CN110658862B - Flexible structure vibration energy integrated control method based on distributed angular momentum - Google Patents

Flexible structure vibration energy integrated control method based on distributed angular momentum Download PDF

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CN110658862B
CN110658862B CN201910951688.4A CN201910951688A CN110658862B CN 110658862 B CN110658862 B CN 110658862B CN 201910951688 A CN201910951688 A CN 201910951688A CN 110658862 B CN110658862 B CN 110658862B
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flexible structure
angular momentum
flywheel
energy
control moment
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CN110658862A (en
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郭川东
胡权
刘菲
沈东�
张尧
张军
李晓辉
刘维惠
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Beijing Institute of Technology BIT
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D17/00—Control of torque; Control of mechanical power
    • G05D17/02—Control of torque; Control of mechanical power characterised by the use of electric means
    • 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
    • B64G1/28—Guiding or controlling apparatus, e.g. for attitude control using inertia or gyro effect
    • B64G1/285—Guiding or controlling apparatus, e.g. for attitude control using inertia or gyro effect using momentum wheels
    • 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
    • B64G1/28—Guiding or controlling apparatus, e.g. for attitude control using inertia or gyro effect
    • B64G1/286—Guiding or controlling apparatus, e.g. for attitude control using inertia or gyro effect using control momentum gyroscopes (CMGs)
    • 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
    • B64G1/36—Guiding or controlling apparatus, e.g. for attitude control using sensors, e.g. sun-sensors, horizon sensors

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Abstract

The invention discloses a distributed angular momentum-based flexible structure vibration energy integrated control method, and belongs to the technical field of aerospace. The implementation method of the invention comprises the following steps: establishing a vibration equation, a power equation and a measurement matrix of a flexible spacecraft system by installing angular momentum exchange devices and sensors on a flexible spacecraft in a distributed manner; selecting an angular momentum exchange device working mode according to the angular momentum exchange device, wherein the angular momentum exchange device working mode comprises a variable speed control moment gyro mode, a momentum wheel mode and a control moment gyro and momentum wheel combined mode; based on the selected working mode of the angular momentum exchange device, the manipulation law of the angular momentum exchange device is selected, the power requirements of other subsystems are met, vibration suppression of the flexible structure is achieved, and integrated control of vibration energy of the flexible structure based on distributed angular momentum is achieved. The invention can reduce the weight of the energy storage system, thereby reducing the influence of the distributed angular momentum exchange device on the mass and inertia of the whole system.

Description

Flexible structure vibration energy integrated control method based on distributed angular momentum
Technical Field
The invention relates to a flexible structure vibration energy integrated control method based on distributed angular momentum, and belongs to the technical field of aerospace.
Background
With the improvement of the precision and capacity requirements of space missions, the sizes of solar sailboards and antennas of spacecrafts have been developed from ten meters to hundred meters. Different from the traditional 'central rigid body + flexible attachment' spacecraft, the flexible structure of the large-scale spacecraft becomes a system main body, and the control quantity must be applied to the flexible structure in a distributed manner, so that high-precision active control can be realized to meet task requirements. The angular momentum exchange devices such as momentum wheels, control moment gyros and the like are installed on the large flexible structure in a distributed mode, distributed modal force can be applied to achieve structural vibration suppression, and propellant is not consumed at the same time. The system thus obtained is called a gyroscopic flexure.
However, mounting angular momentum exchange devices on flexible structures increases the mass and inertia of the system, which is in conflict with the goal of lightweight design of flexible spacecraft. On the one hand, angular momentum exchange devices of smaller size, lighter weight can be used. On the other hand, the angular momentum exchange device can be fully utilized to have more functions, so that the mass of other subsystems is reduced. The invention provides a flexible structure vibration energy integrated control method based on distributed angular momentum, which makes full use of a flywheel rotating at a high speed in an angular momentum exchange device and stores energy by using the flywheel, so that an energy storage system and a vibration suppression system are integrated into a system. The scheme can reduce the weight of the energy storage system, thereby reducing the influence of the distributed angular momentum exchange device on the mass and inertia of the whole system.
Disclosure of Invention
The invention discloses a flexible structure vibration energy integrated control method based on distributed angular momentum, which solves the technical problems that: the flywheel rotating at high speed in the angular momentum exchange device is fully utilized, energy is stored by utilizing the flywheel, so that the energy storage system and the vibration suppression system are integrated into a system, and when the flexible structure vibrates, the control system can actively suppress the vibration; when the flexible structure does not vibrate or the amplitude is small, the control system can absorb or release energy while keeping the structure well damped; when the power supply of other subsystems is over demand, the control system can absorb the redundant energy of other subsystems, and when the power supply of other subsystems is short demand, the control system can release the energy to supplement the requirements of other subsystems. Through the improvement, the weight of the energy storage system can be reduced, and therefore the influence of the distributed angular momentum exchange device on the mass and inertia of the whole system is reduced.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a distributed angular momentum-based flexible structure vibration energy integrated control method, which is characterized in that a plurality of angular momentum exchange devices and sensors are installed on a flexible spacecraft in a distributed manner, and a vibration equation, a power equation and a measurement matrix of a flexible spacecraft system are established; then selecting the working mode of the angular momentum exchange device according to the angular momentum exchange device, wherein the working mode of the angular momentum exchange device comprises a variable speed control moment gyro mode, a momentum wheel mode and a combined mode of the control moment gyro and the momentum wheel; and finally, based on the selected working mode of the angular momentum exchange device, selecting a manipulation law of the angular momentum exchange device which can meet the power requirements of other subsystems and realize the vibration suppression of the flexible structure, and realizing the integrated control of the vibration energy of the flexible structure based on the distributed angular momentum.
