamic event trigger mechanism.
In one aspect, a computer-readable storage medium is provided, where at least one instruction is stored in the storage medium, and the at least one instruction is loaded and executed by a processor to implement the sliding-mode fault-tolerant control method based on a dynamic event trigger mechanism.
The technical scheme provided by the embodiment of the invention has the beneficial effects that at least:
in the scheme, errors generated by an event trigger mechanism are processed, and on the premise of sensor failure, the problem of sliding-mode fault-tolerant control of a networked control system with a dynamic event trigger mechanism based on an observer method is researched. In the sliding mode fault-tolerant control problem for the first time, the error generated by an event trigger mechanism is taken as a disturbance, and H is utilized∞The norm is bounded for attenuation. By means of the Lyapunov function method, the method for ensuring the asymptotic stability of the closed-loop system and meeting the requirement of H is provided∞And (4) sufficient criterion of performance index. Further, a proper sliding mode fault-tolerant controller is designed, so that the state track of the closed-loop system can reach a preset sliding mode surface and can be kept stable in a limited time.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a schematic flow chart of a sliding mode fault-tolerant control method based on a dynamic event trigger mechanism according to the present invention;
FIG. 2 is a schematic flow chart of a sliding mode fault-tolerant control method based on a dynamic event trigger mechanism according to the present invention;
FIG. 3 is a schematic diagram of a sliding-mode fault-tolerant control system based on a dynamic event trigger mechanism according to the present invention;
FIG. 4 is a block diagram of a sliding-mode fault-tolerant control device based on a dynamic event trigger mechanism according to the present invention;
fig. 5 is a schematic structural diagram of an electronic device according to the present invention.
Detailed Description
In order to make the technical problems, technical solutions and advantages of the present invention more apparent, the following detailed description is given with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, an embodiment of the present invention provides a sliding-mode fault-tolerant control method based on a dynamic event trigger mechanism, where the method is implemented by an electronic device. As shown in fig. 1, a flowchart of a sliding-mode fault-tolerant control method based on a dynamic event trigger mechanism, a processing flow of the method may include the following steps:
and S11, establishing a dynamic model of the discrete networked control system.
And S12, designing a state sliding mode observer of the discrete networked control system based on the condition that the system has sensor faults.
And S13, designing a sliding mode surface based on observer estimation information.
And S14, designing a dynamic event trigger mechanism.
And S15, designing a sliding-mode fault-tolerant controller based on an observer method.
Optionally, the method further comprises: substituting the equivalent control law into the observer to obtain a closed-loop system, and obtaining asymptotic stability and H of the closed-loop system based on the Lyapunov function theory and a linear matrix inequality method∞And (4) sufficient criterion of performance index.
Optionally, the state space form of the dynamic model of the discrete networked control system in S11 is shown as the following formula (1):
Figure BDA0003397625660000088
wherein,
Figure BDA0003397625660000081
is an n-dimensional state vector of the system;
Figure BDA0003397625660000082
representing a set of real numbers;
Figure BDA0003397625660000083
is the m-dimensional control input of the system;
Figure BDA0003397625660000084
is the p-dimensional measurement output of the system;
Figure BDA0003397625660000085
is q-dimension controlled output of the system; a. the1Is a system matrix; b is an input matrix of the system; c is a measurement matrix of the system; d1And D2Is an external disturbance matrix of the system, A2Is the output matrix of the system; a. the1,A2,B,C,D1And D2A known matrix with appropriate dimensions;
Figure BDA0003397625660000086
and
Figure BDA0003397625660000087
respectively w and v dimensions belonging to2External perturbation of [0, ∞) where l2[0, ∞) is the square multiplicative function of Hilbert space; Δ a represents the parameter uncertainty, satisfying Δ a ═ MFN, where F is an unknown matrix, satisfying FTF ≦ I, M and N being known matrices with appropriate dimensions; g (x)k) Non-linear disturbance, satisfies | g (x)k)‖≤r‖xkII, wherein i g (x)k) II is g (x)k) Norm of | xkII is xkR > 0 represents a known constant.
