CN109240081A - The submarine earthquake detection flight node finite time configuration for considering error constraints includes fault tolerant control method - Google Patents
The submarine earthquake detection flight node finite time configuration for considering error constraints includes fault tolerant control method Download PDFInfo
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Abstract
The submarine earthquake detection flight node finite time configuration for considering error constraints includes fault tolerant control method, and being related to submarine earthquake detection flight node configuration error constraints includes control method.In order to solve the problems, such as that the problem of existing control method cannot control effectively when propeller breaks down and control precision are poor.The present invention initially sets up the dynamics and kinematical equation of more submarine earthquake detection flight node systems, the influence that propeller damage generates is expressed as to the variation of thrust profiles matrix, then error function and finite time sliding variable are chosen, and selects nonsingular fast terminal sliding-mode surface；According to the error function of selection, finite time sliding variable and nonsingular fast terminal sliding-mode surface, controller is designed, to realize that submarine earthquake detection flight node finite time configuration includes control.It includes faults-tolerant control that the present invention, which is suitable for submarine earthquake detection flight node finite time configuration,.
Description
Technical field
It include control method the present invention relates to submarine earthquake detection flight node configuration error constraints.
Background technique
In recent years, the collaboration control of more autonomous type underwater robots (Autonomous Underwater Vehicle, AUV)
Problem processed has caused the very big concern of control field, and the application of more AUV Collaborative Control technologies is also high diversity, such as ocean
Measurement and draw, military monitoring and defence, disaster are searched and rescued and resource exploration etc..And becoming more and more important with exploration of ocean resources,
Also more rationally and reliably by more AUV Collaborative Control technical applications to this aspect.To complete to lay automatically on a large scale, certainly in seabed
The synthesis submarine earthquake demodulation system of dynamic recycling, team where inventor propose and use Haiti seismic detection flight node
(Ocean Bottom Flying Node, OBFN) completes surveying tasks, and submarine earthquake detection flight node belongs to autonomous type
One kind of underwater robot.
There are mainly of two types for more AUV Collaborative Controls, i.e., centralized and distributed.For centerized fusion, the control of each AUV
Signal needs processed are transmitted by operator or a certain specific AUV.Compared to centralized control system, since distribution is
Each AUV need to only obtain the information of adjacent AUV in system, so dcs has higher efficiency, expansibility
And stability, the application in engineering are more extensive.For distributed AC servo system, communicate in Turbo codes system between each AUV
Information transfering relation.It generally is classified as two ways, i.e., undirected and oriented communication topology.But it is handed over if existing in system
Stream error, the distributed control method based on undirected communication topology may not work.On the contrary, under oriented communication topology,
There is the communication topology that system need to only be met directed spanning tree distributed AC servo system can be completed, therefore based on oriented communication topology
Control method has more the value further studied.Under oriented communication topology, when the position and direction information of each AUV is with discrete
When time series swaps, " Distributed formation control of 6-DOF autonomous
underwater vehicles networked by sampled-data information under directed
topology.》(Ma,C.,Zeng,Q.:Distributed formation control of 6-DOF autonomous
underwater vehicles networked by sampled-data information under directed
Topology.Neurocomputing.154,33-40 (2015)) Research on Interactive Problem of more AUV is had studied, and be based on being input to shape
State stability characteristic (quality) devises distributed director.It, can be according to the number of pilotage people by its stroke for the distributed AC servo system of more AUV
Consistency control when being divided into no pilotage people includes control there are the tracing control of single pilotage people and there are multiple pilotage peoples
System.But it is studied in the case where no pilotage people, for there are the not applicable comprising control problem of multiple pilotage peoples.It is right
In more OBFN systems, equipment cost can be reduced using comprising control, because whole system can be in only pilotage people
When OBFN receives the information of lash ship, target area is gone to jointly, only needs pilotage people logical over long distances equipped with that can carry out with lash ship in this way
The equipment of news, and follower need to only be loaded with the equipment communicated with neighbouring follower or pilotage people.In marine technology
Field, existing scholar are studied comprising control.Assuming that the dynamics of each AUV and interference are smooth,
《Robust containment control in a leader–follower network of uncertain Euler–
Lagrange systems》(Klota,J.R.,Cheng,T.,Dixon,W.E.:Robust containment control
in a leader–follower network of uncertain Euler–Lagrange systems.Int.J.Robust
Nonlinear Control.26,3791-3805 (2016)) distributed director is devised, so that each follower AUV can
In the convex closure formed with asymptotic convergence to the pilotage people by any amount time-varying.It should be noted that the control method can only be realized is
The asymptotic convergence of system, and it is unable to satisfy the requirement to convergence rate in some cases.Finite-time control technology may be implemented
Time Convergence is limited, the performance of system is improved.When the relative status information between adjacent intelligent body is available, " Robust
finite-time containment control for high-order multi-agent systems with
matched uncertainties under directed communication graphs》(Fu,J.,Wang,J.:
Robust finite-time containment control for high-order multi-agent systems
with matched uncertainties under directed communication
Graphs.Int.J.Control.89 (6), 1137-1151 (2016)) it is devised using sliding formwork control technology for each follower
Distributed director based on observer solves the problems, such as the finite-time control under oriented Communication topology.But do not have
Consider that faults-tolerant control may then be unable to complete successfully task if propeller failure occurs in AUV during navigation.Work as OBFN
When navigating by water in ocean, due to the complexity of environment, it is easy to appear failures for propeller, so the error resilience performance of system is to task
Completion it is most important."Simultaneous fault detection and consensus control design for
a network of multi-agent systems》(Davoodi,M.,Meskin,N.,Khorasani,K.:
Simultaneous fault detection and consensus control design for a network of
Multi-agent systems.Automatica.66,185-194 (2016)) discuss fault detection and consistency control ask
Topic, designs Distributed Detection estimator using only the opposite output information between intelligent body, so that all intelligent bodies all reach
State consistency or model reference are consistent, while coordination with one another detects the generation of failure in group.But error is not considered about
Beam.The presence of propeller failure will make error become larger, so constraint error helps to improve the performance of system.With position with
In the case where track error constraints, " High-gain disturbance observer-based backstepping control
with output tracking error constraint for electro-hydraulic systems》(Won,D.,
Kim,W.,Shin,D.,Chung,C.:High-gain disturbance observer-based backstepping
control with output tracking error constraint for electro-hydraulic
Systems.IEEE Trans.Control Syst.Technol.23 (2), 787-795 (2015)) devise a kind of high-gain
Interference observer, and propose Backstepping Controller using obstacle Lyapunov function, the controller meet output constraint and
Deposit improves position tracking performance in case of interferers."Finite-time consensus of nonlinear multi-
agent system with prescribed performance》(Li,X.,Luo,X.,Wang,J.:Finite-time
consensus of nonlinear multi-agent system with prescribed
Performance.Nonlinear Dyn.91,2397-2409 (2018)) to have studied the finite time with error constraints consistent
Tracking problem, by using the error constraints control and nonsingular quick sliding formwork control skill for applying obstacle Lyapunov function
Art proposes a kind of new distributed director, to guarantee multi-agent system and defined performance synchronization.
Summary of the invention
The present invention is poor and cannot be in propeller in order to solve the problems, such as the existing control precision comprising control method
The problem of controling effectively when breaking down.
The submarine earthquake detection flight node finite time configuration for considering error constraints includes fault tolerant control method, including with
Lower step:
Step 1, the dynamics and kinematical equation for establishing more submarine earthquake detection flight node systems；
Submarine earthquake detection flight node includes pilotage people's flight node and follower's flight node；
The influence that propeller damage generates is expressed as the variation of thrust profiles matrix, is defined as Δ B, practical function is flying
Thrust or torque on node become τ+Δ τ from τ；
Step 2, the dynamics based on flight node and kinematical equation and propeller damage on corresponding flight node
Thrust or torque, choose error function and finite time sliding variable；And select nonsingular fast terminal sliding-mode surface；
During choosing error function, for error functionUse error constraints equation
kaiAnd kbiIt is lower bound and the upper bound of time-varying, k respectivelyaih(t)、kbihIt (t) is respectively kaiAnd kbiElement；Then by error functionIt is converted toWithKAi(t)=diag (kai1(t),…,kain(t)), KBi(t)=
diag(kbi1(t),…,kbin(t))；According to ξai(t) and ξbi(t) nonsingular fast terminal sliding-mode surface s is determinedi；
Step 3, according to the error function of selection, finite time sliding variable and nonsingular fast terminal sliding-mode surface, design
Controller, to realize that submarine earthquake detection flight node finite time configuration includes control.
The invention has the following advantages:
Present invention is fully applicable to the controls of submarine earthquake detection flight node, by Fig. 9 to Figure 12 it is found that when t=0s, institute
Some follower's flight nodes are respectively positioned on except the convex closure that pilotage people's flight node surrounds.When t=20s, all follower fly
Row node has entered in convex closure.When t=50s and t=80s, all follower's flight nodes are still located in convex closure.Figure 13 and figure
18 show that follower's flight node needs bigger power and torque output in the initial stage.But after t=10s, control force
Amplitude is reduced within the scope of 60N, and control moment amplitude is reduced within the scope of 100Nm.Since there are incipient faults by propeller T1, and
Its influence flight node longitudinal direction and head shake movement, so by Fig. 3 with Fig. 8 it is found that before 30s, follower's flight node follows
Pilotage people advances, and angle of yaw degree has converged to 0.After 30s, follower's flight node still follows pilotage people to advance, angle of yaw degree
There is variation, amplitude becomes larger, but still very little when its amplitude maximum, influences on overall performance smaller.From Figure 19 to
Figure 24 can be seen that by using error constraints (16), and error variance is limited in range represented by formula (48), therefore,
Improve the mapping and stable state accuracy of more flight node systems.By being analyzed above it is found that in this condition, using control
It restrains (16), realizing the fault-tolerant error constraints of more flight node system distribution finite times includes control.For more flight nodes
The fault-tolerant error constraints of the finite time of system include that control precision is higher.
Detailed description of the invention
Fig. 1 is the phase locus analysis chart of more flight node systems；
Communication topological diagram of the Fig. 2 between pilotage people's flight node and follower's flight node；
The location track of Fig. 3 flight node surge direction；
The location track in Fig. 4 flight node swaying direction；
The location track in Fig. 5 flight node heave direction；
The variation of Fig. 6 flight node roll angle；
The variation of Fig. 7 flight node pitch angular；
The variation of Fig. 8 flight node yawing angle；
The relative position of pilotage people's flight node and follower's flight node changes when Fig. 9 t=0s；
The relative position of pilotage people's flight node and follower's flight node changes when Figure 10 t=20s；
The relative position of pilotage people's flight node and follower's flight node changes when Figure 11 t=50s；
The relative position of pilotage people's flight node and follower's flight node changes when Figure 12 t=80s；
The control force of 5 surge direction of Figure 13 follower's flight node；
The control force in 5 swaying direction of Figure 14 follower's flight node；
The control force in the heave of Figure 15 follower's flight node 5 direction；
The control moment of 5 roll angle of Figure 16 follower's flight node；
The control moment of 5 pitch angular of Figure 17 follower's flight node；
The control moment of 5 yawing angle of Figure 18 follower's flight node；
The error variance of 5 surge direction of Figure 19 follower's flight node；
The error variance in 5 swaying direction of Figure 20 follower's flight node；
The error variance in the heave of Figure 21 follower's flight node 5 direction；
The error variance of 5 roll angle of Figure 22 follower's flight node；
The error variance of 5 pitch angular of Figure 23 follower's flight node；
The error variance of 5 angle of yaw degree of Figure 24 follower's flight node.
Specific embodiment
Specific embodiment 1:
The submarine earthquake detection flight node finite time configuration for considering error constraints includes fault tolerant control method, including with
Lower step:
Step 1, the dynamics and kinematical equation for establishing more submarine earthquake detection flight node systems；
Submarine earthquake detection flight node includes pilotage people's flight node and follower's flight node；
The influence that propeller damage generates is expressed as the variation of thrust profiles matrix, is defined as Δ B, practical function is flying
Thrust or torque on node become τ+Δ τ from τ；
Step 2, the dynamics based on flight node and kinematical equation and propeller damage on corresponding flight node
Thrust or torque, choose error function and finite time sliding variable；And select nonsingular fast terminal sliding-mode surface；
During choosing error function, for error functionUse error constraints equation
kaiAnd kbiIt is lower bound and the upper bound of time-varying, k respectivelyaih(t)、kbihIt (t) is respectively kaiAnd kbiElement；Then by error functionIt is converted toWithKAi(t)=diag (kai1(t),…,kain(t)), KBi(t)=
diag(kbi1(t),…,kbin(t))；According to ξai(t) and ξbi(t) nonsingular fast terminal sliding-mode surface s is determinedi；
Step 3, according to the error function of selection, finite time sliding variable and nonsingular fast terminal sliding-mode surface, design
Controller, to realize that submarine earthquake detection flight node finite time configuration includes control.
Specific embodiment 2:
Detailed process is as follows for step 1 described in present embodiment:
Establish the dynamics and kinematical equation of more submarine earthquake detection flight node systems:
In formula: footmark i expression parameter is the parameter for flight node i；Mηi=MiJi -1, JiIt is body coordinate system to used
The transition matrix of property coordinate system, MiIt is the inertial matrix for including additional mass；CRBηiFor flight node i and CRBiRelevant matrix, For JiFirst derivative, CRBiFor the centripetal torque of rigid body Coriolis of flight node i
Battle array；CAηi=CAi(νri)Ji -1, CAiIt is additional mass Coriolis centripetal force matrix；Dηi=Di(νri)Ji -1, DiFor damped coefficient matrix；
gηi=gi(ηi), gi(ηi) it is restoring force (torque) vector generated by gravity and buoyancy；For flight node i and νriIt is relevant
Vector,νriSpeed for flight node relative to ocean current；νi=[ui vi wi pi qi ri]TFor flight section
Point i is in the undefined vector about speed of body coordinate system, νri=νi-νci, νciFor speed of the ocean current under fixed coordinate system
Degree；For in the undefined vector about position and direction of inertial coodinate system, xi、yi、ziRespectively
For length travel, lateral displacement, vertical deviation；θi、ψiRespectively roll angle, pitch angular, yawing angle；τiFor effect
In the control force and torque of flight node mass center；
Submarine earthquake detection flight node includes pilotage people's flight node and follower's flight node；
For pilotage people's flight node, there is no interference；For i ∈ vL, have
vLIndicate pilotage people's flight node set；τLiThe controller for indicating pilotage people's flight node, actually navigates
The corresponding τ of person's flight nodei；
Propeller is most common, the most important source of failure, and the influence that propeller damage generates can be expressed as thrust point
The variation of cloth matrix is defined as Δ B, and therefore, thrust or torque of the practical function on flight node become τ+Δ τ from τ；
τ+Δ τ=(Bz- KB) u=(Bz+ΔB)u (3)
Wherein, BzIt is the estimated value of thrust profiles matrix；U is the control input of propeller；K is diagonal matrix, element kii
∈ [0,1] indicates the size of corresponding propeller failure；Δ τ is the variable quantity of thrust or torque；
According to (3), convert (1) to
In formula, subscript z is defined as the corresponding estimated value of each parameter；FiFor general uncertainty, i.e., general disturbance is expressed as
Wherein,Indicate the influence that ocean current disturbance generates；ΔMηi、ΔBi、ΔCRBηi、ΔCAηi、ΔDηi、
ΔgηiRespectively indicate Mηi、Bi、CRBηi、CAηi、Dηi、gηiCorresponding uncertain value.
Other processes are same as the specific embodiment one.
Specific embodiment 3:
Selection error function and finite time sliding variable described in present embodiment step 2 simultaneously select nonsingular fast terminal
The process of sliding-mode surface is as follows:
Choose error function and finite time sliding variable:
The error function being defined as follows:
Wherein, vFIndicate follower's flight node set；aijFor in the weighted adjacent matrix of digraph with flight node i and
The relevant element of flight node j；
By (4) and (7), can obtain
By error constraints theory, it is known that error constraints equation is
In formula, kaiAnd kbiIt is lower bound and the upper bound of time-varying respectively, is vector；kaih(t)、kbihIt (t) is respectively kaiAnd kbi
Element, satisfaction-kaih(t) < kbih(t), h=1 ..., n, n represent the quantity of freedom degree；
Error function is converted to
Wherein, KAi(t)=diag (kai1(t),…,kain(t)), KBi(t)=diag (kbi1(t),…,kbin(t))；
DefinitionAnd qm(x)=diag (qmi(x1),…,qmi(xn))；
Make?
ξi=qmiξbi+(En-qmi)ξai(11)
To (11) derivation, obtain
Wherein,EnFor n × n unit matrix
Wherein,
According to finite time theory, following nonsingular fast terminal sliding-mode surface is selected:
Wherein, α1、α2、β1、β2It is constant, 1 < α1< 2,q1、q2It is positive odd-integral number, α2> α1, β1> 1, β2> 0；
According to ξi=[ξi1,ξi2,…,ξin]TWithΞ is defined respectivelyi=diag (| ξi1|,|ξi2
|,…,|ξin|) and
To (14) derivation and (13) are combined, are obtained
Other processes are the same as one or two specific embodiments.
Specific embodiment 4:
Controller is designed described in present embodiment step 3, thus limited according to control law submarine earthquake detection flight node
Time configuration includes that the process of control is as follows:
The present invention fault-tolerant configuration of more submarine earthquake detection flight Node distribution formula finite times includes that the control law is set
It is calculated as:
ui=ui1+ui2 (16)
Wherein,K is normal number, and sign () is sign function；For in
Between variable,
For wiEstimated value, wiFor weight matrix；φiFor activation primitive；ForEstimated value,It indicates in one
The area of a room；
To realize that submarine earthquake detection flight node finite time configuration includes control.
Other processes are identical as one of specific embodiment one to three.
Specific embodiment 5:
U described in present embodimenti2For compensating general disturbance Fi, by using nerual network technique to general disturbance FiAnd
Estimated that detailed process is as follows in its upper bound:
DesignTo general disturbance FiEstimated, is reintroducedNeural network is estimated
ErrorThe upper bound estimated；
Wherein, forDesign neural network estimation, which is restrained, is
Wherein, ΛiFor normal number；
For neural network evaluated errorThe upper bound, forDesign adaptive law is
Wherein, ΔiFor normal number, and define
Other processes are identical as specific embodiment four.
Specific embodiment 6:
Neural network described in present embodiment is Recurrent neural network, and the activation primitive of Recurrent neural network is height
This equation.
Other processes are identical as specific embodiment five.
Theoretical basis of the invention is as follows: being defined first to parameter: JiInertial coodinate system is arrived for body coordinate system
Transition matrix；Mηi=MiJi -1；MiIt is the inertial matrix for including additional mass；CRBiFor
Rigid body Coriolis centripetal force matrix；CAηi=CAi(νri)Ji-1；CAiFor additional mass Coriolis centripetal force matrix；Dηi=Di(νri)Ji-1；
DiFor damped coefficient matrix；gηi=gi(ηi)；gi(ηi) it is restoring force (torque) vector generated by gravity and buoyancy；νri=νi-νci；νriSpeed for flight node relative to ocean current, νciIt is ocean current under inertial coodinate system
Speed；νiFor in the undefined vector about speed of body coordinate system；τiFor the control force and power for acting on flight node mass center
Square；ηiFor the undefined vector about position and direction of inertial coodinate system；BzFor the estimated value of thrust profiles matrix；FiIt is one
As it is uncertain；1nComplete 1 column vector is tieed up for n；0nFull 0 column vector is tieed up for n；0n×nFor n × n full 0 matrix；EnFor n × n unit matrix；For real number set；Real number column vector set is tieed up for n；For m × n real number matrix set；diag(x1,…,xn) it is pair
Diagonal element is by x1,…,xnThe diagonal matrix of composition；||x||1For vector1- norm；| x | it is vectorIt is every
A element takes absolute value operation；For Kronecker product；Sign () is sign function.
Assuming that 1: for pilotage people's flight node, there is no interference；
When there are multiple pilotage people's flight nodes, Laplacian matrix can be written as follow the form of matrix in block form
Wherein
It enables
Then
Assuming that 2: for any one follower's flight node, at least there is a pilotage people, which, which has to this, follows
The directed walk of person.
Assuming that 3: there are normal number MηLmin, so that
0 < MηL min≤min[||Mη1||,…||MηN+m||]。
Nerual network technique estimates the very competent of nonlinear equation, so more flight node systems can be used
The technology carrys out the disturbance of approximate non-linear uncertainty and environment.When estimating nonlinear terms f with neural network, f can be with table
It is shown as:
Wherein, w is weight matrix；φ is activation primitive, general optional are as follows: sign function, hyperbolic tangent function and Gauss
Equation；For the evaluated error of bounded.The estimated value of nonlinear terms is
Wherein,For the estimated value of w.
In the present invention, we go the general disturbance of estimating system using Recurrent neural network.Gauss equation is selected to make
The activation primitive of Recurrent neural network
In formula, x=[x1,x2,…,xn]TRepresent the input vector of n dimension, cjFor the center of j-th of neuron, bjIt is j-th
The width of neuron.Define φ=[φ1,φ2,…,φn]T, the output of Recurrent neural network is represented by
ym=w1φ1+w2φ2+…+wmφm (24)
Step 1: considering following Lyapunov function
In formula:
To (25) derivation, obtain:
(15), (19) and (20) are substituted into (26), are obtained:
By (7) and (16)-(18), obtain
(28) are brought into (27), are obtained
According to (10) and (11), have
Therefore
By (29) and (31), obtain
Due to qmi(En-qmi)=0, and make?
By?
It is availableTherefore variableIn the feelings for considering error constraints
It is bounded under condition, that is to say, thatWhereinIt is normal number.
Step 2: choosing following Lyapunov function
It to (35) derivation and is further simplified, obtains
WhenWhen, definitionδ is lesser normal number, is obtained
From the foregoing, it will be observed that for any i ∈ vF, k appropriate is chosen, is hadIn this case, pass through selectionIt obtains
According to finite time theory, it is known that there are error constraints, more flight node systems will be limited
Terminal sliding mode face s is converged in timei=0n。
WhenWhen, since δ is a lesser normal number, can reasonably assumeFirstly, it is contemplated thatThe case where.At this point, can be obtained by (8), (13) and (31)
By further analyzing, it has been found that may be assumed that Bui2-Fi=0.The reason is as follows that: firstly, and ui1It compares, ui2Usually
It is very little.Secondly as δ is a lesser normal number, so the region 2 in Fig. 1 is very narrow, so the hypothesis is to more
Influence caused by the overall performance of flight node system is little.Finally, proposing ui2Effect be exactly approximate general disturbance term Fi。
Therefore, comprehensively consider in conjunction with three above reason, it is assumed that Bui2-Fi=0 is reasonable.
Based on the above analysis, can be reduced to
(17) are brought into (40), it is available
ConsiderKnown to
In fact, working asSet up andWhen, for certain j ∈ { 1 ..., n }, according to the shape of control law (17)
Formula, it is also available
Work as sij> 0 and sijWhen < 0, by that can respectively obtainWithThis explanationIt is not attractor.Cause
This,There are a neighborhoods to meetIn this region, haveWithSo the system is each
State can pass through region in finite timeWhenWhen, more flight sections theoretical according to (38) and finite time
Dot system will in finite time incoming terminal sliding-mode surface si=0n.Therefore, under any primary condition, which all can be
Finite-time convergence is to terminal sliding mode face si=0n.Fig. 1 is the phase locus of the system.
According to finite time theory, each state converges to terminal sliding mode face si=0nAfterwards, they will be arrived in finite time
Up to origin, i.e. ξi=0n.Therefore, ξaiAnd ξbiIt also will be in Finite-time convergence to ξai=0nAnd ξbi=0n.It is appropriate by selecting
Lower bound and upper bound kaiAnd kbi, to guarantee to carve ξ at the beginningai1,…,ξain< 1, ξbi1,…,ξbin< 1.So in entire mistake
Cheng Zhong, error constraints equation (9) will all be set up.That is, error variance (6) does not exceed the limitation set.
WhenWhen, by error variance (6), have
From (42), can obtain
Convert (43) to the form of column vector, it is available
Due to L1It is reversible, has
It include definition according to configuration, it is known thatThe convex closure being made of pilotage people's flight node.
From (45) it is found that under the action of control law (16), when there are propeller failure and constraint error, follower flies
Row node in the convex closure that Finite-time convergence is surrounded to pilotage people's flight node, that is, will realize more flight nodes it is limited when
Between fault-tolerant error constraints include control.
Compared with prior art
Have much for the control program of AUV at present, simply introduces four kinds of schemes below, and they and the present invention are carried out
Compare.
Track following scheme
《A novel approach to 6-DOF adaptive trajectory tracking control of an
AUV in the presence of parameter uncertainties》(Rezazadegan,F.,Shojaei,K.,
Sheikholeslam,F.,Chatraei,A.:A novel approach to 6-DOF adaptive trajectory
tracking control of an AUV in the presence of parameter uncertainties.Ocean
Eng.107,246-258 (2015)) it is directed to list AUV system, devise the Trajectory Tracking Control algorithm of six degree of freedom.It is based on
Lyapuno theory and Backstepping, propose adaptive controller, while ensure that the robustness to parameter uncertainty.It is expected that
Track be to change with any time.Compared with other most of correlative studys, this method consider propeller saturation can
Energy property, and another adaptive controller is devised to overcome the problems, such as this, meanwhile, in the controller, use saturation function
Limitation control signal.There are parameter uncertainty, nonlinear autoregressive scheme arrives AUV asymptotic convergence
Reference locus.And using Lyapunov theory and Barbalat lemma demonstrate proposed control law stability and effectively
Property.
But compared with the present invention, the case where which only considered single AUV, and the flexibility of more AUV systems
Height, adaptable, operation is low with maintenance cost, in practical projects using more extensive.Therefore the present invention is for more seabeds
Shake this kind of AUV system of detection flight node devises control algolithm, realizes distributed AC servo system.
More AUV track following schemes
《Flocking control of multiple AUVs based onfuzzy potential functions》
(Sahu,B.K.,Subudhi,b.:Flocking control of multiple AUVs based onfuzzy
Potential functions.Int.J.Fuzzy Syst. (2017)) devise more AUV formation control algorithms.Using navigator
Person-follower's control strategy makes more AUV systems assemble and navigate by water along scheduled expected path.In the algorithm, it is assumed that neck
Boat person AUV has all information of desired trajectory, but does not transmit these information to follower AUV.In order to which all AUV are connected
At one group, Formation Center is estimated.The Formation Center is virtual point, and the position at its per moment can be by using consistency algorithm
To predict.The controller of pilotage people and follower AUV are designed by mathematics and fuzzy artificial potential function.Also, in nothing
Obstacle and having in two kinds of environment of obstacle is simulated, and can be seen that the fuzzy formation control algorithm proposed from the result obtained
More AUV systems are controlled along set path cooperative motion, and avoid barrier.
But compared with the present invention, although which realizes more AUV Collaborative Controls, but is not comprising control
System includes in practical projects that control application is more extensive there are the distribution of multiple pilotage peoples.Particularly with more submarine earthquakes
Detection flight node system can make entire using comprising control when only pilotage people's flight node receives the information of lash ship
System goes to target area jointly, only needs equipment of the pilotage people equipped with that can carry out long range communication with lash ship in this way, and follows
Person need to only be loaded with the equipment communicated with similar follower or pilotage people, reduce the cost of equipment.Therefore this hair
It is bright to devise for more this kind of AUV systems of submarine earthquake detection flight node comprising control algolithm.
More AUV configurations include control program
《Containment control of networked autonomous underwater vehicles with
model uncertainty and ocean disturbances guided by multiple leaders》(Peng,Z.,
Wang,D.,Shi,Y.,Wang,H.,Wang,W.:Containment control of networked autonomous
underwater vehicles with model uncertainty and ocean disturbances guided by
Multiple leaders.Inf.Sci.316,163-179 (2015)) for there are realize pair in the case of multiple pilotage peoples
Multiple AUV's includes control.The key feature of the algorithm can be summarized as follows.Firstly, with traditional neural dynamic surface control method
It compares, proposes a kind of new neural dynamic surface control algorithm for design based on prediction, see formula (46).Use changing for prediction error
The unknown dynamic of AUV is identified for more new law, this learn system can all accurately under stable state and transient state, and can improve
The bad mapping generated in traditional neural dynamic surface control method due to biggish initial tracking error.Then, exist
There are model uncertainty, in the case where unknown ocean interference and unmeasured velocity information, it is defeated to devise a kind of new distribution
Feedback control framework is out to control AUV, also, a neural network is used only in entire design.
Compared with the present invention, although it includes control which realizes more AUV, but does not account for faults-tolerant control,
If propeller failure occurs in AUV during navigation, then task may be unable to complete successfully.When flight node is in ocean
When navigation, due to the complexity of environment, it is easy to appear failures for propeller, so the error resilience performance of system is completed to task
It closes important.Therefore the present invention devises fault-tolerant comprising control algolithm for more this kind of AUV systems of submarine earthquake detection flight node.
More AUV faults-tolerant control schemes
《Consensus control for multiple AUVs under imperfect information
caused by communication faults》(Chen,S.,Ho,D.W.C.:Consensus control for
multiple AUVs under imperfect information caused by communication
Faults.Inf.Sci.370-371,565-577 (2016)) it has studied since communication failure leads to the incomplete more AUV of information
Consistent control problem, designed control algolithm multiple AUV can be made to reach an agreement.Meanwhile designed distribution one
Control algolithm is caused local status information to be used only rather than global information.The main feature of the algorithm has: unanimously grinding with existing
Study carefully result to compare, the problem of this method solve more AUV systems that there is communication failure to influence.For no pilotage people and there is navigator
Two kinds of situations of person devise the consistent control algolithm of more AUV System Fault Tolerances.In addition, the fault model considered in the document by when
Varying function indicates, to embody the actual conditions of marine environment complexity.
Compared with the present invention, although which realizes faults-tolerant control, but there is no consider finite time and error about
The problem of beam, for comprising control, convergence time is a critically important performance indicator, for example, needing when evading danger
Follower is wanted to enter in the convex closure that pilotage people surrounds as soon as possible.And the presence of propeller failure will make error become larger, and constrain error
Help to improve the performance of system.Therefore the present invention has been devised for more this kind of AUV systems of submarine earthquake detection flight node
Fault-tolerant error constraints include control algolithm between in limited time.
Embodiment
It include having for control algolithm to verify the fault-tolerant error constraints of more flight Node distribution formula finite times proposed
Effect property, we choose the more flight nodes being made of 8 follower (number 1 ..., 8) and 5 pilotage peoples's (number 9 ..., 13)
System carries out simulating, verifying.
The dynamics and kinematics model of follower's flight node can be described as
The dynamics and kinematics model of pilotage people's flight node can be described as
Communication topological diagram of the Fig. 2 between pilotage people's flight node and follower's flight node；
Model uncertainty
In order to embody model uncertainty, 30% model error, that is, power in controller are taken in simulation process
The nominal value for learning model is the 70% of actual value.
