CN110083171A - The method and system of the Dynamic sliding mode Attitude tracking control of flexible spacecraft - Google Patents
The method and system of the Dynamic sliding mode Attitude tracking control of flexible spacecraft Download PDFInfo
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Abstract
The present invention provides a kind of method and system of the Dynamic sliding mode Attitude tracking control of flexible spacecraft, this method comprises: step S1: establishing kinematical equation and kinetics equation of the flexible spacecraft based on error attitude quaternion；Step S2: by introducing switching at runtime function, the Dynamic sliding mode Attitude tracking control rule of Flexible Spacecraft tracking problem is devised, and the robust differentiator for devising a finite time convergence control estimates the partial status of flexible spacecraft system.The beneficial effects of the present invention are: the present invention effectively inhibits the problem of buffeting caused by traditional sliding formwork control ratio sign function by the design of switching function, the method for Dynamic sliding mode Attitude tracking control can make Space Vehicle System carry out Attitude Tracking.
Description
Technical field
The present invention relates to the Dynamic sliding mode Attitude tracking controls of flexible spacecraft technical field more particularly to flexible spacecraft
Method.
Background technique
Sliding formwork control has been obtained extensively in Flexible Spacecraft control with its robustness and stronger anti-interference ability
Application.One kind is proposed using the upper bound of adaptive approach estimation unknown disturbance for rigid spacecraft attitude maneuver problem
Based on the anti-adaptive sliding-mode observer rule pushed away.For rigid spacecraft, a kind of Adaptive Integral sliding formwork control ratio is proposed, is avoided
The mistake adjustment of traditional sliding formwork control ratio.It is proposed for Flexible Spacecraft tracking problem using sliding-mode control
A kind of Sliding Mode Attitude tracing control rule.Traditional sliding formwork control ratio is made of equivalent control and switching control two parts.Generally
In the case of, it by adjusting switch control parameter, can solve the uncertainty of control system, improve the anti-interference energy of control system
Power.The switch control of traditional sliding formwork control is made of sign function, and sign function can cause high frequency to be buffeted.For sliding formwork control
Buffeting problem can use the sign function item in the traditional sliding-mode control of saturation function replacement, have studied rigid spacecraft
Attitude maneuver problem proposes Spacecraft During Attitude Maneuver sliding formwork control rule.By introducing sliding formwork boundary layer, buffeting is limited in
In the range of one very little.However, introducing boundary layer method and replacing sign function with saturation function method, sliding formwork control is weakened
Robustness.For rigid spacecraft Attitude Tracking problem, the high-order that discontinuous control variables transformations are sliding formwork switching function is led
Number proposes High-Order Sliding Mode Attitude tracking control rule.The High-Order Sliding Mode attitude control law of proposition can efficiently solve sliding formwork control
Buffeting problem, but high_order sliding mode control rule design limited by opposite order.
To sum up, the defect of background technique are as follows: the switch control of traditional sliding formwork control is made of sign function, sign function meeting
High frequency is caused to be buffeted.By introducing sliding formwork boundary layer, buffeting is limited in the range of a very little.However, introducing boundary layer
Method simultaneously replaces sign function with saturation function method, weakens the robustness of sliding formwork control.High-Order Sliding Mode attitude control law can be effective
Ground solves the problems, such as the buffeting of sliding formwork control, but the design of high_order sliding mode control rule is limited by opposite order.
Summary of the invention
The present invention provides a kind of methods of the Dynamic sliding mode Attitude tracking control of flexible spacecraft, include the following steps:
Step S1: kinematical equation and kinetics equation of the flexible spacecraft based on error attitude quaternion are established；
Step S2: by introducing switching at runtime function, the Dynamic sliding mode appearance of Flexible Spacecraft tracking problem is devised
State tracing control rule, and devise the robust differentiator an of finite time convergence control to the partial status of flexible spacecraft system into
Row estimation.
The present invention also provides a kind of systems of the Dynamic sliding mode Attitude tracking control of flexible spacecraft, comprising:
Establish equation module: for establishing kinematical equation and dynamics of the flexible spacecraft based on error attitude quaternion
Equation；
Processing module: for devising the dynamic of Flexible Spacecraft tracking problem by introducing switching at runtime function
Sliding Mode Attitude tracing control rule, and devise the part of the robust differentiator to flexible spacecraft system an of finite time convergence control
State is estimated.
