CN102749846B - Design method of double parallel configuration VSDGCMGs singularity avoidance steering law - Google Patents
Design method of double parallel configuration VSDGCMGs singularity avoidance steering law Download PDFInfo
- Publication number
- CN102749846B CN102749846B CN201210203414.5A CN201210203414A CN102749846B CN 102749846 B CN102749846 B CN 102749846B CN 201210203414 A CN201210203414 A CN 201210203414A CN 102749846 B CN102749846 B CN 102749846B
- Authority
- CN
- China
- Prior art keywords
- msub
- mrow
- mover
- partiald
- msup
- 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.)
- Expired - Fee Related
Links
- 238000000034 method Methods 0.000 title claims abstract description 19
- 238000013461 design Methods 0.000 title claims abstract description 13
- 239000013598 vector Substances 0.000 claims description 56
- 239000011159 matrix material Substances 0.000 claims description 41
- 230000001133 acceleration Effects 0.000 claims description 21
- 238000000354 decomposition reaction Methods 0.000 claims description 6
- 238000012546 transfer Methods 0.000 claims description 6
- 238000005265 energy consumption Methods 0.000 abstract description 9
- 230000008859 change Effects 0.000 description 8
- 238000005259 measurement Methods 0.000 description 8
- 230000008569 process Effects 0.000 description 7
- 230000007547 defect Effects 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 230000007246 mechanism Effects 0.000 description 2
- 238000012545 processing Methods 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- 102000002274 Matrix Metalloproteinases Human genes 0.000 description 1
- 108010000684 Matrix Metalloproteinases Proteins 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 230000009467 reduction Effects 0.000 description 1
- 230000006641 stabilisation Effects 0.000 description 1
- 238000011105 stabilization Methods 0.000 description 1
- 230000002194 synthesizing effect Effects 0.000 description 1
Images
Landscapes
- Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)
Abstract
The invention discloses a design method of double parallel configuration VSDGCMGs singularity avoidance steering law, which comprises the steps of: firstly creating a dynamical model of double parallel configuration VSDGCMGs, and then, analyzing the singularity states of the double parallel configuration VSDGCMGs, finally, creating a framework control target function based on a singularity measure function, creating a flywheel control target function based on rotating speed balance, and designing the double parallel configuration VSDGCMGs singularity avoidance steering law comprehensively considering the singularity avoidance, energy consumption and rotating speed balance. The design method disclosed by the invention can effectively guarantee the output moment precision of the double parallel configuration VSDGCMGs and lay the foundation for agile maneuver attitude control of spacecrafts.
Description
Technical Field
The invention relates to a singularity avoidance control law design method for two parallel-configuration VSDGCMGs, which can be used for effectively avoiding singularities of the two parallel-configuration VSDGCMGs and improving the output torque precision of a two-parallel-configuration variable-speed double-frame control torque gyroscope.
Background
Control Moment Gyros (CMGs) are a type of executing mechanism for spacecraft attitude Control, and the basic principle is that angular momentum exchange occurs between a Control moment gyro and a carrier by changing the direction of a rotating shaft of a gyro rotor rotating at a high speed, so that the angular speed and the attitude of the carrier are changed. Compared with the traditional attitude control mechanisms such as a jet thruster and a momentum wheel, the control moment gyroscope has the remarkable advantages of large control range, high precision, large output moment, capability of working only by electric energy and the like, and is applied to large spacecrafts such as a space station and the like and spacecrafts such as an optical satellite and the like with higher requirements on attitude control precision. In recent years, the application field of the spacecraft is gradually expanded to various types of spacecrafts. The gyro rotor can be classified into a Single-frame control moment gyro (SGCMG) and a Double-frame control moment gyro (DGCMG) according to the degree of freedom of movement of the gyro rotor in addition to rotation. The gyro rotor of the SGCMG can only rotate around 1 frame shaft; while DGCMG can rotate around 2 frame axes. Compared with SGCMG, the DGCMG increases the freedom of movement and greatly improves the capability of outputting three-dimensional moment.
The DGCMG mainly comprises a flywheel rotor rotating at a constant speed and an inner frame and an outer frame supporting the flywheel rotor, the output torque is large, but the torque resolution is low, and the problem of singularity exists. The flywheel (RW) is an attitude control actuator with a variable rotation speed, and has a high resolution of output torque but a small torque value. In order to fully exert the respective advantages of the DGCMG and the RW in the attitude control system of the spacecraft, the constant-speed flywheel of the DGCMG can be changed into a Variable-speed flywheel, namely a Variable-speed double-gimbal control moment gyro (VSDGCMG). Therefore, the VSDGCMG includes a CMG portion through which a large torque can be output (frame rotation) and a RW portion through which resolution of the output torque can be improved (flywheel shift). The VSDGCMG has the advantages of both the CMG and the RW, so that the VSDGCMG can be used for realizing not only the quick maneuvering of the attitude of the spacecraft, but also the high-precision and high-stability control of the attitude of the spacecraft.