Alternatively, the sensor failure model in S12 is as shown in the following equation (2):
Figure BDA0003397625660000091
wherein,
Figure BDA0003397625660000092
Figure BDA0003397625660000093
Figure BDA0003397625660000094
wherein, Fs＝diag{f1,f2,…,fqPreag, diag is a diagonal matrix;
Figure BDA0003397625660000095
i＝1,2,…,q， ifis fiThe lower bound of (a) is,
Figure BDA0003397625660000096
is fiUpper bound of, satisfy
Figure BDA0003397625660000097
When f isiWhen 1, i is 1,2, …, q, the sensor is in normal operation.
When f isiAt 0, i 1,2, …, q, the sensor is completely inoperable.
When f isiE (0,1), i is 1,2, …, q, the sensor fails.
The measurement output with sensor failure is denoted as yF＝Fsyk。
Alternatively, the sliding mode observer in S12 is represented by the following formula (3):
Figure BDA0003397625660000098
wherein,
Figure BDA0003397625660000099
which represents the state of the observer,
Figure BDA00033976256600000910
representing the controlled output zkL represents the observer gain matrix.
Alternatively, the sliding mode surface function in S13 is represented by the following formula (4):
Figure BDA00033976256600000911
wherein S iskA sliding mode function representing the time k,
Figure BDA00033976256600000912
is a parameter matrix of a sliding mode surface to be designed, G is BTP1，P1> 0 is the positive definite matrix to be solved.
Alternatively, the dynamic event triggering mechanism model in S14 is shown as the following equation (5):
Figure BDA00033976256600000913
wherein,
Figure BDA00033976256600000914
represents a set of positive integers; { l0,l1… is the time sequence from the observer to the current state of the controller; definition of l00; sigma, theta are givenA positive scalar quantity of (c);
Figure BDA00033976256600000915
wherein
Figure BDA00033976256600000916
For the state estimation at the time instant k,
Figure BDA00033976256600000917
is the latest released state; etakRepresents internal dynamic variables, satisfies
Figure BDA0003397625660000101
Where T is the transpose of the matrix, λ ∈ (0,1) is a given constant, η0The initial conditions are given as ≧ 0.
Optionally, designing the sliding-mode fault-tolerant controller based on the observer method in S15 includes:
according to Sk+1＝SkThe equivalent control law is represented by the following formula (6) when 0:
Figure BDA0003397625660000102
wherein,-1is an inverse matrix.
Based on the dynamic event triggering mechanism, the equivalent control law is rewritten into the following formula (7):
Figure BDA0003397625660000103
when the difference of the sliding mode surface functions satisfies the following equations (8) and (9),
ΔSk≤-ωe-μksgn(Sk)-κSkif S isk＞0 (8)
ΔSk≥-ωe-μksgn(Sk)-κSkIf S isk＜0 (9)
Wherein, kappa is more than 0 and less than 1, omega is more than 0, and mu is more than or equal to 0.
Designing a sliding-mode fault-tolerant controller as shown in the following formula (10):
Figure BDA0003397625660000104
wherein,
Figure BDA0003397625660000105
in the embodiment of the invention, errors generated by an event trigger mechanism are processed, and on the premise of a sensor fault, the problem of sliding-mode fault-tolerant control of a networked control system with a dynamic event trigger mechanism based on an observer method is researched. In the sliding mode fault-tolerant control problem for the first time, the error generated by an event trigger mechanism is taken as a disturbance, and H is utilized∞The norm is bounded for attenuation. By means of the Lyapunov function method, the method for ensuring the asymptotic stability of the closed-loop system and meeting the requirement of H is provided∞And (4) sufficient criterion of performance index. Further, a proper sliding mode fault-tolerant controller is designed, so that the state track of the closed-loop system can reach a preset sliding mode surface and can be kept stable in a limited time.