It as further improvement of the invention, is established in equation module described, is based on attitude quaternion, establish flexible boat
The kinematical equation and kinetics equation of its device are as follows:
Wherein, q be spacecraft body coordinate system under unit attitude quaternion, i.e., | | q | |=1 orq0
For the scalar component of q, qvFor the vector portion of q, and qv=[q1 q2 q3]T；For spacecraft ontology seat
Attitude angular velocity under mark system；Matrix T (q0,qv) be
Wherein, I3For 3 × 3 unit matrix；For arbitraryX × expression:
Clearly for the column vector x, x of any one 3 dimension×It is an antisymmetric matrix；For flexible spacecraft
Integrally-built moment of inertia matrix is rigid bodies inertia matrix JmbWith the summation of flexible appendage moment of inertia matrix, i.e. J=
Jmb+δTδ, wherein coupling matrix of the δ between flexible appendage and rigid bodies, to describe flexible appendage to the shadow of rigid bodies
It rings；η is that the flexible mode of flexible appendage is displaced；To act on the spaceborne outer controling force square of rigid body,
For the external disturbance torque acted in main body；C, K are respectively the damping matrix and stiffness matrix of flexible spacecraft；Consider flexible
Spacecraft has there are when N rank flexible mode
C=diag { 2 ξiωni, i=1 ..., N }
Wherein, ωni, i=1 ..., N are the vibration frequency of flexible spacecraft flexible mode, ξi, i=1 ..., N is flexibility
The damping ratio of mode.
It as further improvement of the invention, is established in equation module described, establishes flexible spacecraft and be based on posture four
The error motion equation and kinetics equation of first number are as follows:
Define Attitude Tracking errorqev=[qe1 qe2 qe3]TIt is to expire from ontology reference frame
Hope the opposite quaternary number error of referential, andqdv=[qd1,qd2,qd3]TIt is to be described with unit quaternion
The expectation posture of flexible spacecraft；According to the calculation formula of quaternary number it follows that
Unit quaternion qdAnd qeIt is all satisfied | | qdv| |=1 He | | qev| |=1, then desired attitude motion can indicate
Are as follows:
WhereinAndIt is target angular velocity；It is expected that coordinate system
Spin matrix corresponding between fixed coordinate system can be represented as with ontologyAnd meetInertia angular speed
Use ωdIt indicates, then the kinematics of relative attitude tracking and kinetics equation can indicate are as follows:
Wherein, I3For 3 × 3 unit matrix；For arbitraryx×It indicates:
Clearly for the column vector x, x of any one 3 dimension×It is an antisymmetric matrix；For flexible spacecraft
Integrally-built moment of inertia matrix is rigid bodies inertia matrix JmbWith the summation of flexible appendage moment of inertia matrix, i.e. J=
Jmb+δTδ, wherein coupling matrix of the δ between flexible appendage and rigid bodies, to describe flexible appendage to the shadow of rigid bodies
It rings；η is that the flexible mode of flexible appendage is displaced；To act on the spaceborne outer controling force square of rigid body,For
Act on the external disturbance torque in main body；C, K are respectively the damping matrix and stiffness matrix of flexible spacecraft；Consider flexible boat
Its device has there are when N rank flexible mode
C=diag { 2 ξiωni, i=1 ..., N }
Wherein, ωni, i=1 ..., N are the vibration frequency of flexible spacecraft flexible mode, ξi, i=1 ..., N is flexibility
The damping ratio of mode.
As further improvement of the invention, in the processing module, the Dynamic sliding mode posture of flexible spacecraft is designed
The control law of tracing control:
Firstly, design switching function s=ωe+λqev, can be released as sliding-mode surface s=0Work as flexibility
System model can tend to Asymptotic Stability after spacecraft reaches sliding-mode surface；Redesign a new switching at runtime function
Wherein,
As σ=0,Asymptotically stable first-order dynamic system, when t tends to be infinite s=0 andIt is right
Switching at runtime function σ derivation is available
It enablesIt is then available
V is the true input of the first-order dynamic system, it can be seen that, will not be even if v is discontinuousPlane generation is trembled
Vibration；
As d=0, following control law is designed:
W=-k | | σ | |βsign(σ)
Wherein k > 0, β ∈ (0,1).Under the action of above-mentioned control law, spacecraft attitude quaternary number error qevAnd attitude angle
Velocity error ωeIt can level off to 0；
As d ≠ 0, following control law is designed:
W=-k | | σ | |βsign(σ),
wdis=-l1ζ-l2sign(ζ),
Assuming that | | d | | andEqual bounded, andIn the work of above-mentioned control law
Under, spacecraft attitude quaternary number error qevWith attitude angular velocity error ωeIt can level off to 0.
As further improvement of the invention, in the processing module, the robust for designing a finite time convergence control is micro-
Device is divided to estimate the partial status of flexible spacecraft system:
Wherein, γ1> γ2> 0, andBe respectively A (ω, q, ψ, η) andIn real time estimate
Evaluation.
The beneficial effects of the present invention are: the present invention effectively inhibits traditional sliding formwork control ratio to accord with by the design of switching function
The problem of being buffeted caused by number function, the method for Dynamic sliding mode Attitude tracking control can make Space Vehicle System carry out posture with
Track.
Detailed description of the invention
Fig. 1 is flow chart of the method for the present invention.
Specific embodiment
As shown in Figure 1, the invention discloses a kind of methods of the Dynamic sliding mode Attitude tracking control of flexible spacecraft, including
Following steps:
Step S1: kinematical equation and kinetics equation of the flexible spacecraft based on error attitude quaternion are established；
Step S2: by introducing switching at runtime function, the Dynamic sliding mode appearance of Flexible Spacecraft tracking problem is devised
State tracing control rule, and devise the robust differentiator an of finite time convergence control to the partial status of flexible spacecraft system into
Row estimation.
In step sl, it is based on attitude quaternion, kinematical equation and the kinetics equation for establishing flexible spacecraft are as follows:
Wherein, q be spacecraft body coordinate system under unit attitude quaternion, i.e., | | q | |=1 orq0
For the scalar component of q, qvFor the vector portion of q, and qv=[q1 q2 q3]T；For spacecraft ontology seat
Attitude angular velocity under mark system；Matrix T (q0,qv) be
Wherein, I3For 3 × 3 unit matrix；For arbitraryX × expression:
Clearly for the column vector x, x of any one 3 dimension×It is an antisymmetric matrix；For flexible spacecraft
Integrally-built moment of inertia matrix is rigid bodies inertia matrix JmbWith the summation of flexible appendage moment of inertia matrix, i.e. J=
Jmb+δTδ, wherein coupling matrix of the δ between flexible appendage and rigid bodies, to describe flexible appendage to the shadow of rigid bodies
It rings；η is that the flexible mode of flexible appendage is displaced；To act on the spaceborne outer controling force square of rigid body,
For the external disturbance torque acted in main body；C, K are respectively the damping matrix and stiffness matrix of flexible spacecraft.Consider flexible
Spacecraft has there are when N rank flexible mode
C=diag { 2 ξiωni, i=1 ..., N }
Wherein, ωni, i=1 ..., N are the vibration frequency of flexible spacecraft flexible mode, ξi, i=1 ..., N is flexibility
The damping ratio of mode.
In step s 2, the control law of the Dynamic sliding mode Attitude tracking control of flexible spacecraft is designed:
Wherein, λ, k, β, α > 0, γ1> γ2> 0.
Firstly, design switching function s=ωe+λqev, can be released as sliding-mode surface s=0Work as flexibility
System model can tend to Asymptotic Stability after spacecraft reaches sliding-mode surface.Redesign a new switching at runtime function:
Wherein,
As σ=0,Asymptotically stable first-order dynamic system, when t tends to be infinite s=0 andIt is right
Switching at runtime function σ derivation is available
It enablesIt is then available
V is the true input of the first-order dynamic system.It, will not be even if can be seen that v is discontinuousPlane generation is trembled
Vibration.
1. when d=0, designing following control law:
W=-k | | σ | |βsign(σ)
Wherein k > 0, β ∈ (0,1).Under the action of above-mentioned control law, spacecraft attitude quaternary number error qevAnd attitude angle
Velocity error ωeIt can level off to 0；
2. when d ≠ 0, designing following control law:
W=-k | | σ | |βsign(σ),
wdis=-l1ζ-l2sign(ζ),
Assuming that | | d | | andEqual bounded, andIn the work of above-mentioned control law
Under, spacecraft attitude quaternary number error qevWith attitude angular velocity error ωeIt can level off to 0.
In step sl, error motion equation and kinetics equation of the flexible spacecraft based on attitude quaternion are established such as
Under:
Define Attitude Tracking errorqev=[qe1 qe2 qe3]TIt is from ontology reference frame to expectation
The opposite quaternary number error of referential, andqdv=[qd1,qd2,qd3]TIt is to be scratched with what unit quaternion described
The expectation posture of property spacecraft；According to the calculation formula of quaternary number it follows that
Unit quaternion qdAnd qeIt is all satisfied | | qdv| |=1 He | | qev| |=1, then desired attitude motion can indicate
Are as follows:
WhereinAndIt is target angular velocity；It is expected that coordinate system
Spin matrix corresponding between fixed coordinate system can be represented as with ontologyAnd meetInertia angle speed
Degree uses ωdIt indicates, then the kinematics of relative attitude tracking and kinetics equation can indicate are as follows:
In step s 2, the method for the Dynamic sliding mode Attitude tracking control of flexible spacecraft is established:
Step 201 is directed to the SYSTEM ERROR MODEL (3) of flexible spacecraft, designs following switching at runtime function:
S=ωe+λqev (4)
Assuming that flexible spacecraft reaches sliding-mode surface s=0, it is defined as follows Lyapunov function:
V0(t)=2 (1-qe0)≥0
To above-mentioned Lyapunov function seeking time derivative, can obtain:
Therefore, haveIt sets up；
Step 202 designs a new switching at runtime function:
Assuming that flexible spacecraft reaches new sliding-mode surface σ=0:
1. when d=0, being defined as follows Lyapunov function:
To above-mentioned Lyapunov function seeking time derivative, and the control law as designed by equation (2) can obtain:
Wherein k > 0, β ∈ (0,1).Under the action of above-mentioned control law, as d=0, it can be obtained by equation (4) and (5), it is sliding
Die face σ, s can converge on 0, then spacecraft attitude quaternary number error qevWith attitude angular velocity error ωeIt can also level off to 0.；
2. when d ≠ 0, the integral switching function that is defined as follows:
It is defined as follows Lyapunov function:
To above-mentioned Lyapunov function seeking time derivative, and the control law as designed by equation (2) can obtain:
It is availableIt can be obtained by equation (6)
Step 203 is defined as follows Lyapunov function:
Above-mentioned Lyapunov function seeking time derivative can be obtained:
Under the action of above-mentioned control law, as d ≠ 0, it can be obtained by equation (4) and (5), sliding-mode surface σ, s can converge on 0,
Then spacecraft attitude quaternary number error qevWith attitude angular velocity error ωeIt can also level off to 0.
Therefore, have known to the result of Step 202 and Step 203
Step S2 further include: part shape of the robust differentiator of one finite time convergence control of design to flexible spacecraft system
State is estimated:
In fact, in control law (2)It hardly results in, therefore devises following finite time convergence control
Robust differentiator its estimated:
Wherein, γ1> γ2> 0, andBe respectively A (ω, q, ψ, η) andIn real time estimate
Evaluation.
To sum up, the method for the Dynamic sliding mode Attitude tracking control of flexible spacecraft of the invention, specifically includes as follows:
Firstly, it is as follows to establish kinematical equation and kinetics equation of the rigid body spacecraft based on attitude quaternion:
It is as follows to establish kinematical equation and kinetics equation of the flexible spacecraft based on attitude quaternion:
Define Attitude Tracking errorqev=[qe1qe2qe3]TIt is to join from ontology reference frame to expectation
The opposite quaternary number error for being is examined, andqdv=[qd1,qd2,qd3]TIt is the flexibility described with unit quaternion
The expectation posture of spacecraft；According to the calculation formula of quaternary number it follows that
Unit quaternion qdAnd qeIt is all satisfied | | qdv| |=1 He | | qev| |=1, then desired attitude motion can indicate
Are as follows:
WhereinAndIt is target angular velocity；It is expected that coordinate system
Spin matrix corresponding between fixed coordinate system can be represented as with ontologyAnd meetInertia angle speed
Degree uses ωdIt indicates, then the error motion of relative attitude tracking and kinetics equation can indicate are as follows:
Wherein, I3For 3 × 3 unit matrix；For arbitraryx×It indicates:
Clearly for the column vector x, x of any one 3 dimension×It is an antisymmetric matrix；For flexible spacecraft
Integrally-built moment of inertia matrix is rigid bodies inertia matrix JmbWith the summation of flexible appendage moment of inertia matrix, i.e. J=
Jmb+δTδ, wherein coupling matrix of the δ between flexible appendage and rigid bodies, to describe flexible appendage to the shadow of rigid bodies
It rings；η is that the flexible mode of flexible appendage is displaced；To act on the spaceborne outer controling force square of rigid body,For
Act on the external disturbance torque in main body；C, K are respectively the damping matrix and stiffness matrix of flexible spacecraft.Consider flexible boat
Its device has there are when N rank flexible mode
C=diag { 2 ξiωni, i=1 ..., N }
Wherein, ωni, i=1 ..., N are the vibration frequency of flexible spacecraft flexible mode, ξi, i=1 ..., N is flexibility
The damping ratio of mode.Next, establishing the Dynamic sliding mode Attitude tracking control algorithm of flexible spacecraft (7).
Step 1 is firstly, design switching function s=ωe+λqev, can be released as sliding-mode surface s=0I.e.
System model can tend to Asymptotic Stability after flexible spacecraft reaches sliding-mode surface.Redesign a new switching at runtime function
Wherein,
As σ=0,Asymptotically stable first-order dynamic system, when t tends to be infinite s=0 andIt is right
Switching at runtime function σ derivation is available
It enablesIt is then available
V is the true input of the first-order dynamic system.It, will not be even if can be seen that v is discontinuousPlane generation is trembled
Vibration.
Step 2 1. d=0 when, design following control law:
W=-k | | σ | |βsign(σ)
Wherein k > 0, β ∈ (0,1).Under the action of above-mentioned control law, spacecraft attitude quaternary number error qevAnd attitude angle
Velocity error ωeIt can level off to 0；
2. when d ≠ 0, designing following control law:
W=-k | | σ | |βsign(σ),
wdis=-l1ζ-l2sign(ζ),
Assuming that | | d | | andEqual bounded, andIn the work of above-mentioned control law
Under, spacecraft attitude quaternary number error qevWith attitude angular velocity error ωeIt can level off to 0.
The robust differentiator that Step 3 designs a finite time convergence control carries out the partial status of flexible spacecraft system
Estimation:
In fact, in control law (2)It hardly results in, therefore devises following finite time convergence control
Robust differentiator its estimated:
Wherein, γ1> γ2> 0, andBe respectively A (ω, q, ψ, η) andIn real time estimate
Evaluation.
The present invention will illustrate the control effect of Dynamic sliding mode Attitude tracking control algorithm by example below.Consider that band is flexible
The rotary inertia J of attachment spacecraft are as follows:
Coupling matrix between the rigid bodies and flexible appendage of flexible spacecraft is
Consider that flexible spacecraft has the case where quadravalence mode, natural frequency (rad/s) are as follows:
ωn1=0.7400, ωn2=0.7500,
ωn3=0.7600, ωn4=0.7600
Corresponding damping are as follows:
ξ1=0.004, ξ2=0.005,
ξ3=0.0064, ξ4=0.008.
In simulations, initial angular speed are as follows:
ω (0)=[0 0 0]Trad/s.
Desired angular speed are as follows:
ωd=[0 0 0]Trad/s.
Initial attitude quaternion are as follows:
Desired attitude quaternion are as follows:
qd=[1,0,0,0]T.
Define the initial value of flexible spacecraft flexible mode variable are as follows:
ηi(0)=0, ψi(0)=0, i=1,2,3,4.
Following parameter is used to the dynamic sliding mode control rule (2) proposed:
λ=0.9, k=0.9, β=0.3,
α=0.2, γ1=5.5, γ2=0.25
A kind of method and system of the Dynamic sliding mode Attitude tracking control of flexible spacecraft disclosed by the invention are to disappear
Except the buffeting that there are problems that and generate in traditional sliding formwork control due to symbol item.The purpose of the invention is to solve flexible space flight
Device Attitude tracking control problem.The kinematics side that the invention indicates Flexible Spacecraft error using attitude quaternion method
Journey establishes the error dynamics equation of flexible spacecraft；By designing switching at runtime function, and Lyapunov direct method is combined,
Gradually have devised Dynamic sliding mode Attitude tracking control method.Finally, being designed with the simulink module verification in MATLAB
Control algolithm validity.
The present invention effectively inhibits buffeting caused by traditional sliding formwork control ratio sign function by the design of switching function
Problem, the method for Dynamic sliding mode Attitude tracking control can make Space Vehicle System carry out Attitude Tracking.
The present invention is solved and is trembled as caused by signal function in traditional sliding formwork control ratio by design switching at runtime function
Vibration problem, simulation result show that proposed Dynamic sliding mode Attitude tracking control rule can effectively inhibit to buffet, have preferable control
Effect processed.
The above content is a further detailed description of the present invention in conjunction with specific preferred embodiments, and it cannot be said that
Specific implementation of the invention is only limited to these instructions.For those of ordinary skill in the art to which the present invention belongs, exist
Under the premise of not departing from present inventive concept, a number of simple deductions or replacements can also be made, all shall be regarded as belonging to of the invention
Protection scope.
Claims (10)
1. a kind of method of the Dynamic sliding mode Attitude tracking control of flexible spacecraft, which comprises the steps of:
Step S1: kinematical equation and kinetics equation of the flexible spacecraft based on error attitude quaternion are established；
Step S2: by introducing switching at runtime function, devise the Dynamic sliding mode posture of Flexible Spacecraft tracking problem with
Track control law, and the robust differentiator for devising a finite time convergence control estimates the partial status of flexible spacecraft system
Meter.
2. foundation is scratched the method according to claim 1, wherein in the step S1, being based on attitude quaternion
The kinematical equation and kinetics equation of property spacecraft are as follows:
Wherein, q be spacecraft body coordinate system under unit attitude quaternion, i.e., | | q | |=1 orq0For q's
Scalar component, qvFor the vector portion of q, and qv=[q1 q2 q3]T；For spacecraft body coordinate system
Under attitude angular velocity；Matrix T (q0,qv) be
Wherein, I3For 3 × 3 unit matrix；For arbitraryx×It indicates:
Clearly for the column vector x, x of any one 3 dimension×It is an antisymmetric matrix；For flexible spacecraft entirety
The moment of inertia matrix of structure is rigid bodies inertia matrix JmbWith the summation of flexible appendage moment of inertia matrix, i.e. J=Jmb+
δTδ, wherein coupling matrix of the δ between flexible appendage and rigid bodies, to describe influence of the flexible appendage to rigid bodies；
η is that the flexible mode of flexible appendage is displaced；To act on the spaceborne outer controling force square of rigid body,To make
With the external disturbance torque in main body；C, K are respectively the damping matrix and stiffness matrix of flexible spacecraft；Consider flexible space flight
Device has there are when N rank flexible mode
C=diag { 2 ξiωni, i=1 ..., N }
Wherein, ωni, i=1 ..., N are the vibration frequency of flexible spacecraft flexible mode, ξi, i=1 ..., N is flexible mode
Damping ratio.
