A method and system for capturing and controlling a test mass of a drag-free satellite combining ESO and tube-MPC

Abstract

This invention proposes a dragless satellite verification mass acquisition control method and system combining ESO and tube-MPC, belonging to the aerospace field. The method uses a V-shaped dual-mass dragless satellite, commonly used for gravitational wave detection, as the control design object. An ESO is designed based on a dynamic model, and an innovative method is obtained to acquire a robust positive invariant set from the ESO estimation error. An MPC controller is designed for the nominal model of tube-MPC, and constraints are reduced based on the robust positive invariant set. Simultaneously, an auxiliary feedback gain is designed to ensure the convergence of the minimum robust positive invariant set. This method overcomes the problem that traditional Tube-MPC is unsuitable for handling bias disturbances, while also considering the dynamic performance and robustness of the TM acquisition control process. This invention can be naturally extended to more general disturbance cases, not just slowly varying disturbances. Furthermore, it can be extended to higher-dimensional controlled objects.

Description

Technical Field

[0001] This invention belongs to the aerospace field, specifically relating to a method for quality capture and control of drag-free satellites. Background Technology

[0002] This invention mainly involves three areas: "dragless satellite verification quality capture control", "extended state observer", and "Tube-based model predictive control theory". The background technology of these three aspects will be introduced below.

[0003] 1. Dragless satellite inspection quality capture control

[0004] Dragless satellites originated in the 1960s, and the corresponding dragless control technology is currently widely used in scientific missions such as gravity measurement and gravitational wave detection. The idea is to place a test mass (TM) inside the satellite's enclosed cavity. Due to the satellite's shielding effect, the TM is almost entirely affected by gravity. If the control satellite strictly follows the TM, the satellite will also operate in the same purely gravitational orbit, thus meeting the prerequisites for scientific detection. With technological advancements, new-generation dragless satellites employ multiple TMs to improve the overall performance of the dragless control system. Satellites such as GOCE and LISA Pathfinder have already verified the feasibility of this technology.

[0005] The inertial sensor, also known as the gravitational reference sensor (GRS), is a core component of drag-free satellites, primarily consisting of a telescopic reference sensor (TM) and a surrounding polar plate frame. The capacitance between the TM and the polar plates allows for the measurement of the TM's displacement and attitude, and also generates electrostatic force to control the TM's motion, forming an electrostatic levitation system. During the launch and orbit insertion process, the TM is fixed to the satellite body via a locking mechanism. Before drag-free control during the scientific mission phase, the satellite needs to release the locked TM at a certain relative velocity. After the release mechanism recovers the TM, the GRS uses electrostatic force to capture and stabilize it at the center of its cavity. If the TM is cubic, its attitude must typically be aligned with the GRS cavity to meet the initial conditions for transitioning to drag-free control. However, the low actuation capability of the GRS and the randomness of the initial conditions make the capture and control during the TM release phase a challenging task.

[0006] Early research on TM capture control during the release phase mainly focused on sliding mode control and time-optimal control. Sliding mode control is characterized by its simplicity and robustness, while time-optimal control uses time as the optimization objective to design a control law with the shortest capture time. However, these methods did not fully consider the low drive capability and small measurement range of GRS. Furthermore, in the 2016 LISA Pathfinder flight test, the unexpected initial release velocity prevented the sliding mode controller from effectively capturing the TM, causing the TM to collide with the plunger. This prompted further research on TM capture control, particularly for gravitational wave detection satellites with more stringent control conditions and higher accuracy requirements.

[0007] Model Predictive Control (MPC), as a method capable of online rolling optimization to obtain the current optimal control input, can fully consider various constraints and achieve optimal control in the prediction time domain, characterized by fast convergence and high accuracy. To capture time-shifting objects (TMs) as effectively as possible under the constraints of GRS's driving and measurement capabilities, researchers have begun to apply MPC to this problem. Considering that conventional MPC methods require all state information and have high model accuracy requirements, while GRS can only measure the relative displacement and attitude of the TM, and taking into account the numerous uncertainties in the TM release phase, it is necessary to design a robust state observer and a robust output feedback MPC method to ensure the success rate of capture control.