The control law design of the VSDGCMG means that a moment command required by attitude control is decomposed into a frame angular rate command and a flywheel rotor angular acceleration command of each VSDGCMG. To design a good law of steering, the first problem to be solved is the singular avoidance. Theoretically, a single VSDGCMG has three degrees of freedom such as the angular velocity of an inner frame and an outer frame and the angular acceleration of a flywheel rotor, and can output three-dimensional torque. However, in the process of practical application, the magnitude of the torque output through the angular acceleration of the rotor is very small, and the demand of the command torque cannot be met generally, so that when the command torque is large, the rotation of the inner frame and the outer frame is required to have the capacity of outputting the three-dimensional torque.
The parallel configuration Variable speed double-frame control moment gyros (VSDGCMGs) mean that all VSDGCMGs are installed in parallel, namely the outer frame shafts of all the gyros are parallel to each other. For two parallel VSDGCMGs, when the rotation of the inner frame and the outer frame of each gyro does not have the three-dimensional moment output capacity, the gyro is in a singular state.
In the prior art, research results about DGCMG manipulation law design exist, and research about VSDGCMG manipulation law is not reported yet. The design of the DGCMG singular avoidance control law mainly comprises a generalized robust pseudo-inverse control law and a pseudo-inverse control law with zero motion. The generalized robust pseudo-inverse steering law is that when the DGCMG is close to the singularity, the equality constraint problem is relaxed to be a minimum value problem, the frame angular rate output torque is allowed to be not equal to the expected torque, and a large output torque error exists, so that the steering law is not preferable in the situation that the output torque precision requirement is high. The pseudo-inverse law of operation with zero motion is that when the DGCMG is close to the singularity, the DGCMG escapes from the singularity as soon as possible by adding the zero motion. The pseudo-inverse manipulation law with zero motion can cause large frame angular rate fluctuation and large energy consumption in the singularity avoidance process, and inconvenience is brought to DGCMG high-precision high-efficiency torque output.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the design method overcomes the defects in the existing method, provides a method for designing the singular avoidance control law of the VSDGCMGs with two parallel configurations, realizes smooth change of the angular rate of the frame and reduction of the total energy consumption when outputting the same command torque as that of the existing singular avoidance control law, ensures the accuracy of the output torque of the VSDGCMGs with the two parallel configurations, and provides a good basis for the control of the agile maneuvering attitude of the spacecraft.
The technical solution of the invention is as follows: a method for designing singular avoidance steering laws of two parallel-configuration VSDGCMGs comprises the following steps:
(1) establishing a dynamic model of two parallel-configuration VSDGCMGs:
i＝1,2
wherein M isBiIs the output torque of the ith VSDGCMG, MBIs the output torque of two parallel-configuration VSDGCMGs; omegabIs the angular velocity of rotation of the satellite relative to the inertial system; j. the design is a squareriIs the polar moment of inertia of the ith VSDGCMG rotor;respectively represent the axial unit vector of the outer frame, the axial unit vector of the inner frame and the axial unit vector of the rotor of the ith VSDGCMG. Rotor speed vector Ω ═ Ω1,Ω2]T，ΩiIs the rotor speed of the ith VSDGCMG; angular rate vector of outer frame 
Is the outer frame angular rate of the ith VSDGCMG; inner gimbal angular rate vector
Is the inner frame angular rate of the ith VSDGCMG; angular acceleration vector of rotor
Is the rotor angular acceleration of the ith VSDGCMG.
Is the current time frame angular rate vector; q is the output torque and
the transfer matrix between the two or more of them,
is the frame angular rate output torque; e is the output torque and
the transfer matrix between the two or more of them,
is the flywheel output torque.
