A flexible spacecraft attitude active fault-tolerant control method without angular velocity measurement

Abstract

A flexible spacecraft attitude active fault-tolerant control method without angular velocity measurement is proposed to solve the problems of actuator faults, flexible appendage vibrations and external disturbances in the process of spacecraft on-orbit attitude maneuver. The method considers the actuator faults, space environment external disturbances and flexible appendage vibrations, establishes the spacecraft attitude kinematics and dynamics model, designs the fixed-time sliding mode observer based on cosine sliding mode function and the flexible vibration observer, uses the estimation results of the two types of observers to rewrite the dynamics model equivalently, and designs the adaptive learning observer to estimate the comprehensive uncertainty caused by actuator faults, angular velocity estimation error, flexible vibration estimation error and external disturbances. Finally, the specified time fault-tolerant controller is designed according to the estimated value of the comprehensive uncertainty. The method has strong fault-tolerant ability, good flexible vibration suppression performance and robustness to external disturbances.

Description

Technical Field

[0001] This invention relates to the field of spacecraft attitude control technology in aerospace control technology, specifically to an active fault-tolerant control method for the attitude of flexible spacecraft that does not require angular velocity measurement. Background Technology

[0002] In recent years, with the increasing demands of space missions, space missions have become increasingly complex and diverse. To cope with the harsh space environment, spacecraft commonly incorporate structures such as large solar panels and large flexible antennas. Recent advancements in space technology have highlighted the growing importance of spacecraft attitude control systems in critical missions such as Earth observation, formation flying, and orbital rendezvous. As mission complexity increases, the demand for high-precision, high-speed attitude maneuvers continues to grow, and this goal still faces significant challenges. Most existing control algorithms are based on full-state information and cannot handle scenarios where angular velocity is unmeasurable. Furthermore, spacecraft operate for extended periods in harsh environments with intense radiation, microgravity, and drastic temperature variations, and may encounter unpredictable actuator failures during long-term missions, severely degrading spacecraft control performance. The flexural vibrations of flexible spacecraft with large flexible appendages, if not effectively suppressed, will also affect control accuracy. Currently, most control methods can only achieve asymptotic convergence, failing to meet rapid response requirements and increasing the complexity of control system design. These issues warrant in-depth research.

[0003] Research on attitude control of spacecraft to cope with external disturbances in a fault-free state has been extensive. For fault-free conditions, most inventions have proposed various nonlinear control strategies, including sliding mode control, neural network control, adaptive control, fuzzy control, and observer-based control. However, during the on-orbit operation of a spacecraft, actuators can hardly maintain a completely fault-free state in all times. Therefore, fault-tolerant control methods for spacecraft have emerged and have been widely used in recent years. Fault-tolerant control refers to control strategies that can maintain closed-loop performance even in the presence of actuator / sensor faults, and is generally divided into two categories: passive fault-tolerant control and active fault-tolerant control. Passive fault-tolerant control uses a single fixed controller, which is simple in structure but has limited fault tolerance and is difficult to achieve fast and high-precision control. Active fault-tolerant control feeds data back to the controller through a real-time fault estimation module for compensation. Currently, most fault-tolerant control strategies assume the availability of full-state measurement data; however, sensor faults or size limitations may prevent the measurement of angular velocity, prompting research into fault-tolerant control strategies without angular velocity.

[0004] To address the aforementioned problems, the present invention presents a method for active fault-tolerant attitude control of flexible spacecraft that does not require angular velocity measurement, which is of great significance. Summary of the Invention

[0005] This invention addresses the problems of unmeasurable angular velocity and performance degradation caused by actuator failures, flexible appendage vibrations, and external disturbances during attitude maneuvers in existing flexible spacecraft. It provides an active fault-tolerant attitude control method for flexible spacecraft that eliminates the need for angular velocity measurement. This method involves designing a sliding mode observer to estimate the attitude derivative and obtain an estimated angular velocity, designing a flexible vibration observer to estimate flexible vibrations, and designing a learning observer to estimate the combined uncertainty composed of actuator failures, external disturbances, and observer errors. Based on this, a class of time-specified active fault-tolerant controllers is designed. This method solves the problems of unmeasurable angular velocity, actuator failures, flexible appendage vibrations, and external disturbances during attitude maneuvers in flexible spacecraft, ensuring the overall fault tolerance, rapid maneuverability, and robustness to external disturbances and vibrations of the spacecraft.