[0008] 2. Extended State Observer and Tube-based Model Predictive Control Theory

[0009] Extended State Observer (ESO) is one of the core technologies of Active Disturbance Rejection Control (ADDC). The basic idea is to reduce the uncertainty of external disturbances and internal models to a total disturbance. Only the output information of the object is needed to estimate the system state and the total disturbance, which has strong anti-disturbance and robustness. ESO has various forms, such as the linear form proposed by Gao Z. Scaling and bandwidth-parameterization based controller tuning[C] / / Acc. 2003, 4: 989-4., which has the characteristics of easy parameter tuning; and the method based on nonlinear Fal function proposed by Qin Yao, Yang Jie, Liu Shuyun, et al. Research on filter and extended state observer based on improved Fal function[J]. Control and Decision, 2025, 40(2):684-692., which has the gain conforming to the empirical knowledge in the control engineering community: "large error, small gain, small error, large gain". By estimating and compensating for disturbances, ESO can compensate the actual controlled object into a standard integral system. While obtaining state estimation information, it simplifies the design of the controller. It is a general and effective observer with great application value.

[0010] Model predictive control (MPC), an advanced control technique originating in the 1970s, is characterized by predicting the future dynamic behavior of a system using models and system state information. It then applies current and future uncertainties and physical constraints to a finite-time domain optimization control problem, and obtains the optimal control input sequence by solving the optimization problem through a rolling time-domain optimization control strategy. Tube-based MPC is an advanced robust MPC control method. This method stabilizes a nominal system with tightened constraints through open-loop optimization control, then designs a feedback control law using robust invariant sets, and finally combines the two. This approach confines the system trajectory to a tubular region around the nominal trajectory, hence the name "Tube-based method." Tube-based MPC effectively handles system constraints and uncertainties, ensuring the robust stability of the controlled system.

[0011] Combining ESO with tube-MPC allows the system to estimate and compensate for low-frequency disturbances, enhancing its disturbance rejection capability. The estimation error of ESO can be converted into an additive bounded high-frequency disturbance, guiding the parameter design of Tube-MPC. Tube-MPC ensures that the system state remains within a tubular region near the nominal trajectory under the aforementioned disturbances, thus guaranteeing the system's robustness and control performance. Currently, there is no research on the application of combining ESO and tube-MPC in TM capture control.

[0012] Therefore, this invention addresses the acquisition control problem during the mass release phase of a dragless satellite by designing a control method that combines ESO and tube-MPC. Summary of the Invention

[0013] To achieve mass acquisition control for towed satellites, this invention proposes a control method combining ESO and tube-MPC. This method uses a V-shaped, dual-mass, towless satellite commonly used for gravitational wave detection as the control design object. An ESO is designed based on a dynamic model, and a method for obtaining robust positive invariant sets from ESO estimation errors is innovatively derived. An MPC controller is designed for the nominal model of tube-MPC, and constraints are reduced based on the robust positive invariant sets. An auxiliary feedback gain is designed to ensure the convergence of the minimum robust positive invariant set. This control method overcomes the problem of traditional tube-MPC's inability to handle bias disturbances while simultaneously ensuring the dynamic performance and robustness of the TM acquisition control process.

[0014] To achieve the above objectives, the present invention provides the following technical solution:

[0015] This invention provides a drag-free satellite inspection quality acquisition control method combining ESO and tube-MPC:

[0016] A dynamic model of a drag-free dual-mass satellite is constructed, and the two TM satellites are stabilized in the GRS cavity coordinate system using this dynamic model. Center, and make its posture consistent with Alignment;

[0017] Construct a control system, including building an extended state observer (ESO) and an MPC controller based on the nominal model of the tube-MPC;

[0018] Based on the constructed control system, the optimal control commands are obtained.