When J isr1＝Jr2＝Jr，Ω1＝Ω2When Ω, then:
wherein, <math>
<mrow>
<mi>D</mi>
<mo>=</mo>
<mo>[</mo>
<msub>
<mover>
<mi>g</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>j</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>×</mo>
<msub>
<mover>
<mi>g</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>s</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mover>
<mi>g</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>j</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>×</mo>
<msub>
<mover>
<mi>g</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>s</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mover>
<mi>g</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>g</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>×</mo>
<msub>
<mover>
<mi>g</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>s</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mover>
<mi>g</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>g</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>×</mo>
<msub>
<mover>
<mi>g</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>s</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>]</mo>
<mo>.</mo>
</mrow>
</math>
(2) performing singular value decomposition on the D array obtained in the step (1), and defining a singular measurement function according to the singular states of two parallel configuration VSDGCMGs:
wherein σ1、σ3The maximum and minimum singular values obtained after singular value decomposition of the matrix D can be expressed as a function of ρ, where ρ ═ α, β]TFor the current time frame angle vector, α ═ α1,α2]T，αiIs the outer frame angle of the ith VSDGCMG, beta ═ beta1,β2]T，βiIs the inner frame angle of the ith VSDGCMG. The closer the k value is to 0, the further away the matrix D is from the singularity,it also means that the further apart the two parallel configurations VSDGCMGs are from the singularity, (i ═ 1, 2).
(3) Neglecting the high-order terms, and obtaining the Taylor expansion of the singular measure function in the step (2) as:
where ρ is0Is the frame angle at the previous time, Δ t is the time interval, H is the Hessian matrix, and g is the gradient vector.
(4) Establishing a frame control target function based on a singular measure function, and obtaining a frame angular rate instruction by solving a minimum value of the control target function
Attitude control command torque LrCan be decomposed into frame angular rate command torque LCMGAnd flywheel command torque LRWConsidering the frame angular rate command torque LCMGSingular avoidance and energy consumption, obtaining a control objective function:
wherein, W1Is a positive definite weighting matrix with the value of aI4×4，a∈[0.5,0.9]，λ1Is the framework Lagrange multiplier vector. And (3) solving a minimum value of the frame control objective function to obtain a frame angular rate instruction:
wherein the intermediate variable matrix
Intermediate variable matrix
Intermediate variable matrix H1＝H+W1。
(5) According to the flywheel output torque in the dynamic model, a flywheel control objective function is established, and the minimum value of the control objective function is solved to obtain the flywheel rotor angular acceleration instruction
Taking into account the flywheel command torque LRWRotating speed balance and energy consumption to obtain a control objective function:
wherein, W2Z is a positive definite weighting array, and values are all bI2×2，b∈[0.002,0.009]，λ2Is a fly-wheel Lagrange multiplier vector,
is the target angular acceleration of the rotor and,
is determined by the following formula:
in the above formula, omegad＝[Ωd1，Ωd2]For a balanced speed vector to be approximated, Ωd1、Ωd2Are taken as the mean value of the rotor speed.
And (3) solving a minimum value of the flywheel control objective function to obtain a flywheel rotor angular acceleration instruction:
wherein the intermediate variable matrix
Intermediate variable matrix
Intermediate variable matrix H2＝Z+W2。
The principle of the invention is as follows:
however, in the process of practical application, the magnitude of the output torque generated by the speed change of the flywheel is very small, and the requirement of the command torque can not be met generally, so that when the command torque is large, the angular rate of the frame is required to have the three-dimensional torque output capability. For two parallel-configuration VSDGCMGs, when the frame angular rate outputs moment vectors in a common plane, the frame angular rate does not have three-dimensional moment output capacity, and the two parallel-configuration VSDGCMGs are in a singular state. Since the frame angular distribution determines the frame angular rate output moment direction, the frame angular distribution of the two parallel configurations VSDGCMGs determines their singular states. By defining a singular measurement function, the singular states of the two parallel-configuration VSDGCMGs can be quantitatively described.
The design principle of the singular measurement function is as follows: in a matrixIn (1),
is the unit vector in the direction of the 1 st VSDGCMG outer frame angular rate output torque,
is the unit vector in the direction of the 2 nd VSDGCMG outer frame angular rate output torque,
is a unit vector in the angular rate output torque direction of the 1 st VSDGCMG inner frame,the vector is a unit vector in the angular rate output moment direction of the 2 nd VSDGCMG inner frame, therefore, the three-dimensional space distribution of each vector in the matrix D represents the three-dimensional moment output capability of two parallel-configuration VSDGCMGs, and the singular measurement function of the two parallel-configuration VSDGCMGs can be designed by utilizing the singular value of the matrix.
Based on a singular measure function, a frame control target function is established, and a frame angular rate instruction which can output instruction torque and change frame angular distribution is designed by solving a minimum value of the control target function so as to enable the frame control target function to escape from singularity.