The invention discloses a distributed angular momentum-based flexible structure vibration energy integrated control method, which comprises the following steps of:
the method comprises the following steps: and a plurality of angular momentum exchange devices and sensors are arranged on the flexible structure in a distributed manner.
Step two: and establishing a vibration equation, a power equation and a measurement matrix of the flexible structure system.
Step three: and selecting the working mode of the angular momentum exchange device according to the angular momentum exchange device, and selecting the control law of the angular momentum exchange device which can meet the power requirements of other subsystems and realize the vibration suppression of the flexible structure, namely realizing the integrated control of the vibration energy of the flexible structure based on the distributed angular momentum.
The other subsystems refer to: all subsystems on the flexible structure except for distributed angular momentum.
The finger meeting other subsystem power requirements means: when the power supply of other subsystems is over demand, the control system can absorb the redundant energy of other subsystems, and when the power supply of other subsystems is short demand, the control system can release the energy to supplement the requirements of other subsystems.
The flexible structure vibration suppression implementation means that: when the flexible structure vibrates, the control system can actively inhibit the vibration; when the flexible structure is not vibrating or has small amplitude, the control system is able to absorb or release energy while maintaining good damping of the structure.
The working modes of the angular momentum exchange device comprise the following three modes:
the first method is as follows: "variable speed control moment gyro" mode: the angular momentum exchange device is a variable speed control moment gyro which mainly comprises a flywheel rotating at a high speed and a frame outputting moment. The system works in a mode of 'variable speed control moment gyro', fully utilizes a flywheel rotating at a high speed in an angular momentum exchange device to store or release energy by selecting an acceleration law of the flywheel, and meets the power requirements of other subsystems by storing or releasing the energy of the flywheel; meanwhile, the frame shaft outputs vibration suppression modal force by selecting the manipulation law of the frame shaft so as to meet the vibration suppression requirement of the flexible structure, namely, the energy storage system and the vibration suppression system are integrated into a system by simultaneously selecting the acceleration law of the flywheel and the manipulation law of the frame shaft, so that the flexible structure vibration energy integrated control based on the distributed angular momentum is realized.
The second method comprises the following steps: "momentum wheel" mode: the angular momentum exchange device is a control moment gyro, a momentum wheel or various configurations derived from a variable speed control moment gyro and the momentum wheel. The angular momentum exchange device works in a 'momentum wheel' mode, a flywheel acceleration law is selected based on a projection matrix method, the flywheel acceleration law is in a column matrix form, the flywheel acceleration law is divided into two parts which are orthogonal to each other, one part is used for storing or releasing energy to meet the power requirements of other subsystems, the other part is used for outputting vibration suppression modal force to meet the vibration suppression requirements of a flexible structure, namely the flywheel acceleration law is selected based on the projection matrix method, so that an energy storage system and a vibration suppression system are integrated into a system, and the flexible structure vibration energy integrated control based on distributed angular momentum is realized.
The third method comprises the following steps: the combined mode of the control moment gyro and the momentum wheel is as follows: the angular momentum exchange device is a control moment gyro, a momentum wheel or various configurations derived from a variable speed control moment gyro and the momentum wheel. When the amplitude of the flexible structure is large, the variable-speed control moment gyroscope works in a 'control moment gyroscope' mode, and vibration suppression is quickly realized by selecting a frame shaft steering law to output large moment; when the flexible structure does not vibrate or the amplitude is small, the variable-speed control moment gyroscope works in a momentum wheel mode, a flywheel acceleration law is selected based on a projection matrix method, the flywheel acceleration law is divided into two parts which are orthogonal to each other, one part is used for storing energy or releasing energy to meet the power requirements of other subsystems, the other part is used for outputting vibration suppression modal force to meet the vibration suppression requirements of the flexible structure, namely the flywheel acceleration law is selected based on the projection matrix method, so that the energy storage system and the vibration suppression system are integrated into a system, and the flexible structure vibration energy integrated control based on distributed angular momentum is realized.
The small amplitude range and the medium amplitude range of the flexible structure are set according to task precision requirements.
Preferably, the sensors include a MEMS angular velocity meter and a linear velocity meter.
Preferably, for a constraint boundary gyroscope flexible structure for installing a variable speed control moment gyroscope, the vibration energy integrated control method of the flexible structure based on distributed angular momentum disclosed by the invention comprises the following steps:
the method comprises the following steps: n variable speed control moment gyroscopes are installed on the constraint boundary flexible structure in a distributed mode, and n angular speed meters are installed in a co-location mode.
Step two: and establishing a vibration equation, a power equation and a measurement matrix of the constraint boundary gyroscope flexible structure.
Step 2.1: and establishing a vibration equation of the flexible structure of the constraint boundary gyroscope.
Establishing a constraint boundary gyroscope flexible structure vibration equation as
Figure BDA0002225964370000031
Wherein:
Figure BDA0002225964370000032
is the modal coordinate of the flexible structure, k is the order of the modal coordinate describing the elastic movement of the flexible structure; eaA modal mass matrix representing a flexible structure with a variable speed control moment gyro; dbAnd ΛbRespectively representing a rigidity matrix and a damping matrix; g is a gyro coupling matrix;
Figure BDA0002225964370000033
representing the generalized modal force generated by the acceleration of a rotor of the variable speed control moment gyroscope; omega is a rotor speed matrix, and omega is [ omega ]1,...,Ωn]T，ΩiThe rotor speed of the ith variable speed control moment gyro is controlled;
Figure BDA0002225964370000034
is a generalized modal force generated by the rotation of a frame shaft of the variable-speed control moment gyroscope;
Figure BDA0002225964370000035
is a matrix of the rotational speed of the frame shaft,
Figure BDA0002225964370000036
the frame shaft rotation speed of the ith variable speed control moment gyro. Wherein the content of the first and second substances,
Figure BDA0002225964370000037
Figure BDA0002225964370000038
Figure BDA0002225964370000039
Figure BDA00022259643700000310
Figure BDA00022259643700000311
wherein:
Figure BDA00022259643700000312
and
Figure BDA00022259643700000313
respectively a translational modal vector and a rotational modal vector of a mass infinitesimal dm on a flexible structure; m isgiThe mass of the ith variable speed control moment gyro; j. the design is a squaregiThe moment of inertia of the frame shaft of the ith variable speed control moment gyro; j. the design is a squareriThe moment of inertia of the gyro flywheel is the ith variable speed control moment,
Figure BDA00022259643700000314
Ab,gigyro frame axis coordinate system f for ith variable speed control momentgiTo the flexible structure body coordinate system fbThe coordinate transformation matrix of (a) is,
Figure BDA0002225964370000041
Figure BDA0002225964370000042
and
Figure BDA0002225964370000043
is Ab,giThe column submatrix of (1);
Figure BDA0002225964370000044
and
Figure BDA0002225964370000045
is that
Figure BDA0002225964370000046
The term (2) is used in (1),
Figure BDA0002225964370000047
and
Figure BDA0002225964370000048
is RgiThe row submatrix. The frame shaft moves by a small amount
Figure BDA0002225964370000049
Wherein:
Figure BDA00022259643700000410
chinese superscript "0"means
Figure BDA00022259643700000411
Is equal to
Figure BDA00022259643700000412
The value at the initial instant.
Step 2.2: and establishing a power equation of the flexible structure of the constraint boundary gyroscope.
The energy storage and discharge power of the flexible structure of the constraint boundary gyroscope is
Figure BDA00022259643700000413
Wherein:
Figure BDA00022259643700000414
step 2.3: and establishing a measurement matrix of the constraint boundary gyroscope flexible structure.
The measuring direction of each angular velocity sensor is consistent with the torque direction generated when the variable speed control moment gyro works in the 'control moment gyro' mode at the initial time, and the measuring matrix is
Figure BDA00022259643700000415
Wherein:
Figure BDA00022259643700000416
for the measurement of the i-th sensor,
Figure BDA00022259643700000417
then there is
Figure BDA00022259643700000418
Wherein
Figure BDA00022259643700000419
Step three: and selecting an angular momentum exchange device control law which can meet the power requirements of other subsystems and realize flexible structure vibration suppression at the same time according to the selected working mode of the angular momentum exchange device, namely realizing the flexible structure vibration energy integrated control based on the distributed angular momentum.
The working modes of the angular momentum exchange device comprise the following three modes:
the first method is as follows: "variable speed control moment gyro" mode: the angular momentum exchange device is a variable speed control moment gyro which mainly comprises a flywheel rotating at a high speed and a frame outputting moment. The system works in a mode of 'variable speed control moment gyro', fully utilizes a flywheel rotating at a high speed in an angular momentum exchange device to store or release energy by selecting an acceleration law of the flywheel, and meets the power requirements of other subsystems by storing or releasing the energy of the flywheel; meanwhile, the frame shaft outputs vibration suppression modal force by selecting the manipulation law of the frame shaft so as to meet the vibration suppression requirement of the flexible structure, namely, the energy storage system and the vibration suppression system are integrated into a system by simultaneously selecting the acceleration law of the flywheel and the manipulation law of the frame shaft, so that the flexible structure vibration energy integrated control based on the distributed angular momentum is realized.
The specific implementation method comprises the following steps: the energy is stored or released by fully utilizing the flywheel rotating at high speed in the angular momentum exchange device through selecting the acceleration law of the flywheel, and the power requirements of other subsystems are met through the energy storage or release of the flywheel; meanwhile, the frame shaft outputs vibration suppression modal force by selecting the manipulation law of the frame shaft so as to meet the vibration suppression requirement of the flexible structure.
Step 3.1.1: based on a projection matrix method, a flywheel acceleration law is selected as
Figure BDA0002225964370000051
Wherein: pdPower requirements for other subsystems;
Figure BDA0002225964370000052
wherein InIs an n × n identity matrix;
Figure BDA0002225964370000053
S1S1＝S1，
Figure BDA0002225964370000054
that is, the selected flywheel acceleration laws can only output power to meet the system power demand, without applying modal forces to the structure.
Step 3.1.2: selecting the frame axis manipulation law as
Figure BDA0002225964370000055
Wherein: feedback parameter kd＝diag[kd1,...,kdn]，kdi>0。
The second method comprises the following steps: "momentum wheel" mode: the angular momentum exchange device is a control moment gyro, a momentum wheel or various configurations derived from a variable speed control moment gyro and the momentum wheel. The angular momentum exchange device works in a 'momentum wheel' mode, a flywheel acceleration law is selected based on a projection matrix method, the flywheel acceleration law is in a column matrix form, the flywheel acceleration law is divided into two parts which are orthogonal to each other, one part is used for storing or releasing energy to meet the power requirements of other subsystems, the other part is used for outputting vibration suppression modal force to meet the vibration suppression requirements of a flexible structure, namely the flywheel acceleration law is selected based on the projection matrix method, so that an energy storage system and a vibration suppression system are integrated into a system, and the flexible structure vibration energy integrated control based on distributed angular momentum is realized.