[0019] Furthermore, the method for constructing the above-mentioned drag-free satellite dynamics model with dual mass blocks is as follows:

[0020] Both TMs are placed inside the GRS cavity, with their nominal orientations at a 60° angle, and an auxiliary coordinate system is defined, including a heliocentric inertial reference coordinate system. Satellite coordinate system GRS cavity coordinate system and TM fixed coordinate system ,in correspond and ;

[0021] Establish TM relative to The attitude dynamics equations and translation dynamics equations of the satellite, relative to The attitude and orbital dynamics equations, and based on the TM and [other equations] during mass capture control. Relative posture between Relative attitude angular velocity and relative displacement All of these are small quantities, resulting in the dynamic system equations for a drag-free satellite with two mass blocks;

[0022] Based on the dynamic system equations of a drag-free satellite with two mass blocks, the two TM satellites are stabilized in the GRS cavity coordinate system. Center, and make its posture consistent with Alignment.

[0023] Furthermore, the construction method of the above extended state observer (ESO) is as follows:

[0024] The obtained dynamic system equations are decomposed, and the system is decoupled into 12 time-invariant SISO systems by utilizing the physical properties of TM as a uniform metal cube and introducing equivalent perturbations.

[0025] The forward Euler method is used to discretize any SISO system to obtain a discrete model containing bounded measurement noise and bounded process noise.

[0026] By defining extended states, the obtained discrete model is extended to obtain an ESO with linear discreteness.

[0027] Furthermore, the method for constructing the MPC controller of the aforementioned nominal system is as follows:

[0028] The robust positive invariant set is obtained by estimating the ESO error, and the robust positive invariant set is calculated offline. The MPC controller is designed based on the robust positive invariant set calculated offline.

[0029] Furthermore, a reduction constraint is applied to the nominal system using a robust positive invariant set.

[0030] Furthermore, the final control command is obtained through auxiliary control laws.

[0031] Furthermore, the auxiliary control law is specifically as follows:

[0032]

[0033] in, The nominal control input solved by MPC, For the feedback auxiliary control section, This is an estimate of the ESO information.

[0034] The dragless satellite inspection quality capture and control method combining ESO and tube-MPC described in this invention can be entirely implemented using computer software. Therefore, correspondingly, this invention also provides a dragless satellite inspection quality capture and control system combining ESO and tube-MPC. The system includes a storage device for executing the dragless satellite inspection quality capture and control method combining ESO and tube-MPC proposed above.

[0035] The present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, performs a drag-free satellite inspection quality capture control method combining ESO and tube-MPC as described above.

[0036] The present invention also provides a computer device including a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes a dragless satellite inspection quality capture control method combining ESO and tube-MPC as described in any of the above-mentioned embodiments.

[0037] The beneficial effects of this invention are as follows:

[0038] 1. This invention proposes a dragless satellite verification mass acquisition control method combining ESO and tube-MPC. This method uses a dragless satellite with a "V"-shaped configuration and dual mass blocks, commonly used for gravitational wave detection, as the control design object. An ESO is designed based on a dynamic model, and an innovative method for obtaining the robust positive invariant set when combined with the ESO is presented. An MPC controller is designed for the nominal model of tube-MPC, and constraints are reduced based on the robust positive invariant set. Simultaneously, an auxiliary feedback gain is designed to ensure the convergence of the minimum robust positive invariant set. This control method overcomes the problem that traditional Tube-MPC is unsuitable for handling bias disturbances, while also ensuring both dynamic performance and robustness of the TM acquisition control process.

[0039] Furthermore, by combining the output feedback MPC method of ESO, this invention only needs to obtain the position / attitude information given by GRS. It can take into account the constraints brought about by the measurement range and drive range of GRS in the towless satellite TM acquisition control problem, and give the optimal control command in the finite time domain to obtain excellent control effect.

[0040] Furthermore, by introducing ESO, this invention enhances the ability of the dragless satellite TM acquisition control system to cope with disturbances and uncertainties. Its disturbance estimation information enables the system to compensate for disturbances, making up for the shortcomings of the conventional tube-MPC method in dealing with large bias disturbances.

[0041] Furthermore, by introducing the Tube, this invention ensures the robust stability of the dragless satellite™ acquisition control system, which can cope with the effects of uncertainties such as measurement noise and process noise.

