Method and system for realizing F-M II state space model based on gyro flywheel

Abstract

The invention provides an F-M II state space model implementation method and system based on a gyro flywheel, and the method comprises the steps: constructing non-zero power product terms in a transfer function matrix into a special matrix through the full combination of the properties of an F-M II model and the structural characteristics of the transfer function matrix, so as to reduce redundant terms; solving according to the relation between the special matrix and the transfer function matrix to obtain a realization matrix; the order of the realization matrix directly corresponds to the order of the constructed special matrix, so that the model order and the system complexity are obviously reduced; the method is simple and visual in implementation process and high in calculation efficiency, and the high-order implementation problem of the multi-dimensional system is effectively solved. According to the method, the F-M II state space model which is lower in order and easier to implement is adopted to describe the multi-dimensional system, so that the method has remarkable practical application value, the system expression is simplified, the system analysis and design efficiency is improved, and the implementation method of the gyro flywheel system and the application of the F-M II state space model in a practical system are expanded.

Description

Technical Field

[0001] This invention belongs to the field of spatial model technology, specifically relating to the implementation method and system of FM II state-space model based on gyroscope flywheel. Background Technology

[0002] With the rapid development of the aerospace industry, the system implementation technology of micro-spacecraft has become a research hotspot in the aerospace field. Compared with traditional spacecraft, micro-spacecraft have more stringent requirements for indicators such as mass, size, development cycle, and manufacturing cost. The attitude control subsystem is a core component of micro-spacecraft, including attitude sensors and actuator controllers. Among the sensors, gyroscopes are commonly used; among the actuators, flywheels and control torque gyroscopes are commonly used. The performance of the attitude control subsystem directly affects the mission execution effect of micro-spacecraft, and it is also a key factor in the mass, size, power consumption, and cost of micro-spacecraft implementation. Optimizing the design of the attitude control subsystem to achieve lightweighting, miniaturization, and cost reduction while ensuring its performance is of great significance for promoting the advancement of aerospace technology.

[0003] The gyro-flywheel is a novel spacecraft attitude measurement and control device. It integrates the mechanical structures of a gyroscope, flywheel, and control torque gyroscope, combining attitude sensing and control functions to reduce the mass, size, and cost of the attitude control subsystem. As a measurement component, it can measure attitude changes along two axes, while as an actuation component, it can output control torques along three axes to the spacecraft. Analyzing the gyro-flywheel system and studying its simplification methods can provide a feasible research direction for miniaturizing and multifunctionalizing attitude control systems.

[0004] Similarly, with the deepening of modern control theory research, the controlled objects are becoming increasingly complex, and realizing these systems presents many difficulties. These challenges bring new impetus to the study of multidimensional system theory. A multidimensional system is not a simple superposition of one-dimensional systems, but rather a system controlled by the combined action of multiple independent variables. While the complexity of multidimensional systems far exceeds that of one-dimensional systems, they offer a better description of the dynamic characteristics of control systems. The Fornasini-Marchesini II (FM II) state-space model is a typical model built upon multidimensional system theory. The FM II model uses internal state variables to describe the dynamic characteristics of the system. Its main advantage lies in simplifying the mathematical expression of the system, thereby improving computational efficiency. Solving the implementation problem is fundamental to the study of multidimensional system theory. For a given transfer function or matrix, there may actually be multiple FM II implementation matrices. These implementation matrices may have different orders, and even those with the same order may have different computational complexities. Therefore, using the lower-order and more easily implemented FM II state-space model to describe multidimensional systems has significant practical application value, not only simplifying system expressions but also improving the efficiency of system analysis and design.

[0005] Dynamic analysis shows that the characteristics of the gyro flywheel system are those of a highly coupled, complex, multidimensional system. The transfer function derived from its dynamic modeling has a very high dimension and order, making it suitable for low-order implementation using the FM II state-space model in multidimensional systems, thus simplifying its system expression.