The second specific implementation method comprises the following steps: the method comprises the steps of selecting an acceleration law of a flywheel based on a projection matrix method, wherein the acceleration law of the flywheel is in a column matrix form, dividing the acceleration law of the flywheel into two parts which are orthogonal to each other, wherein one part is used for storing energy or releasing energy to meet the power requirements of other subsystems, and the other part is used for outputting vibration suppression modal force to meet the vibration suppression requirements of a flexible structure.
Step 3.2: based on a projection matrix method, a flywheel acceleration law is selected as
Figure BDA0002225964370000056
Wherein:
Figure BDA0002225964370000057
Figure BDA0002225964370000058
Figure BDA0002225964370000059
wherein: t iscObtaining the expected vibration suppression modal force through negative feedback of a sensor measured value; s1Is N (B)Ω) Of the projection matrix, thus S1u1At BΩIn the null space of (1), i.e. S1u1Modal force cannot be generated; pfThe flywheel power due to the vibration suppression requirement, i.e. the stored energy power, excluding the vibration suppression power, is subtracted from the total flywheel power.
The third method comprises the following steps: the combined mode of the control moment gyro and the momentum wheel is as follows: the angular momentum exchange device is a control moment gyro, a momentum wheel or various configurations derived from a variable speed control moment gyro and the momentum wheel. When the amplitude of the flexible structure is large, the variable-speed control moment gyroscope works in a 'control moment gyroscope' mode, and vibration suppression is quickly realized by selecting a frame shaft steering law to output large moment; when the flexible structure does not vibrate or the amplitude is small, the variable-speed control moment gyroscope works in a momentum wheel mode, a flywheel acceleration law is selected based on a projection matrix method, the flywheel acceleration law is divided into two parts which are orthogonal to each other, one part is used for storing energy or releasing energy to meet the power requirements of other subsystems, the other part is used for outputting vibration suppression modal force to meet the vibration suppression requirements of the flexible structure, namely the flywheel acceleration law is selected based on the projection matrix method, so that the energy storage system and the vibration suppression system are integrated into a system, and the flexible structure vibration energy integrated control based on distributed angular momentum is realized.
The third concrete implementation method comprises the following steps: when the amplitude of the flexible structure is large, the variable-speed control moment gyroscope works in a 'control moment gyroscope' mode, and vibration suppression is quickly realized by selecting a frame shaft steering law to output large moment; when the flexible structure does not vibrate or the amplitude is small, the variable-speed control moment gyroscope works in a momentum wheel mode, a flywheel acceleration law is selected based on a projection matrix method, the flywheel acceleration law is divided into two parts which are orthogonal to each other, one part is used for storing energy or releasing energy to meet the power requirements of other subsystems, and the other part is used for outputting vibration suppression modal force to meet the vibration suppression requirements of the flexible structure.
Step 3.3.1: when the amplitude of the flexible structure is large, the variable-speed control moment gyro works in a 'control moment gyro' mode, and the frame axis manipulation law is selected as
Figure BDA0002225964370000061
Wherein: feedback parameter k＝diag[k1,...,kn]，ki>0。
Step 3.3.2: when the flexible structure does not vibrate or the amplitude is small, the variable speed control moment gyroscope works in a momentum wheel mode, and based on a projection matrix method, a flywheel acceleration law is selected as
Figure BDA0002225964370000062
Wherein:
Figure BDA0002225964370000063
Figure BDA0002225964370000064
Figure BDA0002225964370000065
has the advantages that:
1. the invention discloses a flexible structure vibration energy integrated control method based on distributed angular momentum, which fully utilizes a flywheel rotating at a high speed in an angular momentum exchange device, utilizes the flywheel to store energy, and enables an energy storage system and a vibration suppression system to be integrated into a system, and when a flexible structure vibrates, the control system can actively suppress the vibration; when the flexible structure does not vibrate or the amplitude is small, the control system can absorb or release energy while keeping the structure well damped; when the power supply of other subsystems is over demand, the control system can absorb the redundant energy of other subsystems, and when the power supply of other subsystems is short demand, the control system can release the energy to supplement the requirements of other subsystems.
2. According to the distributed angular momentum-based flexible structure vibration energy integrated control method disclosed by the invention, the weight of an energy storage system can be reduced through the improvement, so that the influence of a distributed angular momentum exchange device on the mass and inertia of the whole system is reduced.
3. The distributed angular momentum-based flexible structure vibration energy integrated control method is suitable for flexible spacecrafts in any shapes, has larger expanded space, and can be applied to space structures with more complicated shapes, wherein the complicated space structures comprise flexible structures such as parabolic antennas, large aircrafts and large mechanical devices, and the energy storage capacity of the system is enhanced while the structural vibration is inhibited and the overall control precision of the system is improved.
4. The invention discloses a distributed angular momentum-based flexible structure vibration energy integrated control method, which is characterized in that an angular momentum exchange device working mode is selected according to the angular momentum exchange device, the angular momentum exchange device working mode comprises a variable speed control moment gyro mode, a momentum wheel mode and a control moment gyro and momentum wheel combined mode, and an angular momentum exchange device control law which can meet the power requirements of other subsystems and realize flexible structure vibration suppression is selected according to the angular momentum exchange device, namely the flexible structure vibration energy integrated control based on the distributed angular momentum is realized.
