Construction method and system of LPF closed-loop system based on state space model

Abstract

The invention belongs to the technical field of LPF closed-loop system simulation, and particularly discloses an LPF closed-loop system construction method and system based on a state space model. The method comprises the following steps: establishing a state space model of each subsystem included in the LPF closed-loop system; according to the data sampling time, classifying subsystems except the noise model into a continuous system and a discrete system; respectively connecting the continuous system and the discrete system; discretizing the connected continuous system and the noise model respectively, and then connecting the discretized system and the connected discrete system to form a complete LPF closed-loop system; and recombining and simulating the state space model of the LPF closed-loop system. According to the LPF closed-loop system construction method provided by the invention, the operation is more simplified, a required function can be realized by using a simple function, the operation efficiency is high, and a model basis is provided for subsequent data processing and analogue simulation.

Description

Technical Field

[0001] This application belongs to the technical field of LPF closed-loop system simulation. More specifically, it relates to a construction method and system of an LPF closed-loop system based on a state space model. Background Art

[0002] Gravitational waves were predicted by Einstein in the general theory of relativity in 1916. When the mass distribution moves in an asymmetric manner, a perturbation will be generated in spacetime, just like ripples in water, which is the gravitational wave. Since the 1980s, laser interferometers based on the Michelson interferometer principle have been applied to gravitational wave detection. Space gravitational wave detection is a method of using satellite formations or constellations to construct large laser interferometers for gravitational wave detection. LPF (Laser Interferometer Space Antenna Pathfinder) aims to test the inertial reference technology and laser interferometry ranging technology of the space gravitational wave detection program LISA (Laser Interferometer Space Antenna). It is necessary to develop a detailed and accurate system model to simulate the dynamic behavior of LPF and implement the data analysis function, with the purpose of verifying the behavior of all subsystems before launch and designing the experiments to be carried out during flight. During mission operations, the system can analyze the operations of the satellite in detail, estimate its most important characteristics, and process all telemetry data.

[0003] The LISA team developed a toolbox LTPDA (LISA Technology Package Data Analysis) for object-oriented modeling according to the requirements of data analysis. This toolbox allows the use of repositories, processes data sets in different ways, tracks all operations, and conducts parameter estimation procedures. There are some problems with this toolbox: currently, the description file of this toolbox abroad is only limited to a description website, and the parameter sources and methods for building models are not publicly available, causing great difficulties for domestic researchers to learn and use; to use this toolbox, an installation package must be obtained for installation, and it needs to be started by entering a start command before each use, and the existing new version of MATLAB software cannot be compatible with it; this toolbox is based on object-oriented classes, and corresponding classes must be called first before use. After obtaining data, the content in these classes must be defined, which increases the complexity of use and is slower than procedural code or matrix operations when frequently creating, copying, or calling methods.

[0004] Therefore, how to solve the problems of complex operation and low operation efficiency of traditional simulation models is a difficult problem in current research. Summary of the Invention

[0005] Aiming at the defects of the existing technology, the purpose of this application is to provide a construction method and system for an LPF closed-loop system based on a state-space model, which is improved on the basis of the traditional LTPDA toolbox, can achieve the required functions, and at the same time the operation is more simplified. The required functions can be realized by using simple functions, and the operation efficiency is high, providing a model basis for subsequent data processing and simulation.

[0006] To achieve the above object, in the first aspect, this application provides a construction method for an LPF closed-loop system based on a state-space model, including the following steps: S10, establish the state-space models of each subsystem included in the LPF closed-loop system; S20, classify the subsystems other than the noise model according to the data sampling time into continuous systems and discrete systems; S30, connect the continuous system and the discrete system respectively; S40, discretize the connected continuous system and the noise model respectively, and then connect the discretized system and the discrete system connected in step S30 to form a complete LPF closed-loop system; S50, recombine and simulate the state-space model of the LPF closed-loop system according to the simulation requirements.