[0006] In existing technologies, there are limitations in implementing the FM II state-space model of a system. For example, when implementing the system's transfer function or matrix, the implementation matrix is ​​constructed only by using the degree of the transfer function or matrix (the degree of the highest-power term in the transfer function or matrix). This results in a large number of terms with zero coefficients in the transfer function or matrix participating in the construction of the implementation matrix, leading to an excessively high order of the final implementation matrix, which seriously affects the efficiency of system analysis. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a method and system for implementing the FM II state-space model based on a gyroscope flywheel, for the low-order implementation and simplification of multidimensional systems.

[0008] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a method for implementing the FM II state-space model based on a gyroscope flywheel, comprising the following steps: S1: Analyze the system, select state variables and establish a mathematical model, and construct the FM II state-space model based on the transfer function matrix obtained by transforming the mathematical model; S2: Represent the transfer function matrix as a right matrix fraction, and construct a polynomial matrix using the matrix obtained by subtracting the denominator matrix from the numerator matrix and the identity matrix as elements of the column vectors. S3: Obtain the non-zero power product terms of each column of the polynomial matrix, remove duplicate terms, and arrange them in ascending order of power to construct a special matrix; S4: Add new terms to a special matrix to satisfy the condition: there exist other terms such that the non-delayed operator terms are equal to the product of the delayed operator and other terms; S5: Generate the implementation matrix based on the algebraic relationship between the special matrix and the transfer function matrix.

[0009] According to the above scheme, the specific steps in step S1 are as follows: S11: Perform dynamic analysis on the gyro flywheel system, and establish a mathematical model of the gyro flywheel system with radial rotational inertia and axial angular momentum as state variables through Euler's dynamic equations; perform Laplace transform on the mathematical model to obtain the three-dimensional rational transfer function matrix of rotor tilt angle and torque in the shell system of the gyro flywheel system; S12: Construct an FM II state-space model based on the transfer function matrix, including the relationship between the state vectors of adjacent dimensions and the external disturbance input, and the controlled output obtained by applying the external disturbance input to the state vectors according to the dimensions; the coefficients of each term in the model are different real number matrices; S13: The FM II state-space model is rearranged into a relationship between the controlled output and the external disturbance input, and further transformed to obtain the transfer function represented by the realization matrix and delay operator.

[0010] Furthermore, in step S4, the specific steps are as follows: For each non-delayed operator term in the special matrix, determine whether there exists another term that includes the delay operator such that the non-delayed operator term is equal to the product of the delay operator and the other term: If it does not exist, a new term is inserted before the non-delayed operator term, and the new term is recursively checked to see if it meets the above conditions. If the conditions are not met, continue inserting new items until the above conditions are met. Under the premise of satisfying the above conditions, minimize the number of elements in the special matrix; After completing the supplementary insertion operation, rearrange all items of the special matrix in ascending order of power.

[0011] Furthermore, in step S5, the specific steps are as follows: S51: Construct a first-class matrix based on the relationships between the elements in a special matrix; S52: Construct a second type of matrix based on the relationship between the special matrix and the transfer function matrix; S53: The realization matrix is ​​obtained based on the algebraic relationship between the first type matrix and the second type matrix, including the first realization matrix, the second realization matrix, the third realization matrix and the fourth realization matrix.

[0012] Furthermore, in step S51, the specific steps are as follows: The first type of matrix includes the first intermediate matrix and the second intermediate matrix; The first intermediate matrix is ​​a diagonal matrix, and the elements on the main diagonal are square matrices corresponding to each delay operator. The order of the square matrices is equal to the number of elements in the special matrix. The elements in the special matrix are represented in such a way that the non-delayed operator terms are equal to the product of the delay operator and other terms. The square matrix is ​​initialized as a zero matrix. The elements in the special matrix are judged as follows: if there exists an array (row, column) such that the element in the th row of the special matrix is ​​equal to the product of the delay operator and the element in the th column, then the elements in the square matrix indexed by (row, column) are set to 1. The second intermediate matrix is ​​a diagonal matrix, and the elements on the main diagonal are column vectors corresponding to each delay operator. The order of the column vectors is equal to the number of elements in the special matrix. Initialize the column vectors as zero matrices, and then check the elements in the special matrix: if there exists an element in the i-th column that is equal to the delay operator, then set the element in the i-th column vector to 1.