5. On the basis of the distributed angular momentum-based flexible structure vibration energy integrated control method, the invention also discloses a distributed variable speed control moment gyro-based constrained boundary gyro flexible structure vibration energy integrated control method for a constrained boundary gyro flexible structure, so as to realize the integrated control of the constrained boundary gyro flexible structure vibration energy based on the distributed variable speed control moment gyro.
Drawings
Fig. 1 is a working principle diagram of the distributed angular momentum-based flexible structure vibration energy integrated control method disclosed by the invention.
Fig. 2 is a schematic diagram of a mode of "variable speed control moment gyro".
FIG. 3 is a schematic diagram of the "momentum wheel" mode.
Fig. 4 is a schematic diagram of a combined mode of 'control moment gyro & momentum wheel'.
Fig. 5 is a schematic structural diagram of a constraint boundary gyroscope flexible truss in the embodiment.
Fig. 6 is a variation curve of the modal coordinates of the truss in the present embodiment.
Fig. 7 is a variation curve of the frame angle of the speed control moment gyro in the present embodiment.
Fig. 8 is a variation curve of the angular velocity of the gyro frame of the speed control moment in the present embodiment.
Fig. 9 is a variation curve of the rotation speed of the gyro rotor for the speed control moment in the present embodiment.
Fig. 10 is a power variation curve in the present embodiment.
Fig. 11 is a deformation curve of the truss end in the present embodiment.
Detailed Description
As shown in fig. 1, the flexible structure vibration energy integrated control method based on distributed angular momentum disclosed in this embodiment can be applied to any flexible structure with distributed control. To better illustrate the objects and advantages of the present invention, the following description will be made in detail with reference to the accompanying drawings by taking the vibration energy integrated control of a constrained boundary flexible truss structure carrying 8 variable speed control moment gyros as an example.
The method comprises the following steps: 8 identical angular momentum exchange devices are installed on the constraint boundary gyroscope flexible truss in a distributed mode, and 8 angular velocimeters are installed in a co-location mode.
Designing a constraint boundary gyroscope flexible truss as shown in figure 5, wherein the truss is 10m long, the cross section dimension is 500 × 300mm, the base frequency of the truss is 1.824Hz when the variable speed control moment gyroscope is not mounted, the first four-order mode of the truss is selected to describe the vibration of the truss, a variable speed control moment gyroscope is mounted every 0.5m from the end part of the truss to the inside, an angular speed sensor is mounted on the mounting position of each variable speed control moment gyroscope in a co-location manner, and the variable speed control moment gyroscope has the weight of mg1kg, the flywheel and rotor moments of inertia are Jg＝diag[3,5,3]×10-5kg·m2And Jr＝diag[3,16,3]×10-5kg·m2. The frame angular rate of the variable speed control moment gyroscope can work within the range of +/-0.001-1 rad/s. The mounting matrix of the 8 variable speed control moment gyros is shown in table 1.
TABLE 1 variable speed control moment gyro mounting matrix
Figure BDA0002225964370000081
Step two: and establishing a vibration equation, a power equation and a measurement matrix of the constraint boundary gyroscope flexible truss.
Step 2.1: and establishing a vibration equation of the flexible truss of the constraint boundary gyroscope.
Establishing a constraint boundary gyroscope flexible structure vibration equation as
Figure BDA0002225964370000082
Wherein:
Figure BDA0002225964370000083
is the modal coordinate of the flexible truss; eaRepresenting a modal mass matrix of a flexible truss with a variable speed control moment gyro; dbAnd ΛbRespectively representing a rigidity matrix and a damping matrix; g is a gyro coupling matrix;
Figure BDA0002225964370000084
the generalized modal force generated by the acceleration of the rotor of 8 variable-speed control moment gyros is characterized, wherein omega is [ omega ]1,...,Ω8]T；
Figure BDA0002225964370000085
Is a generalized modal force generated by the rotation of a frame shaft of 8 variable-speed control moment gyros,
Figure BDA0002225964370000086
wherein the content of the first and second substances,
Figure BDA0002225964370000087
Figure BDA0002225964370000088
Figure BDA0002225964370000089
Figure BDA00022259643700000810
Figure BDA00022259643700000811
wherein the content of the first and second substances,
Figure BDA00022259643700000812
and
Figure BDA00022259643700000813
respectively a translation modal vector and a rotation modal vector of a mass infinitesimal dm on the truss;
Figure BDA00022259643700000814
Ab,gigyro frame axis coordinate system f for ith variable speed control momentgiTo the flexible truss body coordinate system fbThe coordinate transformation matrix of (a) is,
Figure BDA00022259643700000815
and
Figure BDA00022259643700000816
is Ab,giThe column submatrix of (1);
Figure BDA00022259643700000817
and
Figure BDA0002225964370000091
is that
Figure BDA0002225964370000092
The term (2) is used in (1),
Figure BDA0002225964370000093
and
Figure BDA0002225964370000094
is RgiThe row submatrix. The frame shaft moves by a small amount
Figure BDA0002225964370000095
Wherein:
Figure BDA0002225964370000096
the superscript "0" in (A) represents
Figure BDA0002225964370000097
Is equal to
Figure BDA0002225964370000098
The value at the initial instant.
Step 2.2: and establishing a power equation of the constraint boundary gyroscope flexible truss.
