CN109116730B - Hybrid execution mechanism energy optimization management method based on TU cooperative game - Google Patents

Hybrid execution mechanism energy optimization management method based on TU cooperative game Download PDF

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CN109116730B
CN109116730B CN201810755402.0A CN201810755402A CN109116730B CN 109116730 B CN109116730 B CN 109116730B CN 201810755402 A CN201810755402 A CN 201810755402A CN 109116730 B CN109116730 B CN 109116730B
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cmg
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吴云华
郑墨泓
何梦婕
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Nanjing University of Aeronautics and Astronautics
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
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Abstract

The invention discloses a hybrid execution mechanism energy optimization management method based on TU cooperative game, which comprises the following steps: designing a dynamic performance index matrix S controlled by a hybrid actuating mechanism, an energy minimization function E and a constraint condition f; designing function H, and respectively deriving relation g of lambda, CMG frame angular velocity set and RW rotation angular acceleration setx，gΩ(ii) a Establishing a TU cooperative game model of a hybrid executing mechanism; calculating a pure strategy and a mixed strategy; designing two-person zero-sum game pay moments and calculating the total income V (N) of the game and the maximum income V ({ lambda) of people in each officei(ii) }) (i ═ 1,2, 3); according to V (N) and V ({ lambdai}) the optimal solution for each person in the office is calculated. The invention solves the CMG singularity problem and the RW saturation problem, does not need iterative operation, can output large torque without error, improves the agility of the satellite attitude maneuver, optimizes and manages the energy of the hybrid actuating mechanism, and greatly reduces the energy consumption of the hybrid actuating mechanism system.

Description

Hybrid execution mechanism energy optimization management method based on TU cooperative game
Technical Field
The invention belongs to the technical field of satellite attitude control, and particularly relates to a hybrid execution mechanism energy optimization management method based on TU cooperative game.
Background
With the increasing number of orbit fragments and dead spacecrafts, the demand of space-based close-range observation tasks such as monitoring the orbit fragments is larger and larger, and the agile maneuver and the attitude dynamic tracking of the spacecrafts become research hotspots. For example, the maximum attitude maneuvering angular speed of the United states World View 1 reaches 4.5 deg/s; as another example, the Earth observation satellite Ple-iades-HR in France can perform a large angle maneuver of 60deg within 25 s. Obviously, agile maneuver and attitude dynamic tracking have higher requirements on the actuator, and the actuator is required to output a larger attitude control torque, and the torque output by the actuator is also required to have higher precision.
Because the single type of executing mechanism has respective limitations, the high requirement of outputting large torque with high precision is difficult to meet, and a hybrid executing mechanism is usually adopted for agile maneuver and attitude dynamic tracking. A tethered satellite is designed by Mohammad Amin Alandedi Hallaj of the university of Schefflerf of Iranderland, and the relative position and RW are controlled by electromagnetic force to carry out attitude maneuver. A RW and thruster hybrid execution mechanism designed by Dong Y of Harbin university of industry and the like is used for solving the problem of high-precision large-angle quick redirection of a spacecraft. Junquan Li, et al, at the university of York, used a hybrid actuator based on RW and a magnetic torquer to solve the problem of attitude control for nano-satellites. And the CMGRW based on the CMG and RW has the characteristics of large torque output and high control precision, and is more suitable for large-angle mobile satellites.
Since the CMG has the problem of geometric singularity, the RW has the problem of saturation, and how to make the CMG and the RW work together becomes the main problem of the manipulation law design of the CMGRW of the hybrid execution mechanism, namely how to solve the problem of CMG singularity and the problem of RW saturation at the same time. At present, no hybrid actuator manipulation law based on TU cooperative game design is found. Cole Doupe and the like of the air force engineering college evaluate the performance of the CMGRW of the hybrid execution mechanism by adopting mathematical simulation and physical experiments, and designs a closed-loop control method, which can solve the strange problem of the CMG and ensure that the frame angle of the CMG rotates to a target value by the shortest path. A hybrid actuating mechanism control method facing imaging agile satellites is designed by Van national Wei and the like of Changchun optical precision machinery and physical research institute of Chinese academy of sciences, aiming at a CMG and RW hybrid actuating mechanism, the hybrid actuating mechanism is composed of Legendre pseudo-spectrum feedforward control and feedback control for realizing an optimal track, and the feedforward control can realize optimal planning of the angular speed of a CMG system frame; the feedback control takes flywheel output torque and the like as constraints to compensate control errors caused by initial state and rotational inertia deviation, but the method adopts an optimal track and is difficult to meet the requirement of high dynamic real-time performance. Cao Xibin et al, Harbin Industrial university, have devised a torque distribution method based on a hybrid actuator CMGRW that enables smooth switching between CMG and RW, but the torque output by RW may not match the CMG. A hybrid actuator control method is designed for satellite fast maneuvering in Shanghai aviation and space control engineering research institute, and the like, but the control method is only suitable for a single-axis attitude fast maneuvering task. A hybrid execution mechanism control law based on CMG and RW is designed by the Wanglogjie of the university of Beijing aerospace and the like based on the Gauss pseudo-common method, the problem of singularity of CMG is solved, but frequent switching between RW and CMG can be caused. A moment distribution algorithm based on a CMG and RW hybrid execution mechanism is designed in Gunn cloud sea of Harbin industry university, the problems of CMG singularity, dead zone and RW saturation and zero crossing can be solved, RW and CMG optimization management is not achieved, and energy consumption of the system is high.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the prior art, the energy optimization management method of the hybrid execution mechanism based on the TU cooperative game is provided for solving the singularity problem of CMG and the saturation problem of RW and performing energy management and optimization.
The technical scheme is as follows: in order to solve the technical problem, the invention provides a hybrid execution mechanism energy optimization management method based on a TU cooperative game, which is characterized by comprising the following steps of:
(1) constructing a dynamic performance index matrix S ═ S controlled by a CMGRW hybrid actuator1,S2,…,S7]TEnergy minimization function
Figure GDA0003198166570000021
And constraint conditions
Figure GDA0003198166570000022
Wherein
Figure GDA0003198166570000023
For the set of angular velocities of the CMG frame,
Figure GDA0003198166570000024
is RW rotation angular acceleration set;
(2) constructing functions
Figure GDA0003198166570000025
Figure GDA0003198166570000026
Where the matrix λ ═ λ1,λ2,λ3]According to
Figure GDA0003198166570000027
And
Figure GDA0003198166570000028
separately deriving lambda and CMG frame angular velocity sets
Figure GDA0003198166570000029
And RW rotational angular acceleration sets