3. according to right want 1 described in method, which is characterized in that in the step S1, establish flexible spacecraft be based on posture
The error motion equation and kinetics equation of quaternary number are as follows:
Define Attitude Tracking errorqev=[qe1 qe2 qe3]TIt is to be referred to from ontology reference frame to expectation
The opposite quaternary number error of system, andqdv=[qd1,qd2,qd3]TIt is the flexible boat described with unit quaternion
The expectation posture of its device；According to the calculation formula of quaternary number it follows that
Unit quaternion qdAnd qeIt is all satisfied | | qdv| |=1 He | | qev| |=1, then desired attitude motion can indicate are as follows:
WhereinAndIt is target angular velocity；It is expected that coordinate system and sheet
Corresponding spin matrix can be represented as between the fixed coordinate system of bodyAnd meetInertia angular speed
Use ωdIt indicates, then the kinematics of relative attitude tracking and kinetics equation can indicate are as follows:
Wherein, I3For 3 × 3 unit matrix；For arbitraryx×It indicates:
Clearly for the column vector x, x of any one 3 dimension×It is an antisymmetric matrix；It is integrally tied for flexible spacecraft
The moment of inertia matrix of structure is rigid bodies inertia matrix JmbWith the summation of flexible appendage moment of inertia matrix, i.e. J=Jmb+δT
δ, wherein coupling matrix of the δ between flexible appendage and rigid bodies, to describe influence of the flexible appendage to rigid bodies；η
It is displaced for the flexible mode of flexible appendage；To act on the spaceborne outer controling force square of rigid body,For effect
External disturbance torque in main body；C, K are respectively the damping matrix and stiffness matrix of flexible spacecraft；Consider flexible spacecraft
There are when N rank flexible mode, have
C=diag { 2 ξiωni, i=1 ..., N }
Wherein, ωni, i=1 ..., N are the vibration frequency of flexible spacecraft flexible mode, ξi, i=1 ..., N is flexible mode
Damping ratio.
4. wanting 1 to 3 described in any item methods according to right, which is characterized in that in the step S2, design flexible spacecraft
Dynamic sliding mode Attitude tracking control control law:
Firstly, design switching function s=ωe+λqev, can be released as sliding-mode surface s=0Work as flexible spacecraft
System model can tend to Asymptotic Stability after reaching sliding-mode surface；Redesign a new switching at runtime function
Wherein,
As σ=0,Asymptotically stable first-order dynamic system, when t tends to be infinite s=0 andTo dynamic
Switching function σ derivation is available
It enablesIt is then available
V is the true input of the first-order dynamic system, it can be seen that, will not be even if v is discontinuousPlane generates buffeting；
As d=0, following control law is designed:
W=-k | | σ | |βsign(σ)
Wherein k > 0, β ∈ (0,1).Under the action of above-mentioned control law, spacecraft attitude quaternary number error qevAnd attitude angular velocity
Error ωeIt can level off to 0；
As d ≠ 0, following control law is designed:
W=-k | | σ | |βsign(σ),
wdis=-l1ζ-l2sign(ζ),
Assuming that | | d | | andEqual bounded, andUnder the action of above-mentioned control law,
Spacecraft attitude quaternary number error qevWith attitude angular velocity error ωeIt can level off to 0.
5. according to right want 4 described in method, which is characterized in that in the step S2, design a finite time convergence control
Robust differentiator estimates the partial status of flexible spacecraft system:
Wherein, γ1> γ2> 0, andBe respectively A (ω, q, ψ, η) andReal-time estimation value.
6. a kind of system of the Dynamic sliding mode Attitude tracking control of flexible spacecraft characterized by comprising establish equation mould
Block: for establishing kinematical equation and kinetics equation of the flexible spacecraft based on error attitude quaternion；
Processing module: for devising the Dynamic sliding mode of Flexible Spacecraft tracking problem by introducing switching at runtime function
Attitude tracking control rule, and devise the partial status of the robust differentiator to flexible spacecraft system an of finite time convergence control
Estimated.
