CN107315421A - The distributed speed sensor fault diagnostic method that a kind of time delay unmanned plane is formed into columns - Google Patents

The distributed speed sensor fault diagnostic method that a kind of time delay unmanned plane is formed into columns Download PDF

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CN107315421A
CN107315421A CN201710554280.4A CN201710554280A CN107315421A CN 107315421 A CN107315421 A CN 107315421A CN 201710554280 A CN201710554280 A CN 201710554280A CN 107315421 A CN107315421 A CN 107315421A
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msub
msubsup
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unmanned plane
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CN107315421B (en
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周东华
秦利国
何潇
卢晓
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Shandong University of Science and Technology
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Shandong University of Science and Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/10—Simultaneous control of position or course in three dimensions
    • G05D1/101—Simultaneous control of position or course in three dimensions specially adapted for aircraft
    • G05D1/104—Simultaneous control of position or course in three dimensions specially adapted for aircraft involving a plurality of aircrafts, e.g. formation flying

Abstract

The invention discloses a kind of distributed speed sensor fault diagnostic method for being directed to the unmanned plane fleet system with communication time-delay, belong to unmanned plane fleet system field, including calculate communication topological parameter；Based on communication topological parameter, given trace, formation vector sum preparatory condition, distributed formation control rule is obtained；Measured based on fleet system closed loop model and each unmanned plane and the relative status of neighbours, obtain distributed fault detection Residual Generation device and corresponding residual error evaluation function；Further obtain a distribution type fault reconstruction Residual Generation device and corresponding residual error evaluation function；Open loop models based on unmanned plane, obtain distributing fault reconstruction Residual Generation device and corresponding residual error evaluation function；Based on residual error evaluation function and corresponding threshold value, fault detect and separation are carried out.Communication between unmanned plane is by under the interference of fixed length time delay, and this method remains able to make each unmanned plane realize detection and separation to faults itself and neighbours' unmanned plane failure.

Description

The distributed speed sensor fault diagnostic method that a kind of time delay unmanned plane is formed into columns
Technical field
The invention belongs to unmanned plane fleet system field, and in particular to point that a kind of unmanned plane with communication time-delay is formed into columns Cloth speed sensor fault diagnostic method.
Background technology
In recent years, unmanned plane fleet system is searched and rescued etc. in field by increasingly in forest fire protection, ground mapping and personnel Many concerns.Unmanned plane fleet system by the collaboration between unmanned plane can realize function that single unmanned plane can not realize or Person has the premium properties that single unmanned plane can not have.Due to having communication connection, the event of single unmanned plane between unmanned plane Barrier can cause the formation of whole fleet system not keep, and then influence the function and performance of fleet system, or even can hit Machine accident.The fault diagnosis of fleet system is the important technology for ensureing the safe formation flight of unmanned plane.
The method for diagnosing faults of current unmanned plane fleet system is broadly divided into centralized fault diagnosis and distributed fault is examined It is disconnected two kinds.Under centralized fault diagnosis framework, fault diagnosis algorithm is concentrated in single unmanned plane or the earth station of system, This unmanned plane or earth station carry out fault diagnosis using the information of all unmanned planes.The shortcoming of the method is reliability not Height, communication load is big.Under distributed diagnostics framework, fault diagnosis algorithm is distributed in all unmanned planes, it is each nobody Fault diagnosis algorithm in machine is identical.Each unmanned plane is only carried out failure and examined using the information of itself and neighbours to itself and neighbours It is disconnected.The method communication load is low, and reliability is higher.
During unmanned plane is formed into columns, the communication between unmanned plane is held due to being influenceed by factors such as environmental disturbances, communication bandwidth It is also easy to produce time delay.In the distributed type fault diagnosis method of current unmanned plane fleet system, time delay is not accounted for Influence.Time delay causes the result of current distributed diagnostics to produce very big error even mistake.
The content of the invention
When can not have communication suitable for forming into columns for the distributed type fault diagnosis method of current unmanned plane fleet system Situation about prolonging, the invention provides a kind of distributed velocity pick-up for being directed to the unmanned plane fleet system with fixed length communication time-delay Device method for diagnosing faults.The sensor that this method can effectively realize permanent deviation sensor failure or the cycle is fixed length time delay The distributed diagnostics of failure.