[0006] An active fault-tolerant attitude control method for flexible spacecraft that does not require angular velocity measurement includes the following steps:

[0007] Step 1: Define the attitude kinematics and attitude dynamics equations of the flexible spacecraft and the actuator fault modeling equations. Based on the actuator fault modeling equations and the flexible spacecraft attitude dynamics equations, obtain the flexible spacecraft fault attitude dynamics equations.

[0008] Step 2: Based on the flexible spacecraft fault attitude dynamics equation described in Step 1, determine the second-order nonlinear state-space model of the spacecraft. Design a fixed-time sliding mode observer based on a cosine nonsingular sliding mode function to obtain the estimated value of the attitude derivative, and then obtain the estimated value of the attitude angular velocity. Design a flexible vibration observer to estimate the flexible modes, and rewrite the flexible spacecraft fault attitude dynamics equation based on the estimated values ​​obtained by the fixed-time sliding mode observer and the flexible vibration observer.

[0009] Step 3: Design based on The adaptive learning observer estimates the comprehensive uncertainty of the function, which includes actuator failure, external disturbances, and observer estimation error;

[0010] Step 4: Using the comprehensive uncertainty estimate obtained by the observer described in Step 3, establish a second-order spacecraft dynamics system design controller; and implement active fault-tolerant control of the flexible spacecraft's attitude based on the controller.

[0011] The beneficial effects of this invention are:

[0012] The control method described in this invention establishes the attitude kinematics and dynamic equations of a flexible spacecraft, with the dynamic equations considering actuator failure models; designs a fixed-time sliding mode observer based on a cosine sliding mode function to estimate the attitude, and calculates the attitude angular velocity estimate using a one-step method; designs a flexible vibration observer to estimate the flexible vibration modes, and rewrites the flexible spacecraft dynamic equations based on the estimation results, where the overall uncertainty includes actuator failure, external disturbances, and observer estimation errors; and designs a flexible vibration observer based on... The adaptive learning observer estimation of the function integrates uncertainties, ensuring uniform eventual bounded convergence of the observer. Finally, based on the observer estimation information, a second-order adaptive non-singular terminal sliding mode fault-tolerant controller with a specified time is designed. This invention presents an active fault-tolerant control method for flexible spacecraft attitude without the need for angular velocity measurement. It effectively achieves convergence of spacecraft attitude and attitude angular velocity estimates within a specified time bound, exhibits strong fault compensation capabilities, and suppresses environmental disturbances and flexible vibrations.

[0013] The present invention proposes a fixed-time sliding mode observer, a flexible vibration observer, and a method based on a cosine sliding mode function. The adaptive learning observer of the function can achieve high-precision estimation. Attached Figure Description

[0014] Figure 1 This is a system block diagram of the active fault-tolerant attitude control method for flexible spacecraft that does not require angular velocity measurement, as described in this invention.

[0015] Figure 2 To estimate the angular velocity of a fixed-time sliding mode observer based on a cosine sliding mode function Renderings;

[0016] Figure 3 Observing flexible vibration with a flexible vibration observer Renderings;

[0017] Figure 4 For based on Adaptive learning observer of function observes comprehensive uncertainty Renderings;

[0018] Figure 5 For attitude quaternions and attitude angular velocity estimates Response diagram;

[0019] Figure 6 Modal displacement and modal velocity The response diagram. Detailed Implementation

[0020] Combination Figures 1 to 6This embodiment describes an active fault-tolerant attitude control method for flexible spacecraft that does not require angular velocity measurement. The method first considers the influence of actuator failures and external disturbances in flexible spacecraft, establishing the kinematics, dynamics, and dynamics equations of the flexible spacecraft's attitude. Second, a fixed-time sliding mode observer based on a cosine sliding mode function is designed to estimate the attitude derivative, and the estimated angular velocity is calculated using a one-step method. Subsequently, a flexible vibration observer is designed to estimate unavailable flexible modes, and the spacecraft dynamics model is rewritten based on the estimates from the first two observers. