CN108227503A - The attitude-adaptive fault tolerant control method of near-earth magnetic control cube star - Google Patents

The attitude-adaptive fault tolerant control method of near-earth magnetic control cube star Download PDF

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CN108227503A
CN108227503A CN201810068717.8A CN201810068717A CN108227503A CN 108227503 A CN108227503 A CN 108227503A CN 201810068717 A CN201810068717 A CN 201810068717A CN 108227503 A CN108227503 A CN 108227503A
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formula
control
adaptive
neural network
robust
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张敏
李涛
申晓宁
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Nanjing University of Information Science and Technology
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Nanjing University of Information Science and Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Abstract

The attitude-adaptive fault tolerant control method of near-earth magnetic control cube star provided by the invention according to the external disturbance situation being subject to, constructs H∞Robust performance index determines closed loop feedback gain, with the influence of disturbance suppression；For actuator saturated conditions, saturation isolation link is designed, improves robust control, forms the H with saturation isolation∞Robust control keeps normal control action, and system is made to avoid causing control performance deterioration due to actuator saturation；On this basis, introduce the control compensator based on dynamic structure adaptive neural network, the change of control system model caused by offset actuator glitch, so as to construct adaptive fusion rule, realize quickly and effectively control reconfiguration, posture is kept in the preferred range, it is ensured that the reliable and stable operation of satellite.To be directed to it is a kind of there is external disturbance, the adaptive fusion of the uncertain nonlinear time_varying system under actuator glitch and saturated conditions.

Description

The attitude-adaptive fault tolerant control method of near-earth magnetic control cube star
Technical field
The present invention relates to the ADAPTIVE ROBUST Fault Tolerance Control Technology field of uncertain time-variant nonlinear continuous control system, especially It is related to a kind of attitude-adaptive fault tolerant control method of near-earth magnetic control cube star.
Background technology
Cube star is the hot spot in microsatellite field in recent years, is widely used in university and carries out space science research and education, has Have that light-weight, at low cost, the lead time is short, enters the orbit the features such as fast, Space-borne can be used as, realized to ocean, atmospheric environment, ship The monitoring of oceangoing ship, aviation aircraft etc..Obviously, the accurate positionin of cube star and gesture stability will directly influence telemetry Precision, in order to meet the reliable and stable and accuracy requirement of higher and higher Space-borne, design is a kind of effective, functional Posture fault-tolerant control system have important Practical significance and value.
Failure tolerant control is an important topic urgently to be resolved hurrily in the research of present satellites gesture stability, is had at present The achievement in research of certain depth, and the achievement studied the posture faults-tolerant control of near-earth magnetic control cube star be not also it is very much, it is existing Fault tolerant control method employed in document is mostly both for flywheel failure, for using magnetic torquer completely as execution machine The near-earth cube star of structure is then without correlative study.The bar magnet in three directions is respectively adopted to realize three-axis stabilization control in magnetic torquer System, and bar magnet then generates magnetic torque by the coil that is powered, coil passes through prolonged operational heat, performance it is possible that decline, This will cause gesture stability effect to be deteriorated, therefore, fault-tolerant when needing to consider actuator partial injury for magnetic control satellite Control strategy.Magnetic torquer in actual work, is limited by the physical characteristic of magnetic bar, and output amplitude usually all must be In the range of allowing, it is impossible to which otherwise unlimited increase just will appear the situation of actuator saturation, so as to cannot normally perform control The instruction of device so that the control performance of system declines even unstable.Generally be not in actuator in satellite normal operation Saturation, but start to start operation and break down control is reconstructed when, due to the variation that system mode is violent, just Actuator saturation quickly can be caused, adjusted in time without measure once saturation time is long, it will lead to system control action Failure, so, in order to avoid this case occurs, also need to fully consider the place of actuator saturation in posture faults-tolerant control Reason method increases saturation signal isolation link in control method, system can be made not influenced by actuator saturation, and keep Satisfied dynamic property.