To achieve these goals, the present invention is adopted the following technical scheme that：
A kind of distributed speed sensor fault diagnostic method of time delay unmanned plane fleet system, comprises the following steps：
Step 1：The communication topological parameter that unmanned plane is formed into columns is calculated, for the fleet system being made up of N number of unmanned plane, G= { V, E } is the undirected communication topology of fleet system, and wherein V={ 1,2 ..., N } is communication topological node, each communication topology section Point represents a unmanned plane；For the side of communication topology, each edge represents the communication between a pair of unmanned planes；
Order matrix Ag=[aij] to communicate topological adjacency matrix, if (i, j) ∈ E, claim node i and node j adjacent each other Occupying has communication between node, i.e. node i and node j, then aij=aji=1, otherwise aij=aji=0；
Make NiFor the neighborhood of i-th of unmanned plane, | Ni| it is set NiThe number of middle element；
Order matrix Dg=[dij] to communicate topological degree matrix, the off diagonal element of degree matrix is zero, diagonal entry Value is
Order matrix LgFor the Laplacian Matrix of communication topology, then Lg=Dg-Ag；Make 0≤λ1＜ λ2≤...≤λNFor Lg's N number of characteristic value from small to large；
Step 2：Communication topological parameter, given trace based on unmanned plane formation, formation vector sum preparatory condition, design point Cloth formation control is restrained, specific as follows：
Open loop models of i-th of unmanned plane on space coordinates x-axis direction are as follows：
Wherein, i=1,2 ..., N,For the displacement of i-th of unmanned plane,For the speed of i-th of unmanned plane,For the control law of i-th of unmanned plane,For the displacement sensor value of i-th of unmanned plane,For i-th The velocity sensor measured value of unmanned plane,For the speed sensor fault of i-th of unmanned plane, and form is as follows：
Wherein,Occur the moment for the failure of i-th of unmanned plane,For the failure width of i-th of unmanned plane Value, χi(t) it is steady state value or function that the cycle is τ,For the communication time-delay between neighbours' unmanned plane；
The given trace of fleet system isUsing the 1st unmanned plane as pilotage people, d is made1=0 and order form into columns vector For d=[d1,d2,...,dN]T, whereinFor the distance between i-th of unmanned plane and the 1st unmanned plane, i-th of unmanned plane Distributed AC servo system rule it is as follows：
Wherein, The respectively first derivative and second dervative of given trace, k1＞ 0, k2＞ 0, k3＞ 0, k4 ＞ 0 and meet following preparatory condition：With
Step 3：Measured based on fleet system closed loop model and each unmanned plane and the relative status of neighbours, design is distributed Fault detect Residual Generation device and corresponding fault detect residual error evaluation function, it is specific as follows：
Based on the open loop models and distributed AC servo system rule of i-th of unmanned plane, the closed loop model of i-th of unmanned plane can be obtained such as Under：
Wherein, The displacement of respectively j-th unmanned plane and speed,For the speed of j-th of unmanned plane Spend sensor fault,For the reference locus of the closed loop model of i-th of unmanned plane, concrete form is as follows：
Make x=[ξ1,ξ2,...ξN,ζ1,ζ2,...,ζN]T, v=[v1,v2,...,vN]T, f=[f1,f2,...,fN]T；Order yi(t) it is that i-th of unmanned plane and the relative status of neighbours are measured, form is as follows：
Wherein, i1,i2,...,i|Ni|The 1,2nd of respectively i-th node ..., | Ni| individual neighborhood；
Based on i-th of unmanned plane closed loop model and yi(t), the closed loop model of whole fleet system is as follows：
Wherein,
Wherein, iiWithRespectively unit matrix INAnd I2NKth row；
Closed loop model and i-th of unmanned plane based on fleet system and the relative status of neighbours are measured, i-th unmanned plane Distributed fault detection Residual Generation device design is as follows：
Wherein,The state of Residual Generation device is detected for distributed fault,Examined for distributed fault The residual error of Residual Generation device is surveyed, pole-assignment, design matrix is utilizedMakeTo stablize square Battle array；
Distributed fault based on i-th of unmanned plane detects Residual Generation device, designs corresponding fault detect residual error and evaluates Function is as follows：
Wherein,2 norms；
Step 4：Closed loop model and each unmanned plane and the relative status of neighbours based on fleet system are measured, in each nothing In man-machine, a distribution type fault reconstruction Residual Generation device and one group of corresponding failure point are designed for its all neighbor node It is specific as follows from residual error evaluation function：
In i-th of unmanned plane, for k-th of neighbor node design distributed fault separation Residual Generation device, specific shape Formula is as follows：
Wherein, k ∈ Ni,The state of Residual Generation device is separated for distributed fault,For distribution The residual error of fault reconstruction Residual Generation device；WithBe calculated as follows：
Wherein,Respectively E1, E2And Γi,2Kth row,To makeStable matrix；
K-th of distributed fault based on i-th of unmanned plane separates Residual Generation device, designs corresponding fault reconstruction residual error Evaluation function is as follows：
Step 5：Based on the open loop models of each unmanned plane, distributed fault reconstruction Residual Generation device and correspondingly is designed Fault reconstruction residual error evaluation function；The distributing fault reconstruction Residual Generation implement body form of i-th of unmanned plane is as follows：
Wherein,For the state of the distributing fault reconstruction Residual Generation device of i-th of unmanned plane,For the residual error of the distributing fault reconstruction Residual Generation device of i-th of unmanned plane,For the open loop control of i-th of unmanned plane System input,For the measurement output of i-th of unmanned plane；Wherein,WithValue it is as follows：
Designed using pole-assignmentMakeFor stable matrix；
Based on the distributing fault reconstruction Residual Generation device of i-th of unmanned plane, design corresponding fault reconstruction residual error and evaluate Function is as follows：
Step 6：Detect that residual error evaluation function and corresponding failure determination threshold value carry out fault detect based on distributed fault, It is specific as follows：
OrderForCorresponding failure determination threshold value,Can be detectable according to noise, Unmarried pregnancy and failure The requirement of property, is obtained according to practical experience；The fault detection logic of i-th of unmanned plane is as follows：
IfThen there is a unmanned plane to break down in system；IfThen there is no nobody in system Machine breaks down；
Step 7：Fault reconstruction is carried out based on fault reconstruction residual error evaluation function and corresponding fault reconstruction threshold value, specifically such as Under：
OrderForCorresponding fault reconstruction threshold value, wherein k ∈ Ni, orderForCorresponding fault reconstruction threshold value；WithIt can be obtained according to the requirement of noise, Unmarried pregnancy and the isolabilily according to practical experience；I-th of nothing Man-machine fault reconstruction logic is as follows：
IfThen i-th of unmanned plane breaks down；Otherwise, letter is evaluated if there is a fault reconstruction residual error Numberk∈Ni, and every other fault reconstruction Residual Generation devicep∈Ni{ k }, meetAndThen k-th of neighbour of i-th of unmanned plane break down；Otherwise, if evaluated for all fault reconstruction residual errors FunctionAll meetThe unmanned plane then broken down is to remove i-th of unmanned plane and its neighbours Other unmanned planes；
Step 8：The kinematics model of unmanned plane be in space coordinates x-axis, y-axis and z-axis decoupling, i-th nobody Kinematics model of the machine on space coordinates y-axis direction is identical with the kinematics model in step 2 on x-axis direction, repeats to walk Rapid 2 to step 7, obtains the fault diagnosis result of unmanned plane fleet system on the y axis；
Step 9：The kinematics model of unmanned plane be in space coordinates x-axis, y-axis and z-axis decoupling, i-th nobody Kinematics model of the machine on space coordinates z-axis direction is identical with the kinematics model in step 2 on x-axis direction, repeats to walk Rapid 2 to step 7, obtains fault diagnosis result of the unmanned plane fleet system in z-axis.