Compared with the prior art, the invention has the advantages that: the method overcomes the defects that the frame angular rate fluctuation is large, the total energy consumption is large and the frame servo control is inconvenient when the existing singular avoidance control law is close to singularity, establishes a control target function through the definition of the singular measurement functions of the two parallel-configuration VSDGCMGs to obtain the singular avoidance control law of the two parallel-configuration VSDGCMGs, realizes that the frame angular rate changes smoothly and the total energy consumption is reduced when the same instruction torque is output and utilized by the existing control law, ensures the output torque precision of the two parallel-configuration VSDGCMGs, and provides a good basis for the agile maneuvering attitude control of the spacecraft.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of the coordinate systems of two parallel-configuration VSDGCMGs of the present invention;
FIG. 3 is a graph of experimental results of angular rates of inner and outer frames for the 1 st VSDGCMG;
FIG. 4 is a graph of the experimental results of the inner and outer frame angular rates of the 2 nd VSDGCMG.
Detailed Description
A Variable speed double-frame Control moment gyro (VSDGCMG) is mainly composed of a flywheel rotor with a Variable rotation speed and inner and outer frames supporting the flywheel rotor, and thus, the VSDGCMG includes a flywheel (RW) portion and a Control Moment Gyro (CMG) portion. To facilitate the dynamic modeling of two parallel configuration VSDGCMGs systems, a schematic diagram of the coordinate system is established as shown in FIG. 2. Wherein OxbybzbIs a coordinate system of the spacecraft body,
the axial unit vector of the outer frame, the axial unit vector of the inner frame and the axial unit vector of the rotor of the ith VSDGCMG are respectively,is the unit vector in the direction of the 1 st VSDGCMG outer frame angular rate output torque,
is the unit vector in the direction of the 2 nd VSDGCMG outer frame angular rate output torque,
is a unit vector in the angular rate output torque direction of the 1 st VSDGCMG inner frame,
is the unit vector in the angular rate output torque direction of the 2 nd VSDGCMG inner frame.
The specific implementation of the invention is shown in fig. 1, and the steps are as follows:
(1) establishing a dynamic model of two parallel-configuration VSDGCMGs by utilizing a momentum moment theorem:
i＝1,2
wherein M isBiIs the output torque of the ith VSDGCMG, MBIs the output torque of two parallel-configuration VSDGCMGs; omegabIs the angular velocity of rotation of the satellite relative to the inertial system; j. the design is a squareriIs the polar moment of inertia of the ith VSDGCMG rotor;
respectively represent the axial unit vector of the outer frame, the axial unit vector of the inner frame and the axial unit vector of the rotor of the ith VSDGCMG. Rotor speed vector Ω ═ Ω1,Ω2]T，ΩiIs the rotor speed of the ith VSDGCMG; angular rate vector of outer frame
Is the outer frame angular rate of the ith VSDGCMG; inner gimbal angular rate vector
Is the inner frame angular rate of the ith VSDGCMG; angular acceleration vector of rotor
Is the rotor angular acceleration of the ith VSDGCMG.
Is the current time frame angular rate vector; q is the output torque and
the transfer matrix between the two or more of them,
is the frame angular rate output torque; e is the output torque and
the transfer matrix between the two or more of them,is the flywheel output torque.
When J isr1＝Jr2＝Jr，Ω1＝Ω2When Ω, then:
wherein, <math>
<mrow>
<mi>D</mi>
<mo>=</mo>
<mo>[</mo>
<msub>
<mover>
<mi>g</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>j</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>×</mo>
<msub>
<mover>
<mi>g</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>s</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mover>
<mi>g</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>j</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>×</mo>
<msub>
<mover>
<mi>g</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>s</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mover>
<mi>g</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>g</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>×</mo>
<msub>
<mover>
<mi>g</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>s</mi>
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mover>
<mi>g</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>g</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>×</mo>
<msub>
<mover>
<mi>g</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>s</mi>
<mn>2</mn>
</mrow>
</msub>
<mo>]</mo>
<mo>.</mo>
</mrow>
</math>
(2) performing singular value decomposition on the D array obtained in the step (1), defining a singular measurement function according to the singular state of two parallel configuration VSDGCMGs, and solving a Taylor expansion of the singular measurement function;
(a) singular state analysis of two parallel configuration VSDGCMGs
Although a single VSDGCMG has three degrees of freedom such as rotation of an inner frame and an outer frame and speed change of a flywheel, and can output three-dimensional torque, in the practical application process, the magnitude of the output torque generated by speed change of the flywheel is very small, and the demand of the command torque cannot be met generally, so that when the command torque is large, the angular rate of the frame is required to have three-dimensional torque output capacity. For two parallel-configuration VSDGCMGs, when the frame angular rate outputs moment vectors in a common plane, the frame angular rate does not have three-dimensional moment output capacity, and the two parallel-configuration VSDGCMGs are in a singular state.
The closer the two parallel-configuration VSDGCMGs are to the singular state, the larger the frame angular rate amplitude fluctuation is; the farther two parallel configurations VSDGCMGs are away from the singular state, the more stable the frame angular rate amplitude is. By defining a singular measurement function, the singular states of the VSDGCMGs can be described quantitatively.
(b) Defining a singular measure function:
wherein σ1、σ3After singular value decomposition of the matrix D, respectivelyThe resulting maximum and minimum singular values may be expressed as a function of p, where p ═ α, β]TFor the current time frame angle vector, α ═ α1,α2]T，αiIs the outer frame angle of the ith VSDGCMG, beta ═ beta1,β2]T，βiIs the inner frame angle of the ith VSDGCMG. The closer the k value is to 0, the farther the matrix D is from the singularity, and the farther the two parallel configurations VSDGCMGs are from the singularity. (i ═ 1, 2) (c) neglecting higher order terms, and obtaining taylor expansion of the singular measure function in step (2) as:
where ρ is0Is the frame angle at the previous moment, Δ t is the time interval, H is the Hessian matrix, g is the gradient vector; the first and second partial derivatives of the singular measure function k ═ V (ρ) with respect to the inner and outer frame angles are:
wherein:
wherein, i is 1,2, j is 1, 2.
According to the VSDGCMGs output torque direction change condition caused by the inner and outer frame angles, the first and second partial derivatives of the matrix D relative to the inner and outer frame angles can be obtained:
the singular values of matrix D are decomposed as:
D＝U∑VT
wherein U, V is an orthogonal matrix obtained by decomposing D singular values, and Σ is a diagonal matrix obtained by decomposing D singular values: sigma is diag (sigma)1,σ2,σ3)，σ1、σ2、σ3Is the singular value of D.
Let ujJ-th column vector of U, vjThe jth column vector of V is then the sigma1、σ3The first and second partial derivatives with respect to the inner and outer frame angles are as follows:
j＝1,3;i＝1,2;k＝1,2
(3) establishing a frame control target function based on a singular measure function, and obtaining a frame angular rate instruction by solving a minimum value of the control target function;
attitude control command torque LrCan be decomposed into frame angular rate command torque LCMGAnd flywheel command torque LRWConsidering the frame angular rate command torque LCMGSingular avoidance and energy consumption to obtain a frame control objective function:
wherein, W1Is a positive definite weighting matrix with the value of aI4×4，a∈[0.5,0.9]，λ1Is the framework Lagrange multiplier vector.
And (3) solving a minimum value of the frame control objective function to obtain a frame angular rate instruction:
wherein the intermediate variable matrix
Intermediate variable matrix
Intermediate variable matrix H1＝H+W1。
(4) And establishing a flywheel control objective function according to the flywheel output torque in the dynamic model, and obtaining a flywheel rotor angular acceleration instruction by solving a minimum value of the control objective function.
Taking into account the flywheel command torque LRWRotating speed balance and energy consumption to obtain a flywheel control objective function:
wherein, W2Z is a positive definite weighting array, and values are all bI2×2，b∈[0.002,0.009]，λ2Is a fly-wheel Lagrange multiplier vector,
is the target angular acceleration of the rotor and,
is determined by the following formula:
in the above formula, omegad＝[Ωd1，Ωd2]For a balanced speed vector to be approximated, Ωd1、Ωd2Are taken as the mean value of the rotor speed.
And (3) solving a minimum value of the flywheel control objective function to obtain a flywheel rotor angular acceleration instruction:
wherein the intermediate variable matrix
Intermediate variable matrix
Intermediate variable matrix H2＝Z+W2。
And (3) synthesizing the frame angular rate instruction and the flywheel rotor angular acceleration instruction to obtain two parallel configuration VSDGCMGs control laws:
setting the maximum value of the frame angular rate to
Then pairAfter the amplitude limiting processing is carried out, the following results are obtained:
let the maximum value of the angular acceleration of the rotor be
Then pair
After the amplitude limiting processing is carried out, the following results are obtained:
when the manipulation law is applied, the total command torque L given by the attitude control systemrDecomposed into frame angular rate command torque LCMGAnd flywheel command torque LRWThe method comprises the following steps:
(a) when the spacecraft is in the attitude maneuver stage, if the VSDGCMGs are far away from the singular state, the following steps are carried out: l isCMG＝Lr，L RW0; if VSDGCMGs approach the singular state, the flywheel speed change is used to compensate for the output torque error due to the frame angular rate limit: l isCMG＝Lr，
(b) When the spacecraft is in the attitude stabilization stage, the output torque of the flywheel speed change is taken as the main, the output torque of the frame rotation is taken as the auxiliary, and the output of the instruction torque is completed: l isRW＝Lr，
The VSDGCMG control law mainly comprises a frame control law and a flywheel control law, and the singular avoidance is mainly realized by the frame control law. In order to verify the singular avoidance performance of the singular avoidance steering law of the present invention VSDGCMG, the singular avoidance steering law of the present invention VSDGCMG was compared with the existing singular avoidance steering law of the DGCMG experimentally, and the results are shown in fig. 3 and 4. The experimental parameters were as follows:
command torque: l isr＝[0.5,0.5,0.5]TN.m; initial frame angle: rho is [0 °,0 °,195 °,0 °]TMaximum angular velocity of inner and outer frames
Average rotating speed of the rotor: omega 3762 rpm; moment of inertia J of rotorri＝diag[0.062,0.102,0.062]kg·m2I 1,2, wherein the moment of inertia of the rotor pole Jr＝0.102kg·m2(ii) a Moment of inertia J of the outer frameji＝diag[0.722,0.722,0.7224]kg·m2Inner frame moment of inertia Jgi＝diag[0.297,0.098,0.098]kg·m2(ii) a The parameter a is 0.8, and the parameter b is 0.008.