As shown in fig. 2, an embodiment of the present invention provides a sliding-mode fault-tolerant control method based on a dynamic event trigger mechanism, where the method is implemented by an electronic device. As shown in fig. 2, a flowchart of a sliding-mode fault-tolerant control method based on a dynamic event trigger mechanism, a processing flow of the method may include the following steps:
s21, establishing a dynamic model of the discrete networked control system, wherein the state space form of the dynamic model is shown as the following formula (1):
Figure BDA00033976256600001115
wherein,
Figure BDA0003397625660000111
is an n-dimensional state vector of the system;
Figure BDA0003397625660000112
representing a set of real numbers;
Figure BDA0003397625660000113
is the m-dimensional control input of the system;
Figure BDA0003397625660000114
is the p-dimensional measurement output of the system;
Figure BDA0003397625660000115
is q-dimension controlled output of the system; a. the1Is a system matrix; b is an input matrix of the system; c is a measurement matrix of the system; d1And D2Is an external disturbance matrix of the system, A2Is the output matrix of the system; a. the1,A2,B,C,D1And D2A known matrix with appropriate dimensions;
Figure BDA0003397625660000116
and
Figure BDA0003397625660000117
respectively w and v dimensions belonging to2External perturbation of [0, ∞) where l2[0, ∞) is the square multiplicative function of Hilbert space; Δ a represents the parameter uncertainty, satisfying Δ a ═ MFN, where F is an unknown matrix, satisfying FTF ≦ I, M and N being known matrices with appropriate dimensions; g (x)k) Non-linear disturbance, satisfies | g (x)k)‖≤r‖xkII, wherein i g (x)k) II is g (x)k) Norm of | xkII is xkR > 0 represents a known constant.
Wherein the dynamic model of the discrete networked control system may be a dynamic model of the networked control system with uncertainty and external disturbances;
s22, establishing a sensor fault model as shown in the following formula (2):
Figure BDA0003397625660000118
wherein,
Figure BDA0003397625660000119
Figure BDA00033976256600001110
Figure BDA00033976256600001111
wherein, Fs＝diag{f1,f2,…,fqPreag, diag is a diagonal matrix;
Figure BDA00033976256600001112
i＝1,2,…,q， ifis fiThe lower bound of (a) is,
Figure BDA00033976256600001113
is fiUpper bound of, satisfy
Figure BDA00033976256600001114
Wherein the sensor failure and the matrix FsThe relationship between may be:
when f isiWhen 1, i is 1,2, …, q, the sensor is in normal operation.
When f isiAt 0, i 1,2, …, q, the sensor is completely inoperable.
When f isiE (0,1), i is 1,2, …, q, the sensor fails.
Thus, the measurement output with sensor failure can be expressed as yF＝Fsyk。
S23, establishing a dynamic event trigger mechanism model as shown in the following formula (3):
Figure BDA0003397625660000121
wherein, in order to save computer resources, defining
Figure BDA0003397625660000122
Represents a set of positive integers; definition l0,l1… is the time sequence from the observer to the current state of the controller; definition of l00; sigma and theta are given positive numbers;
Figure BDA0003397625660000123
wherein
Figure BDA0003397625660000124
For the state estimation at the time instant k,
Figure BDA0003397625660000125
is the latest released state; etakRepresents internal dynamic variables, satisfies
Figure BDA0003397625660000126
Where T is the transpose of the matrix, λ ∈ (0,1) is a given constant, η0The initial conditions are given as ≧ 0.
S24, designing a sliding mode observer, which is represented by the following formula (4):
Figure BDA0003397625660000127
wherein,
Figure BDA0003397625660000128
which represents the state of the observer,
Figure BDA0003397625660000129
representing the controlled output zkL represents the observer gain matrix.
In one possible embodiment, a sliding mode observer is designed by using measurement information of a sensor fault; the sliding mode observer can be a sliding mode observer which obtains the measurement information of the sensor fault based on the sensor fault model of the formula (2) and obtains the formula (4) according to the measurement information.
S25, designing a sliding mode surface function, which is represented by the following formula (5):
Figure BDA00033976256600001210
wherein S iskA sliding mode function representing the time k,
Figure BDA00033976256600001211
is a parameter matrix of a sliding mode surface to be designed, G is BTP1，P1> 0 is the positive definite matrix to be solved.