[0013] Furthermore, in step S52, the specific steps are as follows: Construct a diagonal special matrix such that the elements on the main diagonal of the diagonal special matrix are special matrices; The second type of matrix includes the third intermediate matrix and the fourth intermediate matrix; The third and fourth intermediate matrices are obtained by applying the formula that the numerator matrix is ​​equal to the product of the third intermediate matrix and the diagonal special matrix, and the formula that the denominator matrix is ​​equal to the product of the fourth intermediate matrix and the diagonal special matrix.

[0014] Furthermore, in step S53, the specific steps are as follows: The first realization matrix is ​​obtained by adding the product of the first intermediate matrix and the second and fourth intermediate matrices to the first intermediate matrix; The column vector corresponding to the delay operator is used as the second intermediate matrix with the main diagonal elements as the second realization matrix; The third intermediate matrix corresponding to the molecular matrix is ​​used as the third realization matrix; The limit value of the transfer function matrix when each delay operator approaches 0 is used as the fourth realization matrix.

[0015] According to the above plan, the following steps are also included: S6: Substitute the realization matrix into the FM II state-space model for verification, and determine whether the verified transfer function matrix is ​​consistent with the theoretically derived transfer function matrix.

[0016] The system is implemented based on the FM II state-space model of a gyroscope flywheel. The modeling submodule is used to analyze the system, select state variables and establish a mathematical model, construct an FM II state-space model based on the transfer function matrix obtained by transforming the mathematical model, and obtain the realization matrix and delay operator. The transfer function matrix is ​​represented by the realization matrix and delay operator. The polynomial matrix submodule is used to represent the transfer function matrix in right matrix fractional form and construct a polynomial matrix using the matrix obtained by subtracting the denominator matrix from the numerator matrix and the identity matrix as the elements of the column vector. The special matrix submodule is used to obtain the non-zero power product terms of each column of the polynomial matrix, remove duplicate terms, and arrange them in ascending order of power to construct a special matrix. The supplementary insertion submodule is used to insert new terms into special matrices to satisfy the condition: there exist other terms such that the non-delayed operator term is equal to the product of the delayed operator and the other terms; Implement the matrix submodule, which is used to generate the implementation matrix based on the algebraic relationship between the special matrix and the transfer function matrix.

[0017] A computer memory storing a computer program executable by a computer processor, the computer program executing a method for implementing an FM II state-space model based on a gyroscope flywheel.

[0018] The beneficial effects of this invention are as follows: 1. The FM II state-space model implementation method and system based on gyroscope flywheel of the present invention constructs a special matrix for each non-zero power product term according to the structural characteristics of the transfer function matrix, and then obtains the realization matrix according to the relationship between the special matrix and the transfer function matrix. The order of the realization matrix is ​​transformed to be consistent with the order of the constructed special matrix. This not only makes the implementation process simple and intuitive, but also significantly reduces the order of the system realization matrix, thereby reducing system complexity, improving computational efficiency, and realizing the function of low-order implementation and simplification of multidimensional systems.

[0019] 2. This invention uses a lower-order and easier-to-implement FM II state-space model to describe multidimensional systems, which has significant practical application value. It not only simplifies the system expression but also improves the efficiency of system analysis and design. It provides a new approach for the practical application of the FM II state-space model and the lightweight implementation of gyroscope flywheel systems, expands the implementation methods of gyroscope flywheel systems, and also expands the application of the FM II state-space model in practical systems.

[0020] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the 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 based on these drawings without creative effort.