In gesture stability in relation to near-earth magnetic control moonlet, it is also necessary to which a major issue of consideration is external disturbance to defending The influence of star posture, such as gravity torque, solar radiation, air drag and internal noise, this can cause under control performance Drop.For this problem, control system must be made to have certain robust ability when designing control algolithm, with the shadow of disturbance suppression It rings.The H of use∞Robust control is disturbed with good inhibiting effect outside to unknown present in system, by setting certain model Number boundary conditions, it can be ensured that system mode is always in the range of allow, so as to which controlled system be made to influence to protect without interruption Hold preferable control performance.
The attitude control system of near-earth magnetic control cube star usually have stronger non-linear, more external disturbance, it is long when Between work the efficiency of magnetic torquer caused to decline and situations such as actuator saturation, general H∞Robust control cannot be complete The closed-loop stabilization of realization system introduces a kind of dynamic self-adapting neural network on this basis, small former to eliminate actuator with this Model uncertainty caused by barrier plays the role of reconfigurable control algorithm.When satellite executing mechanism occurs under a degree of efficiency During drop, a kind of glitch can be considered, by adaptively adjusting controller parameter, fault tolerance is realized in reconfigurable control effect, it is ensured that The stable operation of system.
Invention content
The present invention for the above-mentioned prior art in deficiency, propose that a kind of attitude-adaptive of near-earth magnetic control cube star is fault-tolerant Control method, enabling under designed faults-tolerant control rule effect, pass through H of the design with saturation isolation∞Robust control Rule, and the control compensator based on dynamic structure adaptive neural network is introduced on this basis, construction ADAPTIVE ROBUST is fault-tolerant Control method effectively inhibits influence of the external disturbance to system, and solves actuator saturation problem and realize the small event of actuator Control reconfiguration function during barrier, by the undulated control at attitude of satellite angle in permissible range, it is ensured that the reliable and stable fortune of cube star Row.
To solve the above-mentioned problems, the present invention provides a kind of attitude-adaptive faults-tolerant control sides of near-earth magnetic control cube star Method, which is characterized in that include the following steps：
Step 1, the uncertain continuous time-varying systems model containing internal perturbation, external disturbance and actuator failures is determined：
Step 1.1, determine near-earth magnetic control cube star dynamics and kinematics model be formula (1) and formula (2), wherein q0, q1, q2, q3For four element variables, ωx、ωy、ωzRespectively rolling, pitching, the angular speed for yawing three directions, matrix IsBy Rotary inertia used is formed, Tx, Ty, TzIt inputs in order to control, wdx, wdy, wdzFor external disturbance, (the I in formula (2)sω)x、(Is ω)yAnd (Isω)zDefinition be formula (3)；
(Isω)x=Ixxωx+Ixyωy+Ixzωz
(Isω)y=Iyxωx+Iyyωy+Iyzωz
(Isω)z=Izxωx+Izyωy+Izzωz (3)
Step 1.2, if the posture of satellite is [q0 q1 q2 q3]=[1 00 0], formula (1) and formula (2) are linearized simultaneously Abbreviation is the form of formula (4) and formula (5), wherein, x1=[q0 q1 q2 q3]T, x2=[ωx ωy ωz]T, T=[0 0.5 0.5 0.5], u=[Tx Ty Tz]T, wd=[wdx wdy wdz]T,
Step 1.3, formula (4) and formula (5) are rewritten into an accepted way of doing sth (6), wherein x=[x1 x2]T∈R7, B=[0 I3×3]-1∈R7 ×3, △ f (x, u, t) are that Continuous Nonlinear function is not known as caused by failure, and t is time variable；
Step 2, fault tolerant control method is set：
Step 2.1, for given attitude signalDefining attitude error is：E (t)=x-xd, then Error dynamics equation is obtained as formula (7)；
Step 2.2, it designs such as the control law of formula (8), wherein, udFor robust control, unIt is adaptively refreshing to be based on dynamic structure Through network-based control compensator；
Step 3, design can inhibit the robust control u of actuator saturationd：
Step 3.1, determine that model during actuator saturation defines such as formula (9), wherein, δ0iMaximum limit for actuation means Amplitude, δ=[δ01,…δ0m]；
Step 3.2, definition control isolation signals are uh=δ-un, in robust controller udMiddle addition control isolation signals, Robust controller form is formula (10)；
ud=Ke-uh (10)
Step 3.3, according to the H of formula (11)∞Control performance standard, the feedback gain matrix K designed in robust controller are Formula (12), wherein γ are given normal numbers, and Q is given symmetric positive definite constant matrices, and P is symmetric positive definite constant matrices, and P expires Algebraic Riccati equations shown in sufficient formula (13)；
K=-BTQ-1BBTP (12)
Step 4, the control compensator u based on dynamic structure adaptive neural network is constructedn：
Step 4.1, design one kind adjusts adaptive radial base neural net entirely, caused by approach actuator failures not really Determine nonlinear function, mathematical description is formula (14), wherein, X=[xT,uT,t]T∈R11It is the input vector of neural network, and X ∈Ad, AdConjunction is compacted for one；W*、ξ*、η*It is one by one default optimal weights, presets optimal center, default optimal width；ε (X) is has Boundary's approximate error meets
Step 4.2, the control compensator based on the neural network is constructed as formula (15), wherein, unnFor the defeated of neural network Go out, expression formula is formula (16)；Wherein：The estimated value of weight, the estimated value at center, width is set as one by one to estimate Evaluation, specific calculating formula is respectively referring to formula (19), formula (20) and formula (21), unsIt exports and compensates for network, expression formula is Formula (17)；Wherein,It isEstimated value, calculating formula is referring to formula (22), sgn (BTPe) it is vectorial BTThe symbol square of Pe Battle array；
un=unn+uns (15)
Step 4.3, shown in the operation rule such as formula (18) of design threshold values comparing element TLU, so as to fulfill on-line tuning god Number through network hidden neuron, wherein, L be hidden neuron number, etra=| | e (n) | | it is approximate error；For the error accumulation in a sliding window M；E1, E2It is given boundary value, 0<α<1 It is impact factor；The initial parameter value of the hidden neuron is set as：ξL+1=x (n), ηL+1=λ etra, λ is regulatory factor；
Operation rule：ρ=α exp (etra-E1)+(1-α)exp(erms-E2)
Logic compares：
Step 4.4, design the adaptive updating rule of the weight of neural network, center and width, respectively formula (19), (20), (21), so that it is guaranteed that on the basis of robust control, after introducing neural network adaptive compensator, system remains able to reality Existing closed loop bounded stability；
In formula, σ1, σ2, σ3It is the regulatory factor of dynamic neural network and is positive constant.
The attitude-adaptive fault tolerant control method of near-earth magnetic control cube star provided by the invention, is disturbed according to the outside of cube star Emotionally condition constructs H∞Robust performance index, so that it is determined that closed loop feedback gain, with the influence of disturbance suppression；Satisfy for actuator And situation, robust control is improved, adds in saturation isolation link, forms a kind of H with saturation isolation∞Robust control avoids satisfying Deteriorate with the system control performance of initiation；On this basis, the control based on dynamic structure adaptive neural network is re-introduced into mend Device is repaid, constructs adaptive fusion, by network on-line study, the model for accurately approaching actuator failures initiation is not known Property, to offset its influence to stability of control system, quickly and effectively control reconfiguration is realized, by stabilization of carriage angle in certain model In enclosing, it is ensured that satellite reliability service.To be directed to it is a kind of there is external disturbance, the time-varying under actuator glitch and saturated conditions The adaptive fusion of uncertain continuous system.Specific advantage is as follows：
(1) according to the external disturbance situation of cube star complexity, H is constructed∞Robust performance index determines closed loop feedback gain, To inhibit uncertain influence of the external disturbance to system stability；
(2) for actuator saturated conditions, robust control is improved, adds in saturation isolation link, is formed a kind of with saturation The H of isolation∞Robust control can compensate actuator saturation signal by control action, so as to keep original control action, keep away The system control performance for exempting from saturation initiation deteriorates；
(3) in the H being isolated with saturation∞On the basis of robust control, construct based on dynamic structure adaptive neural network Compensator is controlled, adaptive fusion is formed, is learnt by Neural Network Online, accurately approaches the mould of actuator failures initiation Type is uncertain, and the variation of Controlling model, can carry out quickly and effectively control reconfiguration, by the appearance of cube star during offsetting failure State angle all-the-time stable is in a certain range, it is ensured that its reliability service.
