A Linear Robust H∞ Control Method for Flexible Satellite Based on Dynamic Observer

Abstract

The present invention relates to a flexible satellite linear robust control method based on a dynamic observer, comprising: S1, constructing a flexible satellite attitude system with partially immeasurable states, external disturbances and parameter perturbations, and constructing a linear state space model containing convex polyhedron uncertainty and input constraints; S2, designing a linear dimension reduction dynamic observer and a linear state feedback robust controller, and obtaining a closed-loop system based on the linear dimension reduction dynamic observer and the linear state feedback robust controller and with partially immeasurable states, convex polyhedron uncertainty and external disturbances; S3, deriving the solvability conditions of the linear robust control problem of the closed-loop system based on the linear dimension reduction dynamic observer under the constraint condition of input constraints; S4, solving the solvability conditions, obtaining solutions of the linear dimension reduction dynamic observer and the state feedback robust controller for the flexible satellite attitude system, and controlling the flexible satellite through the solutions.

Description

Technical Field

[0001] The present invention relates to the field of flexible satellite attitude control methods, and specifically refers to a flexible satellite linear robust attitude control method based on a dynamic observer. Control method. Background Art

[0002] Modern satellites need to be equipped with a variety of flexible accessories to assist in mission execution because they undertake complex missions and have long flight times. However, the strong coupling between the satellite's central rigid body and these flexible accessories will have an adverse effect on the performance of the attitude control system, and in extreme cases may cause system instability. Therefore, how to effectively suppress flexible vibration is a core hot issue in the field of flexible satellite attitude control.

[0003] For the attitude system of flexible satellites, if the existing technology generally uses state feedback control to suppress flexible vibration, it is necessary to install additional sensors and measuring devices to detect flexible modes, which is too costly and difficult to implement. However, the observer-based control method does not require the installation of additional sensors. The parameter perturbation term of the flexible satellite can be considered as a convex polyhedron. The current research on convex polyhedron uncertainty mostly focuses on linear systems and mainly relies on state feedback control methods. It rarely involves situations where the state is unmeasurable. The dynamic observer control method of flexible satellites has not yet achieved substantial integration with the convex polyhedron uncertainty method.

[0004] Aiming at the above problems in the prior art, a flexible satellite linear robustness algorithm based on dynamic observer is designed. The control method is the purpose of this invention. Summary of the invention

[0005] In view of the problems existing in the above-mentioned prior art, the present invention provides a flexible satellite linear robust The control method can effectively solve at least one problem existing in the above-mentioned prior art.

[0006] The technical solution of the present invention is:

[0007] A Linear Robust Method for Flexible Satellite Based on Dynamic Observer The control method comprises the following steps:

[0008] S1, construct a flexible satellite attitude system with some unmeasurable states, external disturbances and parameter perturbations, and construct a linear state space model containing convex polyhedron uncertainties and input constraints based on the flexible satellite attitude system;

[0009] S2, design a linear dimension reduction dynamic observer and a linear state feedback robustness for the linear state space model A controller is obtained based on the linear dimension reduction dynamic observer and the linear state feedback robust Controller and closed-loop system with some unmeasurable states, convex polyhedral uncertainties and external disturbances;

[0010] S3, deriving the linear robustness of the closed-loop system based on the linear dimension reduction dynamic observer under the constraint condition of input limitation The solvability conditions of the control problem;

[0011] S4, using Matlab / LMI toolbox to solve the solvability condition, and obtain the linear dimension reduction dynamic observer and the state feedback robustness for the flexible satellite attitude system. The controller solution is robustly implemented through the linear dimension reduction dynamic observer and the state feedback The controller controls the flexible satellite.

[0012] Furthermore, constructing a flexible satellite attitude system with partially unmeasurable states, external disturbances and parameter perturbations includes:

[0013] S1.1, introducing interference torque and perturbation term into the flexible satellite attitude kinematics and dynamics equations, so that the flexible satellite attitude kinematics and the dynamics equations have external interference and parameter perturbation;

[0014] S1.2, introducing auxiliary variables into the flexible satellite attitude kinematics and the dynamic equations and performing approximate linearization processing at the zero equilibrium point, expressing the flexible satellite attitude kinematics and the dynamic equations as the linear state space model, expressing the parameter perturbation terms in the state space model as a convex polyhedron form and restricting its control input, and obtaining a linear state space model containing convex polyhedron uncertainties and input constraints.