[0022] Figure 1 This is a flowchart of an embodiment of the present invention.

[0023] Figure 2 This is a modeling flowchart of an embodiment of the present invention.

[0024] Figure 3 This is a flowchart of the generation implementation matrix in an embodiment of the present invention. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0026] Example 1 See Figure 1 The specific steps of the FM II state-space model implementation method based on the gyroscope flywheel are as follows: S1: Analyze the system, establish a model and select state variables, and construct the F-MII state-space model based on the obtained rational transfer function matrix; see [link / reference]. Figure 2 The specific steps are as follows: S11: In the application scenario of gyroscope flywheel, the dynamics of the gyroscope flywheel system are analyzed. The mathematical model of the gyroscope flywheel system is established through Euler's dynamic equation. The mathematical model is then subjected to Laplace transform to obtain the three-dimensional transfer function matrix of rotor tilt angle and torque under the shell system of the gyroscope flywheel system, which is the rational transfer function matrix.

[0027] S12: The FM II state-space model is constructed based on the transfer function matrix of the gyroscope flywheel system as follows: +

[0028]

[0029] in Represents the state vector. This indicates an external disturbance input. Indicates the controlled output. For the first realization matrix, For the second realization matrix, These are the third and fourth implementation matrices.

[0030] S13: After z The transformation yields the transfer function as follows:

[0031] in It is an r-order identity matrix. Represents the delay operator, .

[0032] S2: Construct a polynomial matrix based on the transfer function matrix; the specific steps are as follows: Represent the transfer function matrix in right matrix fractional form:

[0033] make , Then construct the polynomial matrix. .

[0034] S3: Construct a special matrix based on a polynomial matrix; the specific steps are as follows: Obtaining a polynomial matrix No. The non-zero power product terms in the column, after removing duplicates, are arranged in ascending order of power to construct a special matrix. :

[0035] in For polynomial matrices The number of columns, For polynomial matrices No. The number of non-zero power product terms in the column.

[0036] S4: Perform a supplementary operation on a special matrix to meet preset conditions; the specific steps are as follows: For matrix Each non- item Determine whether another item exists. satisfy = If it does not exist, then in Insert new item before supplement The process recursively checks whether the new item meets the condition. If not, it repeats the insertion operation until the following condition is met: all non- Each item can be connected to other items. Generate by multiplication; under the premise of satisfying the above conditions, such that The matrix has the smallest number of elements. After completing the insertion operation, the matrix will be... All items are rearranged in ascending order of power and assigned subscripts. ,in After performing the supplementary insertion operation, the matrix The number of elements in it.

[0037] S5: Generate implementation matrices A1, A2, A3, B1, B2, B3, C, and D based on the algebraic relationship between the special matrices and the transfer function matrix; see also Figure 3 The specific steps are as follows: S51: According to the matrix Construct a matrix of relationships between elements in the matrix. , The specific steps are as follows: Constructing a matrix :Will The elements in Method representation, initialization matrix for The zero matrix, for the matrix Judge the elements in: If it exists Make , Then matrix elements ; If it exists Make , Then matrix elements ; If it exists Make , Then matrix elements ; Constructing a matrix Initialize the matrix for The zero matrix, for the matrix Judge the elements in: like There exists satisfy Then let ; like There exists satisfy Then let ; like There exists satisfy Then let ; Then we can get: , .

[0038] S52: According to the matrix Construct a matrix based on the relationship between the transfer function matrix and the matrix. The specific steps are as follows: make ,according to , get and .

[0039] S53: According to the matrix , With matrix The algebraic relations yield the system implementation matrix. , , , The specific steps are as follows: make That is, , , , , .

[0040] The system implementation matrix is ​​then... .

[0041] S6: Verify using MATLAB to implement the matrix. Substitute into the FM II state-space model In this process, the resulting transfer function is consistent with the original function.

[0042] In this embodiment, each non-zero power product term is constructed into a special matrix based on the structural characteristics of the transfer function matrix. Then, the realization matrix is ​​obtained by solving the relationship between the special matrix and the transfer function matrix. The order of the realization matrix is ​​transformed to be consistent with the order of the constructed special matrix. This not only makes the implementation process simple and intuitive, but also significantly reduces the order of the system realization matrix, thereby reducing system complexity, improving computational efficiency, and realizing the function of low-order realization and simplification of multidimensional systems.

[0043] Example 2 The steps in this embodiment are the same as in Embodiment 1, except that each step is applied to a specific instance. Specifically, it includes the following steps: S1: Analyze the system, establish a model and select state variables, and construct an F-MII state-space model based on the obtained rational transfer function matrix; the specific steps are as follows: S11: In the application scenario of gyroscope flywheel, the dynamics of the gyroscope flywheel system are analyzed. The mathematical model of the gyroscope flywheel system is established through Euler's dynamic equation. The mathematical model is then subjected to Laplace transform to obtain the three-dimensional transfer function matrix of rotor tilt angle and torque under the shell system of the gyroscope flywheel system, which is the rational transfer function matrix.

[0044] S12: The FM II state-space model is a representative multidimensional state-space model proposed for analyzing and solving practical engineering problems. The FM II state-space model is constructed based on the transfer function matrix of the gyroscope flywheel system as follows: +

[0045]

[0046] in Represents the state vector. This indicates an external disturbance input. Indicates the controlled output. It is a real matrix.

[0047] S13: The transfer function is rearranged as follows:

[0048] in It is an r-order identity matrix. Represents the delay operator, .

[0049] In this embodiment, the radial moment of inertia and axial angular momentum of the gyroscope flywheel are selected as state variables, resulting in the following three-dimensional sixth-order transfer function matrix with two inputs and two outputs:

[0050] in Represents the coefficients of each item in the system. Represents the delay operator, This represents the Laplace operator after performing a Laplace transform on the mathematical model. These represent the radial moment of inertia and axial angular momentum of the gyroscope flywheel, respectively.

[0051] The system implementation matrix is ​​obtained as follows: .

[0052] S2: Construct a polynomial matrix based on the transfer function matrix; the specific steps are as follows: Represent the transfer function matrix in right matrix fractional form:

[0053] In this embodiment:

[0054]

[0055] make , ,get:

[0056]

[0057] Then construct the polynomial matrix:

[0058] S3: Construct a special matrix based on a polynomial matrix; the specific steps are as follows: Obtaining a polynomial matrix No. The non-zero power product terms in the column are sorted in ascending order of power after removing duplicates (when powers are the same, they are sorted by the variable index, e.g., ...). hour, The order is (Previously), construct a special matrix :

[0059] in For polynomial matrices The number of columns, For polynomial matrices No. The number of non-zero power product terms in the column. In this embodiment, the special matrix is: = , in , , = , .

[0060] S4: Perform a supplementary operation on a special matrix to meet preset conditions; the specific steps are as follows: In this embodiment, for the matrix The elements in the table are used for judgment because Only need to Element determination in: Each element in the array cannot be connected to any other element. If the product is multiplied, then an insertion and supplementation operation is required: in Pre-insertion item Further evaluation of the inserted item reveals that more items need to be added. Pre-insertion item ;exist Pre-insertion item Then, for the item Judging from this, we can know No further insertion is needed; in Pre-insertion item Then, for the item By making a judgment, we can determine that an item needs to be inserted before it. Continue with the inserted items Judging from this, we can know No further insertion is needed; because Can be inserted from previously inserted items Multiply The matrix obtained no longer requires insertion and completion. The matrix after insertion and completion... The elements in the matrix are rearranged in ascending order to obtain a new column vector matrix. :

[0061] New matrix Except Each item outside can be connected to other items. Multiplying them together yields the result, i.e. A matrix that meets the requirements.