The attitude-adaptive fault tolerant control method of near-earth magnetic control cube star provided by the present invention, has as one kind External disturbance, the time-varying under actuator glitch and saturated conditions do not know the adaptive fusion method of continuous system, tool There is certain application value, it is easy to accomplish, real-time is good, and accuracy is high, can effectively improve control system safety and can grasp The property made is strong, efficient to can be widely applied in the actuator failures faults-tolerant control of uncertain Continuous Nonlinear control system.
Description of the drawings
Attached drawing 1 is the stream of the attitude-adaptive fault tolerant control method of near-earth magnetic control cube star in the specific embodiment of the invention Cheng Tu；
Attached drawing 2 is the attitude control system structure diagram in the specific embodiment of the invention；
Attached drawing 3 is that the attitude angle time response of three directions (rolling, pitching, yaw) in the specific embodiment of the invention is bent Line chart；
Attached drawing 4 is three direction (rolling, pitching, yaw) angular speed time response curves in the specific embodiment of the invention Figure；
Attached drawing 5 is the controlling curve figure of three directions (rolling, pitching, yaw) in the specific embodiment of the invention.
Specific embodiment
Below in conjunction with the accompanying drawings to the tool of the attitude-adaptive fault tolerant control method of near-earth magnetic control cube star provided by the invention Body embodiment elaborates.
Present embodiment provides a kind of attitude-adaptive fault tolerant control method of near-earth magnetic control cube star, attached drawing 1 It is the flow chart of the attitude-adaptive fault tolerant control method of near-earth magnetic control cube star in the specific embodiment of the invention, attached drawing 2 is Attitude control system structure diagram in the specific embodiment of the invention, attached drawing 3 are three in the specific embodiment of the invention The attitude angle time response curve graph in direction (rolling, pitching, yaw), attached drawing 4 are three sides in the specific embodiment of the invention To (rolling, pitching, yaw) angular speed time response curve graph, attached drawing 5 is three direction (rollings in the specific embodiment of the invention Turn, pitching, yaw) controlling curve figure.