[0015] Furthermore, a linear dimension reduction dynamic observer and a linear state feedback robustness are designed for the linear state space model. The controller includes:

[0016] S2.1, establishing the linear dimension reduction dynamic observer according to the input signal and the output signal of the state space model;

[0017] S2.2, based on the estimated information of the linear dimension reduction dynamic observer, establish the linear state feedback robust Controller.

[0018] Furthermore, a robust linear state feedback observer based on the linear dimension reduction dynamic observer and the linear state feedback Closed-loop systems with controllers and partial unmeasurable states, convex polyhedral uncertainties, and external disturbances include:

[0019] S2.3, the linear dimension reduction dynamic observer and the linear state feedback robust The controller is applied to the linear state space model to obtain a closed-loop system with partial state immeasurability, convex polyhedral uncertainty and external disturbances.

[0020] Furthermore, the linear robustness of the closed-loop system based on the linear dimension reduction dynamic observer under the constraint condition of input limitation is derived. The solvability conditions of the control problem include:

[0021] S3.1, according to Lyapunov stability theory, for the closed-loop system Performance criteria;

[0022] S3.2, in Based on the performance criteria, the variable substitution method and the design idea of ​​LMIs are used to derive a linear robust dynamic observer based on the linear dimension reduction under the constraint of limited input. Solvability conditions of the control problem.

[0023] Furthermore, the solvability condition is:

[0024] The closed-loop system satisfies the constraint of input limitation, and the closed-loop system is asymptotically stable at the zero equilibrium point;

[0025] The closed-loop system Gain ,in The gain is Control performance indicators, is a given constant.

[0026] Further, solving the solvability condition using the Matlab / LMI toolbox includes:

[0027] The kinematic and dynamic parameters of the attitude control process of the flexible satellite are determined, the control input range is limited, and the solvability conditions are solved by Matlab / LMI toolbox.

[0028] Further, after step S4, the following steps are included:

[0029] S5, build a flexible satellite attitude control simulation platform through Matlab / Simulink to verify the obtained linear dimension reduction dynamic observer and state feedback robustness Controller effectiveness and reliability.

[0030] Therefore, the present invention provides the following effects and / or advantages:

[0031] The dynamic observer method adopted by the present invention is an extension of the traditional observer structure. Its uniqueness lies in the fact that the gain has a dynamic adjustment characteristic. This design greatly enriches the flexibility and strategy diversity of the control design. At the same time, the convex polyhedron uncertainty system of the flexible satellite shows a more intuitive and concise modeling advantage compared to other uncertainty systems, making the analysis and control of system uncertainty more convenient. More importantly, this control method shows strong robustness in the face of external interference or parameter changes.

[0032] The control method designed in the present invention cleverly combines the flexible adjustment capability of the dynamic observer with the convex polyhedron uncertainty system, and has the characteristics of simple modeling and strong robustness. This method achieves accurate tracking of the flexible mode, which not only successfully helps the satellite to achieve rapid maneuvers at large angles, but also effectively suppresses the vibration of the flexible attachment, ensuring the stable operation of the system. In addition, when facing external interference and parameter perturbations, this method also demonstrates superior robust performance, providing a strong guarantee for the reliable operation of the system.

[0033] Other features and advantages of the present invention will be described in the following description, and partly become apparent from the description, or understood by practicing the present invention. The purpose and other advantages of the present invention are realized and obtained by the structures particularly pointed out in the description and the drawings.

[0034] It is to be understood that both the foregoing general description and the following detailed description of the present invention are exemplary and explanatory and are intended to provide further explanation of the invention as claimed. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 A flowchart diagram of one embodiment of the present invention is provided.

[0036] Figure 2 It is a partial schematic diagram of the calculation results of the solvability condition.

[0037] Figure 3 Schematic diagram of the flexible satellite attitude control simulation platform.

[0038] Figure 4 is the external disturbance of the uncertain disturbance system Graph.

[0039] Figure 5 For limited control input A curve diagram, which defines Less than 100.

[0040] Figure 6 for The trajectory curve.

[0041] Figure 7 is the attitude angular velocity trajectory.

[0042] Figure 8 for and Schematic diagram of the trajectory.

[0043] Fig. 9 For and Schematic diagram of the derivation trajectory.