[0007] The beneficial effect of this application is that the construction method for the LPF closed-loop system based on the state-space model provided by this application uses the basic form of the state-space equation to establish the state-space models of each subsystem according to the existing parameters and form a complete closed-loop system. Each model can be simulated separately to test the functions of the subsystems, and the LPF of the connected closed-loop system can also be simulated and tested to verify the correctness of the system theory. Compared with the traditional LTPDA toolbox, the operation is more simplified. The required functions can be realized by using simple functions, it can be compatible with the new version of MATLAB, and the operation efficiency is high, providing a model basis for subsequent data processing and simulation.

[0008] As a further preference, in step S10, the subsystems are an inertial sensing system, a spaceborne tracker system, an interferometer system, a delay system, a drag-free attitude control system, a capacitive displacement sensing system, a micro-thruster system, a satellite dynamics system, acceleration noise and models of different expected noise sources, and this model includes actuator noise, sensor noise and external noise.

[0009] As a further preference, in step S10, the process of establishing the state-space models of each subsystem is specifically as follows: Determine the input, output and state of the subsystem; Determine the information of the state matrix, input matrix, output matrix and feedforward matrix of the subsystem and write out the state-space equation; Information on the state - space model of the complete subsystem, including the time model and name, where the time model is determined by the data sampling time of the subsystem.

[0010] As a further preference, in step S20, the continuous system includes an inertial sensing system, a space - borne tracker system, an interferometer system, a satellite dynamics system, and a micro - thruster system.

[0011] As a further preference, step S30 specifically includes: Traverse all the subsystems to be connected after classification, and obtain all the information of the subsystems to be connected; Compare the names of the input and output variables of the subsystems to be connected, and distinguish their internal inputs and external inputs; Obtain and rearrange the input matrices and feed - forward matrices of all the subsystems to be connected according to the positions of the internal inputs in the output matrix; Place the state matrices and output matrices of the subsystems to be connected in the diagonal positions of the state matrix and output matrix of the connected system; Reset the state - space equation of the connected system according to the state - space equation of the model with set - point input feedback; Organize all the information to form a state - space model of the connected system.

[0012] As a further preference, in step S40, the discretization method is: using the zero - order hold method for the state matrix and input matrix of the connected continuous system, and using the linear averaging method for the output matrix and feed - forward matrix of the connected continuous system.

[0013] As a further preference, in step S50, use internal noise generation and / or use an injection signal to reorganize and simulate the state - space model of the closed - loop system.

[0014] As a further preference, the internal noise is generated using a random noise function.

[0015] In a second aspect, the present application provides a construction system for an LPF closed - loop system based on a state - space model, including: A model - building module for building the state - space models of the subsystems included in the LPF closed - loop system; A classification module for classifying the subsystems other than the noise model into continuous systems and discrete systems according to the data sampling time; A connection module for connecting the continuous system and the discrete system respectively; A closed-loop system construction module is used to discretize the connected continuous system and noise model respectively, and then connect the discretized system and the discretized system after connecting the connection module to form a complete LPF closed-loop system; A simulation module is used to reconstruct and simulate the state space model of the LPF closed-loop system according to simulation requirements.

[0016] It can be understood that the beneficial effects of the second aspect above can be referred to the relevant descriptions in the first aspect, and will not be elaborated here. Description of the Drawings

[0017] Figure 1 It is a theoretical model diagram of the LPF closed-loop system provided by the embodiment of the present application; Figure 2 It is a flowchart of the construction method of the LPF closed-loop system based on the state space model provided by the embodiment of the present application; Figure 3 It is a flowchart of step S30 provided by the embodiment of the present application; Figure 4 It is a schematic diagram of the system connection process of step S30 provided by the embodiment of the present application; Figure 5 It is a system block diagram with a set input feedback provided by the embodiment of the present application; Figure 6 It is a complete closed-loop LPF system dynamic simulation model diagram provided by the embodiment of the present application; Figure 7 It is the interferometer output IFO.x1, IFO.x provided by the embodiment of the present application 12 Simulation result diagram; Figure 8 It is the interferometer reading IFO.x1, IFO.x provided by the embodiment of the present application 12 Power spectral density diagram; Figure 9 It is the power spectral density diagram of the command forces DFACS.sc_x and DFACS.tm2_x of the two control loops of the drag-free attitude control system provided by the embodiment of the present application. Detailed Embodiments