Figure GDA00031981665700000210
In relation to (2)
Figure GDA00031981665700000211
Figure GDA00031981665700000212
(3) Constructing a TU game model G ═ { N, V }, wherein N is a person in the game and V is a profit value;
(4) calculating a pure strategy and a mixed strategy according to the established TU game model;
(5) calculating a two-person zero sum game payment matrix, and calculating the total income and the maximum income of the persons in the game;
(6) and obtaining the optimal solution of the people in the bureau.
Further, the specific steps of calculating the pure policy and the mixed policy in the step (4) are as follows:
(4.1) 3 people in the TU game model G ═ { N, V }, and then the people in the TU are gathered N ═ lambda { (λ)1,λ2,λ3The people are respectively set as person in office 1, person in office 2 and person in office 3;
(4.2) based on the command torque ucPure strategies for persons 1,2,3 in the bureau were designed separately:
party 1: { D1,1,D1,2,D1,3}
Person in office 2: { D2,1,D2,2,D2,3}；
Party 3: { D3,1,D3,2,D3,3}
(4.3) strategy D selected according to local person i (i ═ 1,2,3)i,j(j ═ 1,2,3), to give a mixtureStrategy:
Figure GDA0003198166570000031
further, the specific steps of calculating the two-person zero-sum game payment matrix in the step (5) and calculating the total income and the maximum income of the persons in the game are as follows:
(5.1) setting up alliance and its complementary alliance according to person union in bureau
Figure GDA0003198166570000032
And respectively calculate CPiAnd
Figure GDA0003198166570000033
the two-person zero sum game payout matrix;
(5.2) calculating the total income V (N) of the game and the maximum income V ({ lambda) of all the game players according to the two-player zero-sum game payment matrix1})、V({λ2}) and V ({ lambda. })3})。
Further, the CMGRW hybrid actuator in the step (1) is composed of a CMG system and a RW system.
Further, the CMGRW hybrid actuator in step (1) is controlled by using a hybrid actuator TU cooperative game theory manipulation law.
Further, the manipulation law of the TU cooperative game theory of the hybrid executing mechanism is as follows:
Figure GDA0003198166570000034
wherein u isoJ is a system matrix of the hybrid actuator and is related to the configuration of the CMG system and the RW system for the hybrid actuator to output the control torque.
Compared with the prior art, the invention has the advantages that:
the invention adopts TU cooperative game theory design for the first time and is based on the control law of the CMG and RW hybrid executing mechanism, thereby solving the problem of CMG singularity and the problem of RW saturation, needing no iterative operation, outputting large torque without error, improving the agility of satellite attitude maneuver, optimizing and managing the energy of the hybrid executing mechanism, and greatly reducing the energy consumption of the hybrid executing mechanism system.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The invention is further elucidated with reference to the drawings and the detailed description. The described embodiments of the present invention are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, other embodiments obtained by a person of ordinary skill in the art without any creative effort belong to the protection scope of the present invention.
As shown in fig. 1, the present invention comprises the steps of:
(1) designing dynamic performance index matrix S ═ S controlled by CMGRW hybrid actuator1,S2,…,S7]TEnergy minimization function
Figure GDA0003198166570000041
And constraint conditions
Figure GDA0003198166570000042
Wherein
Figure GDA0003198166570000043
For the set of angular velocities of the CMG frame,
Figure GDA0003198166570000044
is RW rotation angular acceleration set;
(2) setting function
Figure GDA0003198166570000045
Figure GDA0003198166570000046
Wherein matrix λ ═[λ1,λ2,λ3]According to
Figure GDA0003198166570000047
And
Figure GDA0003198166570000048
separately deriving lambda and CMG frame angular velocity sets
Figure GDA0003198166570000049
And RW rotational angular acceleration sets
Figure GDA00031981665700000410
In relation to (2)
Figure GDA00031981665700000411
Figure GDA00031981665700000412
(3) And setting the TU cooperative game G as { N, V }, wherein N is a person in the game and V is a profit value. The game has 3 players, and the player group is N ═ lambda1,λ2,λ3And the numbers are respectively set as person in office 1, person in office 2 and person in office 3. According to the command torque ucPure strategies for persons 1,2,3 in the bureau were designed separately:
party 1: { D1,1,D1,2,D1,3}
Person in office 2: { D2,1,D2,2,D2,3}
Party 3: { D3,1,D3,2,D3,3}
(4) Strategy D selected according to local person i (i is 1,2,3)i,j(j ═ 1,2,3), resulting in a hybrid strategy:
Figure GDA0003198166570000051
(5) setting up alliance C according to person union in bureauPi(i ═ 1,2,3) and its complementary alliances
Figure GDA0003198166570000052
And respectively calculate CPiAnd
Figure GDA0003198166570000053
two-person zero sum game payout moments;
(6) calculating the total income V (N) of the game and the maximum income V ({ lambda) of all the game players according to the two-player zero sum game payment matrix1})、V({λ2}) and V ({ lambda. })3})；
(7) Obtaining the optimal solution of people 1,2 and 3 in the bureau:
Figure GDA0003198166570000054
the game ends.
The CMGRW hybrid actuating mechanism consists of a CMG system and a RW system in certain configurations. As shown in fig. 1, the CMGRW hybrid executing mechanism plays a game under the control of a hybrid executing mechanism TU cooperative game theory manipulation law, wherein the hybrid executing mechanism TU cooperative game theory manipulation law is as follows:
Figure GDA0003198166570000055
wherein u isoJ is a system matrix of the hybrid actuator and is related to the configuration of the CMG system and the RW system for the hybrid actuator to output the control torque. The hybrid execution mechanism TU can output the command torque without error in cooperation with the game theory manipulation law.

Claims (4)

1. A hybrid execution mechanism energy optimization management method based on TU cooperative game is characterized by comprising the following steps:
(1) constructing a dynamic performance index matrix S ═ S controlled by a CMGRW hybrid actuator1,S2,…,S7]TEnergy minimization function
Figure FDA0003199777110000011
And constraint conditions
Figure FDA0003199777110000012
Wherein
Figure FDA0003199777110000013
For the set of angular velocities of the CMG frame,
Figure FDA0003199777110000014
is RW rotation angular acceleration set;
(2) constructing functions
Figure FDA0003199777110000015
Figure FDA0003199777110000016
Where the matrix λ ═ λ1,λ2,λ3]According to
Figure FDA0003199777110000017
And
Figure FDA0003199777110000018
separately deriving lambda and CMG frame angular velocity sets
Figure FDA0003199777110000019
And RW rotational angular acceleration sets
Figure FDA00031997771100000110
In relation to (2)
Figure FDA00031997771100000111
Figure FDA00031997771100000112
(3)And constructing a TU game model G ═ { N, V }, wherein N ═ λ1,λ2,λ3The person in the office is designated as V, and the income value is designated as V;
(4) calculating a pure strategy and a mixed strategy according to the established TU game model;
(5) calculating a two-person zero sum game payment matrix, and calculating the total income and the maximum income of the persons in the game;
(6) obtaining the optimal solution of the people in the bureau;
the specific steps of calculating the pure strategy and the mixed strategy in the step (4) are as follows:
(4.1) 3 people in the TU game model G ═ { N, V }, and then the people in the TU are gathered N ═ lambda { (λ)1,λ2,λ3The people are respectively set as person in office 1, person in office 2 and person in office 3;
(4.2) based on the command torque ucPure strategies for persons 1,2,3 in the bureau were designed separately:
party 1: { D1,1,D1,2,D1,3}
Person in office 2: { D2,1,D2,2,D2,3}；
Party 3: { D3,1,D3,2,D3,3}
(4.3) strategy D selected according to local person i, i ═ 1,2,3i,jJ ═ 1,2,3, resulting in a hybrid strategy:
Figure FDA00031997771100000113
the specific steps of calculating the two-person zero-sum game payment matrix in the step (5) and calculating the total income and the maximum income of the persons in the game are as follows:
(5.1) setting alliance C according to people union in bureauPi1,2,3 and their complementary alliances
Figure FDA0003199777110000021
And respectively calculate CPiAnd
Figure FDA0003199777110000022
the two-person zero sum game payout matrix;
(5.2) calculating the total income V (N) of the game and the maximum income V ({ lambda) of all the game players according to the two-player zero-sum game payment matrix1})、V({λ2}) and V ({ lambda. })3})。
2. The method as claimed in claim 1, wherein the CMGRW hybrid actuator in step (1) is composed of a CMG system and a RW system.
3. The method as claimed in claim 1, wherein the CMGRW hybrid actuator in step (1) is controlled by using a hybrid actuator TU cooperative game theory manipulation law.
4. The energy optimization management method for the hybrid execution mechanism based on the TU cooperative game as claimed in claim 3, wherein the manipulation law of the TU cooperative game theory of the hybrid execution mechanism is as follows:
Figure FDA0003199777110000023
wherein u isoJ is a system matrix of the hybrid actuator and is related to the configuration of the CMG system and the RW system for the hybrid actuator to output the control torque.
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