The energy storage and discharge power of the flexible truss of the constraint boundary gyroscope is
Figure BDA0002225964370000099
Wherein
Figure BDA00022259643700000910
Step 2.3: and establishing a measurement matrix of the constraint boundary gyroscope flexible truss.
The measuring direction of each angular velocity sensor is consistent with the torque direction generated when the variable speed control moment gyro works in the 'control moment gyro' mode at the initial time, and the measuring matrix is
Figure BDA00022259643700000911
Wherein:
Figure BDA00022259643700000912
for the measurement of the i-th sensor,
Figure BDA00022259643700000913
then there is
Figure BDA00022259643700000914
Wherein
Figure BDA00022259643700000915
Step three: and selecting an angular momentum exchange device control law which can meet the power requirements of other subsystems and realize flexible truss vibration suppression at the same time according to the selected working mode of the angular momentum exchange device, namely realizing the flexible truss vibration energy integrated control based on the distributed angular momentum.
In the embodiment, the variable speed control moment gyro is installed on the flexible truss, so that the mode of the variable speed control moment gyro is selected as the working mode of the flexible truss. The system works in a mode of 'variable speed control moment gyro', fully utilizes a flywheel rotating at a high speed in an angular momentum exchange device to store or release energy by selecting an acceleration law of the flywheel, and meets the power requirements of other subsystems by storing or releasing the energy of the flywheel; meanwhile, the frame shaft outputs vibration suppression modal force by selecting the manipulation law of the frame shaft so as to meet the vibration suppression requirement of the flexible structure, namely, the energy storage system and the vibration suppression system are integrated into a system by simultaneously selecting the acceleration law of the flywheel and the manipulation law of the frame shaft, so that the flexible structure vibration energy integrated control based on the distributed angular momentum is realized.
The specific implementation method comprises the following steps: the energy is stored or released by fully utilizing the flywheel rotating at high speed in the angular momentum exchange device through selecting the acceleration law of the flywheel, and the power requirements of other subsystems are met through the energy storage or release of the flywheel; meanwhile, the frame shaft outputs vibration suppression modal force by selecting the manipulation law of the frame shaft so as to meet the vibration suppression requirement of the flexible structure.
Step 3.1.1: based on a projection matrix method, a flywheel acceleration law is selected as
Figure BDA00022259643700000916
Wherein, PdPower requirements for other subsystems;
Figure BDA00022259643700000917
wherein I8Is an 8 × 8 identity matrix.
Figure BDA00022259643700000918
S1S1＝S1，
Figure BDA00022259643700000919
That is, the flywheel acceleration law is designed to output power only to meet the system power demand, and modal force is not applied to the truss.
Step 3.1.2: selecting the frame axis manipulation law as
Figure BDA0002225964370000101
Wherein: feedback parameter kd＝diag[kd1,...,kd8]，kdi>0。
The validity of this embodiment is verified by numerical simulation.
The system orbit period is set to be 5750s, wherein the duration of the sunshine area is 3750s, and the duration of the terrestrial shadow area is 2000 s. The variable-speed control moment gyroscope on the truss structure is charged in a sunshine area, and the power is 5W; in the front 1750s of the ground shadow area, the output power requirement of the variable speed control moment gyroscope is 5W; at the rear 250s of the shadowy area, the variable speed control moment gyro output power demand is 40W. At the beginning τb＝[1,1,0,0]T，
Figure BDA0002225964370000102
The rotor angular rate was 30000r/min and all initial frame angles were zero. At 3000s per orbital period, a 57.5s perturbation is applied to the frame angular rate, which is 0.5 rad/s. The feedback control parameter matrix is selected to be kd＝diag[1000,...,1000]。
12000s simulation shows that, in the embodiment, under the mode of a variable speed control moment gyro, the designed frame axis steering law and the designed flywheel acceleration law can restrain the vibration of the truss while meeting the power requirement, and the vibration energy integrated control of the flexible structure is realized. Fig. 6 shows that the control scheme in this embodiment enables flexible structure vibration suppression. Fig. 7 and 8 show that the variable speed control moment gyro frame shaft moves by a small amount. FIG. 9 depicts a time-varying process of rotor angular rate as a function of power demand. Fig. 10 shows that the power requirements are well met throughout the simulation. Fig. 6 and 11 show that the elastic deformation of the truss is initially damped rapidly and remains well damped at all times under active vibration suppression.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (6)

1. The flexible structure vibration energy integrated control method based on distributed angular momentum is characterized by comprising the following steps: comprises the following steps of (a) carrying out,
the method comprises the following steps: a plurality of angular momentum exchange devices and sensors are arranged on the flexible structure in a distributed manner;
step two: establishing a vibration equation, a power equation and a measurement matrix of the flexible structure system;