In fig. 3a, the dotted line is the inner frame angular rate curve of the 1 st VSDGCMG obtained by using the conventional steering law, the solid line is the inner frame angular rate curve of the 1 st VSDGCMG obtained by using the steering law of the present invention, the amplitude fluctuation of the dotted line is 13.48 °/s, the amplitude fluctuation of the solid line is 4.353 °/s, which is 68% lower than that of the dotted line; in fig. 3b, the dotted line is the outer frame angular rate curve of the 1 st VSDGCMG obtained by using the conventional manipulation law, the solid line is the outer frame angular rate curve of the 1 st VSDGCMG obtained by using the manipulation law of the present invention, the amplitude fluctuation of the dotted line is 9.089 °/s, the amplitude fluctuation of the solid line is 3.056 °/s, which is reduced by 66% compared with the dotted line; in fig. 4a, the dotted line is the inner frame angular rate curve of the 2 nd VSDGCMG obtained by using the conventional steering law, the solid line is the inner frame angular rate curve of the 2 nd VSDGCMG obtained by using the steering law of the present invention, the amplitude fluctuation of the dotted line is 14.082 °/s, the amplitude fluctuation of the solid line is 4.583 °/s, which is 67% lower than that of the dotted line; in fig. 4b, the dotted line is the outer frame angular rate curve of the 2 nd VSDGCMG obtained using the conventional steering law, the solid line is the outer frame angular rate curve of the 2 nd VSDGCMG obtained using the steering law of the present invention, the amplitude fluctuation of the dotted line is 10.23 °/s, the amplitude fluctuation of the solid line is 3.615 °/s, which is 65% lower than that of the dotted line. From the above, the frame angular rate fluctuation in the steering law of the present invention is significantly smaller than that of the existing steering law.
In the experimental process, the frame angular rate of the existing singular avoidance control law fluctuates in the first 30s, which indicates that the two parallel configuration VSDGCMGs are close to the singular state, the frame angular rate tends to be stable in the second 20s, which indicates that the two parallel configuration VSDGCMGs are far away from the singular state, and the total energy consumed in the whole process is about 0.0535J; the frame angular rate of the singular avoidance control law of the invention fluctuates in the first 20s, which indicates that the two parallel configuration VSDGCMGs are close to the singular state, the frame angular rate tends to be stable in the second 30s, which indicates that the two parallel configuration VSDGCMGs are far away from the singular state, and the total energy consumed in the whole process is about 0.0083J. From the above, the time for the maneuver law of the present invention to escape from singularity is 10s shorter than the existing maneuver law, and the total energy consumed is 84% less than the existing maneuver law.
Those skilled in the art will appreciate that the invention may be practiced without these specific details.