7. system according to claim 6, which is characterized in that it is established in equation module described, is based on attitude quaternion,
Kinematical equation and the kinetics equation for establishing flexible spacecraft are as follows:
Wherein, q be spacecraft body coordinate system under unit attitude quaternion, i.e., | | q | |=1 orq0For q's
Scalar component, qvFor the vector portion of q, and qv=[q1 q2 q3]T；For spacecraft body coordinate system
Under attitude angular velocity；Matrix T (q0,qv) be
Wherein, I3For 3 × 3 unit matrix；For arbitraryx×It indicates:
Clearly for the column vector x, x of any one 3 dimension×It is an antisymmetric matrix；For flexible spacecraft entirety
The moment of inertia matrix of structure is rigid bodies inertia matrix JmbWith the summation of flexible appendage moment of inertia matrix, i.e. J=Jmb+
δTδ, wherein coupling matrix of the δ between flexible appendage and rigid bodies, to describe influence of the flexible appendage to rigid bodies；
η is that the flexible mode of flexible appendage is displaced；To act on the spaceborne outer controling force square of rigid body,To make
With the external disturbance torque in main body；C, K are respectively the damping matrix and stiffness matrix of flexible spacecraft；Consider flexible space flight
Device has there are when N rank flexible mode
C=diag { 2 ξiωni, i=1 ..., N }
Wherein, ωni, i=1 ..., N are the vibration frequency of flexible spacecraft flexible mode, ξi, i=1 ..., N is flexible mode
Damping ratio.
8. according to right want 6 described in system, which is characterized in that established in equation module described, establish flexible spacecraft base
It is as follows in the error motion equation and kinetics equation of attitude quaternion:
Define Attitude Tracking errorqev=[qe1 qe2 qe3]TIt is to be referred to from ontology reference frame to expectation
The opposite quaternary number error of system, andqdv=[qd1,qd2,qd3]TIt is the flexible boat described with unit quaternion
The expectation posture of its device；According to the calculation formula of quaternary number it follows that
Unit quaternion qdAnd qeIt is all satisfied | | qdv| |=1 He | | qev| |=1, then desired attitude motion can indicate are as follows:
WhereinAndIt is target angular velocity；It is expected that coordinate system and sheet
Corresponding spin matrix can be represented as between the fixed coordinate system of bodyAnd meetInertia angle speed
Degree uses ωdIt indicates, then the kinematics of relative attitude tracking and kinetics equation can indicate are as follows:
Wherein, I3For 3 × 3 unit matrix；For arbitraryx×It indicates:
Clearly for the column vector x, x of any one 3 dimension×It is an antisymmetric matrix；For flexible spacecraft entirety
The moment of inertia matrix of structure is rigid bodies inertia matrix JmbWith the summation of flexible appendage moment of inertia matrix, i.e. J=Jmb+
δTδ, wherein coupling matrix of the δ between flexible appendage and rigid bodies, to describe influence of the flexible appendage to rigid bodies；
η is that the flexible mode of flexible appendage is displaced；To act on the spaceborne outer controling force square of rigid body,To make
With the external disturbance torque in main body；C, K are respectively the damping matrix and stiffness matrix of flexible spacecraft；Consider flexible space flight
Device has there are when N rank flexible mode
C=diag { 2 ξiωni, i=1 ..., N }
Wherein, ωni, i=1 ..., N are the vibration frequency of flexible spacecraft flexible mode, ξi, i=1 ..., N is flexible mode
Damping ratio.
9. wanting 6 to 8 described in any item systems according to right, which is characterized in that in the processing module, design flexible space flight
The control law of the Dynamic sliding mode Attitude tracking control of device:
Firstly, design switching function s=ωe+λqev, can be released as sliding-mode surface s=0Work as flexible spacecraft
System model can tend to Asymptotic Stability after reaching sliding-mode surface；Redesign a new switching at runtime function
Wherein,
As σ=0,Asymptotically stable first-order dynamic system, when t tends to be infinite s=0 andTo dynamic
Switching function σ derivation is available
It enablesIt is then available
V is the true input of the first-order dynamic system, it can be seen that, will not be even if v is discontinuousPlane generates buffeting；
As d=0, following control law is designed:
W=-k | | σ | |βsign(σ)
Wherein k > 0, β ∈ (0,1).Under the action of above-mentioned control law, spacecraft attitude quaternary number error qevAnd attitude angular velocity
Error ωeIt can level off to 0；
As d ≠ 0, following control law is designed:
W=-k | | σ | |βsign(σ),
wdis=-l1ζ-l2sign(ζ),
Assuming that | | d | | andEqual bounded, andUnder the action of above-mentioned control law,
Spacecraft attitude quaternary number error qevWith attitude angular velocity error ωeIt can level off to 0.
10. according to right want 9 described in system, which is characterized in that in the processing module, design a finite time convergence control
Robust differentiator the partial status of flexible spacecraft system is estimated:
Wherein, γ1> γ2> 0, andBe respectively A (ω, q, ψ, η) andReal-time estimation value.