step three: selecting a working mode of the angular momentum exchange device according to the angular momentum exchange device, and selecting an angular momentum exchange device control law which can meet the power requirements of other subsystems and realize flexible structure vibration suppression at the same time, namely realizing flexible structure vibration energy integrated control based on distributed angular momentum;
the other subsystems refer to: all subsystems on the flexible structure except for distributed angular momentum;
the finger meeting other subsystem power requirements means: when the power supply of other subsystems is over, the control system can absorb the redundant energy of other subsystems, and when the power supply of other subsystems is short, the control system can release the energy to supplement the requirements of other subsystems;
the flexible structure vibration suppression implementation means that: when the flexible structure vibrates, the control system can actively inhibit the vibration; when the flexible structure does not vibrate or the amplitude is small, the control system can absorb or release energy while keeping the structure well damped;
for a constraint boundary gyroscope flexible structure for installing a variable speed control moment gyroscope, the method comprises the following steps,
the method comprises the following steps: n variable speed control moment gyroscopes are installed on the constraint boundary flexible structure in a distributed mode, and n angular speed meters are installed in a co-location mode;
step two: establishing a vibration equation, a power equation and a measurement matrix of a flexible structure of the constraint boundary gyroscope;
step 2.1: establishing a vibration equation of a flexible structure of a constraint boundary gyroscope;
establishing a constraint boundary gyroscope flexible structure vibration equation as
Figure FDA0002521108410000011
Wherein:
Figure FDA0002521108410000012
is the modal coordinate of the flexible structure, k is the order of the modal coordinate describing the elastic movement of the flexible structure; eaA modal mass matrix representing a flexible structure with a variable speed control moment gyro; dbAnd ΛbRespectively representing a rigidity matrix and a damping matrix; g is a gyro coupling matrix;
Figure FDA0002521108410000013
representing the generalized modal force generated by the acceleration of a rotor of the variable speed control moment gyroscope; omega is a rotor speed matrix, and omega is [ omega ]1,...,Ωn]T，ΩiThe rotor speed of the ith variable speed control moment gyro is controlled;
Figure FDA0002521108410000014
is a generalized modal force generated by the rotation of a frame shaft of the variable-speed control moment gyroscope;
Figure FDA0002521108410000015
is a matrix of the rotational speed of the frame shaft,
Figure FDA0002521108410000016
Figure FDA0002521108410000017
controlling the frame shaft rotation speed of the moment gyro for the ith variable speed; wherein the content of the first and second substances,
Figure FDA0002521108410000018
Figure FDA0002521108410000019
Figure FDA00025211084100000110
Figure FDA00025211084100000111
Figure FDA0002521108410000021
wherein:
Figure FDA0002521108410000022
and
Figure FDA0002521108410000023
respectively a translational modal vector and a rotational modal vector of a mass infinitesimal dm on a flexible structure; m isgiThe mass of the ith variable speed control moment gyro; j. the design is a squaregiThe moment of inertia of the frame shaft of the ith variable speed control moment gyro; j. the design is a squareriThe moment of inertia of the gyro flywheel is the ith variable speed control moment,
Figure FDA0002521108410000024
Ab,gigyro frame axis coordinate system f for ith variable speed control momentgiTo the flexible structure body coordinate system fbThe coordinate transformation matrix of (a) is,
Figure FDA0002521108410000025
Figure FDA0002521108410000026
Figure FDA0002521108410000027
and
Figure FDA0002521108410000028
is Ab,giThe column submatrix of (1);
Figure FDA0002521108410000029
and
Figure FDA00025211084100000210
is that
Figure FDA00025211084100000211
The term (2) is used in (1),
Figure FDA00025211084100000212
Figure FDA00025211084100000213
and
Figure FDA00025211084100000214
is RgiThe row submatrix of (a); the frame shaft moves by a small amount
Figure FDA00025211084100000215
Wherein:
Figure FDA00025211084100000216
chinese superscript "0"means
Figure FDA00025211084100000217
Is equal to
Figure FDA00025211084100000218
A value at an initial time;
step 2.2: establishing a power equation of a flexible structure of the constraint boundary gyroscope;
the energy storage and discharge power of the flexible structure of the constraint boundary gyroscope is
Figure FDA00025211084100000219
Wherein:
Figure FDA00025211084100000220
step 2.3: establishing a measuring matrix of a constraint boundary gyroscope flexible structure;
the measuring direction of each angular velocity sensor is consistent with the torque direction generated when the variable speed control moment gyro works in the 'control moment gyro' mode at the initial time, and the measuring matrix is
Figure FDA00025211084100000221
Wherein:
Figure FDA00025211084100000222
for the measurement of the i-th sensor,
Figure FDA00025211084100000223
then there is
Figure FDA00025211084100000224
Wherein
Figure FDA00025211084100000225
Step three: and selecting an angular momentum exchange device control law which can meet the power requirements of other subsystems and realize flexible structure vibration suppression at the same time according to the selected working mode of the angular momentum exchange device, namely realizing the flexible structure vibration energy integrated control based on the distributed angular momentum.