[0018] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0019] It should be understood that in the description of this application, the term "a number of" means at least one, such as one, two, etc., unless otherwise specifically defined; the term "a plurality of" means two or more, unless otherwise specifically defined; the terms "first" and "second" etc. are used to distinguish different objects, rather than to describe a specific order of the objects; the term "and / or" includes any and all combinations of one or more of the related listed items.

[0020] In addition, throughout this specification, the reference to "one embodiment"; the language such as "one embodiment", "one example" or the like means that the specific features, structures or characteristics described in connection with that embodiment are included in at least one embodiment of this application. Therefore, the appearance of the phrase "in one embodiment;" throughout this specification, "in one embodiment" and similar language may or may not all refer to the same embodiment.

[0021] To solve the problems of complex operation and low operation efficiency of the traditional LTPDA toolbox, in this regard, this application provides a construction method of an LPF closed-loop system based on a state space model, so as to generate a model and perform time-domain simulation, inheriting and improving the method of establishing a state space model to represent a system in the LTPDA toolbox.

[0022] The theoretical model of the LPF closed-loop system provided by this application is as Figure 1 shown. Place the first test mass TM1 in the LPF to let it fall freely. Place TM2 and perform differential measurement to evaluate the differential acceleration of the two test masses. The spacecraft protects the two test masses from external influences. The relative noise jitter of the spacecraft is measured by the on-board tracker system. The jitter of the spacecraft relative to TM1 is adjusted by a drag-free control loop using microthrusters connected to the spacecraft. The differential position of the two test masses is controlled by an electrostatic actuator around TM2, and the full control scheme is called a drag-free attitude control system. The LPF contains two main sensor systems for reading the different degrees of freedom of the two test masses relative to each other and the spacecraft. The gravity reference system uses capacitive reading of the relative motion of the spacecraft-test mass along six degrees of freedom to achieve the inertial sensing function. Electrostatic forces and torque moments can also be applied according to the command forces and torques from the controller in the drag-free attitude control system to reposition and rotate the test masses themselves. The interferometer readout system in the optical metrology system provides the reading of the x-axis position of TM1 relative to the spacecraft (O1) and the differential position of the two test masses (O 12 ) and reads the interference angle of each test mass through differential wavefront sensing.

[0023] As Figure 2 shown, the construction method of the LPF closed-loop system based on the state space model provided by this application includes steps S10 to S50, which are described in detail as follows: Step S10: Based on the theoretical knowledge of the LPF closed-loop system and the existing parameters, establish the state-space models of each subsystem included in the LPF closed-loop system.

[0024] In this embodiment, the subsystems in the LPF closed-loop system include the LTP system (LISA Technology Package, mainly a hardware system) and the noise model. Among them, the LTP system includes an inertial sensing system, an on-board tracker system, an interferometer system, a delay system, a drag-free attitude control system, a capacitive displacement sensing system, a micro-propulsion system, a satellite dynamics system, and acceleration noise; the noise model includes actuator noise, sensor noise, and external noise.

[0025] Step S20: According to the data sampling time, classify the subsystems other than the noise model into continuous systems and discrete systems.

[0026] In this embodiment, the continuous systems include an inertial sensing system, an on-board tracker system, an interferometer system, a satellite dynamics system, and a micro-propulsion system.

[0027] Step S30: Connect the continuous systems and discrete systems separately.

[0028] In this embodiment, connection functions can be constructed to connect the continuous systems and discrete systems separately.