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Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110844122A (en) * | 2019-11-20 | 2020-02-28 | 中山大学 | Satellite attitude control method for restraining attitude tracking error |
| CN111413995A (en) * | 2020-03-24 | 2020-07-14 | 北京科技大学 | Method and system for tracking relative position and synchronously controlling posture between double rigid body characteristic points |
| CN111498147A (en) * | 2020-04-03 | 2020-08-07 | 哈尔滨工业大学(深圳)(哈尔滨工业大学深圳科技创新研究院) | Finite time segmentation sliding mode attitude tracking control algorithm of flexible spacecraft |
| CN111874266A (en) * | 2020-03-27 | 2020-11-03 | 哈尔滨工业大学(深圳)(哈尔滨工业大学深圳科技创新研究院) | Unwinding-resistant sliding mode attitude maneuver control method and system of rigid spacecraft |
| CN113697131A (en) * | 2021-08-27 | 2021-11-26 | 哈尔滨工业大学（深圳） | Unwinding-resistant sliding mode attitude tracking control method and system for rigid spacecraft |
| CN113859589A (en) * | 2021-10-18 | 2021-12-31 | 南京工业大学 | Spacecraft attitude control method based on model predictive control and sliding mode control |
| CN113885547A (en) * | 2021-10-20 | 2022-01-04 | 河北工业大学 | Fault-tolerant attitude control strategy for rigid spacecraft in preset time |
| CN114229039A (en) * | 2021-12-14 | 2022-03-25 | 内蒙古工业大学 | Self-adaptive non-angular-velocity compound control method for liquid-filled flexible spacecraft |
| CN115685761A (en) * | 2022-11-10 | 2023-02-03 | 哈尔滨工业大学 | Flexible spacecraft preset performance attitude control method, computer equipment and storage medium |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101708780A (en) * | 2009-11-26 | 2010-05-19 | 哈尔滨工业大学 | Method for controlling rigid spacecraft for target attitude tracking |
| CN107065913A (en) * | 2017-05-10 | 2017-08-18 | 哈尔滨工业大学深圳研究生院 | The sliding moding structure gesture stability algorithm of Spacecraft |
| CN109213184A (en) * | 2018-11-06 | 2019-01-15 | 哈尔滨工业大学（深圳） | The multi-modal Sliding Mode Attitude control algolithm of the finite time of flexible spacecraft |
-
2019
- 2019-04-30 CN CN201910364543.4A patent/CN110083171A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101708780A (en) * | 2009-11-26 | 2010-05-19 | 哈尔滨工业大学 | Method for controlling rigid spacecraft for target attitude tracking |
| CN107065913A (en) * | 2017-05-10 | 2017-08-18 | 哈尔滨工业大学深圳研究生院 | The sliding moding structure gesture stability algorithm of Spacecraft |
| CN109213184A (en) * | 2018-11-06 | 2019-01-15 | 哈尔滨工业大学（深圳） | The multi-modal Sliding Mode Attitude control algolithm of the finite time of flexible spacecraft |
Non-Patent Citations (2)
| Title |
|---|
| 朱庆华等: "基于动态滑模控制的挠性航天器姿态控制", 《控制理论与应用》 * |
| 荆武兴等: "喷嘴为执行机构的空间飞行器基于误差四元数的非线性姿态跟踪控制", 《CHINESE JOURNAL OF AERONAUTICS》 * |
Cited By (13)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
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| CN110844122B (en) * | 2019-11-20 | 2022-08-16 | 中山大学 | Satellite attitude control method for restraining attitude tracking error |
| CN111413995A (en) * | 2020-03-24 | 2020-07-14 | 北京科技大学 | Method and system for tracking relative position and synchronously controlling posture between double rigid body characteristic points |
| CN111874266A (en) * | 2020-03-27 | 2020-11-03 | 哈尔滨工业大学(深圳)(哈尔滨工业大学深圳科技创新研究院) | Unwinding-resistant sliding mode attitude maneuver control method and system of rigid spacecraft |
| CN111498147B (en) * | 2020-04-03 | 2021-09-21 | 哈尔滨工业大学(深圳)(哈尔滨工业大学深圳科技创新研究院) | Finite time segmentation sliding mode attitude tracking control algorithm of flexible spacecraft |
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| CN113859589B (en) * | 2021-10-18 | 2023-05-30 | 南京工业大学 | Spacecraft attitude control method based on model predictive control and sliding mode control |
| CN113885547A (en) * | 2021-10-20 | 2022-01-04 | 河北工业大学 | Fault-tolerant attitude control strategy for rigid spacecraft in preset time |
| CN114229039A (en) * | 2021-12-14 | 2022-03-25 | 内蒙古工业大学 | Self-adaptive non-angular-velocity compound control method for liquid-filled flexible spacecraft |
| CN114229039B (en) * | 2021-12-14 | 2023-09-15 | 内蒙古工业大学 | Self-adaptive non-angular velocity composite control method for liquid-filled flexible spacecraft |
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