[0062] S5: Generate implementation matrices A1, A2, A3, B1, B2, B3, C, and D based on the algebraic relationship between the special matrix and the transfer function matrix; the specific steps are as follows: S51: According to the matrix Construct a matrix of relationships between elements in the matrix. , The specific steps are as follows: In this embodiment, The elements in The method of representation, because = ,by To explain, have: , , , , , , ,

[0063] Initialization matrix for The zero matrix, combined with the above relationships, for the matrix Judge the elements in: right exist Make: , , ,

[0064] Then matrix elements , , , ,Right now

[0065] right exist Make: ,

[0066] Then matrix elements , ,Right now

[0067] right exist Make ,

[0068] Then matrix elements , ,Right now

[0069] Then construct the matrix. for The zero matrix, for elements in Make a judgment: exist satisfy ,but ,Right now ; because There are no elements in and ,so and for The zero matrix, i.e. = = ; because ,so , , , Right now , , , , = , .

[0070] S52: According to the matrix Construct a matrix based on the relationship between the transfer function matrix and the matrix. The specific steps are as follows: In this embodiment, let ,pass ,

[0071] get , ,in:

[0072]

[0073] S53: According to the matrix , With matrix The algebraic relations yield the system implementation matrix. The specific steps are as follows: In this embodiment, let , , , , = , , , .

[0074] That is, the system implementation matrix They are respectively: , , , , matrix The non-zero elements are: , , = = , All other items are zero; matrix The non-zero elements are: All other items are zero; matrix The non-zero elements are: All other items are zero.

[0075] The obtained FM II state-space model has an implementation order of 18.

[0076] S6: Verify using MATLAB to implement the matrix. Substitute into the FM II state-space model In this process, the resulting transfer function is consistent with the original function.

[0077] This embodiment considers the properties of the FM II model and the structural characteristics of the transfer function or matrix. It constructs a special matrix only through the non-zero power terms in the transfer function or matrix to reduce redundant terms, effectively reducing the order of the implementation matrix and improving the efficiency of the system implementation process.

[0078] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0079] Example 3 This embodiment is used to implement the principle of the above method embodiment to construct an FM II state-space model implementation system based on a gyroscope flywheel, including a modeling submodule, a polynomial matrix submodule, a special matrix submodule, a supplementary insertion submodule, and an implementation matrix submodule.

[0080] The modeling submodule is used to analyze the system, select state variables and establish a mathematical model, construct an FM II state-space model based on the transfer function matrix obtained by transforming the mathematical model, and obtain the realization matrix and delay operator. The transfer function matrix is ​​represented by the realization matrix and delay operator. The polynomial matrix submodule is used to represent the transfer function matrix in right matrix fractional form and construct a polynomial matrix using the matrix obtained by subtracting the denominator matrix from the numerator matrix and the identity matrix as the elements of the column vector. The special matrix submodule is used to obtain the non-zero power product terms of each column of the polynomial matrix, remove duplicate terms, and arrange them in ascending order of power to construct a special matrix. The supplementary insertion submodule is used to insert new terms into special matrices to satisfy the condition: there exist other terms such that the non-delayed operator term is equal to the product of the delayed operator and the other terms; Implement the matrix submodule, which is used to generate the implementation matrix based on the algebraic relationship between the special matrix and the transfer function matrix.

[0081] Each submodule is mainly used to implement the various steps of the method implementation, which will not be elaborated here.

[0082] It should be noted that, depending on the implementation needs, the various steps / components described in this application can be broken down into more steps / components, or two or more steps / components or parts of the operation of steps / components can be combined into new steps / components to achieve the purpose of this invention.

[0083] This embodiment also includes a processor, a communication interface, a memory, and a communication bus; wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; the memory stores a computer program, and when the program is executed by the processor, the processor performs the steps of the FM II state-space model implementation method based on a gyroscope flywheel.

[0084] This embodiment also provides a computer-readable storage medium storing executable instructions that, when executed by a processor, enable the processor to implement a gyroscope flywheel-based FM II state-space model implementation method.

[0085] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects.

[0086] Furthermore, this application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0087] This application is described with reference to the flowchart of the method and computer program product according to Embodiment 1 and the block diagram of the device (system) according to Embodiment 3. It should be understood that each step or block in the flowchart or block diagram, as well as combinations of steps or blocks in the flowchart or block diagram, can be implemented by computer program instructions.

[0088] These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions, which are executable by the processor of the computer or other programmable data processing device, produce instructions for implementing the process. Figure 1 One or more processes or boxes Figure 1 A system implementing the functions specified in one or more boxes using the FM II state-space model based on a gyroscope flywheel.

[0089] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes or boxes Figure 1 The function specified in one or more boxes.

[0090] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes or boxes Figure 1 The steps of the FM II state-space model implementation method based on the gyroscope flywheel are specified in one or more boxes.

[0091] The above embodiments are only used to illustrate the design concept and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications made based on the principles and design ideas disclosed in the present invention are within the protection scope of the present invention.

Claims

1. A method for implementing the FM II state-space model based on a gyroscope flywheel, characterized in that: Includes the following steps: S1: Analyze the system, select state variables and establish a mathematical model, and construct the FM II state-space model based on the transfer function matrix obtained by transforming the mathematical model; S2: Represent the transfer function matrix as a right matrix fraction, and construct a polynomial matrix using the matrix obtained by subtracting the denominator matrix from the numerator matrix and the identity matrix as elements of the column vectors. S3: Obtain the non-zero power product terms of each column of the polynomial matrix, remove duplicate terms, and arrange them in ascending order of power to construct a special matrix; S4: Add new terms to a special matrix to satisfy the condition: there exist other terms such that the non-delayed operator terms are equal to the product of the delayed operator and other terms; S5: Generate the implementation matrix based on the algebraic relationship between the special matrix and the transfer function matrix.

2. The method for implementing the FM II state-space model based on a gyroscope flywheel according to claim 1, characterized in that: The specific steps in step S1 are as follows: S11: Perform dynamic analysis on the gyro flywheel system, and establish a mathematical model of the gyro flywheel system with radial rotational inertia and axial angular momentum as state variables through Euler's dynamic equations; perform Laplace transform on the mathematical model to obtain the three-dimensional rational transfer function matrix of rotor tilt angle and torque in the shell system of the gyro flywheel system; S12: Construct an FM II state-space model based on the transfer function matrix, including the relationship between the state vectors of adjacent dimensions and the external disturbance input, and the controlled output obtained by applying the external disturbance input to the state vectors according to the dimensions; the coefficients of each term in the model are different real number matrices; S13: The FM II state-space model is rearranged into a relationship between the controlled output and the external disturbance input, and further transformed to obtain the transfer function represented by the realization matrix and delay operator.

3. The method for implementing the FM II state-space model based on a gyroscope flywheel according to claim 2, characterized in that: The specific steps in step S4 are as follows: For each non-delayed operator term in the special matrix, determine whether there exists another term that includes the delay operator such that the non-delayed operator term is equal to the product of the delay operator and the other term: If it does not exist, a new term is inserted before the non-delayed operator term, and the new term is recursively checked to see if it meets the above conditions. If the conditions are not met, continue inserting new items until the above conditions are met. Under the premise of satisfying the above conditions, minimize the number of elements in the special matrix; After completing the supplementary insertion operation, rearrange all items of the special matrix in ascending order of power.

4. The method for implementing the FM II state-space model based on a gyroscope flywheel according to claim 3, characterized in that: The specific steps in step S5 are as follows: S51: Construct a first-class matrix based on the relationships between the elements in a special matrix; S52: Construct a second type of matrix based on the relationship between the special matrix and the transfer function matrix; S53: The realization matrix is ​​obtained based on the algebraic relationship between the first type matrix and the second type matrix, including the first realization matrix, the second realization matrix, the third realization matrix and the fourth realization matrix.