[0044] Fig.10 is an uncertain vector Range of variation. DETAILED DESCRIPTION

[0045] In order to facilitate understanding by those skilled in the art, the present invention is now described in further detail by way of examples:

[0046] refer to Figure 1 , a linear robust method for flexible satellite based on dynamic observer The control method comprises the following steps:

[0047] S1, construct a flexible satellite attitude system with some unmeasurable states, external disturbances and parameter perturbations, and construct a linear state space model containing convex polyhedron uncertainties and input constraints based on the flexible satellite attitude system;

[0048] S2, design a linear dimension reduction dynamic observer and a linear state feedback robustness for the linear state space model A controller is obtained based on the linear dimension reduction dynamic observer and the linear state feedback robust Controller and closed-loop system with some unmeasurable states, convex polyhedral uncertainties and external disturbances;

[0049] S3, deriving the linear robustness of the closed-loop system based on the linear dimension reduction dynamic observer under the constraint condition of input limitation The solvability conditions of the control problem;

[0050] S4, using Matlab / LMI toolbox to solve the solvability condition, and obtain the linear dimension reduction dynamic observer and the state feedback robustness for the flexible satellite attitude system. The controller solution is robustly implemented through the linear dimension reduction dynamic observer and the state feedback The controller controls the flexible satellite.

[0051] The following describes in detail how to implement each step S1-S4.

[0052] Furthermore, constructing a flexible satellite attitude system with partially unmeasurable states, external disturbances and parameter perturbations includes:

[0053] S1.1, introducing interference torque and perturbation term into the flexible satellite attitude kinematics and dynamics equations, so that the flexible satellite attitude kinematics and the dynamics equations have external interference and parameter perturbation;

[0054] S1.2, introducing auxiliary variables into the flexible satellite attitude kinematics and the dynamic equations and performing approximate linearization processing at the zero equilibrium point, expressing the flexible satellite attitude kinematics and the dynamic equations as the linear state space model, expressing the parameter perturbation terms in the state space model as a convex polyhedron form and restricting its control input, and obtaining a linear state space model containing convex polyhedron uncertainties and input constraints.

[0055] The flexible satellite attitude kinematics and dynamics equations in this step are directly adopted from the prior art. The following steps illustrate how to make the flexible satellite attitude kinematics and the dynamics equations have external interference, parameter perturbation, unmeasurable partial states and input restriction.

[0056] First, the kinematics and dynamics equations of the flexible satellite attitude are expressed as the following model:

[0057] ;

[0058] ;

[0059] in is the Rodrigues parameter vector, is the attitude angular velocity vector, , is the moment of inertia matrix, is the perturbation term of the moment of inertia matrix, for The corresponding cross product matrix is, is the rigid-flex coupling coefficient matrix, is the flexible mode coordinate vector ( represents the truncated mode order), is the modal damping matrix, is the natural frequency matrix, and are the control torque and disturbance torque respectively.

[0060] Since the flexible mode measurement of the satellite attitude system is too expensive, here we consider the case where only the attitude angle and angular velocity can be directly measured, so the flexible satellite attitude kinematics and dynamics equations themselves have some states that cannot be measured. The external disturbance it carries. Furthermore, So that there is parameter perturbation, while limiting This makes it have the characteristics of limited input.

[0061] This embodiment takes the modal order b=2 of the flexible mode intercept as an example, and introduces the auxiliary vector and , and approximate linearization is performed at the zero balance point, the flexible satellite attitude kinematics and the dynamic equations can be expressed as the state space model:

[0062] ;

[0063] in is the system status, and They are the measurable and unmeasurable sub-states of , and They are control input, controlled output and measured output respectively; It is external interference and satisfaction ; , , , is a known constant matrix; , is the uncertainty matrix, specifically, , , , ,

[0064] , .

[0065] At the same time, the system meets:

[0066] Assumption 1:

[0067] There is a saturation constraint , specifically:

[0068] , ;

[0069] in , They are , No. OK.

[0070] Assumption 2:

[0071] Given a vector And define the following polyhedron set :

[0072] ,

[0073] For , assuming:

[0074] , ,

[0075] in and is a given constant matrix, Represents the number of vertices of a convex polyhedron.

[0076] visible, Constrained by vertices , , This indicates that the system has the uncertainty of the convex polyhedron form described above. All abbreviated as .

[0077] The symbol regulations are as follows: , , and Respectively dimensional real vector set, The set of real matrices of dimension, the identity matrix of appropriate dimension, and the zero matrix.

[0078] One of the cases of the convex polyhedron obtained in this step can be Fig.10 shown.

[0079] Furthermore, a linear dimension reduction dynamic observer and a linear state feedback robustness are designed for the linear state space model. The controller includes:

[0080] S2.1, establishing the linear dimension reduction dynamic observer according to the input signal and the output signal of the state space model;

[0081] S2.2, based on the estimated information of the linear dimension reduction dynamic observer, establish the linear state feedback robust Controller.