[0029] Specifically, step S30 can be as follows: Step S31: Traverse all the subsystems that need to be connected after classification, and obtain all the information of the subsystems that need to be connected. Step S32: Compare the names of the input and output variables of the subsystems that need to be connected, and distinguish their internal inputs and external inputs. Step S33: Obtain and rearrange the input matrices and feedforward matrices of all the subsystems that need to be connected according to the positions of the internal inputs. Step S34: Place the state matrices and output matrices of the subsystems that need to be connected in the diagonal positions of the state matrix and output matrix of the connected system. Step S35: Reset the state-space equation of the connected system according to the state-space equation of the model with set-point input feedback. Step S36: Organize all the information to form a state-space model of the connected system.

[0030] Step S40: Discretize the connected continuous system and the noise model separately, and then connect the discretized systems and the discrete system connected in step S30 to form a complete LPF closed-loop system.

[0031] In this embodiment, a discrete function can be used to discretize the connected continuous system and noise model respectively. Specifically, the zero-order hold method can be used for the state matrix and input matrix of the connected continuous system, and the linear averaging method can be used for the output matrix and feedforward matrix of the connected continuous system to realize the discretization process of the connected continuous system.

[0032] In this embodiment, the systems other than the noise model can be connected first through the function of the connection system to form an LTP system, preparing for subsequent segmented processing; then the noise model of the expected noise source is discretized and then all connected to the LTP system to form a complete LPF closed-loop system.

[0033] Step S50, reorganize and simulate the state-space model of the LPF closed-loop system according to the simulation requirements.

[0034] The method for constructing an LPF closed-loop system based on a state-space model provided in this embodiment is different from the traditional LTPDA toolbox. In this embodiment, the model can be directly studied and learned by scholars, and the data of each module are all double-precision data models that can be directly processed by MATLAB; the basic information of the model is stored in the form of a structure during the model establishment process, and users can adjust the fields and field values in the structure according to their needs at any time; all the contents of the model are directly stored in a folder, and when using it, only need to put the folder into MATLAB and call the relevant functions to use it, which can realize fast time-domain simulation and adapt to scenarios with low computing power; this model is a basic model, providing a model basis for the data analysis activities of gravitational wave detectors, and more functions can be realized on this basis in the future.

[0035] The beneficial effects of the method for constructing an LPF closed-loop system based on a state-space model provided in this embodiment are as follows: In this embodiment, the state-space models of each subsystem are established according to the existing parameters using the basic form of the state-space equation and combined into a complete closed-loop system. Each model can be simulated separately to test the functions of the subsystems, and the connected closed-loop system LPF can also be simulated and tested to verify the correctness of the system theory. Compared with the traditional LTPDA toolbox, the operation is more simplified, and the required functions can be realized using simple functions. It is compatible with the new version of MATLAB and has high operation efficiency, providing a model basis for subsequent data processing and simulation.

[0036] Based on the same inventive concept, the present application also provides a system for constructing an LPF closed-loop system based on a state-space model, including a model establishment module, a classification module, a connection module, a closed-loop system construction module, and a simulation module.

[0037] Among them, the model establishment module is used to establish the state-space models of the subsystems included in the LPF closed-loop system.

[0038] The classification module is used to classify the subsystems other than the noise model according to the data sampling time, and is divided into a continuous system and a discrete system.

[0039] The connection module is used to connect the continuous system and the discrete system respectively.

[0040] The closed-loop system construction module is used to discretize the connected continuous system and the noise model respectively, and then connect the discretized system and the discrete system connected by the connection module to form a complete LPF closed-loop system.

[0041] The simulation module is used to reorganize and simulate the state space model of the LPF closed-loop system according to the simulation requirements.

[0042] It should be noted that for the functions of the modules provided in this embodiment, reference may be made to the description of the foregoing method embodiment, and details are not described herein again.

[0043] Next, a specific embodiment is used to illustrate the method for constructing an LPF closed-loop system based on a state space model provided in this application.

[0044] The method for constructing an LPF closed-loop system based on a state space model provided in this specific embodiment includes the following steps: Step 1: Based on the theoretical knowledge of the LPF closed-loop system and the existing parameters, establish the state space models of the various subsystems included in the LPF closed-loop system, including: inertial sensing system (IS), spaceborne tracker system (ST), interferometer system (IFO), delay system (DELAY), drag-free attitude control system (DFACS), capacitive displacement sensing system (CAPACT), micropropulsion system (FEEPS), satellite dynamics system (EOM), acceleration noise (ACCNOISE), and models of different expected noise sources: actuator noise, sensor noise, and external noise. A linear, time-invariant, dynamic system can be represented in state space form with time-independent coefficient matrices. In this case, a set of first-order differential equations is represented in matrix form, and the classical state space representation is: (1) In Equation (1), is the state, represents the input, is the output of the system, A is the state matrix of the system, B is the input matrix, C is the output matrix, and D is the feedforward matrix.

[0045] In Step 1, the establishment process of each subsystem is specifically as follows: 1) Determine the inputs, outputs, and states of the subsystem. Based on the functions of the subsystem in the theory, the inputs, outputs, and states of the subsystem can be determined. Classify these inputs, states, and outputs and store them in the form of blocks. For example, the specific applied forces and noises in the inputs can be divided into two categories, and each category contains specific variables in different directions.

[0046] 2) Determine the information of the state matrix, input matrix, output matrix, and feedforward matrix and write the state - space equation. The state matrix A, input matrix B, output matrix C, and feedforward matrix D are parameters set according to the theory. These matrices are stored in the form of blocks. Through a certain block, the rows and columns of the corresponding matrix can be quickly found, preparing for the connection and recombination of the subsequent matrices. The form of the state - space equation is as shown in formula (1).

[0047] 3) Improve the information of the subsystem model. According to the previous steps, the basic contents included in the subsystem structure are: the information of the four matrices stored in the form of blocks; the state - space model established by the MATLAB built - in model; the input variables, state variables, and output variables of the subsystem; the name of the subsystem; the time model timestep determined by the subsystem according to the sampling time, which can be discrete or continuous.

[0048] Step 2: Classify the subsystems according to their time models into continuous systems and discrete systems.

[0049] In Step 2, the time model of the subsystem is determined by setting the sampling rate of the system according to the characteristics of the input data in the system. In subsequent operations, all systems need to be combined, and different time models will cause system errors. Therefore, here, systems other than the noise model need to be classified. If the time - model value is 0, it is a continuous - type system; otherwise, it is a discrete - type system.

[0050] Step 3: Connect the discrete systems and continuous systems separately. Connect the systems classified in the previous step into two complete systems respectively, construct a connection function for operation, and the connection - step flow chart is as Figure 3 shown. The specific process is as follows: 1) Traverse all the subsystems that need to be connected after classification, obtain all the information of the subsystems that need to be connected, and compare the names of the input and output variables of all the subsystems that need to be connected to distinguish their internal inputs and external inputs.

[0051] As Figure 4 shown, the i - th subsystem contains input blocks inputs i 1, inputs i 2, inputs i 3, respectively corresponding to the input matrix B i 1, B i 2, B i3, and the feedforward matrix D i 1. D i 2. D i 3. The output block is outputs i 1. outputs i 2. outputs i 3. The state - space equation is as follows: (2) In Equation (2), A i is the state matrix, and C i is the output matrix.

[0052] The (i + 1)-th subsystem contains the input block inputs i+1 1. inputs i+1 2. inputs i+1 3. They respectively correspond to the input matrix B i+1 [[ID=3,2]]1. B i+1 2. B i+1 3. and the feedforward matrix D i+1 1. D i+1 2. D i+1 3. The output block is inputs i 2. The state - space equation is as follows: (3) In Equation (3), A i+1 is the state matrix, and C i+1 is the output matrix.

[0053] The input of the i - th subsystem and the output of the (i + 1)-th subsystem have the same term inputs i 2. Then inputs i 2 is determined as the internal input, and the other inputs inputs i 1. inputs i 3 are the external inputs.

[0054] 2) Obtain and rearrange the input matrices and feedforward matrices of all subsystems to be connected according to the positions of the internal inputs in the output matrix. The corresponding state - space equation is: (4) In Equation (4), A is the state matrix, B in , B ext are the input matrices of the internal input and the external input respectively, and the corresponding u in and u ext are the input variables of the internal input and the external input, C is the output matrix, and D in , D ext are the feedforward matrices of the internal input and the external input respectively. Store the output blocks of all subsystems in traversal order, here it is outputs i 1. outputs i 2. outputs i 3. inputs i 2. Obtain the positions of the internal input matrices in the output blocks, here it is inputs i If 2 is recorded as the 4th block, then the new internal input matrix B in The block in the i-th row and 4th column is the input block of the i-th subsystem, inputs i The corresponding input matrix B of 2 i 2. If the remaining blocks are empty, then the new internal feedforward matrix D in The block in the i-th row and 4th column is the input block of the i-th subsystem, inputs i The corresponding feedforward matrix D of 2 i 2. If the remaining blocks are empty; the new external input matrix B ext and the preposed matrix D ext Then it is the matrix at the corresponding position of the external input.

[0055] 3) Place the state matrix A and output matrix C of the subsystems to be connected on the diagonal positions of the state matrix and output matrix of the connected system. According to the above state space equations, it can be seen that the state matrix A and output matrix C do not change during the classification of the inputs. Therefore, they can be directly placed on the diagonal positions of the state matrix and output matrix of the connected system in the system traversal order.

[0056] 4) Reset the state space equation of the connected system according to the state space equation of the model with setpoint input feedback. It is known that the whole system is a closed-loop system. Therefore, the state space model selected is the system with set input feedback. The system block diagram is as Figure 5 shown. According to the block diagram, the corresponding state space equation can be written as: (5) The variable names in Equation (5) are the variable names in Equation (4). A is the state matrix, B in 、B ext are the input matrices of the internal input and external input respectively. The corresponding u in and u ext are the internal input and external input variables. C is the output matrix, D in 、D ext are the feedforward matrices of the internal input and external input respectively. According to the results of the state equation, the values of the corresponding input-output matrices, state matrix and feedforward matrix can be directly set by the formula in MATLAB.

[0057] 5) Organize all the information to form a state - space model of the connected system. Rearrange the state matrix, input matrix, output matrix, and feed - forward matrix of the connected system according to the above formulas (4) and (5). Here, the matrices are stored in block form; convert these matrices to double - precision type and use the built - in functions in MATLAB to generate the state - space model; organize the input, output, and state variables. The input variables only include external inputs, and the output variables only include the combined external outputs; rename the system as the sum of all the added subsystems; the sampling time is the original sampling time of this system category.

[0058] Step 4: Discretize the connected continuous system. The LPF closed - loop system finally uses discrete data results, so discretize the continuous system by constructing a discrete function. From the sampling information, the continuous systems are the spaceborne tracker system, inertial sensing system, interferometer system, satellite dynamics system, and micro - thruster system. Discretize the continuous system after connecting these systems. According to the state - space equation, during the discretization process, the structure of the system does not change, so all variables do not change, only the system matrices change. The discretization method adopted is combined discretization, that is, use the zero - order hold method for the state matrix and input matrix of the connected continuous system, and use the linear averaging method for the output matrix and feed - forward matrix of the connected continuous system. The processing process is as follows: 1) Obtain the basic information of the continuous system, confirm that the conversion type is continuous - to - discrete, and determine the sampling time after discretization.

[0059] 2) Use the zero - order hold method for the state matrix A and input matrix B to obtain the discrete equation: (6) In formula (6), x n+1 is the difference value of the discrete state variable, x n is the discrete state variable, A is the state matrix, B is the input matrix, and u n is the discrete input variable.

[0060] According to the above formula, the discrete state matrix and input matrix of the system can be obtained: (7) Substitute the results in the formula into the system. dt is the sampling time after discretization. The state matrix A can be directly converted using the exponential function in MATLAB, and the input matrix B is calculated by integrating the matrix using the Taylor expansion method.