5. The method for implementing the FM II state-space model based on a gyroscope flywheel according to claim 4, characterized in that: The specific steps in step S51 are as follows: The first type of matrix includes the first intermediate matrix and the second intermediate matrix; The first intermediate matrix is ​​a diagonal matrix, and the elements on the main diagonal are square matrices corresponding to each delay operator. The order of the square matrix is ​​equal to the number of elements in the special matrix. The elements in the special matrix are represented in such a way that the non-delayed operator terms are equal to the product of the delay operator and other terms. The square matrix is ​​initialized as a zero matrix. The elements in the special matrix are judged as follows: if there exists an array (row, column) such that the element in the th row of the special matrix is ​​equal to the product of the delay operator and the element in the th column, then the elements in the square matrix indexed by (row, column) are set to 1. The second intermediate matrix is ​​a diagonal matrix, and the elements on the main diagonal are column vectors corresponding to each delay operator. The order of the column vectors is equal to the number of elements in the special matrix. Initialize the column vectors as zero matrices, and then check the elements in the special matrix: if there exists an element in the i-th column that is equal to the delay operator, then set the element in the i-th column vector to 1.

6. The method for implementing the FM II state-space model based on a gyroscope flywheel according to claim 5, characterized in that: The specific steps in step S52 are as follows: Construct a diagonal special matrix such that the elements on the main diagonal of the diagonal special matrix are special matrices; The second type of matrix includes the third intermediate matrix and the fourth intermediate matrix; The third and fourth intermediate matrices are obtained by applying the formula that the numerator matrix is ​​equal to the product of the third intermediate matrix and the diagonal special matrix, and the formula that the denominator matrix is ​​equal to the product of the fourth intermediate matrix and the diagonal special matrix.

7. The method for implementing the FM II state-space model based on a gyroscope flywheel according to claim 6, characterized in that: The specific steps in step S53 are as follows: The first realization matrix is ​​obtained by adding the product of the first intermediate matrix and the second and fourth intermediate matrices to the first intermediate matrix; The column vector corresponding to the delay operator is used as the second intermediate matrix with the main diagonal elements as the second realization matrix; The third intermediate matrix corresponding to the molecular matrix is ​​used as the third realization matrix; The limit value of the transfer function matrix when each delay operator approaches 0 is used as the fourth realization matrix.

8. The method for implementing the FM II state-space model based on a gyroscope flywheel according to claim 1, characterized in that: It also includes the following steps: S6: Substitute the realization matrix into the FM II state-space model for verification, and determine whether the verified transfer function matrix is ​​consistent with the theoretically derived transfer function matrix.

9. A system implementing the FM II state-space model based on a gyroscope flywheel, characterized in that: The modeling submodule is used to analyze the system, select state variables and establish a mathematical model, construct an FM II state-space model based on the transfer function matrix obtained by transforming the mathematical model, and obtain the realization matrix and delay operator. The transfer function matrix is ​​represented by the realization matrix and delay operator. The polynomial matrix submodule is used to represent the transfer function matrix in right matrix fractional form and construct a polynomial matrix using the matrix obtained by subtracting the denominator matrix from the numerator matrix and the identity matrix as the elements of the column vector. The special matrix submodule is used to obtain the non-zero power product terms of each column of the polynomial matrix, remove duplicate terms, and arrange them in ascending order of power to construct a special matrix. The supplementary insertion submodule is used to insert new terms into special matrices to satisfy the condition: there exist other terms such that the non-delayed operator term is equal to the product of the delayed operator and the other terms; Implement the matrix submodule, which is used to generate the implementation matrix based on the algebraic relationship between the special matrix and the transfer function matrix.

10. A computer memory, characterized in that: It contains a computer program that can be executed by a computer processor, which performs the FM II state-space model implementation method based on a gyroscope flywheel as described in any one of claims 1 to 8.

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