The advantageous effects that the present invention is brought：
In this method, each unmanned plane merely with itself output signal and measure to all residual with the relative status of neighbours The state of difference function is updated, and under the communication between unmanned plane is disturbed by fixed length time delay, remains able to make each nothing Man-machine fault detect and the fault reconstruction for realizing itself and neighbours' unmanned plane, that is, realize accurate distributed diagnostics.
Brief description of the drawings
Fig. 1 is the flow chart of the inventive method.
Fig. 2 is the communication topological diagram of three four rotor wing unmanned aerial vehicles formation in example 1.
Fig. 3 is the flight result schematic diagram of three four rotor wing unmanned aerial vehicles formation in embodiment 1.
Fig. 4 is fault detect and the separating resulting schematic diagram of four rotor wing unmanned aerial vehicles 1 in embodiment 1.
Fig. 5 is fault detect and the separating resulting schematic diagram of four rotor wing unmanned aerial vehicles 2 in embodiment 1.
Fig. 6 is fault detect and the separating resulting schematic diagram of four rotor wing unmanned aerial vehicles 3 in embodiment 1.
Embodiment
Below in conjunction with the accompanying drawings and embodiment is described in further detail to the present invention：
With reference to Fig. 1 to Fig. 6, for the unmanned plane fleet system with fixed length communication time-delay and speed sensor fault, A kind of distributed speed sensor fault diagnostic method of time delay unmanned plane fleet system is provided, below for by the rotor of 3 frame four The fleet system of unmanned plane composition, is illustrated, its flow is as shown in Figure 1 to the method for diagnosing faults of the present invention.
Embodiment 1
Step 1：For the communication topology of given unmanned plane, obtain communicating topological parameter.Calculate communication topological sum and draw general The characteristic value of Lars matrix.For the fleet system being made up of 3 unmanned planes, the communication topology of four rotor wing unmanned aerial vehicles is such as Fig. 2 institutes Show.The communication topology that G={ V, E } is fleet system is made, and is undirected UNICOM figure.Wherein, V={ 1,2,3 } is communication topology section Point, each communication topological node represents a unmanned plane.E={ (1,2), (2,3), (3,1) } is the side of communication topology, each edge Represent the communication between a pair of unmanned planes.
Order matrix Ag=[aij] it is the topological adjacency matrix of communication.If node (i, j) ∈ E, claim node i and node j mutual To there is communication between neighbours, i.e. node i and node j, then aij=aji=1, otherwise aij=aji=0.Make NiFor the neighbours of node i Set.|Ni| it is set NiThe number of middle element.Order matrix Dg=[dij] to communicate topological degree matrix, spend the non-right of matrix Diagonal element is zero, and diagonal entry value isMake dmFor degree matrix greatest member value.Order matrix LgOpened up for communication The Laplacian Matrix flutterred, then Lg=Dg-Ag.Make 0≤λ1≤λ2≤...≤λNFor LgN number of characteristic value from small to large.Then may be used Obtain parameters value as follows：
N1={ 2,3 }, N2={ 1,3 }, N3={ 1,2 }, | N1|=| N2|=| N3|=2.
Step 2：Based on described communication topological parameter, given trace, formation vector sum preparatory condition, distributed volume is obtained Team's control law.Open loop models of i-th of unmanned plane on space coordinates x-axis direction are as follows：
Wherein, i=1,2,3,For the displacement of i-th of unmanned plane,For the speed of i-th of unmanned plane,For The control law of i-th of unmanned plane,For the displacement sensor value of i-th of unmanned plane,For i-th unmanned plane Velocity sensor measured value.In embodiment 1, unmanned plane 1 is set to occur permanent deviation fault, unmanned plane 2 and 3 in 655.2025s Do not break down.The failure concrete form of unmanned plane 1 is as follows：
The pursuit path in the direction of the x axis of fleet system is r (t)=43.5-0.5t (m).Vector of forming into columns is d= [0m,-5m,-5m]T.Pursuit path in y-axis and z-axis direction is to be used on y-axis and z-axis direction in constant, this example Control law is similar with x-axis direction, does not elaborate in the present invention.The present invention is examined just for x-axis direction controlling and failure It is disconnected to be described in detail.
The distributed AC servo system rule of i-th of unmanned plane is as follows：
Wherein The respectively first derivative and second dervative of given trace.k1＞ 0, k2＞ 0, k3＞ 0, k4 ＞ 0 and meet preparatory condition：k1＞ k2λNAnd
According to preparatory condition, it is k that control law parameter is selected in embodiment 11=3, k2=0.17, k3=3, k4=0.37. Formation result is as shown in Figure 3.First subgraph is three frame UAV Formation Flight tracks in Fig. 3, and 3 rhombuses represent 3 framves respectively The triangle that line between unmanned plane, unmanned plane is constituted, which is represented, forms into columns, and three curves represent the flight path of unmanned plane.Second Individual subgraph represents the formation tracking error of 3 frame unmanned planes.From the figure 3, it may be seen that during fault-free, triangle is formed into columns normal and formation error Smaller, i.e., control law can realize stable formation；After failure occurs, formation produces deviation and formation error magnitude significantly increases this Although when control law can not ensure the convergence of formation error, still can make formation error keep within the specific limits.
Step 3：Measured based on fleet system closed loop model and each unmanned plane and the relative status of neighbours, design is distributed Fault detect Residual Generation device and corresponding fault detect residual error evaluation function, it is specific as follows：
Based on the open loop models and distributed AC servo system rule of i-th of unmanned plane, the closed loop model of i-th of unmanned plane can be obtained such as Under：
Wherein, The displacement of respectively j-th unmanned plane and speed.Passed for the speed of j-th of unmanned plane Sensor failure.For the reference locus of the closed loop model of i-th of unmanned plane, concrete form is as follows：
Make x=[ξ1,ξ2,ξ3,ζ1,ζ2,ζ3]T, v=[v1,v2,v3]T, f=[f1,f2,f3]T.I-th of unmanned plane and neighbours Relative status observation yi(t) concrete form is as follows：
Based on i-th of unmanned plane closed-loop dynamic model and yi(t), the closed loop model of fleet system is as follows：
Wherein,
In embodiment 1, the value of above-mentioned parameter is specific as follows：
Based on fleet system closed loop model, the distributed fault detection Residual Generation device design of i-th of unmanned plane is as follows：
Wherein,For the state of Residual Generation device,For the residual error of Residual Generation device.Utilize POLE PLACEMENT USING side Method, willWithLimit difference [- 3-6-9-12-15-18] are configured to, [- 2-4-6-8-10-12] and [- 2-4-6-8-10-12] are right The matrix answeredWithValue difference is as follows：
In example 1, the fault detect Residual Generation device based on i-th of unmanned plane, designs corresponding fault detect residual error Evaluation function design is as follows
Wherein, | | ri 0(t) | | it is ri 0(t) 2 norms, i=1,2,3.
Step 4：Closed loop model and each unmanned plane and the relative status of neighbours based on fleet system are measured, in each nothing In man-machine, design a distribution type fault reconstruction Residual Generation device for its all neighbour and one group of corresponding fault reconstruction is residual Poor evaluation function, it is specific as follows：
It is specific as follows for its k-th of neighbours' design distributed fault separation Residual Generation device in i-th of unmanned plane：
Wherein, k ∈ Ni,The state of Residual Generation device is separated for distributed fault,For distributed fault point From the residual error of Residual Generation device.Be calculated as follows：
Wherein,WithRespectively E1, E2And Γi,2Kth row,To makeStable matrix.
In embodiment 1, the parameter value of all distributed faults separation Residual Generation device is as follows：
In embodiment 1, each distributed fault separation Residual Generation device based on each unmanned plane, designs corresponding event Barrier separation residual error evaluation function is as follows：
Step 5：Based on the open loop models of each unmanned plane, distributed fault reconstruction Residual Generation device and correspondingly is designed Fault reconstruction residual error evaluation function；
The form of the distributing fault reconstruction Residual Generation device of i-th of unmanned plane is as follows：
Wherein,For the state of the distributing fault reconstruction Residual Generation device of i-th of unmanned plane,For The residual error of the distributing fault reconstruction Residual Generation device of i-th of unmanned plane,Inputted for the opened loop control of i-th of unmanned plane,For the measurement output of i-th of unmanned plane.WhereinWithValue it is as follows：
In embodiment 1, using pole-assignment, configurationWithLimit Respectively [- 1-2], [- 3-6] and [- 3-6], corresponding matrixValue it is as follows：
In embodiment 1, based on i-th of nobody distributing fault reconstruction Residual Generation device, corresponding failure point is designed It is as follows from residual error evaluation function：
Step 6：Detect that residual error evaluation function and corresponding failure determination threshold value carry out fault detect based on distributed fault, It is specific as follows：
OrderForCorresponding failure determination threshold value.According to wanting for noise, Unmarried pregnancy and fault detectability Ask, and practical experience takesThe fault detection logic of i-th of unmanned plane is as follows：
From Fig. 4 first subgraph, in 655s or so, the distributed fault detection residual error evaluation function of unmanned plane 1More than corresponding threshold valueTherefore unmanned plane 1 judges there is nodes break down in forming into columns.
From Fig. 5 first subgraph, in 655s or so, the distributed fault detection residual error evaluation function of unmanned plane 2More than corresponding threshold valueTherefore unmanned plane 2 judges there is nodes break down in forming into columns.
From Fig. 6 first subgraph, in 655s or so, the distributed fault detection residual error evaluation function of unmanned plane 3More than corresponding threshold valueTherefore unmanned plane 3 judges there is nodes break down in forming into columns.
Step 7：Residual error evaluation function is separated based on distributed fault and corresponding fault reconstruction threshold value carries out fault reconstruction. OrderForCorresponding fault reconstruction threshold value, wherein k ∈ Ni。ForCorresponding fault reconstruction threshold value.According to noise, The requirement of Unmarried pregnancy and the isolabilily, and practical experience takeWithValue it is as follows：
The fault reconstruction logic of i-th of unmanned plane is as follows：
IfThen i-th nobody break down；Otherwise, if there is a fault reconstruction residual error evaluation functionk∈Ni, and every other fault reconstruction residual error evaluation functionp∈Ni{ k }, meetAndThen k-th of neighbour of i-th of unmanned plane break down；Otherwise, if evaluated for all fault reconstruction residual errors Functionk∈Ni, all meetThe unmanned plane then broken down for remove i-th of unmanned plane and its neighbours its His unmanned plane.
From Fig. 4 second subgraph, after fault detect terminates, the distributing fault reconstruction residual error of unmanned plane 1 is evaluated FunctionMore than corresponding threshold valueTherefore unmanned plane 1 judges that itself there occurs failure.Fault reconstruction behind now Step is without carrying out.
From Fig. 5 second subgraph, after fault detect terminates, the distributing fault reconstruction residual error of unmanned plane 2 is evaluated FunctionLess than corresponding threshold valueTherefore unmanned plane 2 judges that itself does not break down.By the 3rd of Fig. 5 Subgraph understands that unmanned plane 2 separates residual error evaluation function to the distributed fault of unmanned plane 1Less than corresponding threshold valueAnd unmanned plane 2 separates residual error evaluation function to the distributed fault of unmanned plane 3More than corresponding threshold valueTherefore unmanned plane 2 judges that unmanned plane 1 there occurs failure.
From Fig. 6 second subgraph, after fault detect terminates, the distributing fault reconstruction residual error of unmanned plane 3 is evaluated FunctionLess than corresponding threshold valueTherefore unmanned plane 3 judges that itself does not break down.By the 3rd of Fig. 6 Subgraph understands that unmanned plane 3 separates residual error evaluation function to the distributed fault of unmanned plane 1Less than corresponding threshold valueAnd unmanned plane 3 separates residual error evaluation function to the distributed fault of unmanned plane 2More than corresponding threshold valueTherefore unmanned plane 3 judges that unmanned plane 1 there occurs failure.
Step 8：The kinematics model of unmanned plane be in space coordinates x-axis, y-axis and z-axis decoupling, i-th nobody Kinematics model of the machine on space coordinates y-axis direction is identical with the kinematics model in step 2 on x-axis direction, repeats to walk Rapid 2 to step 7, obtains the failure analysis result of unmanned plane fleet system on the y axis；
Step 9：The kinematics model of unmanned plane be in space coordinates x-axis, y-axis and z-axis decoupling, i-th nobody Kinematics model of the machine on space coordinates z-axis direction is identical with the kinematics model in step 2 on x-axis direction, repeats to walk Rapid 2 to step 7, obtains failure analysis result of the unmanned plane fleet system in z-axis.
Certainly, described above is not limitation of the present invention, and the present invention is also not limited to the example above, this technology neck The variations, modifications, additions or substitutions that the technical staff in domain is made in the essential scope of the present invention, should also belong to the present invention's Protection domain.

Claims (1)

1. a kind of distributed speed sensor fault diagnostic method of time delay unmanned plane fleet system, it is characterised in that including with Lower step：
Step 1：The communication topological parameter that unmanned plane is formed into columns is calculated, for the fleet system being made up of N number of unmanned plane, G={ V, E } For the undirected communication topology of fleet system, wherein V={ 1,2 ..., N } is communication topological node, each communication topological node generation One unmanned plane of table；For the side of communication topology, each edge represents the communication between a pair of unmanned planes；
Order matrix Ag=[aij] to communicate topological adjacency matrix, if (i, j) ∈ E, claiming node i, neighbours save each other with node j There is communication between point, i.e. node i and node j, then aij=aji=1, otherwise aij=aji=0；
Make NiFor the neighborhood of i-th of unmanned plane, | Ni| it is set NiThe number of middle element；
Order matrix Dg=[dij] to communicate topological degree matrix, the off diagonal element of degree matrix is zero, diagonal entry value For
Order matrix LgFor the Laplacian Matrix of communication topology, then Lg=Dg-Ag；Make 0≤λ1＜ λ2≤...≤λNFor LgFrom small To big N number of characteristic value；
Step 2：Communication topological parameter, given trace based on unmanned plane formation, formation vector sum preparatory condition, design are distributed Formation control is restrained, specific as follows：
Open loop models of i-th of unmanned plane on space coordinates x-axis direction are as follows：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>&amp;xi;</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;zeta;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>&amp;zeta;</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>u</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>y</mi> <mi>i</mi> <mi>&amp;xi;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>y</mi> <mi>i</mi> <mi>&amp;zeta;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;zeta;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>f</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
Wherein, i=1,2 ..., N,For the displacement of i-th of unmanned plane,For the speed of i-th of unmanned plane, For the control law of i-th of unmanned plane,For the displacement sensor value of i-th of unmanned plane,For i-th nobody The velocity sensor measured value of machine,For the speed sensor fault of i-th of unmanned plane, and form is as follows：
<mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>t</mi> <mo>&lt;</mo> <msub> <mi>T</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>&amp;chi;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msub> <mi>T</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mi>t</mi> <mo>&amp;GreaterEqual;</mo> <msub> <mi>T</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
Wherein,Occur the moment for the failure of i-th of unmanned plane,For the failure amplitude of i-th of unmanned plane, χi (t) it is steady state value or function that the cycle is τ,For the communication time-delay between neighbours' unmanned plane；
The given trace of fleet system isUsing the 1st unmanned plane as pilotage people, d is made1=0 and order form into columns vector be d =[d1,d2,...,dN]T, whereinFor the distance between i-th of unmanned plane and the 1st unmanned plane, i-th unmanned plane Distributed AC servo system rule is as follows：
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>&amp;lsqb;</mo> <mi>r</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>-</mo> <msubsup> <mi>y</mi> <mi>i</mi> <mi>&amp;xi;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>&amp;Element;</mo> <msub> <mi>N</mi> <mi>i</mi> </msub> </mrow> </munder> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>&amp;lsqb;</mo> <msubsup> <mi>y</mi> <mi>j</mi> <mi>&amp;xi;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>d</mi> <mi>j</mi> </msub> <mo>-</mo> <msubsup> <mi>y</mi> <mi>i</mi> <mi>&amp;xi;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msub> <mi>k</mi> <mn>3</mn> </msub> <mo>&amp;lsqb;</mo> <mover> <mi>r</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>y</mi> <mi>i</mi> <mi>&amp;zeta;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>+</mo> <msub> <mi>k</mi> <mn>4</mn> </msub> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>&amp;Element;</mo> <msub> <mi>N</mi> <mi>i</mi> </msub> </mrow> </munder> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>&amp;lsqb;</mo> <msubsup> <mi>y</mi> <mi>j</mi> <mi>&amp;zeta;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>y</mi> <mi>i</mi> <mi>&amp;zeta;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>+</mo> <mover> <mi>r</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
Wherein,The respectively first derivative and second dervative of given trace, k1＞ 0, k2＞ 0, k3＞ 0, k4＞ 0 And meet following preparatory condition：k1＞ k2λNWith
Step 3：Measured based on fleet system closed loop model and each unmanned plane and the relative status of neighbours, design distributed fault Residual Generation device and corresponding fault detect residual error evaluation function are detected, it is specific as follows：
Based on the open loop models and distributed AC servo system rule of i-th of unmanned plane, the closed loop model that can obtain i-th of unmanned plane is as follows：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>&amp;xi;</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;zeta;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mover> <mi>&amp;zeta;</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>k</mi> <mn>3</mn> </msub> <msub> <mi>&amp;zeta;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>&amp;Element;</mo> <msub> <mi>N</mi> <mi>i</mi> </msub> </mrow> </munder> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>&amp;lsqb;</mo> <msub> <mi>&amp;xi;</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>&amp;xi;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>-</mo> <msub> <mi>k</mi> <mn>3</mn> </msub> <msub> <mi>f</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <msub> <mi>k</mi> <mn>4</mn> </msub> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>&amp;Element;</mo> <msub> <mi>N</mi> <mi>i</mi> </msub> </mrow> </munder> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>&amp;lsqb;</mo> <msub> <mi>&amp;zeta;</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>&amp;zeta;</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>+</mo> <msub> <mi>k</mi> <mn>4</mn> </msub> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>&amp;Element;</mo> <msub> <mi>N</mi> <mi>i</mi> </msub> </mrow> </munder> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>&amp;lsqb;</mo> <msub> <mi>f</mi> <mi>j</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>f</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
Wherein,The displacement of respectively j-th unmanned plane and speed,For the speed of j-th of unmanned plane Sensor fault,For the reference locus of the closed loop model of i-th of unmanned plane, concrete form is as follows：
<mrow> <msub> <mi>v</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>&amp;lsqb;</mo> <mi>r</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>&amp;rsqb;</mo> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>&amp;Element;</mo> <msub> <mi>N</mi> <mi>i</mi> </msub> </mrow> </munder> <msub> <mi>a</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>&amp;lsqb;</mo> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>d</mi> <mi>j</mi> </msub> <mo>&amp;rsqb;</mo> <mo>+</mo> <msub> <mi>k</mi> <mn>3</mn> </msub> <mover> <mi>r</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mover> <mi>r</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>;</mo> </mrow>
Make x=[ξ1,ξ2,...ξN,ζ1,ζ2,...,ζN]T, v=[v1,v2,...,vN]T, f=[f1,f2,...,fN]T；Make yi(t) It is that i-th of unmanned plane and the relative status of neighbours are measured, form is as follows：
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>y</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>&amp;lsqb;</mo> <msubsup> <mi>y</mi> <mi>i</mi> <mi>&amp;xi;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <msubsup> <mi>y</mi> <msub> <mi>i</mi> <mn>1</mn> </msub> <mi>&amp;xi;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>y</mi> <mi>i</mi> <mi>&amp;xi;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msubsup> <mi>y</mi> <msub> <mi>i</mi> <mrow> <mo>|</mo> <msub> <mi>N</mi> <mi>i</mi> </msub> <mo>|</mo> </mrow> </msub> <mi>&amp;xi;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>y</mi> <mi>i</mi> <mi>&amp;xi;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>y</mi> <mi>i</mi> <mi>&amp;zeta;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <msubsup> <mi>y</mi> <msub> <mi>i</mi> <mn>1</mn> </msub> <mi>&amp;zeta;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>y</mi> <mi>i</mi> <mi>&amp;zeta;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msubsup> <mi>y</mi> <msub> <mi>i</mi> <mrow> <mo>|</mo> <msub> <mi>N</mi> <mi>i</mi> </msub> <mo>|</mo> </mrow> </msub> <mi>&amp;zeta;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>y</mi> <mi>i</mi> <mi>&amp;zeta;</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <msup> <mo>&amp;rsqb;</mo> <mi>T</mi> </msup> </mrow> </mtd> </mtr> </mtable> <mo>;</mo> </mrow>