As shown in Figure 1, the attitude-adaptive fault tolerant control method for the near-earth magnetic control cube star that present embodiment provides, According to the external disturbance situation of cube star, H is constructed∞Robust performance index, so that it is determined that closed loop feedback gain, with disturbance suppression It influences；For actuator saturated conditions, robust control is improved, adds in saturation isolation link, formation is a kind of to have what saturation was isolated H∞Robust control avoids the system control performance that saturation causes from deteriorating；On this basis, it is re-introduced into adaptive based on dynamic structure The control compensator of neural network constructs adaptive fusion, by network on-line study, accurately approaches actuator failures and draw The model uncertainty of hair to offset its influence to stability of control system, realizes quickly and effectively control reconfiguration, by posture Stablize in a certain range at angle, it is ensured that satellite reliability service.To be directed to it is a kind of there is external disturbance, actuator glitch and full Time-varying in the case of does not know the adaptive fusion of continuous system, comprises the following specific steps that：
Step 1, the uncertain continuous time-varying systems model containing internal perturbation, external disturbance and actuator failures is determined：
Step 1.1, determine near-earth magnetic control cube star dynamics and kinematics model be formula (1) and formula (2), wherein q0, q1, q2, q3For four element variables, ωx、ωy、ωzRespectively rolling, pitching, the angular speed for yawing three directions, matrix IsBy Rotary inertia is formed, Tx, Ty, TzIt inputs in order to control, wdx, wdy, wdzFor external disturbance；(I in formula (2)sω)x, (Isω)yWith And (Isω)zDefinition be formula (3)；
(Isω)x=Ixxωx+Ixyωy+Ixzωz
(Isω)y=Iyxωx+Iyyωy+Iyzωz
(Isω)z=Izxωx+Izyωy+Izzωz (3)
Step 1.2, if the posture of satellite is [q0 q1 q2 q3]=[1 00 0], formula (1) and formula (2) are linearized simultaneously Abbreviation is the form of formula (4) and formula (5), wherein, x1=[q0 q1 q2 q3]T, x2=[ωx ωy ωz]T, T=[0 0.5 0.5 0.5], u=[Tx Ty Tz]T, wd=[wdx wdy wdz]T,
Step 1.3, it is contemplated that formula (4) and formula (5) are rewritten an accepted way of doing sth (6), wherein x by the uncertain conditions such as actuator failures =[x1 x2]T∈R7, B=[0 I3×3]-1∈R7×3, △ f (x, u, t) are that Continuous Nonlinear function is not known as caused by failure, T is time variable.
Step 2, fault tolerant control method designs：
Step 2.1, for given attitude signalDefining attitude error is：E=x-xd, then may be used It is formula (7) to obtain error dynamics equation；
Step 2.2, it designs such as the control law of formula (8), wherein, udFor robust control, unIt is adaptively refreshing to be based on dynamic structure Through network-based control compensator.
Step 3, design can inhibit the robust control u of actuator saturationd：
Step 3.1, determine that model during actuator saturation defines such as formula (9), wherein, δ0iMaximum limit for actuation means Amplitude, δ=[δ01,…δ0m], wherein, m is the positive integer more than 1；
Step 3.2, definition control isolation signals are uh=δ-un, in robust controller udMiddle addition control isolation signals, Robust controller form is formula (10)；
ud=Ke-uh (10)
Step 3.3, according to the H of formula (11)∞Control performance standard, the feedback gain matrix K designed in robust controller are Formula (12), wherein γ are given normal numbers, and Q is given symmetric positive definite constant matrices, and P is symmetric positive definite constant matrices, and P expires Algebraic Riccati equations shown in sufficient formula (13).
K=-BTQ-1BBTP (12)
Step 4, the control compensator u based on dynamic structure adaptive neural network is constructedn：
Step 4.1, design one kind adjusts adaptive radial direction base (Radical Basis Function, RBF) nerve net entirely Network, Uncertain nonlinear function caused by approach actuator failures, mathematical description are formula (14), wherein, X=[xT,uT,t ]T∈R11It is the input vector of neural network, and X ∈ Ad, AdConjunction is compacted for one.If W*,ξ*,η*For default optimal weights, preset most Excellent center, default optimal width, wherein, the default optimal weights, default optimal center, default optimal width faithful representation are pre- Weight first set, ideally, center, width；ε (X) is bounded approximate error, is met
△ f (x, u, t)=W*TG*(X,ξ*,η*)+ε(X) (14)
Step 4.2, the control compensator based on the neural network is constructed as formula (15), wherein, unnFor the defeated of neural network Go out, expression formula is formula (16)；Wherein：The estimated value of weight, the estimated value at center, width is set as one by one to estimate Evaluation, specific calculating formula is respectively referring to formula (19), formula (20) and formula (21), unsIt exports and compensates for network, expression formula is Formula (17)；Wherein,It isEstimated value, calculating formula is referring to formula (22), sgn (BTPe) it is vectorial BTThe symbol square of Pe Battle array；
un=unn+uns (15)
Shown in the operation rule such as formula (18) of step 4.3) design threshold values comparing element TLU, so as to fulfill on-line tuning god Number through network hidden neuron, wherein, L be hidden neuron number, etra=| | e (n) | | it is approximate error；For the error accumulation in a sliding window M.E1, E2It is given boundary value, 0<α<1 It is impact factor.The initial parameter value of newly-increased hidden neuron is set as：ξL+1=x (n), ηL+1=λ etra, λ is regulatory factor；
Operation rule ρ=α exp (etra-E1)+(1-α)exp(erms-E2)
Logic compares
The adaptive updating rule of step 4.4) the design weight of neural network, center and width, respectively formula (19) (20) (21), so that it is guaranteed that on the basis of robust control, after introducing neural network adaptive compensator, system still can be realized Closed loop bounded stability, wherein, σ1, σ2, σ3It is the regulatory factor of dynamic neural network and is positive constant.
The attitude-adaptive faults-tolerant control side for the near-earth magnetic control cube star that present embodiment illustrated below provides The effect of method.
This example is using cube star of a low orbit as controlled device, control structure figure such as Fig. 2.The satellite is using three Axis magnetic torquer is as executing agency.Satellite weight is 1.92kg, orbit altitude 320km, rotary inertia Is=diag [0.0115 0.0115 0.00369]kgm2.If external disturbance is gravitational moment, expression formula is as follows：
If original state is：Angular velocity omega=[0.0001 0.0006-0.0003] rad/s,
Attitude angle (roll angle, pitch angle, yaw angle) [φ θ ψ]=[1 2 1]°。
Simulation parameter is set as：γ=1, L=3, λ=1, α=0.6, σ1=σ2=σ3=1, σ4=0.8
Q=diag [1.5 1.5 1.5 1.5 1.5 1.5 1.5],
According to formula (12) and (13), robust feedback can be calculated:
Assuming that after satellite brings into operation 30000 seconds, the magnetic torquer hydraulic performance decline in 3 directions, output is only normal In the case of 80%, using it is proposed by the present invention with saturation isolation adaptive fusion algorithm, to satellite gravity anomaly System carries out simulation study.Fig. 3 is the time response curve of three attitude angles, and Fig. 4 is the time response of three directional angular velocities Curve, Fig. 5 are the controlling curves in three directions.In terms of simulation result, there is the adaptive of saturation isolation using proposed in text Answer faults-tolerant control calculation that posture of cube star in three rolling, pitching and yaw directions can be made comparatively fast to stablize, and almost do not have There is deviation, be maintained in the range of ideal posture.When failure occurs, attitude angle has small fluctuation, but restores quickly and protect Original angle is held, too much influence is not caused to gesture stability, by above-mentioned experimental result it is found that satisfy for there are actuators With actuator glitch and the nonlinear time_varying system of external disturbance, present embodiment proposed have saturation every From adaptive fusion method be effective.
The above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art Member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications also should be regarded as Protection scope of the present invention.

