CN113859585B - Fixed-time unreeling-free attitude control method of spacecraft - Google Patents

Fixed-time unreeling-free attitude control method of spacecraft Download PDF

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CN113859585B
CN113859585B CN202111068565.XA CN202111068565A CN113859585B CN 113859585 B CN113859585 B CN 113859585B CN 202111068565 A CN202111068565 A CN 202111068565A CN 113859585 B CN113859585 B CN 113859585B
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spacecraft
attitude
unwinding
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fixed time
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CN113859585A (en
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王增
陶玙
王春阳
刘长杰
王子硕
梁书宁
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Xian Technological University
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    • 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
    • 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
    • B64G1/245—Attitude control algorithms for spacecraft attitude control
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

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  • Combustion & Propulsion (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)

Abstract

The invention provides a fixed time unwinding-free attitude control method for a spacecraft, which solves the problem of unwinding of the spacecraft in the prior art, and provides a fixed time robust attitude control method without the problem of unwinding, so that the energy consumption of attitude control is reduced, and the control precision of the attitude control is improved. The invention comprises the following steps: step 1, based on a unit quaternion method, taking external interference moment into consideration, and establishing a rigid body space vehicle attitude tracking control model: wherein (q) v ,q 4 )∈R 3 The x R represents the azimuth of the spacecraft body described by the unit quaternion relative to an inertial coordinate system, and the directions satisfy each otherAnd 2, designing a fixed-time robust attitude controller without unwinding problem, and performing stability analysis.

Description

Fixed-time unreeling-free attitude control method of spacecraft
Technical field:
the invention belongs to the technical field of advanced control, and relates to a spacecraft fixed-time unwinding-free attitude control method based on a hybrid system.
The background technology is as follows:
spacecraft described by quaternion method, which belongs to a multi-input multi-output nonlinear equation set, has two balance points, namely (0, ±)1) T . When the initial state of the spacecraft approaches the equilibrium point (0, -1) T Conventional attitude control techniques, in turn, result in the spacecraft converging to a balance point (0, -1) over a longer path T The waste of redundant energy consumption, namely the unwinding problem of the spacecraft, is caused. The existing fixed-time robust attitude control technology not only does not consider the unwinding problem of the spacecraft and causes energy consumption waste of attitude control of the spacecraft, but also has the flutter problem based on the fixed-time attitude control technology of the traditional sliding mode technology, and the system is caused to resonate when serious, so that the accuracy of attitude control is reduced.
The invention comprises the following steps:
the invention aims to provide a fixed-time unwinding-free attitude control method for a spacecraft, which solves the problem of unwinding of the spacecraft in the prior art, and provides a fixed-time robust attitude control method without the problem of unwinding, which reduces the energy consumption of attitude control and improves the control precision of the attitude control.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a fixed time unwinding-free attitude control method of a spacecraft is characterized by comprising the following steps of: the method comprises the following steps:
step 1, based on a unit quaternion method, taking external interference moment into consideration, and establishing a kinematic and dynamic model of the rigid space vehicle:
wherein (q) v ,q 4 )∈R 3 The x R represents the azimuth of the spacecraft body described by the unit quaternion relative to an inertial coordinate system, and the directions satisfy each otherω∈R 3 Representing the angular velocity of a spacecraft, I 3 ∈R 3×3 Represents an identity matrix, J.epsilon.R 3×3 Represents an inertia matrix of positive definite symmetry, u epsilon R 3 And d.epsilon.R 3 Representing control moment and external disturbance, respectively, (. Cndot.) × ∈R 3×3 The representative antisymmetric matrix may be expressed as follows:
and 2, designing a fixed-time robust attitude controller without unwinding problem, and performing stability analysis.
The spacecraft attitude tracking control model in the step 1 is based on a unit quaternion method, and the kinematics and dynamics model is as follows
ω e ＝ω-Cω d (6)
Wherein omega d ∈R 3 And omega e ∈R 3 Representing the desired angular velocity and the angular velocity tracking error of the spacecraft,is the attitude tracking error, where vector e v ＝[e 1 ,e 2 ,e 3 ]∈R 3 Scalar e 4 E R is the relative pose between the actual pose and the desired pose, the corresponding rotation matrix C e R 3×3 Defined as->Wherein the rotation matrix satisfies c=1 and +.>
The fixed-time robust attitude controller in the step 2 is
u＝u 0 +u 1 (7)
S＝ω e +γhsig α (e v )+λhf(e v ) (10)
f(e v )＝[s(e 1 ),s(e 2 ),s(e 3 )] T (11)
Wherein lambda is 1 ,λ 2 And lambda (lambda) 3 Are all normal numbers, alpha > 1, s (. Cndot.) can be expressed as
Wherein y is R, R is more than 0 and less than 1 and R is more than 1 0 ≤2, d is a very small normal number, sign (&) represents the sign function, h.epsilon.H= { -1,1} is an auxiliary variable, H + = -h, successive and skip sets are defined as respectively
C＝{x∈S 3 ×R 3 ×H:he 4 ＞-h} (13)
D＝{x∈S 3 ×R 3 ×H:he 4 ≤-h} (14)
Wherein x= { q e ,ω e H }, η e (0, 1) represents the delay gap;
F(e v )＝diag(l(e 1 ),l(e 2 ),l(e 3 )) (16)
sig(ζ)＝[sign(ζ 1 ),sign(ζ 2 ),sign(ζ 3 )] T ,ζ∈R 3 (18)
wherein diag (·) represents the diagonal matrix.
In step 2, the stability analysis includes the steps of:
firstly, proving that the attitude error reaches the sliding mode surface for a fixed time;
secondly, proving that the attitude tracking error converges to any small neighborhood of the balance point along the fixed time of the sliding mode surface, and then gradually converges to the balance point.
Compared with the prior art, the invention has the following advantages and effects:
1. compared with the existing fixed-time robust attitude control technology, the invention can avoid the problem of the unwinding of the attitude control of the spacecraft described by quaternion, ensure the rapid convergence of the attitude control, ensure the predictable convergence time, greatly reduce the energy consumption of the attitude control, improve the control precision of the attitude control and have strong robustness to external interference.
2. The invention adopts a mixing system and an advanced control theory with stable fixed time, designs the constant-time unwinding-free gesture controller, can effectively avoid the problem of unwinding of gesture control, reduces the energy consumption of gesture control, can estimate convergence time, has strong robustness to external interference, and has higher gesture control precision.
Description of the drawings:
FIG. 1 is a fixed time attitude control diagram with unwinding problems, where a represents attitude tracking error convergence, b represents angular velocity tracking error convergence, c represents control torque, and d represents an enlarged view of attitude tracking error convergence with unwinding problems;
FIG. 2 is a fixed time attitude control diagram without unwind problems, where a represents attitude tracking error convergence, b represents angular velocity tracking error convergence, c represents control torque, and d represents an enlarged view of attitude tracking error convergence without unwind problems;
FIG. 3 is a graph of attitude control energy consumption versus unwind problem versus no unwind problem;
FIG. 4 is a schematic flow chart of the method of the present invention.
The specific embodiment is as follows:
the present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Examples:
in combination with the method flow diagram shown in fig. 4, the proposed fixed time stable robust attitude control without unwinding problem comprises the following steps:
step 1, establishing a gesture control model of a spacecraft;
step 2, designing a fixed-time robust attitude controller without unwinding problem;
the specific process of the step 1 is as follows:
based on a unit quaternion method, taking external disturbance moment into consideration, and establishing a posture control model of the rigid body space vehicle:
wherein (q) v ,q 4 )∈R 3 The x R represents the azimuth of the spacecraft body described by the unit quaternion relative to an inertial coordinate system, and the directions satisfy each otherω∈R 3 Representing the angular velocity of a spacecraft, I 3 ∈R 3×3 Represents an identity matrix, J.epsilon.R 3×3 Represents an inertia matrix of positive definite symmetry, u epsilon R 3 And d.epsilon.R 3 Representing control moment and external disturbance, respectively, (. Cndot.) × ∈R 3×3 The representative antisymmetric matrix may be expressed as follows:
the desired pose is described by the following formula:
the spacecraft kinematics and dynamics model described by the unit quaternion has no singular point, and can describe the spacecraft attitude of 360 degrees. However, the spacecraft described by the quaternion has two balance points, and the existing fixed time control algorithm does not consider the unwinding problem of attitude control, so that the energy consumption of the attitude control is wasted.
Specifically, the spacecraft attitude tracking control model in the step 1 is based on a unit quaternion method, and the kinematics and dynamics model is as follows:
ω e ＝ω-Cω d (6)
wherein ω εR 3 、ω d ∈R 3 And omega e ∈R 3 Representing respectively the actual angular velocity, the desired angular velocity and the angular velocity tracking error of the spacecraft,is the attitude tracking error, where vector e v ＝[e 1 ,e 2 ,e 3 ]∈R 3 Scalar e 4 E R is the relative pose between the actual pose and the desired pose. Corresponding rotation matrix C E R 3×3 Is defined asWherein the rotation matrix satisfies c=1 and +.>I 3 ∈R 3×3 Represents an identity matrix, J.epsilon.R 3×3 Represents an inertia matrix of positive definite symmetry, u epsilon R 3 And d.epsilon.R 3 Representing control moment and external disturbance, respectively, (. Cndot.) × ∈R 3×3 The representative antisymmetric matrix may be expressed as follows:
the fixed-time robust attitude controller in the step 2 is
u＝u 0 +u 1 (7)
S＝ω e +γhsig α (e v )+λhf(e v ) (10)
f(e v )＝[s(e 1 ),s(e 2 ),s(e 3 )] T (11)
Wherein lambda is 1 ,λ 2 And lambda (lambda) 3 Are all normal numbers, alpha > 1, s (. Cndot.) can be expressed as
Wherein y is R, R is more than 0 and less than 1 and R is more than 1 0 ≤2, d is a very small normal number, sign (&) represents the sign function, h.epsilon.H= { -1,1} is an auxiliary variable, H + = -h, successive and skip sets are defined as respectively
C＝{x∈S 3 ×R 3 ×H:he 4 ＞-η} (13)
D＝{x∈S 3 ×R 3 ×H:he 4 ≤-η} (14)
Wherein x= { q e ,ω e H }, η ε (0, 1) represents the delay gap.
F(e v )＝diag(l(e 1 ),l(e 2 ),l(e 3 )) (16)
sig(ζ)＝[sign(ζ 1 ),sign(ζ 2 ),sign(ζ 3 )] T ,ζ∈R 3 (18)
Wherein diag (·) represents the diagonal matrix.
In order to ensure the stability of the system, stability analysis is required to be performed on the designed attitude controller, and the system is mainly divided into two steps. The first step, the fixed time of the attitude error is proved to reach the sliding mode surface. Secondly, proving that the attitude tracking error converges to any small neighborhood of the balance point along the fixed time of the sliding mode surface, and then gradually converges to the balance point.
The first step: the fixed time was demonstrated to reach the slide face.
Deriving the formula (8) to obtain
The inertial matrix J can be obtained by simultaneously multiplying the two ends of the (21)
Substituting the formula (2) into the formula (22) to obtain
Defining a lyapunov candidate function as:
to derive the above type, get
Substituting formula (23) into formula (25), and using formulas (5) to (7)
Since the external interference is bounded and known as a constant, according to the supercoiled fixed time theorem, the sliding mode surface is consistent and fixed time is converged to the original point, and the convergence time is
Where e > 0, m=α+l, m=α -L, h (λ 1 )＝1/λ 1 +(2e/mλ 1 ) 1/3 E is a natural constant, alpha > L, lambda 1 h -1 (λ 1 )＞M，When T (x) 0 ) Taking the minimum value.
And a second step of: and proving that the system state reaches the balance point along the fixed time of the sliding mode surface.
S=0 after the system state reaches the slide face, which is obtained by the formula (8)
Can be obtained by combining (1)
For the system (29), a lyapunov candidate function is defined as:
deriving time to obtain
When |e i When the I is > d, apply h 2 =1, obtainable by formula (31)
Using e 4 When (t) > 0 is used,is available in the form of
Wherein the method comprises the steps of And->
When |e i When the level is less than or equal to d, applying h 2 =1, obtainable by formula (31)
Using 1 < r 0 When the temperature is less than or equal to 2,is available in the form of
When x is D, V 2 Jumping to obtain
V 2 (x + )-V 2 (x)≤2he 4 ≤-2η≤0 (36)
It can be seen that the designed controller can ensure that the system fixed time is stabilized to any small neighborhood near the balance point and then is asymptotically stabilized to the balance point.
FIGS. 1-3 show that in an environment with external disturbance torque, the attitude control method provided by the invention can ensure that the spacecraft with quaternion description can quickly converge to the balance point (0, + -1) T I.e. the initial pose is q (0) = [0.3, -0.2, -0.3,0.8832)] T Near the equilibrium point (0, -1) T When the spacecraft converges to the equilibrium point (0, -1) in the shortest path T (as shown in fig. 2 d), instead of rotating a half turn, the average energy consumption 3.984NM converges to the equilibrium point (0, 1) with a longer path T The average energy consumption 14.22NM (as shown by d in fig. 1), the proposed control method greatly reduces the energy consumption of spacecraft attitude control (as shown by the energy consumption comparison of fig. 3), i.e. the problem of unwinding of the spacecraft is solved.
Experimental example:
in order to verify the effectiveness of the fixed-time robust attitude stabilization controller designed by the patent, the attitude control of the space vehicle is performed under the condition of considering the existence of external interference, and the effectiveness of unwinding problems and whether the energy consumption of the controller is reduced are verified. The validity verification is mainly carried out through numerical simulation in the part, and the validity of the specific implementation mode and the proposed control algorithm is explained. Assume that the nominal inertial matrix of the rigid body spacecraft is j= [ 201.2.0.9; 1.2 171.4;0.9 1.415]kg·m 2 . Initial desired attitude and angular velocity are set to q d (0)＝[0,0,0,1] T And omega d (t)＝0.05[sin(πt/100),sin(2πt/100),sin(3πt/100)]rad/s, external interference d (t) = [0.1sin (t), 0.2sin (1.2 t), 0.3sin (1.5 t)]N.m. The initial attitude and angular velocity are set to q (0) = [0.3, -0.2, -0.3,0.8832, respectively] T And ω (0) = [0.06, -0.04,0.05] T rad/s。
The above-described embodiments are merely illustrative of the principles of the present invention and its effectiveness, and it will be apparent to those skilled in the art that numerous modifications and improvements can be made without departing from the inventive concept.