2. The integrated control method for vibration energy of the flexible structure based on distributed angular momentum as claimed in claim 1, wherein: the working modes of the angular momentum exchange device comprise the following three modes:
the first method is as follows: "variable speed control moment gyro" mode: the angular momentum exchange device is a variable speed control moment gyroscope which mainly comprises a flywheel rotating at a high speed and a frame outputting moment; the system works in a mode of 'variable speed control moment gyro', fully utilizes a flywheel rotating at a high speed in an angular momentum exchange device to store or release energy by selecting an acceleration law of the flywheel, and meets the power requirements of other subsystems by storing or releasing the energy of the flywheel; meanwhile, the frame shaft outputs vibration suppression modal force by selecting the manipulation law of the frame shaft so as to meet the vibration suppression requirement of the flexible structure, namely, the energy storage system and the vibration suppression system are integrated into a system by simultaneously selecting the acceleration law of the flywheel and the manipulation law of the frame shaft, so that the flexible structure vibration energy integrated control based on the distributed angular momentum is realized;
the second method comprises the following steps: "momentum wheel" mode: the angular momentum exchange device is of various configurations derived from a control moment gyro, a momentum wheel or a variable speed control moment gyro and the momentum wheel; the angular momentum exchange device works in a 'momentum wheel' mode, a flywheel acceleration law is selected based on a projection matrix method, the flywheel acceleration law is in a column matrix form, the flywheel acceleration law is divided into two parts which are orthogonal to each other, one part is used for storing or releasing energy to meet the power requirements of other subsystems, the other part is used for outputting vibration suppression modal force to meet the vibration suppression requirements of a flexible structure, namely the flywheel acceleration law is selected based on the projection matrix method, so that an energy storage system and a vibration suppression system are integrated into a system, and the flexible structure vibration energy integrated control based on distributed angular momentum is realized;
the third method comprises the following steps: the combined mode of the control moment gyro and the momentum wheel is as follows: the angular momentum exchange device is of various configurations derived from a control moment gyro, a momentum wheel or a variable speed control moment gyro and the momentum wheel; when the amplitude of the flexible structure is large, the variable-speed control moment gyroscope works in a 'control moment gyroscope' mode, and vibration suppression is quickly realized by selecting a frame shaft steering law to output large moment; when the flexible structure does not vibrate or the amplitude is small, the variable-speed control moment gyroscope works in a momentum wheel mode, a flywheel acceleration law is selected based on a projection matrix method, the flywheel acceleration law is divided into two parts which are orthogonal to each other, one part is used for storing energy or releasing energy to meet the power requirements of other subsystems, the other part is used for outputting vibration suppression modal force to meet the vibration suppression requirements of the flexible structure, namely the flywheel acceleration law is selected based on the projection matrix method, so that the energy storage system and the vibration suppression system are integrated into a system, and the flexible structure vibration energy integrated control based on distributed angular momentum is realized.
3. The integrated control method for vibration energy of the flexible structure based on distributed angular momentum as claimed in claim 2, wherein: the sensors include MEMS angular velocity meters and linear velocity meters.
4. The integrated control method for vibration energy of the flexible structure based on distributed angular momentum as claimed in claim 3, wherein: the specific implementation method is that the energy is stored or released by selecting the acceleration law of the flywheel and fully utilizing the flywheel rotating at high speed in the angular momentum exchange device, and the power requirements of other subsystems are met through the energy storage or release of the flywheel; meanwhile, the frame shaft outputs vibration suppression modal force by selecting the manipulation law of the frame shaft so as to meet the vibration suppression requirement of the flexible structure;
step 3.1.1: based on a projection matrix method, a flywheel acceleration law is selected as
Figure FDA0002521108410000031
Wherein: pdPower requirements for other subsystems;
Figure FDA0002521108410000032
wherein InIs an n × n identity matrix;
Figure FDA0002521108410000033
S1S1＝S1，
Figure FDA0002521108410000034
namely, the selected flywheel acceleration law can only output power to meet the system power requirement, and modal force is not applied to the structure;
step 3.1.2: selecting the frame axis manipulation law as
Figure FDA0002521108410000035
Wherein: feedback parameter kd＝diag[kd1,...,kdn]，kdi＞0。
5. The integrated control method for vibration energy of the flexible structure based on distributed angular momentum as claimed in claim 4, wherein: the method specifically comprises the following steps of selecting an acceleration law of the flywheel based on a projection matrix method, wherein the acceleration law of the flywheel is in a column matrix form, dividing the acceleration law of the flywheel into two parts which are orthogonal to each other, wherein one part is used for storing energy or releasing energy to meet the power requirements of other subsystems, and the other part is used for outputting vibration suppression modal force to meet the vibration suppression requirements of the flexible structure;
step 3.2: based on a projection matrix method, a flywheel acceleration law is selected as
Figure FDA0002521108410000041
Wherein:
Figure FDA0002521108410000042
Figure FDA0002521108410000043
Figure FDA0002521108410000044
wherein: t iscObtaining the expected vibration suppression modal force through negative feedback of a sensor measured value; s1Is N (B)Ω) Of the projection matrix, thus S1u1At BΩIn the null space of (1), i.e. S1u1Modal force cannot be generated; pfThe flywheel power due to the vibration suppression requirement, i.e. the stored energy power, excluding the vibration suppression power, is subtracted from the total flywheel power.
6. The integrated control method for vibration energy of the flexible structure based on distributed angular momentum as claimed in claim 5, wherein: the third concrete implementation method is that when the amplitude of the flexible structure is large, the variable speed control moment gyro works in a control moment gyro mode, and vibration suppression is quickly realized by selecting a frame shaft steering law to output large moment; when the flexible structure does not vibrate or the amplitude is small, the variable-speed control moment gyroscope works in a momentum wheel mode, a flywheel acceleration law is selected based on a projection matrix method, the flywheel acceleration law is divided into two parts which are orthogonal to each other, one part is used for storing energy or releasing energy to meet the power requirements of other subsystems, and the other part is used for outputting vibration suppression modal force to meet the vibration suppression requirements of the flexible structure;
step 3.3.1: when the amplitude of the flexible structure is large, the variable-speed control moment gyro works in a 'control moment gyro' mode, and the frame axis manipulation law is selected as
Figure FDA0002521108410000045
Wherein: feedback parameter k＝diag[k1,...,kn]，ki＞0；
Step 3.3.2: when the flexible structure does not vibrate or the amplitude is small, the variable speed control moment gyroscope works in a momentum wheel mode, and based on a projection matrix method, a flywheel acceleration law is selected as
Figure FDA0002521108410000046
Wherein:
Figure FDA0002521108410000047
Figure FDA0002521108410000048
Figure FDA0002521108410000049
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