Claims (1)
1. A method for designing singular avoidance steering laws of two parallel-configuration VSDGCMGs is characterized by comprising the following steps:
(1) establishing a dynamic model of two parallel-configuration VSDGCMGs as follows:
i＝1,2
wherein M isBiIs the output torque of the ith VSDGCMG, MBIs the output torque of two parallel-configuration VSDGCMGs; omegabIs the angular velocity of rotation of the satellite relative to the inertial system; j. the design is a squareriIs the polar moment of inertia of the ith VSDGCMG rotor;respectively representing the axial unit vector of the outer frame, the axial unit vector of the inner frame and the axial unit vector of the rotor of the ith VSDGCMG; rotor speed vector Ω ═ Ω1,Ω2]T，ΩiIs the rotor speed of the ith VSDGCMG; angular rate vector of outer frame
Is the outer frame angular rate of the ith VSDGCMG; inner gimbal angular rate vector
Is the inner frame angular rate of the ith VSDGCMG; angular acceleration of rotorVector quantityIs the rotor angular acceleration of the ith VSDGCMG,is the current time frame angular rate vector; q is the output torque and
the transfer matrix between the two or more of them,
is the frame angular rate output torque; e is the output torque and
the transfer matrix between the two or more of them,
is the flywheel output torque;
when J isr1＝Jr2＝Jr，Ω1＝Ω2When Ω, there are:
＝JrΩD
wherein,
(2) performing singular value decomposition on the D array obtained in the step (1), and defining singularities according to the singular states of two parallel VSDGCMGsThe measure function is:
wherein σ1、σ3The maximum and minimum singular values obtained after singular value decomposition of the matrix D can be expressed as a function of ρ, where ρ ═ α, β]TFor the current time frame angle vector, α ═ α1,α2]T，αiIs the outer frame angle of the ith VSDGCMG, beta ═ beta1,β2]T，βiThe i-th VSDGCMG inner frame angle is 1, 2;
(3) neglecting high-order terms, and obtaining Taylor expansion of the singular measure function in the step (2) as:
in the formula,
where ρ is0Is the frame angle vector at the previous moment, Δ t is the time interval, H is the Hessian matrix, g is the gradient vector;
(4) based on the singular measure function, establishing a frame control target function as follows:
wherein, W1Is a positive definite weighting matrix with the value of aI4×4，a∈[0.5,0.9]，λ1Is a frame Lagrange multiplier vector, LCMGIs the frame angular rate command torque;
the frame angular rate command is:
wherein the intermediate variable matrix
Intermediate variable matrix
Intermediate variable matrix H1＝H+W1；
Obtaining a frame angular rate instruction by solving a minimum value of a control objective function;
(5) according to flywheel output torque in two parallel configuration VSDGCMGs dynamic models
The flywheel control objective function is established as follows:
wherein, W2Z is a positive definite weighting array, and values are all bI2×2，b∈[0.002,0.009]，λ2Is the Lagrange multiplier vector of the flywheel, LRWIs the command torque of the flywheel,is the target angular acceleration of the rotor and,
is determined by the following formula:
in the above formula, omegad＝[Ωd1,Ωd2]For a balanced speed vector to be approximated, Ωd1、Ωd2Taking the average value of the rotating speed of the rotor;
the angular acceleration instruction of the flywheel rotor is as follows:
wherein the intermediate variable matrix
Intermediate variable matrix
Intermediate variable matrix H2＝Z+W2；
Obtaining a flywheel rotor angular acceleration instruction by solving a minimum value for a control target function, and obtaining two parallel configuration VSDGCMGs manipulation laws by integrating a frame angular rate instruction and the flywheel rotor angular acceleration instruction:
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201210203414.5A CN102749846B (en) | 2012-06-15 | 2012-06-15 | Design method of double parallel configuration VSDGCMGs singularity avoidance steering law |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201210203414.5A CN102749846B (en) | 2012-06-15 | 2012-06-15 | Design method of double parallel configuration VSDGCMGs singularity avoidance steering law |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN102749846A CN102749846A (en) | 2012-10-24 |
| CN102749846B true CN102749846B (en) | 2014-05-07 |
Family
ID=47030130
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201210203414.5A Expired - Fee Related CN102749846B (en) | 2012-06-15 | 2012-06-15 | Design method of double parallel configuration VSDGCMGs singularity avoidance steering law |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN102749846B (en) |
Families Citing this family (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105223961B (en) * | 2015-10-16 | 2018-04-13 | 北京机械设备研究所 | It is a kind of to be used for the unusual Spacecraft Attitude Control method evaded of control-moment gyro |
| CN106441255A (en) * | 2016-09-07 | 2017-02-22 | 哈尔滨工业大学 | Spacecraft angular rate real-time linearization measurement method based on gyroscope flywheel |
| CN111309038B (en) * | 2020-02-21 | 2021-05-11 | 南京航空航天大学 | Hybrid execution mechanism configuration optimization method based on TU cooperative game manipulation law |
| CN111367304B (en) * | 2020-02-25 | 2023-07-14 | 上海航天控制技术研究所 | Actuating mechanism configuration and use method based on dual heterogeneous moment gyro group |
