CN108628165A - Rotary inertia time-varying spacecraft is against optimal Adaptive Attitude Tracking control method - Google Patents
Rotary inertia time-varying spacecraft is against optimal Adaptive Attitude Tracking control method Download PDFInfo
- Publication number
- CN108628165A CN108628165A CN201810429961.2A CN201810429961A CN108628165A CN 108628165 A CN108628165 A CN 108628165A CN 201810429961 A CN201810429961 A CN 201810429961A CN 108628165 A CN108628165 A CN 108628165A
- Authority
- CN
- China
- Prior art keywords
- formula
- attitude
- spacecraft
- varying
- matrix
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 230000003044 adaptive effect Effects 0.000 title claims abstract description 61
- 238000000034 method Methods 0.000 title claims abstract description 53
- 239000011159 matrix material Substances 0.000 claims abstract description 116
- 239000013598 vector Substances 0.000 claims abstract description 79
- 238000013461 design Methods 0.000 claims abstract description 17
- 238000012417 linear regression Methods 0.000 claims abstract description 15
- 238000005457 optimization Methods 0.000 claims abstract description 15
- 238000013178 mathematical model Methods 0.000 claims description 33
- 230000009017 pursuit movement Effects 0.000 claims description 23
- 230000033001 locomotion Effects 0.000 claims description 18
- 238000000205 computational method Methods 0.000 claims description 12
- 230000015572 biosynthetic process Effects 0.000 claims description 5
- 238000005755 formation reaction Methods 0.000 claims description 5
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 claims description 4
- 230000017105 transposition Effects 0.000 claims description 3
- 238000010586 diagram Methods 0.000 description 8
- 238000005516 engineering process Methods 0.000 description 5
- RZVHIXYEVGDQDX-UHFFFAOYSA-N 9,10-anthraquinone Chemical compound C1=CC=C2C(=O)C3=CC=CC=C3C(=O)C2=C1 RZVHIXYEVGDQDX-UHFFFAOYSA-N 0.000 description 2
- 230000008859 change Effects 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 244000290594 Ficus sycomorus Species 0.000 description 1
- 244000131316 Panax pseudoginseng Species 0.000 description 1
- 235000005035 Panax pseudoginseng ssp. pseudoginseng Nutrition 0.000 description 1
- 235000003140 Panax quinquefolius Nutrition 0.000 description 1
- 230000009471 action Effects 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000008901 benefit Effects 0.000 description 1
- 238000004364 calculation method Methods 0.000 description 1
- 239000002131 composite material Substances 0.000 description 1
- 238000013016 damping Methods 0.000 description 1
- 230000007812 deficiency Effects 0.000 description 1
- 235000013399 edible fruits Nutrition 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 239000000446 fuel Substances 0.000 description 1
- 235000008434 ginseng Nutrition 0.000 description 1
- 230000001771 impaired effect Effects 0.000 description 1
- 230000002401 inhibitory effect Effects 0.000 description 1
- 238000005259 measurement Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 230000006641 stabilisation Effects 0.000 description 1
- 238000011105 stabilization Methods 0.000 description 1
- 238000012546 transfer Methods 0.000 description 1
Classifications
-
- 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
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B64—AIRCRAFT; AVIATION; COSMONAUTICS
- B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
- B64G1/00—Cosmonautic vehicles
- B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
- B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
- B64G1/244—Spacecraft control systems
Abstract
The invention discloses a kind of rotary inertia time-varying spacecrafts against optimal Adaptive Attitude Tracking control method, includes the following steps：Step S100：Input instruction posture；Step S200：Attitude error amount between computations posture and practical posture；Step S300：Linear regression matrix F is calculated according to attitude error amount1、F2、F3、G1、G2And G3；Step S400：According to the linear regression matrix F1、F2、F3、G1、G2And G3The estimated value of unknown parameter vector ξ, θ, η are calculated in real timeAccording to the estimated valueThe inverse adaptive control optimization of design is restrained；Controlled spacecraft is controlled against adaptive control optimization rule using this.This method control Space Vehicle System can and consecutive variations unknown in rotary inertia under conditions of, high precision tracking instructs posture, compared to traditional Adaptive Attitude control method, with wider array of adaptability, vulnerability to jamming and strong robustness, effective scheme is provided for the Project Realization of Attitude tracking control.
Description
Technical field
The present invention relates to a kind of rotary inertia time-varying spacecrafts against optimal Adaptive Attitude Tracking control method, belongs to automatic
Control technology field.
Background technology
Spacecraft in orbit when, in order to complete its undertaken task, it is necessary to ensure that its ontology is in space with respect to some
Reference frame has desired direction.Spacecraft Attitude Control is exactly the skill for controlling the ontology of spacecraft and being directed toward in space
Art, including two aspects of attitude maneuver and Attitude Tracking.Attitude maneuver is that spacecraft attitude is adjusted to scheduled instruction posture
Direction, spacecraft attitude is kept constant in space after Spacecraft Attitude Control stabilization.And Attitude Tracking then requires spacecraft
The instruction posture of variation is continuously tracked in posture, and the attitude motion track of spacecraft is protected with instruction attitude motion track after control is stablized
It holds consistent.Many space tasks are required for spacecraft to have remote sensing satellite in Attitude Tracking ability, such as earth observation task
Camera needs to be directed at ground, and the infrared detector needs of early warning satellite will be directed at guided missile on the move in missile warning task.
The Attitude Tracking movement of spacecraft has the characteristics that non-linear, interference is complicated, uncertain, therefore, Attitude Tracking control
System has become the difficult point of Spacecraft Control.The existing research for spacecraft attitude tracing control is all based on greatly rigid model, i.e.,
Assuming that spacecraft is integrally rigid, when not considering in orbit spacecraft rotary inertia can because the consumption or transfer of fuel,
The former resulting non-rigid change such as solar energy sailboard expansion, robotic arm manipulation.Self-adaptation control method is to controlled device
Parameter Perturbation has robustness, and a kind of effective means is provided for spacecraft attitude tracing control.But traditional adaptive appearance
The perturbation of the rotary inertia of spacecraft is only thought of as unknown constant by state tracking and controlling method, and without inhibiting external disturbance to boat
The influence of its device posture.Existing Adaptive Attitude Tracking control method is only capable of making that relatively simple for structure, external disturbance torque is smaller
The effective trace command posture of spacecraft, can not be suitable for rotary inertia consecutive variations the case where, limit self adaptive control side
Method is in large complicated spaceborne application.
Invention content
A kind of parameter time varying spacecraft is provided according to an aspect of the present invention against optimal Adaptive Attitude Tracking controlling party
Method.This method is on the basis of self-adaptation control method, for Large Spacecraft rotary inertia consecutive variations and by external disturbance
Notable problem will be done in conjunction with the inverse adaptive control optimization scheme of nonlinear dampling Technology design by adjusting control parameter
Influence of the torque to Attitude Tracking precision is disturbed to be impaired in arbitrarily small range.
Include the following steps：
Step S100：Input instruction posture (Rd,ωd)；
Step S200：Calculate the attitude error amount between described instruction posture and practical posture；
Step S300：Construct linear regression matrix F1、F2、F3、G1、G2And G3, and institute is calculated according to the attitude error amount
State linear regression matrix F1、F2、F3、G1、G2And G3；
Step S400：According to the linear regression matrix F1、F2、F3、G1、G2And G3, real-time calculating unknown parameter vector ξ,
The estimated value of θ, ηAccording to the estimated valueThe inverse adaptive control optimization of design is restrained；
Step S500：Attitude tracking control amount is calculated according to the inverse adaptive control optimization rule, by the Attitude Tracking
Controlled quentity controlled variable inputs spacecraft to be controlled, and the attitude error angle of the practical posture for judging the spacecraft to be controlled and desired posture is
No satisfaction control requires, and the practical posture of controlled spacecraft is measured if being unsatisfactory for and is returned in the step S200；
Step S600：Step S200~S500 is repeated until the practical posture of the spacecraft to be controlled meets the control
It is required that.
Preferably, instruction posture is the instruction posture that generalized coordinates indicates.
Optionally, attitude error amount includes：Direction of error cosine matrixWith error angular velocity vectorFormula is pressed respectively
(1)~(2) are calculated：
Wherein, RbFor the actual direction cosine matrix of 3 × 3 ranks, ωbFor actual angular speed vector, subscript T indicate vector or
The transposition of matrix.
Optionally, linear regression matrix F is calculated according to the attitude error amount1、F2、F3、G1、G2And G3The step of, including
Following steps：
Step S310：Attitude error vector S is calculated by formula (3)：
Wherein, a1、a2、a3For mutually different positive real number, e1、e2、e3Respectively e1=[1,0,0]T、e2=[0,1,0]T、
e3=[0,0,1]T；
Step S320：Attitude error Matrix C is calculated by formula (4)：
Wherein, matrix I is unit matrix, i.e.,
Step S330：Auxiliary variable z is calculated by formula (5)：
Wherein, K1For 3 × 3 rank positive definite symmetric matrices；
Step S340：According to the attitude error amountThe attitude error vector S, the attitude error square
Battle array C, the auxiliary variable z and spacecraft attitude motion mathematical model, establish the rotary inertia time-varying spacecraft attitude with
The mathematical model of track movement calculates regression matrix according to the mathematical model of the rotary inertia time-varying spacecraft attitude pursuit movement
F1、F2、F3、G1、G2And G3。
Preferably, the mathematical model step for establishing the rotary inertia time-varying spacecraft attitude pursuit movement, including
Following steps：
Step S341：Define the coordinate system and kinematic parameter of the spacecraft attitude pursuit movement：
Step S342：According to the coordinate system and kinematic parameter of the spacecraft attitude pursuit movement, obtain shown in formula (6)
The spacecraft attitude motion mathematical model：
In formula,Indicate RbFirst differential,Indicate ωbFirst differential, u=[u1,u2,u3]TTo act on space flight
Control moment vector on device, u1、u2、u3Respectively OCXbAxis, OCYbAxis, OCZbThe control moment of axis direction, d=[d1,d2,d3
]TTo act on the spaceborne disturbance torque vector, d1、d2、d3Respectively OCXbAxis, OCYbAxis, OCZbAxis direction is done
Torque is disturbed,
J (t)=J0-J1Ψ (t) is the moment of inertia matrix changed over time,Indicate the single order of J (t)
Differential,
Wherein, J0The rigidity parameters not changed over time in rotary inertia, J are indicated as shown in formula (8)1Such as formula (9) institute
Show the coefficient matrix for the nonrigid portions for indicating to be changed over time in rotary inertia,
Ψ (t) in J (t) is the known time-varying function matrix of rotary inertia nonrigid portions, is 3 × 3 rank square formations,
For the first differential of Ψ (t),It indicates to add time-varying parameter matrix caused by rotary inertia variation as shown in formula (10), is
3 × 3 rank square formations：
h0It indicates to add the constant coefficient diagonal matrix in time-varying parameter matrix as shown in formula (11),
Γ (t) is the known 3 dimension time-varying function vector in additional time-varying parameter matrix；
Step S343：According to the attitude error amount, the attitude error vector S, the attitude error Matrix C, described
The attitude motion mathematical model of auxiliary variable z and the spacecraft obtains the rotary inertia time-varying boat as shown in formula (14)
The mathematical model of its device Attitude Tracking movement：
In formula,For instruction angular speed vector ωdFirst differential.
Preferably, the regression matrix F1And G1Computational methods be：The rotary inertia time-varying spacecraft attitude is enabled to track
J in the mathematical model of movement1=h0=03×3, obtain formula (18)：
In formula,
If ξ=[J0(1,1),J0(1,2),J0(1,3),J0(2,2),J0(2,3),J0(3,3)]T, F is calculated by formula (19)1：
G is calculated by formula (20)1：
In formula, operatorPartial derivative of the bracket [] inner function about vectorial ξ is sought in expression.
Preferably, the regression matrix F2And G2Computational methods be：
Enable the J in the mathematical model of the rotary inertia time-varying spacecraft attitude pursuit movement0=h0=03×3：
If θ=[J1(1,1),J1(1,2),J1(1,3),J1(2,2),J1(2,3),J1(3,3)]T, F is calculated by formula (22)2：
G is calculated by formula (23)2：
In formula, operatorPartial derivative of the bracket [] inner function about vectorial θ is sought in expression.
Optionally, the regression matrix F3And G3Computational methods be：
Enable the J in the mathematical model of the rotary inertia time-varying spacecraft attitude pursuit movement0=J1=03×3：
If η=[h01,h02,h03]T, F is calculated by formula (25)3：
G is calculated by formula (26)3：
In formula, operatorPartial derivative of the bracket { } inner function about vectorial θ is sought in expression.
Preferably, the step S400 includes the following steps：
Step S410：The estimated value is calculated by formula (27)
In formula, γ1、γ2、γ3For the positive number more than zero, function Proj () is projection function, if p is 3 dimensions or 6 dimensions
Vector, ΞiBe also 3 dimension or 6 dimensional vectors, the then definition of Proj () be：
In formula, εi,δi＞ 0 is positive real number；
Step S420：According to the estimated valueDesign obtains inverse adaptive control optimization and restrains：
In formula, ueFor nonlinear dampling controlled quentity controlled variable, u is calculated by formula (30)e：
In formula, K is 3 × 3 rank positive definite symmetric matrices, K-1For the inverse matrix of K；β is the positive number more than 2；
Ψ is calculated by formula (31)1：
Ψ is calculated by formula (32)2：
In formula,γ is positive number, KpFor positive number；
According toThe method of calculating is：
According toIt calculates,It is calculated by formula (34)：
According toIt calculates,It is calculated by formula (35)：
Preferably, the known time-varying function Ψ (t) of rotary inertia nonrigid portions is calculated by formula (12)：
Ψ (t)=ρT(t)ρ(t)I-ρ(t)ρT(t) (12)
Wherein, ρ (t) is 3 dimension time-varying function vectors.ρ (t) herein is the parameter that designer is determined by related experiment.