Wherein,The 1,2nd of respectively i-th node ..., | Ni| individual neighborhood；
Based on i-th of unmanned plane closed loop model and yi(t), the closed loop model of whole fleet system is as follows：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>=</mo> <msub> <mi>A</mi> <mn>1</mn> </msub> <mi>x</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <msub> <mi>A</mi> <mn>2</mn> </msub> <mi>x</mi> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> <mo>+</mo> <mi>B</mi> <mi>v</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <msub> <mi>E</mi> <mn>1</mn> </msub> <mi>f</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <msub> <mi>E</mi> <mn>2</mn> </msub> <mi>f</mi> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>=</mo> <msub> <mi>C</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mi>x</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mi>x</mi> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> <mo>+</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mi>f</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mi>f</mi> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
Wherein,
<mrow> <msub> <mi>A</mi> <mn>1</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mn>0</mn> <mi>N</mi> </msub> </mtd> <mtd> <msub> <mi>I</mi> <mi>N</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>k</mi> <mn>1</mn> </msub> <msub> <mi>I</mi> <mi>N</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>k</mi> <mn>3</mn> </msub> <msub> <mi>I</mi> <mi>N</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>A</mi> <mn>2</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mn>0</mn> <mi>N</mi> </msub> </mtd> <mtd> <msub> <mn>0</mn> <mi>N</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <msub> <mi>L</mi> <mi>g</mi> </msub> </mrow> </mtd> <mtd> <mrow> <mo>-</mo> <msub> <mi>k</mi> <mn>4</mn> </msub> <msub> <mi>L</mi> <mi>g</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>B</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mn>0</mn> <mi>N</mi> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>I</mi> <mi>N</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>E</mi> <mn>1</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mn>0</mn> <mi>N</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>k</mi> <mn>3</mn> </msub> <msub> <mi>I</mi> <mi>N</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msub> <mi>E</mi> <mn>2</mn> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mn>0</mn> <mi>N</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <msub> <mi>k</mi> <mn>4</mn> </msub> <msub> <mi>L</mi> <mi>g</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow>
Wherein, iiWithRespectively unit matrix INAnd I2NKth row；
Closed loop model and i-th of unmanned plane and the relative status of neighbours based on fleet system are measured, the distribution of i-th of unmanned plane The design of formula fault detect Residual Generation device is as follows：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msubsup> <mover> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> <mn>0</mn> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>=</mo> <mo>(</mo> <msub> <mi>A</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>A</mi> <mn>2</mn> </msub> <mo>)</mo> <msubsup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> <mn>0</mn> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <mi>B</mi> <mi>v</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <msubsup> <mi>G</mi> <mi>i</mi> <mn>0</mn> </msubsup> <mo>&amp;lsqb;</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>-</mo> <mo>(</mo> <msub> <mi>C</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>)</mo> <msubsup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> <mn>0</mn> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>&amp;rsqb;</mo> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>r</mi> <mi>i</mi> <mn>0</mn> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>=</mo> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>-</mo> <mo>(</mo> <msub> <mi>C</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>C</mi> <mrow> <mi>i</mi> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>)</mo> <msubsup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> <mn>0</mn> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
Wherein,The state of Residual Generation device is detected for distributed fault,Detect residual for distributed fault The residual error of difference function, utilizes pole-assignment, design matrixMakeTo stablize square Battle array；
Distributed fault based on i-th of unmanned plane detects Residual Generation device, designs corresponding fault detect residual error evaluation function It is as follows：
<mrow> <msubsup> <mi>J</mi> <mi>i</mi> <mn>0</mn> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>|</mo> <mo>|</mo> <msubsup> <mi>r</mi> <mi>i</mi> <mn>0</mn> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> <mo>;</mo> </mrow>
Wherein, | | ri 0(t) | | it is ri 0(t) 2 norms；
Step 4：Closed loop model and each unmanned plane and the relative status of neighbours based on fleet system are measured, in each unmanned plane In, design a distribution type fault reconstruction Residual Generation device for its all neighbor node and one group of corresponding fault reconstruction is residual Poor evaluation function, it is specific as follows：