[0042] 2. This invention innovatively proposes a Tube-MPC method combined with ESO, and provides a corresponding robust positive invariant set derivation method and constraint tightening method, which can be extended to more general control problems.

[0043] The Tube-MPC method combined with ESO proposed in this invention can be naturally extended to more general perturbation cases, rather than being limited to slowly varying perturbations. Furthermore, it can be extended to higher-dimensional controlled objects. Attached Figure Description

[0044] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0045] Figure 1 This is a schematic diagram of the drag-free satellite configuration and coordinate system definition described in this invention;

[0046] Figure 2 This is a schematic diagram of the control system structure described in this invention;

[0047] Figure 3 This is the robust positive invariant set of displacement degrees of freedom described in this invention;

[0048] Figure 4 This is the robust positive invariant set of attitude degrees of freedom described in this invention;

[0049] Figure 5 This refers to the relative displacement control curve of TM1 as described in this invention;

[0050] Figure 6 This refers to the relative displacement control curve of TM2 as described in this invention;

[0051] Figure 7 This refers to the relative attitude control curve of TM1 as described in this invention;

[0052] Figure 8 This refers to the relative attitude control curve of TM2 as described in this invention;

[0053] Figure 9 The GRS control force curve described in this invention;

[0054] Figure 10This is the GRS control torque curve described in this invention. Detailed Implementation

[0055] The following description of the specific implementation details (such as experimental setup, operation procedures, data processing steps, and example parameters) of "a dragless satellite inspection quality capture control method combining ESO and tube-MPC" provided in this specification is primarily intended for illustrative purposes rather than limiting definitions, aiming to help those skilled in the art thoroughly understand the principles and implementation of the invention. However, those skilled in the art should understand that these details represent only one feasible embodiment, and the core concept of the invention can be fully realized through other technical means or alternative solutions not described in detail, without departing from its spirit and essence. Furthermore, the omission of details of conventional experimental methods and apparatus known in the art in the specification is to avoid redundant information interfering with the understanding of the innovation points. This does not mean that these known technologies are not required during implementation, and those skilled in the art should be able to supplement and apply them based on their professional knowledge.

[0056] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention.

[0057] The following description relates to some commonly used symbols and operational rules: express The set of dimensional real numbers, express A set of dimensional real vectors; for the set and The Minkowski addition of a set is defined as follows: The Minkowski (Pontryagin) subtraction of a set is... If set If a set is convex, compact, and contains the origin, then the set is... A set is called a true set if it is also non-empty internally. set; Representation matrix The spectral radius is defined as the maximum value of the moduli of all eigenvalues ​​of the matrix. Represents an n-order identity diagonal matrix. express OK A matrix in which all columns are 0.

[0058] Definition: For the system and constraint set ,gather If satisfied And for any state , ,but It is called a positive invariant set; for the system and constraint set ,gather If satisfied And for any state and disturbance , Then it is called It is a robust positive invariant set.

[0059] Implementation Method 1: To achieve dragless satellite test quality acquisition control, this implementation method proposes a dragless satellite test quality acquisition control method combining ESO and tube-MPC. This method uses a dragless satellite with a "V"-shaped configuration and dual mass blocks, commonly used for gravitational wave detection, as the control design object. An ESO is designed based on a dynamic model, and an innovative method for obtaining the robust positive invariant set when combined with the ESO is presented. An MPC controller is designed for the nominal model of tube-MPC, and constraints are reduced based on the robust positive invariant set. Simultaneously, an auxiliary feedback gain is designed to ensure the convergence of the minimum robust positive invariant set. This control method overcomes the problem that traditional Tube-MPC is unsuitable for handling bias disturbances, while also taking into account the dynamic performance and robustness of the TM acquisition control process.

[0060] The control method includes the following steps:

[0061] A dynamic model of a drag-free satellite with two mass blocks is constructed to simulate the motion state of the drag-free satellite. The control objective is to stabilize the two TM satellites in the GRS cavity coordinate system. Center, and make its posture consistent with Alignment;

[0062] Construct a control system, including building an extended state observer (ESO) and an MPC controller based on the nominal model of the tube-MPC;

[0063] Based on the constructed control system, the optimal control commands are obtained.

[0064] Implementation Method Two: Combination Figure 1 and Figure 2 This embodiment describes in detail a drag-free satellite inspection quality capture and control method combining ESO and tube-MPC proposed in Embodiment 1 above.

[0065] (1) The specific steps for constructing a drag-free satellite dynamics model with dual mass blocks are as follows:

[0066] The satellite's configuration is as follows Figure 1 As shown, two TMs are placed within the GRS cavity, with their nominal orientations at a 60° angle. The auxiliary coordinate systems are the heliocentric inertial reference coordinate system. Satellite body coordinate system GRS cavity coordinate system TM fixed coordinate system ,in correspond and .

[0067] When subscripts are omitted, TM is established relative to The attitude dynamic equations and translation dynamic equations are as follows:

[0068] (1)

[0069] (2)

[0070] Satellite relative The attitude and orbital dynamics are as follows:

[0071] (3)

[0072] (4)

[0073] in, This represents the moment of inertia matrix of the satellite platform (including the telescope). Indicates satellite relative angular velocity, This indicates the control torque exerted by the micro-thrusters on the satellite body. The resultant torque of external disturbances. Let TM be the rotational inertia matrix. and The resultant torque of the electrostatic control torque acting on the TM and the external disturbance torque, The stiffness moment generated by the coupling between TM and the satellite is all within... The expression in the text. For satellite quality, for Location of the satellite's center of mass. μ The gravitational constant of the Sun; This indicates the control force exerted on the satellite by the micro-thrusters. All of these are external interference forces. The expression in the text. For the quality of a single TM, For the relative center of mass of TM The position vector of the origin. and These are the electrostatic control force and the resultant force of external disturbance acting on the TM, respectively. The coupling stiffness force between TM and the satellite is in The expression below. for arrive The coordinate transformation matrix. and It can be modeled as:

[0074] (5)

[0075] in, , , and The coupling stiffness matrix is ​​formed, and its off-diagonal elements are ignored during controller design. , .

[0076] In the mass block capture control process, TM and Relative posture between Relative attitude angular velocity and relative displacement Since both are small quantities, we can conclude that:

[0077] (6)

[0078] in , , and express according to Rotate in sequence to The corresponding roll angle, pitch angle, and yaw angle; , and for Center of mass is The coordinates, i.e., the relative displacement exist Components of each axis.

[0079] The control task at this stage is to stabilize the two TMs. Center, and make its posture consistent with Alignment. The satellite platform performs attitude and orbit maintenance control, with attitude control employing PID control and orbit control using open-loop control to compensate for disturbances. Both are existing technologies, therefore, specific design details are not provided in this implementation.

[0080] The specific steps for building an Extended State Observer (ESO) are as follows:

[0081] (2) Decomposition and discretization of the controlled object:

[0082] Next, the control system will be designed. TM is relative to The displacement and attitude are measured by GRS. To obtain state information, a state observer needs to be designed. At the same time, the TM is subject to some low-frequency disturbances during the acquisition process. To compensate for these disturbances, a disturbance estimator also needs to be designed. ESO can achieve both state estimation and disturbance estimation simultaneously.

[0083] First, the system dynamics equations are processed:

[0084] (7)

[0085] in, , , , , . This refers to the equivalent perturbation input term transformed from coupling terms, nonlinear terms, and parameter uncertainties in dynamics. Let this be the satellite's state vector. This refers to direct perturbations acting on the TM. Furthermore, measurement noise in the GRS is taken into account. .

[0086] for Since TM is a precise, uniform metal cube, its moment of inertia is negligible. The off-diagonal elements, and from equation (7), it can be seen that by introducing equivalent perturbations, the system can be decoupled into 12 time-invariant SISO systems, each with a similar form. Therefore, the controller design results for a single SISO system can be extended to the design of all SISO systems. Any one of the SISO systems can be expressed as:

[0087] (8)

[0088] in, , , For equivalent input disturbance, For measuring noise. , Stiffness matrix The corresponding elements in , b For the input matrix The corresponding elements in.

[0089] Discretize the system (8) using the forward Euler method to obtain:

[0090] (9)

[0091] in, , , , For bounded measurement noise, This refers to bounded process noise present during system updates.

[0092] Before proceeding to the next design step, the following settings are given:

[0093] 1) The system is controllable and observable;

[0094] 2) The main body is a gentle disturbance, which is modeled as follows during the TM capture control process. , It is a small, bounded noise;

[0095] 3) The system's state and input constraints satisfy... ,and and All true set.

[0096] For TM capture control, let , , and These represent the measurement and drive limits of GRS, respectively. Clearly, the system can meet the above settings.

[0097] (3) ESO design

[0098] Based on the construction logic of ESO, let's define the expansion state. The system (9) is extended as follows:

[0099] (10)

[0100] in, , , , This can be viewed as process uncertainty in an extended system.

[0101] Establish the following linear discrete ESO:

[0102] (11)

[0103] This is the observer gain.

[0104] make , The observation error equation is:

[0105] (12)

[0106] definition Select the observer gain satisfy This ensures its stability.

[0107] (4) Combining the ESO tube-MPC theory derivation, we obtain the following: Figure 2 The diagram shows the Tube-MPC control system structure combined with ESO.

[0108] Introduce the nominal system corresponding to the original system (9):

[0109] (13)

[0110] in, To indicate the nominal system status, Input for the nominal system.

[0111] The nominal system is unaffected by uncertainties and can be considered an ideal system. The principle of Tube-MPC is as follows: The initial state of the nominal system is set to be similar to that of the actual system. Then, an open-loop real-time MPC controller is designed for the nominal system to obtain the convergent state sequence of the nominal system, which serves as the center of the Tube. An auxiliary control law is designed; based on the relevant theory of robust positive invariant sets, the state trajectory of the actual system can be maintained within the Tube without violating system constraints, resisting the effects of disturbances and uncertainties. This implementation improves upon the traditional Tube-MPC, resisting unknown, gradual disturbances. The control law is designed as follows:

[0112] (14)

[0113] This control law consists of three parts. The nominal control input solved by MPC; This is a feedback-assisted control section used to maintain the observer's dynamics / actual dynamics near the nominal dynamics, resisting uncertainty disturbances; this embodiment additionally introduces... The term involves feedforward compensation of the disturbance based on the estimated information. Among these, For feedback gain, ,but:

[0114] (15)

[0115] Define the projection matrix , ,but: , , , Combining equations (10), (13), and (14), the control error equation can be obtained:

[0116] (16)

[0117] definition Feedback gain It is necessary to make To ensure the stability of the error system.

[0118] Next, we present the method for obtaining robust positive invariant sets and constraint shrinkage. First, we rewrite the estimation error equation:

[0119] (17)

[0120] in ,and , for Collection. According to existing theories, At that time, the system (17) is in the constraint set There exists a robust positive invariant that can be computed in finite time. set ,satisfy:

[0121] (18)

[0122] Combining the definition of robust positive invariant sets, in , Under the condition that the initial ESO has converged, i.e. the initial observation error is... Then all subsequent observation errors are within This implies the subsequent actual system state. Will always be in ESO state In the central Tube, that is:

[0123] (19)

[0124] (20)

[0125] Next, the control error equation is rewritten:

[0126] (twenty one)

[0127] in ,but , for Collection. Due to The system (17) is in the constraint set There exists a robust positive invariant that can be computed in finite time. set ,satisfy:

[0128] (twenty two)

[0129] Combining the definition of robust positive invariant sets, in , Under the condition that the initial error Then all subsequent error states are in This means the state of the subsequent observers It will always be in the nominal system state In the central Tube:

[0130] (twenty three)

[0131] definition:

[0132] (twenty four)

[0133] Combining (20) and (23), the actual system state at this time satisfies:

[0134] (25)

[0135] Obviously, in , Under these conditions, the actual system state Will be located in Centered on, size is In the Tube.

[0136] Based on equations (18) and (20), robust positive invariant sets can be defined. , and Offline computation is performed using existing algorithms, which are not detailed in this implementation. Before proceeding with the design of the nominal MPC controller, the following settings are made:

[0137] 1) and Small enough that the calculated , satisfy , .

[0138] 2) Before Tube-MPC was enabled, the ESO observation error had converged to the robust positive invariant set. Inside.

[0139] Considering that GRS has high accuracy and there is a plunger retraction time of about 10 seconds during the TM release process, which allows ESO to complete convergence, the above settings can be satisfied for the TM capture control task.

[0140] (5) Design of the MPC controller for the nominal system

[0141] According to equations (14) and (25), in order to satisfy the constraints of the entire system, the nominal system should be tightened accordingly:

[0142] (26)

[0143] (27)

[0144] If the nominal system state Set after tightening In the middle, the original state If the input of the nominal system Then the actual input satisfies . Although affected by equivalent perturbation, online estimation value However, under slowly varying perturbations and when the ESO has converged, the impact is minimal. It will not affect the robustness of the system; during single-step optimization, it can be used... It is considered a constant.

[0145] Both the prediction time domain and the control time domain are taken as... ,exist k At time t, the cost function is defined as follows:

[0146] (28)

[0147] Where Q and R are weight matrices, The terminal weight matrix consists of positive definite symmetric matrices. The optimization objective of MPC in a single step is to obtain the control input sequence. Make the objective function Minimum optimization problem can be expressed as:

[0148] (29)

[0149] This can be further simplified into a quadratic programming (QP) problem, and the solution method is based on existing technology; detailed implementation is not provided here. The optimal nominal control sequence is ultimately obtained. Take the first step of the input As the nominal control command for the current step.

[0150] Finally, the final control command is obtained by combining the auxiliary control law. ,exist , Under reasonable conditions such as ESO convergence, the actual system state trajectory will remain in the Tube centered on the nominal system state trajectory, taking into account dynamic performance and robustness, resisting disturbances and uncertainties, and ultimately achieving stable and reliable capture control in the TM release phase.

[0151] Implementation Method 3: Combination Figures 3 to 10 This embodiment describes the simulation effect of a drag-free satellite inspection quality capture and control method combining ESO and tube-MPC as described in any of the above embodiments.

[0152] Numerical simulation of the dragless satellite TM acquisition control process was performed, with the following parameter settings:

[0153] satellite quality Satellite rotational inertia TM quality TM moment of inertia . At coordinate , At coordinate The solar gravitational constant The initial attitude and angular velocity of the satellite relative to its inertial frame were set to 0.

[0154] Initial relative Displacement ;

[0155] Initial relative speed ;

[0156] Initial relative attitude ;

[0157] Initial relative Attitude angular velocity .

[0158] The corresponding displacement degree of freedom , Upper limit of control State limit ESO gain Auxiliary feedback gain The robust positive invariant set of displacement degrees of freedom is calculated as follows: Figure 3 As shown. The external constant disturbance torque is set to Random values ​​within.

[0159] corresponding to the degrees of freedom of posture , Control torque upper limit State limit ESO gain Auxiliary feedback gain The robust positive invariant set of attitude degrees of freedom is calculated as follows: Figure 4 As shown. The external constant disturbance torque is set to Random values ​​within.

[0160] Single degree of freedom corresponds to MPC prediction in the time domain , , , The control step size is 0.1 seconds. Tube-MPC control is applied 10 seconds after TM release, at which point the ESO has converged. The simulation results of TM capture control are as follows: Figures 5 to 10 As shown, TM was successfully captured and has high control accuracy.

[0161] Implementation Method 4: The dragless satellite inspection quality capture and control method combining ESO and tube-MPC proposed in the above implementation methods can be entirely implemented using computer software. Therefore, this implementation method provides a dragless satellite inspection quality capture and control system combining ESO and tube-MPC, the system comprising:

[0162] This is used to construct a dynamic model for a drag-free dual-mass block satellite, and the dynamic model is used to stabilize the two TM satellites in the GRS cavity coordinate system. Center, and make its posture consistent with Aligned storage devices;

[0163] Storage device for building control systems, including the storage device for the MPC controller that builds the nominal model of the extended state observer ESO and the tube-MPC;

[0164] A storage device for obtaining optimal control commands based on the constructed control system.