[0082] Furthermore, a robust linear state feedback observer based on the linear dimension reduction dynamic observer and the linear state feedback Closed-loop systems with controllers and partial unmeasurable states, convex polyhedral uncertainties, and external disturbances include:

[0083] S2.3, the linear dimension reduction dynamic observer and the linear state feedback robust The controller is applied to the linear state space model to obtain a closed-loop system with partial state immeasurability, convex polyhedral uncertainty and external disturbances.

[0084] In this step, the sub-states designed The linear dimension reduction dynamic observer of is as follows:

[0085] ;

[0086] in yes The estimated amount, is the state quantity representing the observer gain, and is an auxiliary variable, , , and is the observer parameter matrix to be designed.

[0087] The designed linear state feedback robust The controller looks like this:

[0088] ;

[0089] in , , is the observation error; is the controller gain matrix to be designed.

[0090] The designed closed-loop system with some unmeasurable states, convex polyhedron uncertainty and external disturbances is as follows:

[0091] ;

[0092] in , , , , , , .

[0093] For systems that satisfy assumptions 1 and 2, the linear robustness based on dynamic observer The control problem specifically refers to designing a linear dimension reduction dynamic observer and a linear state feedback robust The controller is used to ensure that the closed-loop system is asymptotically stable at the zero equilibrium point and has Gain , Gain is a performance indicator of the system, reflecting the system's ability to suppress interference.

[0094] Furthermore, the linear robustness of the closed-loop system based on the linear dimension reduction dynamic observer under the constraint condition of input limitation is derived. The solvability conditions of the control problem include:

[0095] S3.1, according to Lyapunov stability theory, for the closed-loop system Performance criteria;

[0096] S3.2, in Based on the performance criteria, the variable substitution method and the design idea of ​​LMIs are used to derive a linear robust dynamic observer based on the linear dimension reduction under the constraint of limited input. Solvability conditions of the control problem.

[0097] Furthermore, the solvability condition is:

[0098] The closed-loop system satisfies the constraint of input limitation, and the closed-loop system is asymptotically stable at the zero equilibrium point;

[0099] The closed-loop system Gain ,in The gain is Control performance indicators, is a given constant.

[0100] Further, solving the solvability condition using the Matlab / LMI toolbox includes:

[0101] The kinematic and dynamic parameters of the attitude control process of the flexible satellite are determined, the control input range is limited, and the solvability conditions are solved by Matlab / LMI toolbox.

[0102] Specifically, in this step, according to the Lyapunov stability theory, we can first establish a Performance guidelines.

[0103] Theorem 1: For a known constant , if there exists a scalar function ( and has continuous first-order partial derivatives), so that for all Both have:

[0104] ,

[0105] , ;

[0106] Then the closed-loop system is asymptotically stable at the zero equilibrium point and has Gain ,in .

[0107] Proof: Definition for No. Row elements. For the closed-loop system, we know:

[0108] ;

[0109] ;

[0110] because and , we can get:

[0111] ;

[0112] It is known that When, for and ,have , so the closed-loop system is asymptotically stable at the zero equilibrium point.

[0113] Again Under the condition of arrive By integrating, we can get:

[0114] ;

[0115] This allows us to determine the system’s Gain .

[0116] Based on Theorem 1, we apply the variable substitution method and the design idea of ​​LMIs to obtain the linear robustness based on the linear dimension reduction dynamic observer under the constraint of input restriction. Solvability conditions of the control problem.

[0117] Theorem 2: Given a constant , if there exists a matrix , , as well as , , , and ;satisfy:

[0118] (i) ;

[0119] (ii) , ;

[0120] (iii) , ;

[0121] in:

[0122] ,

[0123] , ,

[0124] , , ,

[0125] .

[0126] in, Represents a symmetric matrix block; for a square matrix , , express The set of dimensional real symmetric positive definite matrices, express No. OK.

[0127] Then when When the linear robustness based on the dynamic observer The control problem can be solved. At this time, the observer parameter matrix and the controller gain matrix are:

[0128] ;

[0129] in, and is a reversible matrix and satisfies:

[0130] ;

[0131] Proof: First, for the system, define the Lyapunov function , we can get:

[0132] ;

[0133] in .