| CN111781833B (en) * | 2020-07-17 | 2021-06-25 | 北京航空航天大学 | Spacecraft online optimal attitude avoidance control method based on state dependence decomposition |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN100559315C (en) * | 2008-04-22 | 2009-11-11 | 北京航空航天大学 | A kind of double-frame magnetic suspension control moment gyroscope control system |
| CN101763038A (en) * | 2009-12-22 | 2010-06-30 | 北京航空航天大学 | Method for controlling structural modal vibration of dual-frame magnetic levitation control moment gyroscope |
| CN101891018A (en) * | 2010-07-09 | 2010-11-24 | 中国科学院长春光学精密机械与物理研究所 | Single frame control moment gyro control method based on moment output capability optimization |
| CN102063521A (en) * | 2010-10-12 | 2011-05-18 | 北京理工大学 | Design method for configuration-adjustable single-framework control moment gyro system |
| CN101750200B (en) * | 2009-12-30 | 2011-06-15 | 航天东方红卫星有限公司 | Method for determining flutter response of high-resolution minisatellites |
-
2012
- 2012-06-15 CN CN201210203414.5A patent/CN102749846B/en not_active Expired - Fee Related
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN100559315C (en) * | 2008-04-22 | 2009-11-11 | 北京航空航天大学 | A kind of double-frame magnetic suspension control moment gyroscope control system |
| CN101763038A (en) * | 2009-12-22 | 2010-06-30 | 北京航空航天大学 | Method for controlling structural modal vibration of dual-frame magnetic levitation control moment gyroscope |
| CN101750200B (en) * | 2009-12-30 | 2011-06-15 | 航天东方红卫星有限公司 | Method for determining flutter response of high-resolution minisatellites |
| CN101891018A (en) * | 2010-07-09 | 2010-11-24 | 中国科学院长春光学精密机械与物理研究所 | Single frame control moment gyro control method based on moment output capability optimization |
| CN102063521A (en) * | 2010-10-12 | 2011-05-18 | 北京理工大学 | Design method for configuration-adjustable single-framework control moment gyro system |
Also Published As
| Publication number | Publication date |
|---|---|
| CN102749846A (en) | 2012-10-24 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN106292681B (en) | A kind of satellite Active Fault-tolerant Control Method distributed based on observer and On-line Control | |
| Zhao et al. | Attitude control for quadrotors subjected to wind disturbances via active disturbance rejection control and integral sliding mode control | |
| CN104527994B (en) | Multi-polar cross-over becomes the track set time soon and holds position sensing tracking and controlling method | |
| CN110794863B (en) | Heavy carrier rocket attitude control method capable of customizing control performance indexes | |
| CN105116910B (en) | A kind of satellite attitude control method to ground point staring imaging | |
| CN106896821B (en) | A kind of angular momentum management method of variable speed control moment gyro | |
| CN103869704B (en) | Based on the robot for space star arm control method for coordinating of expansion Jacobian matrix | |
| CN103592848B (en) | Method for accurately and quickly manipulating variable speed control moment spinning top group | |
| CN103092208B (en) | Spacecraft high-accuracy speediness attitude maneuver method based on single gimbal control moment gyro (SGCMG) and reaction wheel (RW) | |
| Sun et al. | Neural network-based sliding mode control for atmospheric-actuated spacecraft formation using switching strategy | |
| CN104570742B (en) | Feedforward PID (proportion, integration and differentiation) control based rapid high-precision relative pointing control method of noncoplanar rendezvous orbit | |
| CN107688295A (en) | A kind of quadrotor finite time self-adaptation control method based on fast terminal sliding formwork | |
| CN102749846B (en) | Design method of double parallel configuration VSDGCMGs singularity avoidance steering law | |
| Tian et al. | Nonlinear robust control for reusable launch vehicles in reentry phase based on time-varying high order sliding mode | |
| CN105629732B (en) | A kind of spacecraft attitude output Tracking Feedback Control method for considering Control constraints | |
| Zhang et al. | Robust backstepping control for agile satellite using double-gimbal variable-speed control moment gyroscope | |
| CN104238563B (en) | Design method of control moment gyroscopes with surface inclination angles changeable | |
| CN107402516B (en) | Rank saturation the fuzzy PD attitude control method is passed based on joint executing agency | |
| CN104360686B (en) | Nonsingular terminal sliding mode flight path control method for airships | |
| CN107992062B (en) | Spatial high-dynamic target high-precision attitude tracking control method based on hybrid actuating mechanism | |
| CN104656447A (en) | Differential geometry nonlinear control method for aircraft anti-interference attitude tracking | |
| Zhang et al. | Output-feedback super-twisting control for line-of-sight angles tracking of non-cooperative target spacecraft | |
| Romagnoli et al. | High performance two degrees of freedom attitude control for solar sails | |
| Cai et al. | Optimal satellite formation reconfiguration actuated by inter-satellite electromagnetic forces | |
| Zhang et al. | Integrated translational and rotational control for the terminal landing phase of a lunar module |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| C14 | Grant of patent or utility model | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20140507 |