Claims (1)

1. a kind of attitude-adaptive fault tolerant control method of near-earth magnetic control cube star, which is characterized in that include the following steps：
Step 1, the uncertain continuous time-varying systems model containing internal perturbation, external disturbance and actuator failures is determined：
Step 1.1, determine near-earth magnetic control cube star dynamics and kinematics model be formula (1) and formula (2), wherein q0, q1, q2, q3For four element variables, ωx、ωy、ωzRespectively rolling, pitching, the angular speed for yawing three directions, matrix IsBy institute It is formed with rotary inertia, Tx, Ty, TzIt inputs in order to control, wdx, wdy, wdzFor external disturbance, (the I in formula (2)sω)x、(Isω)y And (Isω)zDefinition be formula (3)；
(Isω)x=Ixxωx+Ixyωy+Ixzωz
(Isω)y=Iyxωx+Iyyωy+Iyzωz
(Isω)z=Izxωx+Izyωy+Izzωz (3)
Step 1.2, if the posture of satellite is [q0 q1 q2 q3]=[1 00 0], be by formula (1) and formula (2) linearisation and abbreviation The form of formula (4) and formula (5), wherein, x1=[q0 q1 q2 q3]T, x2=[ωx ωy ωz]T, T=[0 0.5 0.5 0.5], U=[Tx Ty Tz]T, wd=[wdx wdy wdz]T,
Step 1.3, formula (4) and formula (5) are rewritten into an accepted way of doing sth (6), wherein x=[x1 x2]T∈R7, B=[0 I3×3]-1∈R7×3, △ f (x, u, t) is that Continuous Nonlinear function is not known as caused by failure, and t is time variable；
Step 2, fault tolerant control method is set：
Step 2.1, for given attitude signalDefining attitude error is：E (t)=x-xd, then obtain Error dynamics equation is formula (7)；
Step 2.2, it designs such as the control law of formula (8), wherein, udFor robust control, unTo be based on dynamic structure adaptive neural network net The control compensator of network；
Step 3, design can inhibit the robust control u of actuator saturationd：
Step 3.1, determine that model during actuator saturation defines such as formula (9), wherein, δ0iMaximum amplitude limit for actuation means Value, δ=[δ01,…δ0m]；
Step 3.2, definition control isolation signals are uh=δ-un, in robust controller udMiddle addition control isolation signals, robust Controller form is formula (10)；
ud=Ke-uh (10)
Step 3.3, according to the H of formula (11)∞Control performance standard, it is formula to design the feedback gain matrix K in robust controller (12), wherein γ is given normal number, and Q is given symmetric positive definite constant matrices, and P is symmetric positive definite constant matrices, wherein square Battle array P meets the Algebraic Riccati equations shown in formula (13)；
K=-BTQ-1BBTP (12)
Step 4, the control compensator u based on dynamic structure adaptive neural network is constructedn：
Step 4.1, design one kind adjusts adaptive radial base neural net entirely, is not known caused by approach actuator failures non- Linear function, mathematical description are formula (14), wherein, X=[xT,uT,t]T∈R11It is the input vector of neural network, and X ∈ Ad, AdConjunction is compacted for one；W*、ξ*、η*It is one by one default optimal weights, presets optimal center, default optimal width；ε (X) is bounded Approximate error meets
Step 4.2, the control compensator based on the neural network is constructed as formula (15)；Wherein, unnFor the output of neural network, Expression formula is formula (16), wherein：It is estimated value, the estimated value at center, the estimated value of width of weight one by one, Specific calculating formula is respectively formula (19), formula (20) and formula (21)；unsIt exporting and compensates for network, expression formula is formula (17), In,It isEstimated value, calculating formula is referring to formula (22)；sgn(BTPe) it is vectorial BTThe sign matrix of Pe；
un=unn+uns (15)
Step 4.3, shown in the operation rule such as formula (18) of design threshold values comparing element TLU, so as to fulfill on-line tuning nerve net The number of network hidden neuron, wherein, L be hidden neuron number, etra=| | e (n) | | it is approximate error；For the error accumulation in a sliding window M；E1, E2It is given boundary value, 0<α<1 It is impact factor；The initial parameter value of the hidden neuron is set as：ξL+1=x (n), ηL+1=λ etra, λ is regulatory factor；
Operation rule：ρ=α exp (etra-E1)+(1-α)exp(erms-E2)
Logic compares：
Step 4.4, design the adaptive updating rule of the weight of neural network, center and width, respectively formula (19), (20), (21), so that it is guaranteed that on the basis of robust control, after introducing neural network adaptive compensator, system remains able to realize closed loop Bounded stability；
In formula, σ1, σ2, σ3It is the regulatory factor of dynamic neural network and is positive constant.
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Citations (3)

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