[0165] Storage device used to build an extended state observer (ESO) based on the constructed construction dynamics model;

[0166] Implementation Method 5: This implementation method provides a computer-readable storage medium storing a computer program. When the computer program is run by a processor, it executes the drag-free satellite inspection quality capture and control method combining ESO and tube-MPC as described in any of the above implementation methods.

[0167] Implementation Method Six: This implementation method provides a computer device, which includes a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes a dragless satellite inspection quality capture and control method combining ESO and tube-MPC as described in any of the above implementation methods.

[0168] This embodiment provides a computer device, the hardware of which is a general-purpose model and not shown in the figure. The system includes a processor and a memory, which can be connected via a bus or other means. The memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs, non-transitory computer-executable programs and modules, as well as corresponding program instructions / modules. The processor executes various functional applications and data processing by running the non-transitory software programs, instructions and modules stored in the memory, so as to realize the drag-free satellite inspection quality capture control method and steps combining ESO and tube-MPC in the above method embodiment.

[0169] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of the claims of the present invention.

Claims

1. A method for capturing and controlling a test mass of a drag-free satellite that combines ESO and tube-MPC, characterized by, The method is as follows: A dynamic model of a dual-mass drag-free satellite is constructed, and through the dynamic model, two TMs are stabilized in the GRS cavity coordinate system center and make their attitudes align with each other; The method for constructing a drag-free satellite dynamics model with two mass blocks is as follows: Both TMs are placed in the GRS cavity, with nominal orientations at a 60° angle and defining auxiliary coordinate systems, including a heliocentric inertial reference coordinate system , a satellite body coordinate system , a GRS cavity coordinate system , and a TM-fixed coordinate system , wherein corresponds to the first test mass and the second test mass ; The attitude dynamics equation and the translational dynamics equation of TM relative to , the attitude and orbit dynamics equation of the satellite relative to , and the relative attitude , the relative attitude angular velocity , and the relative displacement between TM and are all small during the mass capture control process are established respectively, and the dynamics equation of the double-mass satellite without drag is obtained. According to the double-mass-block non-drag satellite dynamic system equation, two TM satellites are stabilized in the GRS cavity coordinate system center, and their attitudes are aligned with each other; Construct a control system, including building an extended state observer (ESO) and a tube-MPC nominal system MPC controller; The method for constructing the Extended State Observer (ESO) is as follows: The obtained dynamic system equations of the drag-free satellite with dual mass blocks are decomposed, and the system is decoupled into 12 time-invariant SISO systems by utilizing the physical properties of TM as a uniform metal cube and introducing equivalent perturbations. The forward Euler method is used to discretize any SISO system to obtain a discrete model containing bounded measurement noise and bounded process noise. By defining extended states, the obtained discrete model is extended to obtain an ESO with linear discreteness. The method for constructing the MPC controller of the nominal system is as follows: The robust positive invariant set is obtained by estimating the ESO error, and the robust positive invariant set is calculated offline. The MPC controller is designed based on the robust positive invariant set after offline calculation. Based on the constructed control system, obtain the optimal control commands; Specifically: The final control command is obtained through auxiliary control laws; The auxiliary control law is as follows: wherein, a nominal control input solved for the MPC, a feedback auxiliary control part, an estimation information for the ESO.

2. The method of claim 1, wherein the method is characterized by, Furthermore, a reduction constraint is applied to the nominal system using robust positive invariant sets.

3. A drag-free satellite test mass capture control system that binds ESO and tube-MPC, characterized by, The system includes a storage device for executing a dragless satellite inspection quality capture and control method combining ESO and tube-MPC as described in any one of claims 1-2.

4. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs a drag-free satellite inspection quality capture control method combining ESO and tube-MPC as described in any one of claims 1-2.

5. A computer device, comprising: The device includes a memory and a processor. The memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes a dragless satellite inspection quality capture and control method combining ESO and tube-MPC as described in any one of claims 1-2.

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