[0061] 3) Use the linear averaging method to calculate the output matrix C and feed - forward matrix D of the system to obtain the discrete equation: (8) In Equation (8), A disc and B disc are the discretized state matrix and input matrix in Equation (7), I is the identity matrix, y n is the discrete output, x n and u n correspond to the discrete state variables and input variables Based on the above results, the matrix operations in MATLAB can be directly used to obtain the discretized matrix and organize all the information of the system, thereby obtaining the state - space model of the discretized system.

[0062] Step 5: Connect all subsystems to form a complete closed - loop system. First, connect the systems except the noise model through the connection function of the system. The connection method is the same as that in Step 3 above to form an LTP system, which prepares for the segmented processing in subsequent tests. Then, discretize the model of the expected noise source using the method in Step 4, and then connect it all to the LTP system to form a complete LPF closed - loop system, as Figure 6 shown.

[0063] Step 6: Simulate the system. Here, the simulation function is used for operation. This method has three modes. It can use internal noise generation for simulation, such as generating arbitrary noise using the random noise function; it can also use the injected signal for simulation; or it can use both the injected signal and noise for simulation. The complete LPF closed - loop system has a total of 32 input modules with 294 input variables, 27 output blocks with 264 output variables, and 20 state blocks with 601 state variables. It is impossible to give all the input variables during the simulation or real - data processing. Therefore, for the convenience of data processing, when performing data simulation, it is necessary to determine what input variables to use and which output to simulate, and reorganize the state - space model based on this information. The specific process is as follows: According to the information input for simulation, confirm the input signal and the output to be obtained, compare these input and output names with the variable names in the system, locate the variable block, and then find the corresponding input, output, state, and feed - forward matrix information and extract it and reorganize it into a new state - space equation. Such a state - space model will only have the required inputs, outputs, and states, and directly calling the function for implementing the simulation can obtain the output result.

[0064] The key points of the construction method provided in this specific embodiment are as follows: (1) Determine the inputs, outputs, states, feedforward matrices, and input, output, and state variables of the state-space models of each subsystem according to the theoretical model, which facilitates the establishment of the state-space model and the simulation of a single system; (2) Connect the subsystems, and according to the state-space model with feedback, determine the values of the input matrix and the feedforward matrix before and after connection, which is beneficial to the combination of the entire system; (3) Discretize the continuous system, and use the zero-order hold method and the linear averaging method to obtain the discretized state-space equation, which is beneficial to unifying the sampling time of the system; (4) Recombine the state-space equation according to the inputs, outputs, and state variables before simulation, which reduces the complexity of the simulation.

[0065] The effects of the construction method provided in this specific embodiment are as follows: (1) In this embodiment, the state-space models of each subsystem are established according to the existing parameters using the basic form of the state-space equation, and a complete closed-loop system is formed. Each model can be simulated separately to test the functions of the subsystems, and the closed-loop system LPF after connection can also be simulated and tested, which can verify the correctness of the system theory. For example, in the test of the LTP system, injecting a sine wave signal of 1 nm and 1 mHz on GUIDANCE.ifo_x1 in theory will cause SC to oscillate around TM1 by 1 nm, and the corresponding outputs on the interferometer: DELAY_IFO.x1 and DELAY_IFO.x12. The simulation results are as Figure 7 , which is consistent with the theoretical derivation.

[0066] (2) The closed-loop system established in this embodiment can simulate the output of the system under a given noise or signal input, and the desired simulation results can be obtained according to the specified output after a given input. For example: Enable all the noise sources in the system and require the following outputs: the readings of the interferometer and ; the command force for the drag-free attitude control system to control the spacecraft to follow TM1 along the x-axis; the command force for the actuator in the electrostatic control loop to control TM2 to follow TM1 along the x-axis. Drawing the power spectral density of these outputs can analyze the behavior of the noise and the control effect of the system. For example, Figure 8 is the power spectral density of the interferometer readings, Figure 9 is the power spectral density diagram of the command forces of the two control loops of the drag-free attitude control system. This way of simulating the output can be compared with the real measurement output and can also judge the control effect of the system, which prepares for the data processing of real data.

[0067] (3) This embodiment is improved on the basis of the traditional LTPDA toolbox, which can achieve the required functions. At the same time, the operation is more simplified. The required functions can be realized by using simple functions, and the operation efficiency is high, providing a model basis for subsequent data processing and simulation.

[0068] Those skilled in the art can easily understand that the above are only the preferred embodiments of the present application, which are not intended to limit the present application. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A construction method of an LPF closed-loop system based on a state-space model, characterized in that, It includes the following steps: S10. Establish the state - space models of each subsystem included in the LPF closed - loop system; S20. Classify the subsystems other than the noise model according to the data sampling time into continuous systems and discrete systems; S30. Connect the continuous system and the discrete system respectively; S40. Discretize the connected continuous system and the noise model respectively, and then connect the discretized system and the discrete system connected in step S30 to form a complete LPF closed - loop system; S50. Re - organize and simulate the state - space model of the LPF closed - loop system according to the simulation requirements.

2. The construction method of the LPF closed-loop system based on the state space model according to claim 1, characterized in that, In step S10, the subsystems are an inertial sensing system, a spaceborne tracker system, an interferometer system, a delay system, a drag - free attitude control system, a capacitive displacement sensing system, a micro - thruster system, a satellite dynamics system, an acceleration noise and noise models of different expected noise sources, and the model includes actuator noise, sensor noise and external noise.

3. The construction method of the LPF closed-loop system based on the state space model according to claim 1, characterized in that, In step S10, the process of establishing the state - space models of each subsystem is specifically as follows: Determine the input, output and state of the subsystem; Determine the information of the state matrix, input matrix, output matrix and feed - forward matrix of the subsystem and write out the state - space equation; The information of the state - space model of the complete subsystem, and this information includes the time model and name, and the time model is determined by the data sampling time of the subsystem.

4. The construction method of the LPF closed-loop system based on the state space model according to claim 1, characterized in that, In step S20, the continuous systems include an inertial sensing system, a spaceborne tracker system, an interferometer system, a satellite dynamics system and a micro - thruster system.

5. The construction method of the LPF closed-loop system based on the state space model according to claim 1, characterized in that, Step S30 is specifically as follows: Traverse all the subsystems to be connected after classification and obtain all the information of the subsystems to be connected; Compare the names of the input and output variables of the subsystems to be connected and distinguish their internal inputs and external inputs; Obtain and rearrange the input matrix and feed - forward matrix of all the subsystems to be connected according to the positions of the internal inputs in the output matrix; Place the state matrix and output matrix of the subsystems to be connected in the diagonal positions of the state matrix and output matrix of the connected system; Reset the state - space equation of the connected system according to the state - space equation of the model with set - point input feedback; Organize all the information to form a state - space model of the connected system.

6. The construction method of the LPF closed-loop system based on the state space model according to claim 1, characterized in that, In step S40, the discretization method is: use the zero - order hold method for the state matrix and input matrix of the connected continuous system, and use the linear averaging method for the output matrix and feed - forward matrix of the connected continuous system.

7. The construction method of the LPF closed-loop system based on the state space model according to claim 1, characterized in that, In step S50, use internal noise generation and / or use injection signals to re - organize and simulate the state - space model of the LPF closed - loop system.

8. The method for constructing an LPF closed-loop system based on a state space model according to claim 7, characterized in that The internal noise is generated by a random noise function.

9. A construction system for an LPF closed-loop system based on a state space model, characterized in that, It includes: A model - building module for establishing the state - space models of each subsystem included in the LPF closed - loop system; A classification module for classifying the subsystems other than the noise model into continuous systems and discrete systems according to the data sampling time; A connection module for connecting the continuous system and the discrete system respectively; A closed-loop system construction module, which is used to discretize the connected continuous system and noise model respectively, and then connect the discretized system and the discretized system after connecting the connection module to form a complete LPF closed-loop system; A simulation module, which is used to reorganize and simulate the state space model of the LPF closed-loop system according to simulation requirements.

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