In a feasible implementation mode, a sliding mode surface function can be designed by utilizing observation information obtained by a sliding mode observer; the sliding mode observer based on the formula (4) can obtain observation information, and the sliding mode surface function of the formula (5) can be obtained according to the observation information.
And S26, designing a sliding-mode fault-tolerant controller based on an observer method.
According to Sk+1＝SkThe equivalent control law is represented by the following formula (6) when 0:
Figure BDA00033976256600001212
where, -1 is the inverse matrix.
Based on the dynamic event triggering mechanism, the equivalent control law is rewritten into the following formula (7):
Figure BDA0003397625660000131
when the difference of the sliding mode surface functions satisfies the following equations (8) and (9),
ΔSk≤-ωe-μksgn(Sk)-κSkif S isk＞0 (8)
ΔSk≥-ωe-μksgn(Sk)-κSkIf S isk＜0 (9)
Wherein, kappa is more than 0 and less than 1, omega is more than 0, and mu is more than or equal to 0.
Designing a sliding-mode fault-tolerant controller as shown in the following formula (10):
Figure BDA0003397625660000132
wherein,
Figure BDA0003397625660000133
in a feasible implementation manner, the sliding-mode fault-tolerant control system based on the dynamic event trigger mechanism shown in fig. 3 considers the sensor fault under the dynamic event trigger mechanism, designs a sliding-mode fault-tolerant controller based on an observer method, and ensures accessibility of a sliding-mode surface under a discrete condition and normal operation of the system when the fault occurs. The trajectory of the closed loop system can converge on the slip-form surface and remain stable for a limited time.
In the embodiment of the invention, errors generated by an event trigger mechanism are processed, and on the premise of a sensor fault, the problem of sliding-mode fault-tolerant control of a networked control system with a dynamic event trigger mechanism based on an observer method is researched. In the sliding mode fault-tolerant control problem for the first time, the error generated by an event trigger mechanism is taken as a disturbance, and H is utilized∞The norm is bounded for attenuation. By means of the Lyapunov function method, the method for ensuring the asymptotic stability of the closed-loop system and meeting the requirement of H is provided∞And (4) sufficient criterion of performance index. Further, a proper sliding mode fault-tolerant controller is designed, so that the state track of the closed-loop system can reach a preset sliding mode surface and can be kept stable in a limited time.
As shown in fig. 4, an embodiment of the present invention provides a sliding mode fault-tolerant control apparatus 400 based on a dynamic event trigger mechanism, where the apparatus 400 is applied to implement a sliding mode fault-tolerant control method based on a dynamic event trigger mechanism, and the apparatus 400 includes:
and a dynamic model establishing module 410, configured to establish a dynamic model of the discrete networked control system.
The observer design module 420 is configured to design a state sliding mode observer of the discrete networked control system based on a condition that the system has a sensor fault.
And a sliding mode surface design module 430 for designing a sliding mode surface based on the observer estimation information.
And a dynamic event trigger mechanism designing module 440 for designing the dynamic event trigger mechanism.
And a sliding mode fault-tolerant controller design module 450, configured to design a sliding mode fault-tolerant controller based on the observer method.
Optionally, the method further comprises: substituting the equivalent control law into the observer to obtain a closed-loop system, and obtaining the equivalent control law which satisfies the asymptotic stability and H of the closed-loop system based on the Lyapunov function theory and the linear matrix inequality method∞And (4) sufficient criterion of performance index.
Optionally, the state space form of the dynamic model of the discrete networked control system is as shown in the following equation (1):
Figure BDA00033976256600001415
wherein,
Figure BDA0003397625660000141
is an n-dimensional state vector of the system;
Figure BDA0003397625660000142
representing a set of real numbers;
Figure BDA0003397625660000143
is the m-dimensional control input of the system;
Figure BDA0003397625660000144
is the p-dimensional measurement output of the system;
Figure BDA0003397625660000145
is q-dimension controlled output of the system; a. the1Is a system matrix; b is an input matrix of the system; c is a measurement matrix of the system; d1And D2Is an external disturbance matrix of the system, A2Is the output matrix of the system; a. the1,A2,B,C,D1And D2A known matrix with appropriate dimensions;
Figure BDA0003397625660000146
and
Figure BDA0003397625660000147
respectively w and v dimensions belonging to2External perturbation of [0, ∞) where l2[0, ∞) is the square multiplicative function of Hilbert space; Δ a represents the parameter uncertainty, satisfying Δ a ═ MFN, where F is an unknown matrix, satisfying FTF ≦ I, M and N being known matrices with appropriate dimensions; g (x)k) Non-linear disturbance, satisfies | g (x)k)‖≤r‖xkII, wherein i g (x)k) II is g (x)k) Norm of | xkII is xkR > 0 represents a known constant.
Alternatively, the sensor failure model is as shown in equation (2) below:
Figure BDA0003397625660000148
wherein,
Figure BDA0003397625660000149
Figure BDA00033976256600001410
Figure BDA00033976256600001411
wherein, Fs＝diag{f1,f2,…,fqPreag, diag is a diagonal matrix;
Figure BDA00033976256600001412
i＝1,2,…,q， ifis fiThe lower bound of (a) is,
Figure BDA00033976256600001413
is fiUpper bound of, satisfy
Figure BDA00033976256600001414
When f isiWhen 1, i is 1,2, …, q, the sensor is in normal operation.
When f isiAt 0, i 1,2, …, q, the sensor is completely inoperable.
When f isiE (0,1), i is 1,2, …, q, the sensor fails.
The measurement output with sensor failure is denoted as yF＝Fsyk。
Alternatively, the sliding-mode observer is represented by the following formula (3):
Figure BDA0003397625660000151
wherein,
Figure BDA0003397625660000152
which represents the state of the observer,
Figure BDA0003397625660000153
representing the controlled output zkL represents the observer gain matrix.
Alternatively, the sliding mode surface function is represented by the following formula (4):
Figure BDA0003397625660000154
wherein S iskA sliding mode function representing the time k,
Figure BDA0003397625660000155
is a parameter matrix of a sliding mode surface to be designed, G is BTP1，P1> 0 is the positive definite matrix to be solved.
Alternatively, the event trigger mechanism model is shown as the following equation (5):
Figure BDA0003397625660000156
wherein,
Figure BDA0003397625660000157
represents a set of positive integers; { l0,l1… is the time sequence from the observer to the current state of the controller; definition of l00; sigma and theta are given positive scalars;
Figure BDA0003397625660000158
wherein
Figure BDA0003397625660000159
For the state estimation at the time instant k,
Figure BDA00033976256600001510
is the latest released state; etakRepresents internal dynamic variables, satisfies
Figure BDA00033976256600001511
Where T is the transpose of the matrix, λ ∈ (0,1) is a given constant, η0The initial conditions are given as ≧ 0.
Optionally, the sliding-mode fault-tolerant controller design module 450 is further configured to:
according to Sk+1＝SkThe equivalent control law is represented by the following formula (6) when 0:
Figure BDA00033976256600001512
wherein,-1is an inverse matrix.
Based on the dynamic event triggering mechanism, the equivalent control law is rewritten into the following formula (7):
Figure BDA00033976256600001513
when the difference of the sliding mode surface functions satisfies the following equations (8) and (9),
ΔSk≤-ωe-μksgn(Sk)-κSkif S isk＞0 (8)
ΔSk≥-ωe-μksgn(Sk)-κSkIf S isk＜0 (9)
Wherein, kappa is more than 0 and less than 1, omega is more than 0, and mu is more than or equal to 0.
Designing a sliding-mode fault-tolerant controller as shown in the following formula (10):
Figure BDA0003397625660000161
wherein,
Figure BDA0003397625660000162
in the embodiment of the invention, errors generated by an event trigger mechanism are processed, and on the premise of a sensor fault, the problem of sliding-mode fault-tolerant control of a networked control system with a dynamic event trigger mechanism based on an observer method is researched. In the sliding mode fault-tolerant control problem for the first time, the error generated by an event trigger mechanism is taken as a disturbance, and H is utilized∞The norm is bounded for attenuation. By means of the Lyapunov function method, the method for ensuring the asymptotic stability of the closed-loop system and meeting the requirement of H is provided∞And (4) sufficient criterion of performance index. Further, a proper sliding mode fault-tolerant controller is designed, so that the state track of the closed-loop system can reach a preset sliding mode surface and can be kept stable in a limited time.
Fig. 5 is a schematic structural diagram of an electronic device 500 according to an embodiment of the present invention, where the electronic device 500 may generate a relatively large difference due to different configurations or performances, and may include one or more processors (CPUs) 501 and one or more memories 502, where at least one instruction is stored in the memory 502, and the at least one instruction is loaded and executed by the processor 501 to implement the following sliding mode fault-tolerant control method based on a dynamic event mechanism:
and S1, establishing a dynamic model of the discrete networked control system.
And S2, designing a state sliding mode observer of the discrete networked control system based on the condition that the system has sensor faults.
And S3, designing a sliding mode surface based on observer estimation information.
And S4, designing a dynamic event trigger mechanism.
And S5, designing a sliding-mode fault-tolerant controller based on an observer method.
In an exemplary embodiment, a computer-readable storage medium, such as a memory, including instructions executable by a processor in a terminal to perform the sliding-mode fault-tolerant control method based on a dynamic event trigger mechanism is also provided. For example, the computer readable storage medium may be a ROM, a Random Access Memory (RAM), a CD-ROM, a magnetic tape, a floppy disk, an optical data storage device, and the like.
It will be understood by those skilled in the art that all or part of the steps for implementing the above embodiments may be implemented by hardware, or may be implemented by a program instructing relevant hardware, where the program may be stored in a computer-readable storage medium, and the above-mentioned storage medium may be a read-only memory, a magnetic disk or an optical disk, etc.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (10)

1. A sliding mode fault-tolerant control method based on a dynamic event trigger mechanism is characterized by comprising the following steps:
s1, establishing a dynamic model of the discrete networked control system;
s2, designing a state sliding mode observer of the discrete networked control system based on the condition that the system has sensor faults;
s3, designing a sliding mode surface based on observer estimation information;
s4, designing a dynamic event trigger mechanism;
and S5, designing a sliding-mode fault-tolerant controller based on an observer method.
2. The method of claim 1, further comprising: substituting the equivalent control law into the observer to obtain a closed-loop system, and obtaining the equivalent control law which satisfies the asymptotic stability and H of the closed-loop system based on the Lyapunov function theory and the linear matrix inequality method∞And (4) sufficient criterion of performance index.
3. The method according to claim 1, wherein the state space form of the dynamic model of the discrete networked control system in S1 is represented by the following formula (1):
Figure FDA0003397625650000011
wherein,
Figure FDA0003397625650000012
is an n-dimensional state vector of the system;
Figure FDA0003397625650000013
representing a set of real numbers;
Figure FDA0003397625650000014
is the m-dimensional control input of the system;
Figure FDA0003397625650000015
is the p-dimensional measurement output of the system;
Figure FDA0003397625650000016
is q-dimension controlled output of the system; a. the1Is a system matrix; b is an input matrix of the system; c is a measurement matrix of the system; d1And D2Is an external disturbance matrix of the system, A2Is the output matrix of the system; a. the1,A2,B,C,D1And D2A known matrix with appropriate dimensions;
Figure FDA0003397625650000017
and
Figure FDA0003397625650000018
respectively w and v dimensions belong to
Figure FDA0003397625650000019
Wherein the external disturbance is
Figure FDA00033976256500000110
Is a square integrable function of Hilbert space; Δ a represents the parameter uncertainty, satisfying Δ a ═ MFN, where F is an unknown matrix, satisfying FTF ≦ I, M and N being known matrices with appropriate dimensions; g (x)k) Nonlinear disturbance, satisfies | | g (x)k)||≤r||xkI, where g (x)k) I is g (x)k) Norm of | xkII is xkR > 0 represents a known constant.