In i-th of unmanned plane, for k-th of neighbor node design distributed fault separation Residual Generation device, concrete form is such as Under：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msubsup> <mover> <mi>z</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> <mi>k</mi> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>=</mo> <msubsup> <mi>F</mi> <mi>i</mi> <mi>k</mi> </msubsup> <msubsup> <mi>z</mi> <mi>i</mi> <mi>k</mi> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <msubsup> <mi>M</mi> <mi>i</mi> <mi>k</mi> </msubsup> <mi>v</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <msubsup> <mi>S</mi> <mi>i</mi> <mi>k</mi> </msubsup> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>r</mi> <mi>i</mi> <mi>k</mi> </msubsup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>=</mo> <msubsup> <mi>J</mi> <mi>i</mi> <mi>k</mi> </msubsup> <msup> <mi>z</mi> <mi>k</mi> </msup> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <msubsup> <mi>H</mi> <mi>i</mi> <mi>k</mi> </msubsup> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
Wherein, k ∈ Ni,The state of Residual Generation device is separated for distributed fault,For distributed fault point From the residual error of Residual Generation device；WithBe calculated as follows：
Wherein,WithRespectively E1, E2And Γi,2Kth row,To makeStable matrix；
K-th of distributed fault based on i-th of unmanned plane separates Residual Generation device, designs corresponding fault reconstruction residual error and evaluates Function is as follows：
<mrow> <msubsup> <mi>J</mi> <mi>i</mi> <mi>k</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>|</mo> <mo>|</mo> <msubsup> <mi>r</mi> <mi>i</mi> <mi>k</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> <mo>;</mo> </mrow>
Step 5：Based on the open loop models of each unmanned plane, distributed fault reconstruction Residual Generation device and corresponding event are designed Barrier separation residual error evaluation function；The distributing fault reconstruction Residual Generation implement body form of i-th of unmanned plane is as follows：
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mover> <mover> <mi>x</mi> <mo>^</mo> </mover> <mo>&amp;CenterDot;</mo> </mover> <mi>i</mi> <mi>i</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>A</mi> <mi>i</mi> <mi>i</mi> </msubsup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>B</mi> <mi>i</mi> <mi>i</mi> </msubsup> <msub> <mi>u</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>G</mi> <mi>i</mi> <mi>i</mi> </msubsup> <mo>&amp;lsqb;</mo> <msubsup> <mi>y</mi> <mi>i</mi> <mi>i</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>C</mi> <mi>i</mi> <mi>i</mi> </msubsup> <msubsup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> <mi>i</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>r</mi> <mi>i</mi> <mi>i</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>y</mi> <mi>i</mi> <mi>i</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <msubsup> <mi>C</mi> <mi>i</mi> <mi>i</mi> </msubsup> <msubsup> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>i</mi> <mi>i</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
Wherein,For the state of the distributing fault reconstruction Residual Generation device of i-th of unmanned plane, For the residual error of the distributing fault reconstruction Residual Generation device of i-th of unmanned plane,Opened loop control for i-th of unmanned plane is defeated Enter,For the measurement output of i-th of unmanned plane；Wherein,WithValue it is as follows：
<mrow> <msubsup> <mi>A</mi> <mi>i</mi> <mi>i</mi> </msubsup> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msubsup> <mi>B</mi> <mi>i</mi> <mi>i</mi> </msubsup> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <msubsup> <mi>C</mi> <mi>i</mi> <mi>i</mi> </msubsup> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
Designed using pole-assignmentMakeFor stable matrix；
Based on the distributing fault reconstruction Residual Generation device of i-th of unmanned plane, corresponding fault reconstruction residual error evaluation function is designed It is as follows：
<mrow> <msubsup> <mi>J</mi> <mi>i</mi> <mi>i</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>|</mo> <mo>|</mo> <msubsup> <mi>r</mi> <mi>i</mi> <mi>i</mi> </msubsup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>|</mo> <mo>;</mo> </mrow>
Step 6：Detect that residual error evaluation function and corresponding failure determination threshold value carry out fault detect based on distributed fault, specifically It is as follows：
OrderForCorresponding failure determination threshold value,Can be according to noise, Unmarried pregnancy and fault detectability It is required that, obtained according to practical experience；The fault detection logic of i-th of unmanned plane is as follows：
IfThen there is a unmanned plane to break down in system；IfThen there is no unmanned plane in system Break down；
Step 7：Fault reconstruction is carried out based on fault reconstruction residual error evaluation function and corresponding fault reconstruction threshold value, it is specific as follows：
OrderForCorresponding fault reconstruction threshold value, wherein k ∈ Ni, orderForCorresponding fault reconstruction threshold value；WithIt can be obtained according to the requirement of noise, Unmarried pregnancy and the isolabilily according to practical experience；I-th of unmanned plane Fault reconstruction logic it is as follows：
IfThen i-th of unmanned plane breaks down；Otherwise, if there is a fault reconstruction residual error evaluation functionk∈Ni, and every other fault reconstruction Residual Generation devicep∈Ni{ k }, meetAndThen k-th of neighbour of i-th of unmanned plane break down；Otherwise, if commented for all fault reconstruction residual errors Valency functionk∈Ni, all meetThe unmanned plane then broken down is i-th of unmanned plane of removing and its neighbours Other unmanned planes；
Step 8：The kinematics model of unmanned plane is decoupling in space coordinates x-axis, y-axis and z-axis, and i-th of unmanned plane exists Kinematics model on space coordinates y-axis direction is identical with the kinematics model in step 2 on x-axis direction, repeat step 2 to Step 7, the fault diagnosis result of unmanned plane fleet system on the y axis is obtained；
Step 9：The kinematics model of unmanned plane is decoupling in space coordinates x-axis, y-axis and z-axis, and i-th of unmanned plane exists Kinematics model on space coordinates z-axis direction is identical with the kinematics model in step 2 on x-axis direction, repeat step 2 to Step 7, fault diagnosis result of the unmanned plane fleet system in z-axis is obtained.
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