Claims (3)

1. A fixed time unwinding-free attitude control method of a spacecraft is characterized by comprising the following steps of: the method comprises the following steps:
step 1, based on a unit quaternion method, taking external interference moment into consideration, and establishing a kinematic and dynamic model of the rigid space vehicle:
wherein (q) v ,q 4 )∈R 3 The x R represents the azimuth of the spacecraft body described by the unit quaternion relative to an inertial coordinate system, and the directions satisfy each otherRepresenting the angular velocity of a spacecraft, I 3 ∈R 3×3 Represents an identity matrix, J.epsilon.R 3×3 Represents an inertia matrix of positive definite symmetry, u epsilon R 3 And d.epsilon.R 3 Representing control moment and external disturbance, respectively, (. Cndot.) × ∈R 3×3 The representative antisymmetric matrix may be expressed as follows:
step 2, designing a fixed-time robust attitude controller without unwinding problem, and analyzing stability;
the fixed-time robust attitude controller in the step 2 is
u＝u 0 +u 1 (7)
S＝ω e +γhsig α (e v )+λhf(e v ) (10)
f(e v )＝[s(e 1 ),s(e 2 ),s(e 3 )] T (11)
Wherein lambda is 1 ,λ 2 And lambda (lambda) 3 Are all normal numbers, alpha>1, s (. Cndot.) can be expressed as
Wherein y is R,0<r<1<r 0 ≤2,Delta is a very small normal number, sign (&) represents the sign function, H E H= { -1,1} is an auxiliary variable, H + = -h, successive and skip sets are defined as respectively
C＝{x∈S 3 ×R 3 ×H:he 4 >-η} (13)
D＝{x∈S 3 ×R 3 ×H:he 4 ≤-η} (14)
Wherein x= { q e ,ω e H }, η e (0, 1) represents the delay gap;
F(e v )＝diag(l(e 1 ),l(e 2 ),l(e 3 )) (16)
sig(ζ)＝[sign(ζ 1 ),sign(ζ 2 ),sign(ζ 3 )] T ,ζ∈R 3 (18)
wherein diag (·) represents the diagonal matrix.
2. The method for controlling a fixed time unreeled attitude of a spacecraft of claim 1, wherein: the spacecraft attitude tracking control model in the step 1 is based on a unit quaternion method, and the kinematics and dynamics model is as follows
ω e ＝ω-Cω d (6)
Wherein omega d ∈R 3 And omega e ∈R 3 Representing the desired angular velocity and the angular velocity tracking error of the spacecraft,is the attitude tracking error, where vector e v ＝[e 1 ,e 2 ,e 3 ]∈R 3 Scalar e 4 E R is the relative pose between the actual pose and the desired pose, the corresponding rotation matrix C e R 3×3 Defined as->Wherein the rotation matrix satisfies c=1 and +.>
3. The method for controlling a fixed time unreeled attitude of a spacecraft of claim 1, wherein: in step 2, the stability analysis includes the steps of:
firstly, proving that the attitude error reaches the sliding mode surface for a fixed time;
secondly, proving that the attitude tracking error converges to any small neighborhood of the balance point along the fixed time of the sliding mode surface, and then gradually converges to the balance point.
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