[0134] According to Schur's complement lemma, to make the above equation valid, we only need to make:

[0135] ;

[0136] Next, let and , and and The blocks are:

[0137] , ;

[0138] because , so there is . Based on this, further definition:

[0139] , ;

[0140] at this time, is equivalent to:

[0141] ;

[0142] Therefore, we can get .

[0143] Will Substituting into the above formula:

[0144] ;

[0145] And multiply them respectively by And right multiply it by its transpose, and then make:

[0146] ;

[0147] It can be concluded that .

[0148] Finally When , according to Schur's complement lemma, Equivalent to .

[0149] Through Schwarz inequality, we can also get:

[0150] ;

[0151] in, express The 2-norm of .

[0152] If conditions (i), (ii), and (iii) in the theorem hold, then there exists a linear state feedback robust H∞ controller based on a linear dimension reduction dynamic observer that can make the closed-loop system is asymptotically stable inside, and has Gain .

[0153] Further, after step S4, the following steps are included:

[0154] S5, build a flexible satellite attitude control simulation platform through Matlab / Simulink to verify the obtained linear dimension reduction dynamic observer and state feedback robustness Controller effectiveness and reliability.

[0155] The satellite attitude control simulation platform carried by this step is as follows Figure 3 shown.

[0156] The parameters of the flexible satellite attitude system are as follows:

[0157] , ,

[0158] , ;

[0159] Pick , and , , , limiting the saturation input , given , and Restricted to , , , , and These six vertices form an octahedron.

[0160] Assume that the satellite needs to perform an 80 The initial state of the attitude maneuver is: .

[0161] Simulation studies are carried out for the following three different situations:

[0162] 1) Nominal system (NS):

[0163] , ;

[0164] 2) Uncertain and disturbed system 1 (UDS1):

[0165] ;

[0166] 3) Uncertain and disturbed system 2 (UDS2):

[0167] .

[0168] The experimental data are as follows:

[0169] The NS nominal system is defined to represent the operation of a closed-loop system without disturbances and uncertainties, and UDS1 and UDS2 are the operation of a closed-loop system with different disturbances and uncertainties added.

[0170] The linear reduced-dimensional dynamic observer and the linear state feedback robustness for the flexible satellite attitude system obtained by this method Some parameters of the controller solution are as follows Figure 2 shown.

[0171] Figure 4 is the external disturbance of the uncertain disturbance system Graph in Newton meters.

[0172] Figure 5 For limited control input A curve diagram, which defines Less than 100.

[0173] Figure 6 for The trajectory curve shows that the method provided by the present application can quickly complete the attitude maneuver of the flexible satellite under the conditions of external interference and uncertainty and limited input, and is close to the trajectory curve of the nominal system.

[0174] Figure 7 is the attitude angular velocity The trajectory of the present invention illustrates that the method provided by the present invention can make the attitude angular velocity of the flexible satellite quickly stabilize and be close to the trajectory curve of the nominal system under the conditions of interference, uncertainty and limited input.

[0175] Figure 8 for and The trajectory of Fig. 9 for and The trajectory of the first-order derivative shows that the estimation effect of the observer provided by the present application is good.

[0176] In summary, the linear dimensionality reduction dynamic observer obtained in this embodiment has a good estimation effect on the flexible mode and its derivative. Under the control of the linear dimensionality reduction dynamic observer and the state feedback robust H∞ controller, as time goes by, the influence of external interference and parameter uncertainty on the satellite attitude system gradually weakens and eventually disappears. In particular, after 30 seconds, the simulation curves of the three different situations coincide, and the satellite achieves the predetermined attitude control target. These simulation results show that the designed control method not only realizes the large-angle attitude rapid maneuvering of the satellite, but also effectively suppresses the vibration of the flexible attachment, and also shows good robustness to external interference and parameter perturbation.

[0177] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention 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.

[0178] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0179] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0180] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0181] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms should not be understood as necessarily being directed to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, unless they are contradictory.