Ocean current disturbance
In the present invention, single order Gauss-markoff process is selected to emulate ocean current interference, it is as follows
In formula, VcIndicate the size of ocean current under fixed coordinate system, ω is that mean value is 1, the white Gaussian noise that variance is 1；μ=
3。
Propeller failure
In simulation process, it is assumed that only T1 propeller breaks down, and considers propeller there are incipient faults.It promotes
The expression formula of device failure is such as shown in (47)
Control parameter is chosen for α1=1.8, β1=0.1, α2=2, β2=1, k=175.
For neural network, activation primitive when emulation is selected as
φi(zi)=[φi1(zi),…,φi11(zi)]T, i=1 ..., 8
Wherein, φij(zi) it is Gauss equation
In formulaAssuming that for all follower's flight nodes, the activation primitive of neural network is all
It is identical.The center c of neuronijIt is evenly distributed in region [- 0.1,0.1]6On.The width b of Gauss equationijIt is selected as bij=
60.Other parameters are as follows: Λ1=Λ2=Λ3=Λ4=Λ5=Λ6=Λ7=Λ8=800, Δ1=Δ2=Δ3=Δ4=Δ5
=Δ6=Δ7=Δ8=800,The lower bound of error constraints and the upper bound are set as
The initial position and speed of follower's flight node are as shown in Table 1 and Table 2.
The initial position (angle) of 1 follower's flight node of table
Initial (angle) speed of 2 follower's flight node of table
Parameter in relation to flight node is as shown in Table 3 and Table 4.
The inertial parameter of 3 flight node of table
The hydrodynamic force coefficient of 4 flight node of table
Position (angle) track of pilotage people's flight node is as shown in table 5.
Position (angle) track of 5 pilotage people's flight node of table
Fig. 3 to Figure 12 illustrates the control that the fault-tolerant error constraints of more flight Node distribution formula finite times include controller and imitates
Fruit.
Without loss of generality, the present invention will show the output situation of the controller by taking follower's flight node 5 as an example.Emulation
As a result as shown in Figure 13 to Figure 18.
For error constraints, the present invention will also show the error change of six-freedom degree by taking follower's flight node 5 as an example
Situation of change is measured, as shown in Figure 19 to Figure 24, wherein e5ij(i=1,2；J=1 ..., 6) follower's flight node 5 is represented
In i in situation j-th of freedom degree error variance, i=1 representative there is the case where error constraints, i=2 represents error free constraint
The case where.
It can be seen from Fig. 3 to Fig. 8 under control law (16) effect, which is to set up.By Fig. 9 to Figure 12
It is found that all follower's flight nodes are respectively positioned on except the convex closure that pilotage people's flight node surrounds when t=0s.When t=20s,
All follower's flight nodes have entered in convex closure.When t=50s and t=80s, all follower's flight nodes are still located at
In convex closure.Figure 13 and Figure 18 shows that follower's flight node needs bigger power and torque output in the initial stage.But t
After=10s, control force amplitude is reduced within the scope of 60N, and control moment amplitude is reduced within the scope of 100Nm.Due to propeller T1
There are incipient faults, and its influence flight node longitudinal direction and head shake movement, so by Fig. 3 with Fig. 8 it is found that before 30s, follow
Person's flight node follows pilotage people to advance, and angle of yaw degree has converged to 0.After 30s, follower's flight node still follows pilotage people
Advance, variation occurs in angle of yaw degree, and amplitude becomes larger, but still very little when its amplitude maximum, influences on overall performance
It is smaller.It is can be seen that from Figure 19 to Figure 24 by using error constraints (16), error variance is limited in represented by formula (48)
In range, this improves the mappings and stable state accuracy of more flight node systems.By analyzing above it is found that in the shape
Under condition, using control law (16), realizing the fault-tolerant error constraints of more flight node system distribution finite times includes control.
Claims (6)
1. the submarine earthquake detection flight node finite time configuration for considering error constraints includes fault tolerant control method, feature exists
In, comprising the following steps:
Step 1, the dynamics and kinematical equation for establishing more submarine earthquake detection flight node systems；
Submarine earthquake detection flight node includes pilotage people's flight node and follower's flight node；
The influence that propeller damage generates is expressed as the variation of thrust profiles matrix, is defined as Δ B, practical function is in flight node
On thrust or torque from τ become τ+Δ τ；
Step 2, the dynamics based on flight node and kinematical equation and propeller damage pushing away on corresponding flight node
Power or torque choose error function and finite time sliding variable；And select nonsingular fast terminal sliding-mode surface；
During choosing error function, for error functionUse error constraints equationkai
And kbiIt is lower bound and the upper bound of time-varying, k respectivelyaih(t)、kbihIt (t) is respectively kaiAnd kbiElement；Then by error function
It is converted toWithKAi(t)=diag (kai1(t),…,kain(t)), KBi(t)=
diag(kbi1(t),…,kbin(t))；According to ξai(t) and ξbi(t) nonsingular fast terminal sliding-mode surface s is determinedi；
Step 3, according to the error function of selection, finite time sliding variable and nonsingular fast terminal sliding-mode surface, design control
Device, to realize that submarine earthquake detection flight node finite time configuration includes control.