4. The method according to claim 3, wherein the sensor fault model in S2 is as shown in the following equation (2):
Figure FDA0003397625650000021
wherein,
Figure FDA0003397625650000022
Figure FDA0003397625650000023
Figure FDA0003397625650000024
wherein, Fs＝diag{f1,f2,…,fqPreag, diag is a diagonal matrix;
Figure FDA0003397625650000025
ifis fiThe lower bound of (a) is,
Figure FDA0003397625650000026
is fiUpper bound of, satisfy
Figure FDA0003397625650000027
When f isiWhen 1, i is 1,2, …, q, the sensor is in normal operation;
when f isiWhen 0, i is 1,2, …, q, the sensor is completely inoperable;
when f isiE (0,1), i is 1,2, …, q, the sensor fails.
The measurement output with sensor failure is denoted as yF＝Fsyk。
5. The method according to claim 4, wherein the sliding mode observer in S2 is represented by the following formula (3):
Figure FDA0003397625650000028
wherein,
Figure FDA0003397625650000029
which represents the state of the observer,
Figure FDA00033976256500000210
representing the controlled output zkL represents the observer gain matrix.
6. The method according to claim 5, wherein the sliding mode surface function in S3 is represented by the following equation (4):
Figure FDA00033976256500000211
wherein S iskA sliding mode function representing the time k,
Figure FDA00033976256500000212
is a parameter matrix of a sliding mode surface to be designed, G is BTP1，P1> 0 is the positive definite matrix to be solved.
7. The method according to claim 6, wherein the dynamic event trigger mechanism model in S4 is shown as the following formula (5):
Figure FDA00033976256500000213
wherein,
Figure FDA00033976256500000214
represents a set of positive integers; { l0,l1… is the time sequence from the observer to the current state of the controller; definition of l0＝0；σ、θGiven a positive scalar quantity;
Figure FDA0003397625650000031
wherein
Figure FDA0003397625650000032
For the state estimation at the time instant k,
Figure FDA0003397625650000033
is the latest released state; etakRepresents internal dynamic variables, satisfies
Figure FDA0003397625650000034
Wherein,Tfor the transpose of the matrix, λ ∈ (0,1) is given constant, η0The initial conditions are given as ≧ 0.
8. The method according to claim 7, wherein designing the sliding-mode fault-tolerant controller based on the observer method in S5 comprises:
according to Sk+1＝SkThe equivalent control law is represented by the following formula (6) when 0:
Figure FDA0003397625650000035
wherein,-1is an inverse matrix;
based on the dynamic event triggering mechanism, the equivalent control law is rewritten into the following formula (7):
Figure FDA0003397625650000036
when the difference of the sliding mode surface functions satisfies the following equations (8) and (9),
ΔSk≤-ωe-μksgn(Sk)-κSkif S isk＞0 (8)
ΔSk≥-ωe-μksgn(Sk)-κSkIf S isk＜0 (9)
Wherein, kappa is more than 0 and less than 1, omega is more than 0, mu is more than or equal to 0;
designing a sliding-mode fault-tolerant controller as shown in the following formula (10):
Figure FDA0003397625650000037
wherein,
Figure FDA0003397625650000038
9. a sliding-mode fault-tolerant control apparatus based on a dynamic event trigger mechanism, the apparatus comprising:
the dynamic model establishing module is used for establishing a dynamic model of the discrete networked control system;
the observer design module is used for designing a state sliding mode observer of the discrete networked control system based on the condition that the system has sensor faults;
the sliding mode surface design module is used for designing a sliding mode surface based on observer estimation information;
the dynamic event trigger mechanism design module is used for designing a dynamic event trigger mechanism;
and the sliding mode fault-tolerant controller design module is used for designing the sliding mode fault-tolerant controller based on the observer method.
10. The apparatus of claim 9, further comprising: substituting the equivalent control law into the observer to obtain a closed-loop system, and obtaining the equivalent control law which satisfies the asymptotic stability and H of the closed-loop system based on the Lyapunov function theory and the linear matrix inequality method∞And (4) sufficient criterion of performance index.
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