Attitude-orbit coupling control method for drag-free spacecraft formation for gravitational wave detection

Abstract

The invention proposes an attitude-orbit coupling control method for a drag-free spacecraft formation for gravitational wave detection, which belongs to the field of spacecraft control technology. The method comprises the following steps: S1: establishing a relative attitude motion model of a spacecraft platform and a proof mass block based on an attitude error; S2: establishing a relative translation motion model of a spacecraft platform and a proof mass block based on a relative position error; S3: constructing an attitude-orbit coupling control model for a drag-free navigator formation based on the relative attitude motion model and the relative translation motion model; S4: linearizing the attitude-orbit coupling control model for a drag-free navigator formation given an assumption; S5: decoupling the linearized attitude-orbit coupling control model for a drag-free navigator formation into a drag-free control subsystem, an attitude control subsystem and an electrostatic suspension control subsystem, and designing control laws for each subsystem to control the subsystem.

Description

Technical Field

[0001] The present invention relates to the field of spacecraft control technology, and in particular to a method for attitude-orbit coupling control of a drag-free spacecraft formation for gravitational wave detection. Background Art

[0002] Gravitational waves provide a new window for studying the universe. Space gravitational wave detectors can capture low-frequency signals in the millihertz band, which plays a vital role in basic physics research. One way to achieve this is to use a drag-free controlled spacecraft, using three spacecraft to form a space laser interferometer, and capture gravitational wave signals through displacement measurements between inertial references. This structural form can suppress external interference such as solar wind and solar light pressure, and the distance changes caused by gravitational waves are accurately measured between satellites using lasers.

[0003] Each drag-free spacecraft is equipped with several micro-Newton thrusters and at least one test mass. In the drag-free control loop, the test mass points to the sensitive axes X1 and X2 of the other two spacecraft respectively, and the test mass is also perpendicular to the axis of the interference arm plane; the spacecraft follows the test mass under the action of the micro-thruster. The remaining degrees of freedom of the test mass are controlled by electrostatic force to always keep the test mass at the center of the plate. The controller of this control loop is called a suspension controller. The three rotational degrees of freedom of the satellite must always point to the other two satellites to achieve the alignment of the interferometric laser. The drag-free spacecraft is a highly complex nonlinear system. The existing modeling methods mainly use Euler angles, modified Rodriguez parameters or quaternions to represent the attitude, but Euler angles will cause singularity problems and are not suitable for continuous rotation. Modified Rodriguez parameters will also have singularity problems; quaternions will cause attitude unfolding phenomena.

[0004] Therefore, it is very necessary to propose a drag-free spacecraft formation attitude-orbit coupling control method for gravitational wave detection, which can accurately describe the attitude of the spacecraft and perform multi-degree-of-freedom control of the three-satellite formation to make the spacecraft better suitable for the gravitational wave detection process. Summary of the invention

[0005] In view of this, the present invention proposes a method for attitude-orbit coupling control of a drag-free spacecraft formation for gravitational wave detection, which uses a rotation matrix to describe the spacecraft attitude, avoids the singularity of the Euler angles and modified Rodriguez parameters, lacks external disturbances, and actuator output uncertainty, and is closer to the actual application scenario of gravitational wave detection.

[0006] The present invention provides a method for attitude-orbit coupling control of a drag-free spacecraft formation for gravitational wave detection, comprising the following steps:

[0007] S1: Establish the relative attitude motion model of the spacecraft platform and the proof mass based on attitude error;

[0008] S2: Establish the relative translation motion model of the spacecraft platform and the inspection mass block based on the relative position error;

[0009] S3: Based on the relative attitude motion model and relative translation motion model, the attitude-orbit coupling control model of the towless navigator formation is constructed;

[0010] S4: Given the assumptions, the attitude-orbit coupling control model of the towless navigator formation is linearized;

[0011] S5: Decouple the linearized attitude-orbit coupling control model of the drag-free navigator formation into the drag-free control subsystem, attitude control subsystem and electrostatic suspension control subsystem, and design control laws for each subsystem to control it.

[0012] On the basis of the above technical solution, preferably, the specific content of step S1 is:

[0013] S11: Construct reference coordinate system;

[0014] Let the inertial coordinate system be I ; Let the spacecraft coordinate system be B ; The electrode cage coordinate system is H ; The coordinate system of the inspection mass block is M ; B i Refers to i spacecraft, i =1, 2, 3; let each spacecraft include two test masses, then M ki It refers to i The first of the spacecraft k A proof mass block, k =1,2;

[0015] S12: Obtain the rotational dynamics equations of the spacecraft and the proof mass in the reference coordinate system;

[0016] Based on the rotation matrix representation i spacecraft and k The rotational kinematic equation of the proof mass is: , ;in, It is i Spacecraft B i The rotation matrix The first derivative of ; one dot above the parameter represents the first derivative, and two dots represent the second derivative, It isi The first of the spacecraft k The rotation matrix of the proof mass The first derivative of For parameters X Relative to the coordinate system Y The angular velocity of the coordinate axis Z The amount of It is i The spacecraft is relative to the inertial coordinate system I The angular velocity at i Spacecraft B i The components of the coordinate system; yes The antisymmetric matrix of ; It is k The test mass is relative to the heliocentric inertial coordinate system I The angular velocity at k Components in the coordinate system of the proof mass; yes The antisymmetric matrix of is the antisymmetric matrix operation symbol; k The proof mass represents the i The first spacecraft k A proof mass block;

[0017] Then the rotational dynamics equation of the spacecraft and the proof mass is defined as:

[0018] , ;in is the moment of inertia matrix, yes The first derivative of yes The first derivative of For the i The control input of the spacecraft is For the i The disturbance force of a spacecraft, For the k The control input of the proof mass, For the k The disturbance input of the proof mass block;

[0019] make and For the i spacecraft and k The expected rotation matrix of the proof mass is, and For the i spacecraft and kThe expected angular velocity of the proof mass is defined as i The error rotation matrix of the spacecraft for , No. k The error rotation matrix of the proof mass , the upper right corner T is the rank conversion operation; i The error angular velocity of the spacecraft , No. k The error angular velocity of the proof mass , For the k The angular velocity of the test mass in the electrode cage coordinate system is k Components in the coordinate system of the proof mass;

[0020] S13: Define the attitude error vector; let i The error vector corresponding to the error rotation matrix of a spacecraft is , No. k The error vector corresponding to the error rotation matrix of the proof mass block is ,in is the inverse operation of the cross product operation;

[0021] S14: According to the attitude error vector and the rotational dynamics equation of the spacecraft and the proof mass in the reference coordinate system, the relative attitude motion model of the spacecraft platform is obtained as follows:

[0022] , , among which i The Coriolis force matrix for a spacecraft , No. k Coriolis force matrix of a proof mass , No. i The gyroscopic torque matrix of a spacecraft is: , No. k The gyro torque matrix of the proof mass is:

[0023] ; Indicates i Spacecraft to k The coordinate transformation matrix of the proof mass; is the error function, , , is the trace function, For the i The antisymmetric matrix of the error angular velocity of the spacecraft.

[0024] Preferably, the specific content of step S2 is: the relative translation motion model of the spacecraft platform is: , among which k The conjugate matrix of the Coriolis force matrix of the proof mass , No. k The conjugate matrix of the gyro torque matrix of the proof mass , For the k The proof mass is relative to the i The inertial position of the spacecraft is i Components in the spacecraft coordinate system; For the k The position of the proof mass relative to the electrode cage coordinate system is k Components in the electrode cage coordinate system; For the i The component of the position of a spacecraft relative to the inertial coordinate system in the inertial coordinate system; For the inertial coordinate system to k The coordinate transformation matrix of the electrode cage coordinate system; For the i The spacecraft arrived k The coordinate transformation matrix of the electrode cage coordinate system; For the k The mass of the test mass; For the k The gravitational acceleration of the test mass; and For the i spacecraft and k The input torque of the proof mass; and For the i spacecraft and k The disturbance torque of the test mass block.

[0025] Further preferably, the attitude-orbit coupling control model of the towless navigator formation is constructed in step S3, including the following contents:

[0026] Defining parameters , , ,in It is i The error vector of the expected rotation matrix of the first proof mass of the spacecraft, No. i The error vector of the expected rotation matrix of the second proof mass of the spacecraft; and It is iThe mass of the first and second proof masses of the spacecraft; and It is i The input torque of the first and second proof mass blocks of the spacecraft; and For the i Control inputs for the first and second proof masses of a spacecraft; and For the i The disturbance torque of the first and second proof mass blocks of the spacecraft; and For the i The disturbance force of the first and second proof mass blocks of the spacecraft; For the i The first proof mass of the spacecraft is relative to the i The inertial position of the first electrode cage of the spacecraft is i The component of the first electrode cage of the spacecraft in the coordinate system, For the i The second proof mass of the spacecraft is relative to the i The inertial position of the second electrode cage of the spacecraft is i The component of the coordinate system of the second electrode cage of the spacecraft;

[0027] The coupled translational and rotational relative dynamic equations are: ,in , , , , , , , , ,in To take the diagonal operation; is a 3×3 identity matrix, is a 15×15 identity matrix; For the i The gravitational acceleration of the spacecraft; For the inertial coordinate system to i The coordinate transformation matrix of the first electrode cage coordinate system of the spacecraft, For the inertial coordinate system to i The coordinate transformation matrix of the second electrode cage coordinate system of the spacecraft; For the i Spacecraft to iThe coordinate transformation matrix of the first electrode cage coordinate system of the spacecraft, For the i Spacecraft to i The coordinate transformation matrix of the second electrode cage coordinate system of the spacecraft; For the i Spacecraft to i The coordinate transformation matrix of the coordinate system of the first test mass block of the spacecraft is: For the i Spacecraft to i The coordinate transformation matrix of the coordinate system where the second proof mass block of the spacecraft is located; and They are i The Coriolis force matrix of the first test mass block of the spacecraft and the i The Coriolis force matrix of the second proof mass of the spacecraft is, and They are and The conjugate matrix of ; and They are i The gyro torque matrix of the first test mass block of the spacecraft and the i The gyro torque matrix of the second proof mass of the spacecraft is, and They are and The conjugate matrix of ; and They are i The error rotation matrix of the first proof mass block of the spacecraft and the error rotation matrix of the first proof mass block i The error rotation matrix of the second proof mass of the spacecraft; For the i The first proof mass of the spacecraft is relative to the i The inertial position of the spacecraft is i The components in the spacecraft coordinate system, For the i The second proof mass of the spacecraft is relative to the i The inertial position of the spacecraft is i components in the spacecraft coordinate system.

[0028] More preferably, the content of step S4 is: given the assumption that: let i The spacecraft is relative to the inertial coordinate system I The angular velocity at i Spacecraft B i Components of the coordinate system , ;No. i The first spacecraft k The electrode cage is relative to the i The inertial position of the spacecraft is i Components in the spacecraft coordinate system , ;No. k The angular velocity of the test mass in the electrode cage coordinate system is k Components in the coordinate system of the proof mass ;

[0029] Let the drag-free coordinate system selection matrix and the electrostatic suspension coordinate system selection matrix be and , no drag coordinate system selection matrix for:

[0030] ;

[0031] Electrostatic Suspension Coordinate System Selection Matrix for:

[0032] ; Then the coupled translational and rotational relative dynamic equations are rewritten as: , where the state variable , attitude control variables ; No drag control variable , electrostatic suspension control variable , and the state variable ; Coefficient matrix , where the transfer matrix , intermediate variable and ; state vector , the coefficient matrix , where the variable ;

[0033] In order to improve the performance of the drag-free control subsystem, the coefficient matrix of the drag-free control subloop is transformed into a diagonal unit matrix. i The total input variables for a spacecraft are , where the spacecraft control component , the control component of the inspection mass block is ;No. i The total external disturbance variable of a spacecraft is , where the disturbance variable of the spacecraft is , the disturbance variable of the inspection mass block is ; Based on the above variables, the coupled translational and rotational relative dynamics equations are replaced by: , where the coefficient matrix , the spacecraft coefficient matrix , the drag-free loop coefficient matrix , electrostatic suspension loop coefficient matrix , the state vector The derivative of , the spacecraft state vector , the state vector of the no-drag loop , the state vector of the electrostatic suspension circuit .

[0034] Further preferably, the model of the posture control subsystem in step S5 is: ; Given the following sliding die surface : , is a positive constant; sliding surface The expression of the derivative is: ; Using sliding surface , the adaptive superhelical control law of the attitude control subsystem is designed as: ,in is the equivalent control law, For the switching law, , , where the parameters , ;parameter , is the update rate, , ,parameter ; Intermediate variables ,parameter , initial value , , is a positive definite constant; yes The derivative of It is i The disturbance force of the spacecraft j Quantity; is the symbolic function, τ is the variable of the definite integral, Indicates time t The sliding surface status.

[0035] Further preferably, the model of the drag-free control subsystem in step S5 is: , For the i The input torque vector of the spacecraft is, For the i The perturbation torque vector of a spacecraft; the sliding surface as follows: , is a positive constant; in the disturbance Sliding surface The derivative of ;

[0036] Design the following adaptive superhelical control law: , is the equivalent control law, ; For the switching law, , where the parameters , ,parameter , update law Defined as , ; Control law parameters ; Intermediate variables , where the parameters , initial value , , L 1 is a positive constant; It is i The disturbance torque vector of the spacecraft j A quantity.

[0037] Further preferably, the model of the electrostatic suspension control subsystem is: , design the following sliding die surface: , is a positive constant; the adaptive superhelical control law of the electrostatic suspension control subsystem is as follows: , equivalent control law , switching law , where the parameters , ,parameter , update law Defined as , control law parameters , intermediate variable ,parameter , intermediate parameters , initial value , , is a positive constant, the overall control law .

[0038] The attitude-orbit coupling control method for the drag-free spacecraft formation for gravitational wave detection provided by the present invention has the following beneficial effects compared with the prior art:

[0039] (1) Compared with the conventional modeling method of using Euler angles, modified Rodriguez parameters or quaternions to represent attitude, the present invention uses a rotation matrix to describe the attitude of the spacecraft, avoiding the singularity of using Euler angles and modified Rodriguez parameters, and also avoiding the ambiguity of using quaternions;

[0040] (2) The present invention solves the problem of drag-free spacecraft formation control with dual inspection proof masses. Compared with the controller of the drag-free spacecraft formation that only considers a single inspection proof mass, the present invention involves more degrees of freedom and a more difficult control method, but has higher control accuracy. Compared with the controller of the near-Earth drag-free spacecraft formation, the spatial scale involved in this paper is larger. Since the attitude-orbit coupling control model of the drag-free navigator formation is constructed in the absence of prior knowledge such as external disturbances and actuator output uncertainty, and is further decoupled into a combination of a drag-free control subsystem, an attitude control subsystem and an electrostatic suspension control subsystem, and each control subsystem is solved separately, it can be better used in actual gravitational wave detection applications.

[0041] (3) The present invention is designed to construct models, sliding surfaces and adaptive super-helical sliding film control laws for the drag-free control subsystem, attitude control subsystem and electrostatic suspension control subsystem respectively when the prior knowledge of external disturbance is unknown, which is conducive to the accurate solution of controller parameters. Compared with the controller with a known upper bound of external disturbance, the present invention can perform drag-free spacecraft formation control when the prior knowledge of external disturbance is unknown, which reduces the controller requirements and is closer to practical application. The present invention additionally considers the influence of actuator output uncertainty. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0043] Picture 1 This is a flow chart of a method for attitude-orbit coupling control of a drag-free spacecraft formation for gravitational wave detection according to the present invention;

[0044] Picture 2 It is a schematic diagram of simulation results of a method for attitude-orbit coupling control of a drag-free spacecraft formation for gravitational wave detection according to the present invention. DETAILED DESCRIPTION

[0045] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0046] In the modeling stage, most of the existing three-star formation control problems use Euler angles, modified Rodriguez parameters or quaternions to represent attitude. Among them, Euler angles will cause singularity problems and are not suitable for continuous rotation. Modified Rodriguez parameters will also have singularity problems. Quaternions will cause attitude expansion. In view of this, the present invention provides a gravitational wave detection drag-free spacecraft formation attitude-orbit coupling control method, referring to Picture 1 , the present invention comprises the following steps:

[0047] S1: Establish the relative attitude motion model of the spacecraft platform and the proof mass based on the attitude error.

[0048] The specific content of step S1 is:

[0049] S11: Construct reference coordinate system;

[0050] Let the inertial coordinate system be I ; Let the spacecraft coordinate system be B ; The electrode cage coordinate system is H ; The coordinate system of the inspection mass block is M ; B i Refers to i spacecraft, i =1, 2, 3; let each spacecraft include two test masses, then M ki It refers to i The first of the spacecraft k A proof mass block, k =1,2;

[0051] S12: Obtain the rotational dynamics equations of the spacecraft and the proof mass in the reference coordinate system;

[0052] Based on the rotation matrix representation i spacecraft and k The rotational kinematic equation of the proof mass is: , ;in, It is i Spacecraft B i The rotation matrix The first derivative of ; one dot above the parameter represents the first derivative, and two dots represent the second derivative, It is i The first of the spacecraft k The rotation matrix of the proof mass The first derivative of For parameters X Relative to the coordinate system Y The angular velocity of the coordinate axis Z The weight of It is i The spacecraft is relative to the inertial coordinate system I The angular velocity at i Spacecraft B i The components of the coordinate system; yes The antisymmetric matrix of ; It is k The test mass is relative to the heliocentric inertial coordinate system I The angular velocity at k Components in the coordinate system of the proof mass; yes The antisymmetric matrix of is the antisymmetric matrix operation symbol; k The proof mass represents the i The first spacecraft k proof mass blocks; antisymmetric matrix The definition of is that the transpose of a square matrix N is equal to the inverse of the square matrix, , the antisymmetric matrix The elements on the main diagonal are all 0, and the elements on both sides of the main diagonal are opposite in sign, which is an antisymmetric matrix. The expression is , is an antisymmetric matrix Elements of

[0053] Then the rotational dynamics equation of the spacecraft and the proof mass is defined as:

[0054] , ;in is the moment of inertia matrix, yes The first derivative of yes The first derivative of For the i The control input of the spacecraft is For the i The disturbance force of a spacecraft, For the kThe control input of the proof mass, For the k The disturbance input of the proof mass block;

[0055] make and For the i spacecraft and k The expected rotation matrix of the proof mass is, and For the i spacecraft and k The expected angular velocity of the proof mass is defined as i The error rotation matrix of the spacecraft for , No. k The error rotation matrix of the proof mass , the upper right corner T is the rank conversion operation; i The error angular velocity of the spacecraft , No. k The error angular velocity of the proof mass , For the k The angular velocity of the test mass in the electrode cage coordinate system is k Components in the coordinate system of the proof mass;

[0056] S13: Define the attitude error vector; let i The error vector corresponding to the error rotation matrix of a spacecraft is , No. k The error vector corresponding to the error rotation matrix of the proof mass block is ,in is the inverse operation of the cross product operation;

[0057] S14: According to the attitude error vector and the rotational dynamics equation of the spacecraft and the proof mass in the reference coordinate system, the relative attitude motion model of the spacecraft platform is obtained as follows:

[0058] , , among which i The Coriolis force matrix for a spacecraft , No. k Coriolis force matrix of a proof mass , No. i The gyroscopic torque matrix of a spacecraft is: , No. k The gyro torque matrix of the proof mass is:

[0059] ; Indicates i Spacecraft to k The coordinate transformation matrix of the proof mass; is the error function, , , is the trace function, For the i The antisymmetric matrix of the error angular velocity of the spacecraft.

[0060] S2: Establish the relative translation motion model of the spacecraft platform and the inspection mass block based on the relative position error.

[0061] The specific content is: The relative translation motion model of the spacecraft platform is: , among which k The conjugate matrix of the Coriolis force matrix of the proof mass , No. k The conjugate matrix of the gyro torque matrix of the proof mass , For the k The proof mass is relative to the i The inertial position of the spacecraft is i Components in the spacecraft coordinate system; For the k The position of the proof mass relative to the electrode cage coordinate system is k Components in the electrode cage coordinate system; For the i The component of the position of a spacecraft relative to the inertial coordinate system in the inertial coordinate system; For the inertial coordinate system to k The coordinate transformation matrix of the electrode cage coordinate system; For the i The spacecraft arrived k The coordinate transformation matrix of the electrode cage coordinate system; For the k The mass of the test mass; For the k The gravitational acceleration of the test mass; and For the i spacecraft and k The input torque of the proof mass; and For the i spacecraft and k The disturbance torque of the test mass block.

[0062] S3: Based on the relative attitude motion model and the relative translation motion model, an attitude-orbit coupling control model of the towless navigator formation is constructed.

[0063] In step S3, the attitude-orbit coupling control model of the towless navigator formation is constructed, including the following contents:

[0064] Defining parameters , , ,in It is i The error vector of the expected rotation matrix of the first proof mass of the spacecraft, No. i The error vector of the expected rotation matrix of the second proof mass of the spacecraft; and It is i The mass of the first and second proof masses of the spacecraft; and It is i The input torque of the first and second proof mass blocks of the spacecraft; and For the i Control inputs for the first and second proof masses of a spacecraft; and For the i The disturbance torque of the first and second proof mass blocks of the spacecraft; and For the i The disturbance force of the first and second proof mass blocks of the spacecraft; For the i The first proof mass of the spacecraft is relative to the i The inertial position of the first electrode cage of the spacecraft is i The component of the first electrode cage of the spacecraft in the coordinate system, For the i The second proof mass of the spacecraft is relative to the i The inertial position of the second electrode cage of the spacecraft is i The component of the coordinate system of the second electrode cage of the spacecraft;

[0065] The coupled translational and rotational relative dynamic equations are:

[0066] ,in , , , , , , , , ,in To take the diagonal operation; is a 3×3 identity matrix, is a 15×15 identity matrix; For the i The gravitational acceleration of the spacecraft; For the inertial coordinate system to i The coordinate transformation matrix of the first electrode cage coordinate system of the spacecraft, For the inertial coordinate system to i The coordinate transformation matrix of the second electrode cage coordinate system of the spacecraft; For the i Spacecraft to i The coordinate transformation matrix of the first electrode cage coordinate system of the spacecraft, For the i Spacecraft to i The coordinate transformation matrix of the second electrode cage coordinate system of the spacecraft; For the i Spacecraft to i The coordinate transformation matrix of the coordinate system of the first test mass block of the spacecraft is: For the i Spacecraft to i The coordinate transformation matrix of the coordinate system where the second proof mass block of the spacecraft is located; and They are i The Coriolis force matrix of the first test mass block of the spacecraft and the i The Coriolis force matrix of the second proof mass of the spacecraft is, and They are and The conjugate matrix of ; and They are i The gyro torque matrix of the first test mass block of the spacecraft and the i The gyro torque matrix of the second proof mass of the spacecraft is, and They are and The conjugate matrix of ; and They are i The error rotation matrix of the first proof mass block of the spacecraft and the error rotation matrix of the first proof mass block i The error rotation matrix of the second proof mass of the spacecraft; For the iThe first proof mass of the spacecraft is relative to the i The inertial position of the spacecraft is i The components in the spacecraft coordinate system, For the i The second proof mass of the spacecraft is relative to the i The inertial position of the spacecraft is i components in the spacecraft coordinate system.

[0067] S4: Given the assumptions, the attitude-orbit coupling control model of the towless navigator formation is linearized.

[0068] Given the assumptions: i The spacecraft is relative to the inertial coordinate system I The angular velocity at i Spacecraft B i Components of the coordinate system , ;No. i The first spacecraft k The electrode cage is relative to the i The inertial position of the spacecraft is i Components in the spacecraft coordinate system , ;No. k The angular velocity of the test mass in the electrode cage coordinate system is k Components in the coordinate system of the proof mass .

[0069] Let the drag-free coordinate system selection matrix and the electrostatic suspension coordinate system selection matrix be and , no drag coordinate system selection matrix for:

[0070] ;

[0071] Electrostatic Suspension Coordinate System Selection Matrix for:

[0072] .

[0073] The coupled translational and rotational relative dynamics equations are rewritten as: , where the state variable , attitude control variables ; No drag control variable , electrostatic suspension control variable , and the state variable ; Coefficient matrix , where the transfer matrix , intermediate variable and ; state vector , the coefficient matrix , where the variable .

[0074] In order to improve the performance of the drag-free control subsystem, the coefficient matrix of the drag-free control subloop is transformed into a diagonal unit matrix. i The total input variables for a spacecraft are , where the spacecraft control component , the control component of the inspection mass block is ;No. i The total external disturbance variable of a spacecraft is , where the disturbance variable of the spacecraft is , the disturbance variable of the inspection mass block is ; Based on the above variables, the coupled translational and rotational relative dynamics equations are replaced by: , where the coefficient matrix , the spacecraft coefficient matrix , the drag-free loop coefficient matrix , electrostatic suspension loop coefficient matrix , the state vector The derivative of , the spacecraft state vector , the state vector of the no-drag loop , the state vector of the electrostatic suspension circuit .

[0075] S5: Decouple the linearized attitude-orbit coupling control model of the drag-free navigator formation into the drag-free control subsystem, attitude control subsystem and electrostatic suspension control subsystem, and design control laws for each subsystem to control it.

[0076] Among them, the model of the attitude control subsystem is: ; Given the following sliding die surface : , is a positive constant; sliding surface The expression of the derivative is: ; Using sliding surface , the adaptive superhelical control law of the attitude control subsystem is designed as: ,in is the equivalent control law, For the switching law, , , where the parameters , ;parameter , is the update rate, , ,parameter ; Intermediate variables ,parameter , initial value , , is a positive definite constant; yes The derivative of It is i The disturbance force of the spacecraft j Quantity; is the symbolic function, τ is the variable of the definite integral, Indicates time t The sliding surface status.

[0077] Among them, the model of the drag-free control subsystem is: , For the i The input torque vector of the spacecraft is, For the i The perturbation torque vector of a spacecraft; the sliding surface as follows: , is a positive constant; in the disturbance Sliding surface The derivative of ;

[0078] Design the following adaptive superhelical control law: , is the equivalent control law, ; For the switching law, , where the parameters , ,parameter , update law Defined as , ; Control law parameters ; Intermediate variables , where the parameters , initial value , , L 1 is a positive constant; It is i The perturbation torque vector of the spacecraft j A quantity.

[0079] Among them, the model of the electrostatic suspension control subsystem is: , design the following sliding die surface: , is a positive constant; the adaptive superhelical control law of the electrostatic suspension control subsystem is as follows: , equivalent control law , switching law , where the parameters , ,parameter , update law Defined as , control law parameters , intermediate variable ,parameter , intermediate parameters , initial value , , is a positive constant, the overall control law .

[0080] The following is an embodiment of the present invention: Considering the problem of coordinated control of a formation system consisting of three double-test proof mass-block dragless spacecraft, the orbital parameters of each spacecraft are as follows:

[0081]

[0082] The mass of the untowed spacecraft shell is set to 650 kg, and the mass of each inspection mass block is set to 2.5 kg. The initial position of the spacecraft is set, and the initial attitude error between each spacecraft platform and the inspection mass block is set to 0, the initial position error of each spacecraft platform is set to 0, and the initial position error of the inspection mass block is set to [10 -5 , 0, 0] and [-5×10 -6 , 0, 0]. The control law parameters are as follows: L m = L n = L p =1; L 1 = L 2 = L 3 =0.001; , and Both are 0.01.

[0083] See attached Picture 2 It can be seen that the state errors of all degrees of freedom of each spacecraft eventually converged to 0. Picture 2 (a) Picture 2 (b) and Picture 2 (c) The vertical axes of the three graphs ‖ x1 ‖,‖ x 2 ‖and‖ x 3 ‖ respectively correspond to the degree-of-freedom state errors of three different gravitational wave detection drag-free spacecraft, and converge rapidly to 0 with the passage of time represented by the horizontal axis.

[0084] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for attitude-orbit coupling control of a drag-free spacecraft formation for gravitational wave detection, characterized in that: The steps include: S1: Establish the relative attitude motion model of the spacecraft platform and the proof mass based on attitude error; S2: Establish the relative translation motion model of the spacecraft platform and the inspection mass block based on the relative position error; S3: Based on the relative attitude motion model and relative translation motion model, the attitude-orbit coupling control model of the towless navigator formation is constructed; S4: Given the assumptions, the attitude-orbit coupling control model of the towless navigator formation is linearized; S5: Decouple the linearized drag-free navigator formation attitude-orbit coupling control model into the drag-free control subsystem, attitude control subsystem and electrostatic suspension control subsystem, and design control laws for each subsystem to control it; Let the inertial coordinate system be I ; Let the spacecraft coordinate system be B ; The electrode cage coordinate system is H ; The coordinate system of the inspection mass block is M ; B i Refers to i spacecraft, i =1, 2, 3; Assume that each spacecraft includes two proof masses, then M ki It refers to i The first of the spacecraft k A proof mass block, k =1,2; For the i The component of the position of a spacecraft relative to the inertial coordinate system in the inertial coordinate system; define the i The error rotation matrix of the spacecraft for , the upper right corner T is the rank conversion operation, i Spacecraft B i The rotation matrix is , and For the i spacecraft and ki The expected rotation matrix of the proof mass; Order i The error vector corresponding to the error rotation matrix of a spacecraft is ,in is the inverse operation of the cross product operation; In step S3, the attitude-orbit coupling control model of the towless navigator formation is constructed, including the following contents: Defining parameters , , ,in It is i The error vector of the expected rotation matrix of the first proof mass of the spacecraft, No. i The error vector of the expected rotation matrix of the second proof mass of the spacecraft; and It is i The mass of the first and second proof masses of the spacecraft; and It is i The input torque of the first and second proof mass blocks of the spacecraft; For the i The input torque of the spacecraft; For the i Control inputs for each spacecraft; and For the i Control inputs for the first and second proof masses of a spacecraft; For the i The perturbation torque of a spacecraft; For the i The disturbance force of a spacecraft; and For the i The disturbance torque of the first and second proof mass blocks of the spacecraft; and For the i The disturbance force of the first and second proof mass blocks of the spacecraft; For the i The first proof mass of the spacecraft is relative to the i The inertial position of the first electrode cage of the spacecraft is i The component of the first electrode cage of the spacecraft in the coordinate system, For the i The second proof mass of the spacecraft is relative to the i The inertial position of the second electrode cage of the spacecraft is i The component of the coordinate system of the second electrode cage of the spacecraft; The coupled translational and rotational relative dynamic equations are: ,in , , , , , , , , ,in To take the diagonal operation; is a 3×3 identity matrix, is a 15×15 identity matrix; For the i The gravitational acceleration of the spacecraft; For the inertial coordinate system to i The coordinate transformation matrix of the first electrode cage coordinate system of the spacecraft, For the inertial coordinate system to i The coordinate transformation matrix of the second electrode cage coordinate system of the spacecraft; For the i Spacecraft to i The coordinate transformation matrix of the first electrode cage coordinate system of the spacecraft, For the i Spacecraft to i The coordinate transformation matrix of the second electrode cage coordinate system of the spacecraft; For the i Spacecraft to i The coordinate transformation matrix of the coordinate system of the first test mass block of the spacecraft is: For the i Spacecraft to i The coordinate transformation matrix of the coordinate system where the second proof mass block of the spacecraft is located; and They are i The Coriolis force matrix of the first test mass block of the spacecraft and the i The Coriolis force matrix of the second proof mass of the spacecraft is, and They are and The conjugate matrix of ; and They are i The gyro torque matrix of the first test mass block of the spacecraft and the i The gyro torque matrix of the second proof mass of the spacecraft is, and They are and The conjugate matrix of ; and They are i The error rotation matrix of the first proof mass block of the spacecraft and the error rotation matrix of the first proof mass block i The error rotation matrix of the second proof mass of the spacecraft; For the i The first proof mass of the spacecraft is relative to the i The inertial position of the spacecraft is i The components in the spacecraft coordinate system, For the i The second proof mass of the spacecraft is relative to the i The inertial position of the spacecraft is i components in the spacecraft coordinate system.

2. The method for attitude-orbit coupling control of a drag-free spacecraft formation for gravitational wave detection according to claim 1, characterized in that: The specific content of step S1 is: S11: Construct reference coordinate system; S12: Obtain the rotational dynamics equations of the spacecraft and the proof mass in the reference coordinate system; Based on the rotation matrix representation i spacecraft and ki The rotational kinematic equation of the proof mass is: , ;in, It is i Spacecraft B i The rotation matrix The first derivative of ; one dot above the parameter represents the first derivative, and two dots represent the second derivative, It is i The first of the spacecraft k The rotation matrix of the proof mass The first derivative of For parameters X Relative to the coordinate system Y The angular velocity of the coordinate axis Z The amount of It is i The spacecraft is relative to the inertial coordinate system I The angular velocity at i Spacecraft B i The components of the coordinate system; yes The antisymmetric matrix of ; It is ki The test mass is relative to the heliocentric inertial coordinate system I The angular velocity at ki Components in the coordinate system of the proof mass; yes The antisymmetric matrix of is the antisymmetric matrix operation symbol; ki The proof mass represents the i The first spacecraft k A proof mass block; Then the rotational dynamics equation of the spacecraft and the proof mass is defined as: , ;in is the moment of inertia matrix, yes The first derivative of yes The first derivative of For the ki The control input of the proof mass, For the ki The disturbance input of the proof mass block; and For the i spacecraft and ki The expected angular velocity of the proof mass, ki The error rotation matrix of the proof mass ;No. i The error angular velocity of the spacecraft , No. ki The error angular velocity of the proof mass , For the ki The angular velocity of the test mass in the electrode cage coordinate system is ki Components in the coordinate system of the proof mass; S13: define the attitude error vector; ki The error vector corresponding to the error rotation matrix of the proof mass block is ; S14: According to the attitude error vector and the rotational dynamics equation of the spacecraft and the proof mass in the reference coordinate system, the relative attitude motion model of the spacecraft platform is obtained as follows: , , among which i The Coriolis force matrix for a spacecraft , No. ki Coriolis force matrix of a proof mass , No. i The gyroscopic torque matrix of a spacecraft is: , No. ki The gyro torque matrix of the proof mass is: ; Indicates i Spacecraft to ki The coordinate transformation matrix of the proof mass; is the error function, , , is the trace function, For the i The antisymmetric matrix of the error angular velocity of the spacecraft.

3. The method for attitude-orbit coupling control of a drag-free spacecraft formation for gravitational wave detection according to claim 2, characterized in that: The specific content of step S2 is: The relative translation motion model of the spacecraft platform is: , among which ki The conjugate matrix of the Coriolis force matrix of the proof mass , No. ki The conjugate matrix of the gyro torque matrix of the proof mass , For the ki The proof mass is relative to the i The inertial position of the spacecraft is i Components in the spacecraft coordinate system; For the ki The position of the proof mass relative to the electrode cage coordinate system is ki Components in the electrode cage coordinate system; For the inertial coordinate system to ki The coordinate transformation matrix of the electrode cage coordinate system; For the i The spacecraft arrived ki The coordinate transformation matrix of the electrode cage coordinate system; For the ki The mass of the test mass; For the ki The gravitational acceleration of the test mass; For the ki The input torque of the proof mass; For the ki The disturbance torque of the test mass block.

4. The method for attitude-orbit coupling control of a drag-free spacecraft formation for gravitational wave detection according to claim 3, characterized in that: The content of step S4 is: Given the assumptions: i The spacecraft is relative to the inertial coordinate system I The angular velocity at i Spacecraft B i Components of the coordinate system , ;No. i The first spacecraft k The electrode cage is relative to the i The inertial position of the spacecraft is i Components in the spacecraft coordinate system , ;No. ki The angular velocity of the test mass in the electrode cage coordinate system is ki Components in the coordinate system of the proof mass ; Let the drag-free coordinate system selection matrix and the electrostatic suspension coordinate system selection matrix be and , no drag coordinate system selection matrix for: ； Electrostatic Suspension Coordinate System Selection Matrix for: ； Then the coupled translational and rotational relative dynamics equations are rewritten as: , where the state variable , attitude control variables ; No drag control variable , electrostatic suspension control variable , and the state variable ; Coefficient matrix , where the transfer matrix , intermediate variable and ; state vector , the coefficient matrix , where the variable ; In order to improve the performance of the drag-free control subsystem, the coefficient matrix of the drag-free control subloop is transformed into a diagonal unit matrix. i The total input variables for a spacecraft are , where the control component of the spacecraft is , the control component of the inspection mass block is ;No. i The total external disturbance variable of a spacecraft is , where the disturbance variable of the spacecraft is , the disturbance variable of the test mass block is ; Based on the above variables, the coupled translational and rotational relative dynamics equations are replaced by: , where the coefficient matrix , the spacecraft coefficient matrix , the drag-free loop coefficient matrix , electrostatic suspension loop coefficient matrix , the state vector The derivative of , the spacecraft state vector , the state vector of the no-drag loop , the state vector of the electrostatic suspension circuit .

5. The method for attitude-orbit coupling control of a drag-free spacecraft formation for gravitational wave detection according to claim 4, characterized in that: The model of the attitude control subsystem described in step S5 is: ; Given the following sliding die surface : , is a positive constant; sliding surface The expression of the derivative is: ; Using sliding surface , the adaptive superhelical control law of the attitude control subsystem is designed as: ,in is the equivalent control law, For the switching law, , , where the parameters , ;parameter , is the update rate, , ,parameter ; Intermediate variables ,parameter , initial value , , is a positive definite constant; yes The derivative of It is i The disturbance force of the spacecraft j Quantity; is the symbolic function, τ is the variable of the definite integral, Indicates time t The sliding surface status.

6. The method for attitude-orbit coupling control of a drag-free spacecraft formation for gravitational wave detection according to claim 4, characterized in that: The model of the drag-free control subsystem described in step S5 is: , For the i The input torque vector of the spacecraft is, For the i The perturbation torque vector of a spacecraft; the sliding surface as follows: , is a positive constant; in the disturbance Sliding surface The derivative of ; Design the following adaptive superhelical control law: , is the equivalent control law, ; For the switching law, , where the parameters , ,parameter , update law Defined as , ; Control law parameters ; Intermediate variables , where the parameters , initial value , , L 1 is a positive constant; It is i The perturbation torque vector of the spacecraft j A quantity.

7. The method for attitude-orbit coupling control of a drag-free spacecraft formation for gravitational wave detection according to claim 4, characterized in that: The model of the electrostatic suspension control subsystem is: , design the following sliding die surface: , is a positive constant; the adaptive superhelical control law of the electrostatic suspension control subsystem is as follows: , equivalent control law , switching law , where the parameters , ,parameter , update law Defined as , control law parameters , intermediate variable ,parameter , intermediate parameters , initial value , , is a positive constant, the overall control law .

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