2. considering that the submarine earthquake detection flight node finite time configuration of error constraints includes fault-tolerant according to claim 1
Control method, which is characterized in that detailed process is as follows for the step 1:
Establish the dynamics and kinematical equation of more submarine earthquake detection flight node systems:
In formula: footmark i expression parameter is the parameter for flight node i；Mηi=MiJi -1, JiFor body coordinate system to inertial coordinate
The transition matrix of system, MiIt is the inertial matrix for including additional mass； For JiOne
Order derivative, CRBiFor the rigid body Coriolis centripetal force matrix of flight node i；CAηi=CAi(νri)Ji -1, CAiAdditional mass Coriolis to
Mental and physical efforts matrix；Dηi=Di(νri)Ji -1, DiFor damped coefficient matrix；gηi=gi(ηi), gi(ηi) it is to be generated by gravity and buoyancy
Restore force vector；νriSpeed for flight node relative to ocean current；νi=[ui vi wi pi qi ri]TFor
Flight node i is in the undefined vector about speed of body coordinate system, νri=νi-νci, νciIt is ocean current under fixed coordinate system
Speed；For in the undefined vector about position and direction of inertial coodinate system, xi、yi、zi
Respectively length travel, lateral displacement, vertical deviation；θi、ψiRespectively roll angle, pitch angular, yawing angle；τiFor
Act on the control force and torque of flight node mass center；
Submarine earthquake detection flight node includes pilotage people's flight node and follower's flight node；
For pilotage people's flight node, there is no interference；For i ∈ vL, have
vLIndicate pilotage people's flight node set；τLiIndicate the controller of pilotage people's flight node；
The influence that propeller damage generates is expressed as the variation of thrust profiles matrix, is defined as Δ B, practical function is in flight node
On thrust or torque from τ become τ+Δ τ；
τ+Δ τ=(Bz- KB) u=(Bz+ΔB)u (3)
Wherein, BzIt is the estimated value of thrust profiles matrix；U is the control input of propeller；K is diagonal matrix, element kii∈[0,
1] size of corresponding propeller failure is indicated；Δ τ is the variable quantity of thrust or torque；
According to (3), convert (1) to
In formula, subscript z is defined as the corresponding estimated value of each parameter；FiFor general uncertainty, i.e., general disturbance is expressed as
Wherein,Indicate the influence that ocean current disturbance generates；ΔMηi、ΔBi、ΔCRBηi、ΔCAηi、ΔDηi、Δgηi
Respectively indicate Mηi、Bi、CRBηi、CAηi、Dηi、gηiCorresponding uncertain value.
3. the submarine earthquake detection flight node finite time configuration according to claim 1 or claim 2 for considering error constraints includes
Fault tolerant control method, which is characterized in that selection error function and finite time sliding variable described in step 2 simultaneously select nonsingular fast
The process in fast terminal sliding mode face is as follows:
Choose error function and finite time sliding variable:
The error function being defined as follows:
Wherein, vFIndicate follower's flight node set；aijFor in the weighted adjacent matrix of digraph with flight node i and flight
The relevant element of node j；
It can obtain
Error constraints equation is
In formula, kaiAnd kbiIt is lower bound and the upper bound of time-varying respectively；kaih(t)、kbihIt (t) is respectively kaiAnd kbiElement, meet-
kaih(t) < kbih(t), h=1 ..., n, n represent the quantity of freedom degree；
Error function is converted to
Wherein, KAi(t)=diag (kai1(t),…,kain(t)), KBi(t)=diag (kbi1(t),…,kbin(t))；
DefinitionAnd qm(x)=diag (qmi(x1),…,qmi(xn))；
Make?
ξi=qmiξbi+(En-qmi)ξai (11)
To (11) derivation, obtain
Wherein, EnFor n × n unit matrix
Select following nonsingular fast terminal sliding-mode surface:
Wherein, α1、α2、β1、β2It is constant, 1 < α1< 2,q1、q2It is positive odd-integral number, α2> α1, β1> 1, β2> 0；
According to ξi=[ξi1,ξi2,…,ξin]TWithΞ is defined respectivelyi=diag (| ξi1|,|ξi2|,…,|
ξin|) and
To (14) derivation and (13) are combined, are obtained
4. considering that the submarine earthquake detection flight node finite time configuration of error constraints includes fault-tolerant according to claim 3
Control method, which is characterized in that controller is designed described in step 3, to have according to control law submarine earthquake detection flight node
Configuration includes that the process of control is as follows between in limited time:
The design of control law are as follows:
ui=ui1+ui2 (16)
Wherein,K is normal number, and sign () is sign function；Become for centre
Amount,
For wiEstimated value, wiFor weight matrix；φiFor activation primitive；ForEstimated value,Indicate an intermediate quantity；
To realize that submarine earthquake detection flight node finite time configuration includes control.
5. considering that the submarine earthquake detection flight node finite time configuration of error constraints includes fault-tolerant according to claim 4
Control method, which is characterized in that the ui2For compensating general disturbance Fi, by using nerual network technique to general disturbance Fi
And its upper bound is estimated, detailed process is as follows:
DesignTo general disturbance FiEstimated, is reintroducedTo neural network evaluated errorThe upper bound estimated；
Wherein, forDesign neural network estimation, which is restrained, is
Wherein, ΛiFor normal number；
For neural network evaluated errorThe upper bound, forDesign adaptive law is
Wherein, ΔiFor normal number, and define
6. considering that the submarine earthquake detection flight node finite time configuration of error constraints includes fault-tolerant according to claim 5
Control method, which is characterized in that the neural network is Recurrent neural network, and the activation primitive of Recurrent neural network is
Gauss equation.
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