Preferably, the known 3 dimension time-varying function vector Γ (t) added in time-varying parameter matrix is calculated by formula (13)：
Wherein,For the first differential of 3 dimension time-varying function vector ρ (t).
Beneficial effects of the present invention include but not limited to：
(1) rotary inertia time-varying spacecraft provided by the present invention is against optimal Adaptive Attitude Tracking control method, directly
Non-rigid kinetic model design based on spacecraft attitude pursuit movement, it is contemplated that every non-linear factor and rotary inertia
Consecutive variations act on, and overcome the limitation that rigid model is only suitable for small-sized simple spacecraft.
(2) rotary inertia time-varying spacecraft provided by the present invention is against optimal Adaptive Attitude Tracking control method, in conjunction with
The inverse adaptive control optimization scheme of nonlinear dampling Technology design can will inhibit disturbance torque pair by adjusting control parameter
The influence of Attitude Tracking precision.
(3) rotary inertia time-varying spacecraft provided by the present invention is against optimal Adaptive Attitude Tracking control method, directly
Using spin matrix as gesture feedback, continuous control moment can be integrated out, while avoiding posture appearance during control
Unstable unwinding phenomenon.
(4) rotary inertia time-varying spacecraft provided by the present invention, will be certainly against optimal Adaptive Attitude Tracking control method
Adaptive control method is combined with nonlinear dampling method, has been played respective advantage and has been compensated for mutual deficiency：It is adaptive
It answers control method that cannot compensate the problem of not modeling external disturbance to be made up by the natural robustness that nonlinear dampling controls, rather than
Model parameter needed for linear damping control method, then realize On-line Estimation by adaptive approach.
(5) rotary inertia time-varying spacecraft provided by the present invention overcomes against optimal Adaptive Attitude Tracking control method
Practical Space Vehicle System in orbit during the problem of rotary inertia is unknown and consecutive variations, have wider array of adaptability,
Vulnerability to jamming and strong robustness, the Project Realization for spacecraft attitude tracing control provide effective scheme.
Description of the drawings
Fig. 1 is rotary inertia time-varying spacecraft provided by the invention against optimal Adaptive Attitude Tracking control method step stream
Journey schematic diagram；
Fig. 2 is that rotary inertia time-varying spacecraft provided by the invention shows against optimal Adaptive Attitude Tracking Control system architecture
It is intended to；
Fig. 3 is that space vehicle coordinates system provided by the invention and kinematic parameter define schematic diagram；
Fig. 4 be in the preferred embodiment of the present invention smooth projection adaptive law to the rigidity that is not changed over time in rotary inertia
The estimated result schematic diagram of parameter；
Fig. 5 is that smooth projection adaptive law is non-rigid to what is changed over time in rotary inertia in the preferred embodiment of the present invention
The estimated result schematic diagram of part coefficient；
Fig. 6 is that smooth projection adaptive law estimates constant coefficient in additional time-varying parameter matrix in the preferred embodiment of the present invention
Count result schematic diagram；
Fig. 7 is spacecraft Attitude Tracking angle error control result schematic diagram in the preferred embodiment of the present invention；
Fig. 8 is spacecraft Attitude tracking control angular speed error result schematic diagram in the preferred embodiment of the present invention；
Marginal data：
ωdFor instruction angular speed vector；
RdFor command direction cosine matrix；
Rd(0) it is initial time command direction cosine matrix；
ωbFor actual angular speed vector；
RbFor actual direction cosine matrix；
For error angular velocity vector；
For direction of error cosine matrix；
S is attitude error vector；
C is attitude error matrix；
Z is auxiliary variable；
K1Parameter in order to control
F1、F2、F3、G1、G2And G3For six linear regression matrixes；
For the rigidity ginseng not changed over time in rotary inertia
Number vector；
For the nonrigid portions changed over time in rotary inertia
Coefficient vector；
To add the constant coefficient vector in time-varying parameter matrix；
U is to act on spaceborne control moment vector；
OeXeYeZeTo refer to inertial coodinate system；
OCXbYbZbFor body coordinate system；
ωbx、ωby、ωbzRespectively around OCXbAxis, OCYbAxis, OCZbAxis direction angular speed；
Φ (t) is attitude error angle, and computational methods are
For error angular speedNorm.
Specific implementation mode
In order to make the purpose of the present invention, technical solution and advantageous effect be more clearly understood, below in conjunction with the accompanying drawings and implement
Example, the present invention will be described in further detail.It should be noted that specific embodiment described herein is only explaining this hair
It is bright, it is not intended to limit the present invention.
Referring to Fig. 1, rotary inertia time-varying spacecraft provided by the invention is wrapped against optimal Adaptive Attitude Tracking control method
Include following steps：
Step S100：Input instruction posture (Rd,ωd)；
Preferably, described instruction posture is the instruction posture that generalized coordinates indicates.Instruction posture herein is generalized coordinates
Instruction posture (Rd,ωd), wherein：RdFor 3 × 3 rank command direction cosine matrixs；ωdFor instruction angular speed vector.
Step S200：Calculate the attitude error amount between described instruction posture and practical posture；
Practical posture herein refers to the real-time appearance made by controlled spacecraft after the instruction gesture stability for receiving input
State.Instruction posture refers to that user it is expected posture residing for controlled spacecraft.
Preferably, the attitude error amount between instruction posture and practical posture includes：Direction of error cosine matrixWith
Error angular velocity vectorIt is calculated by formula (1)~(2)：
Wherein, RbFor the actual direction cosine matrix of 3 × 3 ranks, ωbFor actual angular speed vector, subscript T indicate vector or
The transposition of matrix.
Step S300：It constructs and linear regression matrix F is calculated according to the attitude error amount1、F2、F3、G1、G2And G3；
Preferably, described that linear regression matrix F is calculated according to the attitude error amount1、F2、F3、G1、G2And G3Step, packet
Include following steps：
Step S310：Attitude error vector S is calculated by formula (3)：
Wherein, a1、a2、a3For mutually different positive real number, such as a in a particular embodiment1=1, a2=2, a3=3；e1、
e2、e3Respectively indicate 3 × 3 unit matrix I the 1st, 2,3 column vectors, i.e. e1=[1,0,0]T、e2=[0,1,0]T、e3=[0,0,
1]T。
Step S320：Attitude error Matrix C is calculated by formula (4)：
Wherein, matrix I is unit matrix, i.e.,
Step S330：Auxiliary variable z is calculated by formula (5)：
Wherein, K1For 3 × 3 rank positive definite symmetric matrices.
Step S340：According to the attitude error amount, the attitude error vector S, the attitude error Matrix C, described
The attitude motion mathematical model of auxiliary variable z and spacecraft establish the rotary inertia time-varying spacecraft attitude pursuit movement
Mathematical model calculates regression matrix F according to the mathematical model of the rotary inertia time-varying spacecraft attitude pursuit movement1、F2、F3、
G1、G2And G3。
Preferably, the mathematical model namely rotary inertia time-varying of rotary inertia time-varying spacecraft attitude pursuit movement are established
The mathematical model of spacecraft attitude pursuit movement, includes the following steps：
Step S341：Define the coordinate system and kinematic parameter of the spacecraft attitude pursuit movement：
For ease of description, the coordinate system and kinematic parameter of spacecraft attitude pursuit movement are defined as follows.As shown in figure 3, adopting
With with reference to inertial coodinate system OeXeYeZeWith body coordinate system OCXbYbZbThe attitude motion of spacecraft is described, with reference to inertia
Coordinate system OeXeYeZeChoose GB/T 32296-2015《Aerospace craft Common Coordinate》In it is common refer to inertial coodinate system.
OCFor the mass centre of controlled spacecraft.
Kinematic parameter is defined as：
The practical posture of spacecraftElement rbijFor OCXbYbZbSystem and OeXeYeZeIt is corresponding basal orientation
Direction cosines between amount；
Spacecraft actual angular speed ωb=[ωbx,ωby,ωbz]T, ωbx、ωby、ωbzRotating around for OCXbAxis, OCYbAxis,
OCZbAxis direction angular speed；
Note attitude motion generalized coordinates is (Rb,ωb)。
Step S342：According to the coordinate system and kinematic parameter of the spacecraft attitude pursuit movement, obtain shown in formula (6)
The attitude motion mathematical model of the spacecraft：
In formula,Indicate RbFirst differential；Indicate ωbFirst differential；U=[u1,u2,u3]TTo act on space flight
Control moment vector on device, u1、u2、u3Respectively OCXbAxis, OCYbAxis, OCZbThe control moment of axis direction；D=[d1,d2,d3
]TTo act on spaceborne disturbance torque vector, d1、d2、d3Respectively OCXbAxis, OCYbAxis, OCZbThe perturbed force of axis direction
Square；
J (t)=J0-J1Ψ (t) is the moment of inertia matrix changed over time；Indicate the single order of J (t)
Differential；
Wherein, J0Indicate the rigidity parameters not changed over time in rotary inertia, as shown in formula (8), J1Indicate that rotation is used
The coefficient matrix of the nonrigid portions changed over time in amount, as shown in formula (9),
Ψ (t) in J (t) is the known time-varying function matrix of rotary inertia nonrigid portions, is 3 × 3 rank square formations；
For the first differential of Ψ (t)；
It indicates shown in additional time-varying parameter matrix such as formula (10) caused by rotary inertia variation, is 3 × 3 rank sides
Battle array；The multiplication cross matrix of 3 dimensional vector of subscript × expression in formula (10).
h0It indicates to add the constant coefficient diagonal matrix in time-varying parameter matrix, as shown in formula (11)；Γ (t) is additional time-varying
Known 3 dimension time-varying function vector in parameter matrix.
Preferably, the known time-varying function Ψ (t) of rotary inertia nonrigid portions is calculated by formula (12)：
Ψ (t)=ρT(t)ρ(t)I-ρ(t)ρT(t) (12)
Wherein, ρ (t) is 3 dimension time-varying function vectors.
Preferably, the known 3 dimension time-varying function vector Γ (t) in above-mentioned additional time-varying parameter matrix is based on formula (13)
It calculates：
Wherein,For the first differential of 3 dimension time-varying function vector ρ (t).
By formula (1) to formula (6), the number of the parameter time varying spacecraft attitude pursuit movement as shown in formula (14) can be obtained
Learn model：
In formula,For instruction angular speed vector ωdFirst differential.
Formula (14) is the mathematical model of rotary inertia time-varying spacecraft attitude pursuit movement, described with formula (14)
Mathematical model is controlled device, using inverse adaptive control optimization method design control moment u so that auxiliary variable z is converged to
0.According to the mathematical model of parameter time varying spacecraft attitude pursuit movement regression matrix F is calculated by existing method1、F2、F3、G1、G2
And G3.
It will be proven below：When auxiliary variable z converges to 0, direction of error cosine matrixWith error angular velocity vectorRespectively
Converge to unit matrix I and null vector 03×1。
Define the Lyapunov functions as shown in (15)：
In formula, A=diag (a1,a2,a3)。
To formula (15) differential and using formula (5), can obtain：
In formula, λmin(K1) indicate positive definite symmetric matrices K1Minimal eigenvalue.
Formula (16) illustrates when auxiliary variable z converges to 0, error angular velocity vectorIt is equal with attitude error vector S
Converge to null vector 03×1,
According to formula (5) it is found that working as S=03×1When, direction of error cosine matrixPossible there are four values, such as formula (17)
It is shown：
Using the linearization technique in non-Euclidean space it can easily be proven that：It is unique stable equilibrium point,Remaining
3 values are unstable saddle point.So far, i.e., error direction cosine matrix when card auxiliary variable z converges to 0Converge to unit square
Battle array I.Illustrate that the practical posture of controlled spacecraft can converge to instruction posture.
Preferably, regression matrix F1And G1Computational methods be：
Enable J1=h0=03×3, herein 03×3Indicate 3 × 3 rank null matrix.By J1=h0=03×3It substitutes into shown in formula (14)
The mathematical model of parameter time varying spacecraft attitude pursuit movement can obtain formula (18)：
In formula,
If ξ=[J0(1,1),J0(1,2),J0(1,3),J0(2,2),J0(2,3),J0(3,3)]T, F is calculated by formula (19)1：
G is calculated by formula (20)1：
In formula, operatorPartial derivative of the bracket [] inner function about vectorial ξ is sought in expression；Obviously, F1And G1It is 3 × 6
Rank matrix.
Preferably, regression matrix F2And G2Computational methods be：
Enable J0=h0=03×3, by J0=h0=03×3Substitute into formula (14) described parameter time varying spacecraft attitude pursuit movement
Mathematical model in can obtain：
If θ=[J1(1,1),J1(1,2),J1(1,3),J1(2,2),J1(2,3),J1(3,3)]T, F is calculated by formula (22)2：
G is calculated by formula (23)2：
In formula, operatorPartial derivative of the bracket [] inner function about vectorial θ is sought in expression.Obviously, F2And G2It is 3
× 6 rank matrixes.
Preferably, regression matrix F3And G3Computational methods be：
Enable J0=J1=03×3, by J0=J1=03×3Substitute into the parameter time varying spacecraft attitude tracking shown in formula (14)
It can be obtained in the mathematical model of movement：
If η=[h01,h02,h03]T, F is calculated by formula (25)3：
G is calculated by formula (26)3：
In formula, operatorPartial derivative of the bracket { } inner function about vectorial θ is sought in expression；Obviously, F3And G3It is 3 × 3
Rank matrix.
Step S400：Design smooth projection adaptive law：According to the linear regression matrix F1、F2、F3、G1、G2And G3, real
When calculate the estimated value of unknown parameter vector ξ, θ, ηAccording to the estimated valueDesign it is inverse it is optimal from
Suitable solution is restrained.
Preferably, the step S400 includes the following steps：
Step S410：The estimated value is calculated by formula (27)
In formula, γ1、γ2、γ3For the positive number more than zero；In formula (27)Respectively Single order it is micro-
Point,RespectivelyInitial value for integral；Function Proj () is projection function, if p is
3 dimensions or 6 dimensional vectors, ΞiBe also 3 dimension or 6 dimensional vectors, the then definition of Proj () be：
In formula, εi,δi＞ 0 is positive real number, is determined by the prior information of vectorial p.
Step S420：According to the estimated valueDesign obtains inverse adaptive control optimization and restrains：
In formula,For the estimated value of unknown vector ξ, θ, η, calculated according to formula (27)；
ueFor nonlinear dampling controlled quentity controlled variable, u is calculated by formula (30)e：
In formula, K is 3 × 3 rank positive definite symmetric matrices, K-1For the inverse matrix of K；β is the positive number more than 2；
Ψ is calculated by formula (31)1：
Ψ is calculated by formula (32)2：
In formula,γ is positive number；KpFor positive number.
According toThe method of calculating is
According toIt calculates,It is calculated by formula (34)：
According toIt calculates,It is calculated by formula (35)：
Step S500：Attitude tracking control amount is calculated according to the inverse adaptive control optimization rule, by the Attitude Tracking
Controlled quentity controlled variable inputs spacecraft to be controlled, judges whether the attitude error angle of practical posture and desired posture meets control requirement, such as
Fruit is unsatisfactory for, and measures in the practical posture of controlled spacecraft and return to step S200；
Step S600：Step S200~S500 is repeated until the practical posture satisfaction control of the spacecraft to be controlled is wanted
It asks.
As shown in Fig. 2, inverse optimal Adaptive Attitude Tracking Control system architecture block diagram provided by the invention, first according to finger
Enable posture (Rd,ωd) and practical posture (R, ω) calculating attitude error amountThen according to attitude error amountIt calculates
Error vector S, error matrix C and auxiliary variable z；Nonlinear dampling method design inverse optimal control rule is used later；In order to
Solve rotary inertia uncertain problem, according to z,ωdConstruct 6 linear regression matrix Fs1、F2、F3、G1、G2And G3, into
And smooth projection adaptive law is constructed, the time-varying rotary inertia parameter of On-line Estimation spacecraftIt is inverse optimal to obtain
Adaptive Attitude Tracking control law.
By this method control Space Vehicle System can in rotary inertia under conditions of unknown and consecutive variations, in high precision with
Track instructs posture, compared to traditional Adaptive Attitude control method, has more fully adaptability, vulnerability to jamming and strong robust
Property, be conducive to Attitude tracking control and realized in engineering field.
Rotary inertia parameter time varying spacecraft provided by the invention against optimal Adaptive Attitude Tracking control method, first by
Then given instruction posture and practical Attitude Calculation attitude error amount are become by calculating error vector, error matrix and auxiliary
Amount designs inverse optimum attitude tracing control rule using nonlinear dampling method, and uses smooth projection adaptive law real-time estimation
The time-varying rotary inertia of spacecraft.In practical application, what the practical posture of spacecraft was made of star sensor and angular rate gyroscope
Navigation system measurement obtains, and the controlled quentity controlled variable being calculated by this method is transmitted to the execution machine such as control-moment gyro or momentum
Structure, you can realize Attitude tracking control function.
There is preferable control stability in order to better illustrate control method provided by the invention, that is, illustrate in gained control
Under the action of system rule, auxiliary variable z can level off to zero, and the stability analysis of control method is as follows：
It is defined as follows Lyapunov functions
In formula,Indicate the evaluated error of unknown parameter；KpFor positive number.
To formula (36) differential, can obtain：
Using Attitude Tracking modular form (14), control law formula (29) and adaptive law formula (27), letter is carried out to formula (37)
Change, can obtain：
In formula,
According to Young inequalityAndFormula (37) can be rewritten as
Therefore, positive number c is certainly existed1And c2So that
Formula (39) proves under control law (29) effect that spacecraft attitude closed-loop tracking system is that input-output is stablized
, and control parameter γ is smaller, and influence of the external disturbance to Attitude Tracking error is smaller.
Method provided by the invention is described in detail below in conjunction with specific example.It is derived from control according to the following steps
Rule, to the spacecraft of parameter as listed in table 1, using gained control law, and by listed control parameter in table 2 to the controlled spacecraft
It is controlled, gained control result is referring to Fig. 4~8.
Step S100：Instruction posture (the R that given generalized coordinates indicatesd,ωd)
Giving instruction attitude angular velocity vector is：
ωd(t)=[0.3, -0.1,0.2]TRad/s,
Command direction cosine matrix is consecutive variations value, and computational methods are：
For RdFirst differential, initial time command direction cosine matrix be Rd(0)=I.
Step S200：Calculate attitude error amount
Direction of error cosine matrix between computations posture and practical posture：
Error angular velocity vector between computations posture and practical posture：
Wherein, RbFor actual direction cosine matrix；ωbIt is consecutive variations value for actual angular speed vector.
The actual direction cosine matrix of initial time is：
Wherein, ε=0.01rad,
The actual angular speed vector of initial time is：
ωb(0)=[0,0,0]Trad/s
Step S300：Construct linear regression matrix F1、F2、F3、G1、G2And G3；
Step S310：Calculate attitude error vector S
In the present embodiment, a1=1, a2=2, a3=3；e1=[1,0,0]T、e2=[0,1,0]T、e3=[0,0,1]T。
Step S320：Calculate attitude error Matrix C
Step S330：Calculate auxiliary variable z；
In the present embodiment, K1=diag (0.1,0.1,0.1).
Step S340：Calculate regression matrix F1、F2、F3、G1、G2And G3；
Step S341：Establish the mathematical model of rotary inertia time-varying spacecraft attitude pursuit movement
The mathematical model of attitude motion of spacecraft is described as follows：
In formula, RbIndicate spacecraft actual direction cosine matrix, ωbIndicate spacecraft actual angular speed,Indicate RbOne
Rank differential；Indicate ωbFirst differential；U is to act on spaceborne control moment vector；D is to act on spacecraft
Disturbance torque vector；J (t)=J0-J1Ψ (t) is the moment of inertia matrix changed over time；Indicate J (t)
First differential；Ψ (t) is the known time-varying function matrix of rotary inertia nonrigid portions；For the first differential of Ψ (t)；Indicate additional time-varying parameter matrix caused by rotary inertia variation；Γ (t) is in additional time-varying parameter matrix
It is known 3 dimension time-varying function vector；
The rigidity parameters value not changed over time in rotary inertia is
In the present embodiment,
ξ=[J0(1,1),J0(1,2),J0(1,3),J0(2,2),J0(2,3),J0(3,3)]T=[20,1.2,0.9,17,1.4,15]T kg*
m2；
The coefficient matrix of the nonrigid portions changed over time in rotary inertia is
In the present embodiment, θ=[J1(1,1),J1(1,2),J1(1,3),J1(2,2),J1(2,3),J1(3,3)]T=[2,0,0,2,0,2]Tkg*m2；
Constant coefficient diagonal matrix in additional time-varying parameter matrix is
In the present embodiment, η=[h01,h02,h03]T=[5,4,3]Tkg*m2/s；
In the present embodiment, the known time-varying function Ψ (t) of rotary inertia nonrigid portions is
In the present embodiment, the time-varying function vector Γ (t) in additional time-varying parameter matrix is
Γ (t)=[sin (0.1t), sin (0.2t), sin (0.3t)]T
Composite type (40) can be obtained to formula (45)
In formula,For instruction angular speed vector ωdFirst differential.
Formula (46) is the mathematical model of rotary inertia time-varying spacecraft attitude pursuit movement, with number described in formula (46)
Model is controlled device, using inverse adaptive control optimization method design control moment u so that auxiliary variable z converges to 0.
Step S342：Calculate regression matrix F1And G1
Wherein, matrix functionBy vector x=[x1,x2,x3]T3 × 6 rank matrixes are mapped to, i.e.,
Step S343：Calculate regression matrix F2And G2
Step S344：Calculate regression matrix F3And G3
Step S400：Design smooth projection adaptive law
In the present embodiment, γ1=100, γ2=100, γ3=100；Function Proj () is projection function
In the present embodiment, ε1=918.21, ε2=12, ε3=50, δi=10-3, i=1,2,3
Step S500：The inverse adaptive control optimization of design is restrained：
In formula,For the estimated value of unknown vector ξ, θ, η, calculated according to formula (47)；ueFor nonlinear dampling control
Amount processed, computational methods are
In the present embodiment, K=K-1=I；β=2；Ψ1And Ψ2Respectively
In the present embodiment, γ=1 or γ=0.4；Kp=1；
In the present embodiment, spacecraft parameter is shown in Table 1, and control parameter and auto-adaptive parameter are shown in Table 2
1 spacecraft parameter of table
| Parameter | Numerical value | Parameter | Numerical value | Parameter | Numerical value |
| J0(1,1) | 20.0kg*m2 | J0(3,3) | 15.0kg*m2 | J1(2,3) | 0.0kg*m2 |
| J0(1,2) | 1.2kg*m2 | J1(1,1) | 2.0kg*m2 | J1(3,3) | 2.0kg*m2 |
| J0(1,3) | 0.9kg*m2 | J1(1,2) | 0.0kg*m2 | h01 | 5.0kg*m2/s |
| J0(2,2) | 17.0kg*m2 | J1(1,3) | 0.0kg*m2 | h02 | 4.0kg*m2/s |
| J0(2,3) | 1.4kg*m2 | J1(2,2) | 2.0kg*m2 | h03 | 3.0kg*m2/s |
2 control parameter of table and auto-adaptive parameter
| Parameter | Numerical value | Parameter | Numerical value | Parameter | Numerical value |
| K1 | 0.1·I | ε2 | 12.00 | K | I |
| γ1 | 100.00 | ε3 | 50.00 | β | 2.00 |
| γ2 | 100.00 | δ1 | 10-3 | γ | 1.00 or 0.40 |
| γ3 | 100.00 | δ2 | 10-3 | Kp | 1.00 |
| ε1 | 918.21 | δ3 | 10-3 |
Spacecraft attitude tracking result in the present embodiment is as shown in Fig. 4-Fig. 8.
Fig. 4 gives in the present embodiment gained adaptive law to spacecraft parameter J0(1,1)、J0(1,2)、J0(1,3)、J0(2,2)、
J0(2,3)、J0(3,3)Real-time estimation as a result, Fig. 5 gives in the present embodiment gained adaptive law to spacecraft parameter J1(1,1)、
J1(1,2)、J1(1,3)、J1(2,2)、J1(2,3)、J1(3,3)Real-time estimation as a result, Fig. 6 gives in the present embodiment gained adaptive law pair
Spacecraft parameter h01、h02、h03Real-time estimation result.It can be seen that each estimates of parameters converges to constant by Fig. 4-Fig. 6,
Show that the adaptive law that method provided by the invention obtains is convergent.
When Fig. 7 gives γ=1 and γ=0.4, the control result of tracking angle error can be obtained by Fig. 7：The initial appearance of spacecraft
State angle error converges to stable state since 180 ° after 150s, and as γ=1, attitude error stable state accuracy is at 1 °~10 °
Between magnitude, as γ=0.4, attitude error stable state accuracy reaches between 0.1 °~1 ° magnitude.
When Fig. 8 gives γ=1 and γ=0.4, the control result of tracking angular rate error can be obtained by Fig. 8：At the beginning of spacecraft
Beginning attitude error converges to stable state after 150s, and as γ=1, angular speed tracking error is less than 0.0126rad/s, works as γ
When=0.4, angular speed tracking error is less than 0.0050rad/s.Fig. 7 and Fig. 8 shows that controlled spacecraft can be accurate in the present embodiment
True trace command posture, demonstrates the validity of flight tracking control method proposed by the invention, and can pass through adjusting control
Parameter γ inhibits the influence of external disturbance, improves Attitude Tracking precision.
More than, be only one embodiment of the present of invention, any type of limitation not done to the present invention, although the present invention with
Preferred embodiment discloses as above, however not to limit the present invention, any person skilled in the art is not departing from this
In the range of inventive technique scheme, makes a little variation using the technology contents of the disclosure above or modification is equal to equivalent reality
Case is applied, is belonged in technical proposal scope.
Claims (10)
1. a kind of rotary inertia time-varying spacecraft is against optimal Adaptive Attitude Tracking control method, which is characterized in that including following
Step：
Step S100：Input instruction posture (Rd,ωd)；
Step S200：Calculate the attitude error amount between described instruction posture and practical posture；
Step S300：Construct linear regression matrix F1、F2、F3、G1、G2And G3, and the line is calculated according to the attitude error amount
Property regression matrix F1、F2、F3、G1、G2And G3；
Step S400：According to the linear regression matrix F1、F2、F3、G1、G2And G3, unknown parameter vector ξ, θ, η are calculated in real time
Estimated valueAccording to the estimated valueThe inverse adaptive control optimization of design is restrained；
Step S500：Attitude tracking control amount is calculated according to the inverse adaptive control optimization rule, by the Attitude tracking control
Amount inputs spacecraft to be controlled, and whether the attitude error angle of the practical posture for judging the spacecraft to be controlled and desired posture is full
Foot control requires, and the practical posture of controlled spacecraft is measured if being unsatisfactory for and is returned in the step S200；
Step S600：Step S200~S500 is repeated until the practical posture of the spacecraft to be controlled meets the control and wants
It asks.
2. rotary inertia time-varying spacecraft according to claim 1 is against optimal Adaptive Attitude Tracking control method, special
Sign is that described instruction posture is the instruction posture that generalized coordinates indicates.
3. rotary inertia time-varying spacecraft according to claim 1 is against optimal Adaptive Attitude Tracking control method, special
Sign is that the attitude error amount includes：Direction of error cosine matrixWith error angular velocity vectorRespectively press formula (1)~
(2) it is calculated：
Wherein, RbFor the actual direction cosine matrix of 3 × 3 ranks, ωbFor actual angular speed vector, subscript T indicates vector or matrix
Transposition.
4. rotary inertia time-varying spacecraft according to claim 1 is against optimal Adaptive Attitude Tracking control method, special
Sign is, described to calculate linear regression matrix F according to the attitude error amount1、F2、F3、G1、G2And G3The step of, including it is following
Step：
Step S310：Attitude error vector S is calculated by formula (3)：
Wherein, a1、a2、a3For mutually different positive real number, e1、e2、e3Respectively e1=[1,0,0]T、e2=[0,1,0]T、e3=
[0,0,1]T；
Step S320：Attitude error Matrix C is calculated by formula (4)：
Wherein, matrix I is unit matrix, i.e.,
Step S330：Auxiliary variable z is calculated by formula (5)：
Wherein, K1For 3 × 3 rank positive definite symmetric matrices,For error angular velocity vector；
Step S340：According to the attitude error amount, the attitude error vector S, the attitude error Matrix C, the auxiliary
The attitude motion mathematical model of variable z and spacecraft establish the mathematics of the rotary inertia time-varying spacecraft attitude pursuit movement
Model calculates regression matrix F according to the mathematical model of the rotary inertia time-varying spacecraft attitude pursuit movement1、F2、F3、G1、G2
And G3；The mathematical model step for establishing the rotary inertia time-varying spacecraft attitude pursuit movement, includes the following steps：
Step S341：Define the coordinate system and kinematic parameter of the spacecraft attitude pursuit movement：
Step S342：According to the coordinate system and kinematic parameter of the spacecraft attitude pursuit movement, institute shown in formula (6) is obtained
State the attitude motion mathematical model of spacecraft：
In formula,Indicate RbFirst differential,Indicate ωbFirst differential, u=[u1,u2,u3]TTo act on spacecraft
Control moment vector, u1、u2、u3Respectively OCXbAxis, OCYbAxis, OCZbThe control moment of axis direction, d=[d1,d2,d3]TFor
Act on the spaceborne disturbance torque vector, d1、d2、d3Respectively OCXbAxis, OCYbAxis, OCZbThe perturbed force of axis direction
Square,
J (t)=J0-J1Ψ (t) is the moment of inertia matrix changed over time,Indicate the first differential of J (t),
Wherein, J0The rigidity parameters not changed over time in rotary inertia, J are indicated as shown in formula (8)1The table as shown in formula (9)
Show the coefficient matrix of the nonrigid portions changed over time in rotary inertia,
Ψ (t) in J (t) is the known time-varying function matrix of rotary inertia nonrigid portions, is 3 × 3 rank square formations,For Ψ
(t) first differential,It indicates to add time-varying parameter matrix caused by rotary inertia variation as shown in formula (10), is 3 × 3
Rank square formation：
h0It indicates to add the constant coefficient diagonal matrix in time-varying parameter matrix as shown in formula (11),
Γ (t) is the known 3 dimension time-varying function vector in additional time-varying parameter matrix；
Step S343：According to the attitude error amount, the attitude error vector S, the attitude error Matrix C, the auxiliary
The attitude motion mathematical model of variable z and the spacecraft obtains the rotary inertia time-varying spacecraft as shown in formula (14)
The mathematical model of Attitude Tracking movement：
In formula,For instruction angular speed vector ωdFirst differential.
5. rotary inertia time-varying spacecraft according to claim 4 is against optimal Adaptive Attitude Tracking control method, special
Sign is, the regression matrix F1And G1Computational methods be：Enable the number of the rotary inertia time-varying spacecraft attitude pursuit movement
Learn the J in model1=h0=03×3, obtain formula (18)：
In formula,
If ξ=[J0(1,1),J0(1,2),J0(1,3),J0(2,2),J0(2,3),J0(3,3)]T, F is calculated by formula (19)1：
G is calculated by formula (20)1：
In formula, operatorPartial derivative of the bracket [] inner function about vectorial ξ is sought in expression.
6. rotary inertia time-varying spacecraft according to claim 4 is against optimal Adaptive Attitude Tracking control method, special
Sign is, the regression matrix F2And G2Computational methods be：
Enable the J in the mathematical model of the rotary inertia time-varying spacecraft attitude pursuit movement0=h0=03×3：
If θ=[J1(1,1),J1(1,2),J1(1,3),J1(2,2),J1(2,3),J1(3,3)]T, F is calculated by formula (22)2：
G is calculated by formula (23)2：
In formula, operatorPartial derivative of the bracket [] inner function about vectorial θ is sought in expression.
7. rotary inertia time-varying spacecraft according to claim 4 is against optimal Adaptive Attitude Tracking control method, special
Sign is, the regression matrix F3And G3Computational methods be：
Enable the J in the mathematical model of the rotary inertia time-varying spacecraft attitude pursuit movement0=J1=03×3：
If η=[h01,h02,h03]T, F is calculated by formula (25)3：
G is calculated by formula (26)3：
In formula, operatorPartial derivative of the bracket { } inner function about vectorial η is sought in expression.
8. rotary inertia time-varying spacecraft according to claim 1 is against optimal Adaptive Attitude Tracking control method, special
Sign is that the step S400 includes the following steps：
Step S410：The estimated value is calculated by formula (27)
In formula, γ1、γ2、γ3For the positive number more than zero, function Proj () is projection function, if p be 3 dimensions or 6 tie up to
Amount, ΞiBe also 3 dimension or 6 dimensional vectors, the then definition of Proj () be：
In formula, εi,δi＞ 0 is positive real number；
Step S420：According to the estimated valueDesign obtains inverse adaptive control optimization and restrains：
In formula, ueFor nonlinear dampling controlled quentity controlled variable, u is calculated by formula (30)e：
In formula, K is 3 × 3 rank positive definite symmetric matrices, K-1For the inverse matrix of K；β is the positive number more than 2；
Ψ is calculated by formula (31)1：
Ψ is calculated by formula (32)2：
In formula,γ is positive number, KpFor positive number；
According toThe method of calculating is：
According toIt calculates,It is calculated by formula (34)：
According toIt calculates,It is calculated by formula (35)：
9. rotary inertia time-varying spacecraft according to claim 4 is against optimal Adaptive Attitude Tracking control method, special
Sign is, the known time-varying function Ψ (t) of rotary inertia nonrigid portions is calculated by formula (12)：
Ψ (t)=ρT(t)ρ(t)I-ρ(t)ρT(t) (12)
Wherein, ρ (t) is 3 dimension time-varying function vectors.
10. rotary inertia time-varying spacecraft according to claim 4 is against optimal Adaptive Attitude Tracking control method, special
Sign is that the known 3 dimension time-varying function vector Γ (t) in the additional time-varying parameter matrix is calculated by formula (13)：
Wherein,For the first differential of 3 dimension time-varying function vector ρ (t).