Claims

1. A Linear Robust Method for Flexible Satellite Based on Dynamic Observer The control method is characterized by: The following steps are involved: S1, construct a flexible satellite attitude system with some unmeasurable states, external disturbances and parameter perturbations, and construct a linear state space model containing convex polyhedron uncertainties and input constraints based on the flexible satellite attitude system; The construction of a flexible satellite attitude system with some unmeasurable states, external disturbances and parameter perturbations includes: S1.1, introducing interference torque and perturbation term into the flexible satellite attitude kinematics and dynamics equations, so that the flexible satellite attitude kinematics and the dynamics equations have external interference and parameter perturbation; S1.2, introducing auxiliary vectors into the flexible satellite attitude kinematics and the dynamic equations and , and perform approximate linearization processing at the zero balance point, express the flexible satellite attitude kinematics and the dynamic equations as the linear state space model, express the parameter perturbation term in the state space model as a convex polyhedron form and restrict its control input, and obtain a linear state space model containing convex polyhedron uncertainty and input restriction; The kinematics and dynamics equations of the flexible satellite attitude are expressed as the following model: ； ； in is the Rodrigues parameter vector, is the attitude angular velocity vector, , is the moment of inertia matrix, is the perturbation term of the moment of inertia matrix, for The corresponding cross product matrix is, is the rigid-flex coupling coefficient matrix, is the flexible mode coordinate vector, represents the truncated mode order, is the modal damping matrix, is the natural frequency matrix, and are the control torque and the disturbance torque respectively, limiting Make it have the characteristics of limited input; The linear state space model is expressed as: ； in is the system status, and They are the measurable and unmeasurable sub-states of , and They are control input, controlled output and measured output respectively; It is external interference and satisfaction ; , , , is a known constant matrix; , is the uncertainty matrix, specifically, , , , , and denote the identity matrix and the zero matrix respectively, , ; S2, design a linear dimension reduction dynamic observer and a linear state feedback robustness for the linear state space model A controller is obtained based on the linear dimension reduction dynamic observer and the linear state feedback robust The controller has a closed-loop system with some unmeasurable states, convex polyhedral uncertainties and external disturbances; the linear dimension reduction dynamic observer is as follows: ； in yes The estimated amount, is the state quantity representing the observer gain, and is an auxiliary variable, , , and is the observer parameter matrix to be designed; S3, deriving the linear robustness of the closed-loop system based on the linear dimension reduction dynamic observer under the constraint condition of input limitation The solvability conditions of the control problem; deriving the linear robustness of the closed-loop system based on the linear dimension reduction dynamic observer under the constraint condition of input restriction The solvability conditions of the control problem include: S3.1, according to Lyapunov stability theory, for the closed-loop system Performance criteria; S3.2, in Based on the performance criteria, the variable substitution method and the design idea of ​​LMIs are used to derive a linear robust dynamic observer based on the linear dimension reduction under the constraint of limited input. The solvability conditions of the control problem; S4, using Matlab / LMI toolbox to solve the solvability condition, and obtain the linear dimension reduction dynamic observer and the state feedback robustness for the flexible satellite attitude system The controller solution is robustly implemented through the linear dimension reduction dynamic observer and the state feedback The controller controls the flexible satellite.

2. A flexible satellite linear robustness based on a dynamic observer according to claim 1 The control method is characterized by: Design a linear dimension reduction dynamic observer and a linear state feedback robustness for the linear state space model The controller includes: S2.1, establishing the linear dimension reduction dynamic observer according to the input signal and the output signal of the state space model; S2.2, based on the estimated information of the linear dimension reduction dynamic observer, establish the linear state feedback robust Controller.

3. A flexible satellite linear robustness based on a dynamic observer according to claim 2 The control method is characterized by: Based on the linear dimension reduction dynamic observer and the linear state feedback robust Closed-loop systems with controllers and partial unmeasurable states, convex polyhedral uncertainties, and external disturbances include: S2.3, the linear dimension reduction dynamic observer and the linear state feedback robust The controller is applied to the linear state space model to obtain a closed-loop system with partial state immeasurability, convex polyhedral uncertainty and external disturbances.

4. A flexible satellite linear robustness based on a dynamic observer according to claim 1 The control method is characterized by: The solvability condition is: The closed-loop system satisfies the constraint of input limitation, and the closed-loop system is asymptotically stable at the zero equilibrium point; The closed-loop system Gain ,in The gain is Control performance indicators, is a given constant.

5. A flexible satellite linear robustness based on a dynamic observer according to claim 1 The control method is characterized by: Solving the solvability condition using the Matlab / LMI toolbox includes: The kinematic and dynamic parameters of the attitude control process of the flexible satellite are determined, the control input range is limited, and the solvability conditions are solved by Matlab / LMI toolbox.

6. A flexible satellite linear robustness based on a dynamic observer according to claim 1 The control method is characterized by: After step S4, the following steps are included: S5, build a flexible satellite attitude control simulation platform through Matlab / Simulink to verify the obtained linear dimension reduction dynamic observer and state feedback robustness Controller effectiveness and reliability.

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