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810429961.2A CN108628165B (en) | 2018-05-08 | 2018-05-08 | Rotary inertia time-varying spacecraft is against optimal Adaptive Attitude Tracking control method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201810429961.2A CN108628165B (en) | 2018-05-08 | 2018-05-08 | Rotary inertia time-varying spacecraft is against optimal Adaptive Attitude Tracking control method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN108628165A true CN108628165A (en) | 2018-10-09 |
| CN108628165B CN108628165B (en) | 2019-06-25 |
Family
ID=63695823
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201810429961.2A Active CN108628165B (en) | 2018-05-08 | 2018-05-08 | Rotary inertia time-varying spacecraft is against optimal Adaptive Attitude Tracking control method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN108628165B (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5563794A (en) * | 1993-11-22 | 1996-10-08 | Hughes Aircraft Company | Repetitive control of thermal shock disturbance |
| WO2003025685A1 (en) * | 2001-09-14 | 2003-03-27 | Ibex Process Technology, Inc. | Scalable, hierarchical control for complex processes |
| CN102411304A (en) * | 2011-12-15 | 2012-04-11 | 北京航空航天大学 | Optimization method of spacecraft small-angle attitude maneuver control parameters |
| CN103412491A (en) * | 2013-08-27 | 2013-11-27 | 北京理工大学 | Method for controlling index time-varying slide mode of flexible spacecraft characteristic shaft attitude maneuver |
| CN103941273A (en) * | 2014-03-31 | 2014-07-23 | 广东电网公司电力科学研究院 | Adaptive filtering method of onboard inertia/satellite integrated navigation system and filter |
| CN105955284A (en) * | 2016-05-30 | 2016-09-21 | 中国人民解放军国防科学技术大学 | On-orbit refueling spacecraft attitude control method |
| CN106125745A (en) * | 2016-06-29 | 2016-11-16 | 中国人民解放军国防科学技术大学 | A kind of satellite attitude control method to Spatial Cooperation target following imaging |
| CN106548475A (en) * | 2016-11-18 | 2017-03-29 | 西北工业大学 | A kind of Forecasting Methodology of the target trajectory that spins suitable for space non-cooperative |
| CN106886149A (en) * | 2017-02-23 | 2017-06-23 | 哈尔滨工业大学 | A kind of spacecraft robust finite time saturation Attitude tracking control method |
-
2018
- 2018-05-08 CN CN201810429961.2A patent/CN108628165B/en active Active
Patent Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5563794A (en) * | 1993-11-22 | 1996-10-08 | Hughes Aircraft Company | Repetitive control of thermal shock disturbance |
| WO2003025685A1 (en) * | 2001-09-14 | 2003-03-27 | Ibex Process Technology, Inc. | Scalable, hierarchical control for complex processes |
| CN102411304A (en) * | 2011-12-15 | 2012-04-11 | 北京航空航天大学 | Optimization method of spacecraft small-angle attitude maneuver control parameters |
| CN103412491A (en) * | 2013-08-27 | 2013-11-27 | 北京理工大学 | Method for controlling index time-varying slide mode of flexible spacecraft characteristic shaft attitude maneuver |
| CN103941273A (en) * | 2014-03-31 | 2014-07-23 | 广东电网公司电力科学研究院 | Adaptive filtering method of onboard inertia/satellite integrated navigation system and filter |
| CN105955284A (en) * | 2016-05-30 | 2016-09-21 | 中国人民解放军国防科学技术大学 | On-orbit refueling spacecraft attitude control method |
| CN106125745A (en) * | 2016-06-29 | 2016-11-16 | 中国人民解放军国防科学技术大学 | A kind of satellite attitude control method to Spatial Cooperation target following imaging |
| CN106548475A (en) * | 2016-11-18 | 2017-03-29 | 西北工业大学 | A kind of Forecasting Methodology of the target trajectory that spins suitable for space non-cooperative |
| CN106886149A (en) * | 2017-02-23 | 2017-06-23 | 哈尔滨工业大学 | A kind of spacecraft robust finite time saturation Attitude tracking control method |
Non-Patent Citations (1)
| Title |
|---|
| 文坤: "基于空间机械臂的航天器系统惯性参数辨识", 《中国优秀硕士学位论文全文数据库 信息科技辑》 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| 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 |
Also Published As
| Publication number | Publication date |
|---|---|
| CN108628165B (en) | 2019-06-25 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Do et al. | Universal controllers for stabilization and tracking of underactuated ships | |
| Zheng et al. | Path following control for marine surface vessel with uncertainties and input saturation | |
| Wu et al. | Modeling and sliding mode-based attitude tracking control of a quadrotor UAV with time-varying mass | |
| Huang et al. | Adaptive control for space debris removal with uncertain kinematics, dynamics and states | |
| CN108646556B (en) | Input saturation spacecraft is without unwinding Attitude tracking control method | |
| Do et al. | State-and output-feedback robust path-following controllers for underactuated ships using Serret–Frenet frame | |
| Lee et al. | Adaptive sliding mode control for spacecraft body-fixed hovering in the proximity of an asteroid | |
| Singh et al. | Adaptive output feedback control of spacecraft with flexible appendages by modeling error compensation | |
| CN108710303A (en) | Spacecraft relative attitude control method containing multi-source disturbance and actuator saturation | |
| CN104483973B (en) | Low-orbit flexible satellite attitude tracking control method based on sliding-mode observer | |
| Park | Inverse optimal and robust nonlinear attitude control of rigid spacecraft | |
| CN108663936B (en) | Model does not know spacecraft without unwinding Attitude Tracking finite-time control method | |
| Forbes | Passivity-based attitude control on the special orthogonal group of rigid-body rotations | |
| Han et al. | Incremental twisting fault tolerant control for hypersonic vehicles with partial model knowledge | |
| Wu et al. | Adaptive control for spacecraft relative translation with parametric uncertainty | |
| Sasaki et al. | Attitude and vibration control with double-gimbal variable-speed control moment gyros | |
| Wood et al. | Attitude control of magnetically actuated satellites with an uneven inertia distribution | |
| Liu et al. | Tether tension control law design during orbital transfer via small-gain theorem | |
| Michałek et al. | Robust output-feedback cascaded tracking controller for spatial motion of anisotropically-actuated vehicles | |
| Warier et al. | Line-of-sight based spacecraft attitude and position tracking control | |
| CN108628165B (en) | Rotary inertia time-varying spacecraft is against optimal Adaptive Attitude Tracking control method | |
| Akella et al. | Rigid body attitude control with inclinometer and low-cost gyro measurements | |
| She et al. | Quasi-model free control for the post-capture operation of a non-cooperative target | |
| Yin et al. | Extended state observer-based attitude fault-tolerant control of rigid spacecraft | |
| Zhao et al. | Quaternion-based adaptive trajectory tracking control of a rotor-missile with unknown parameters identification |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |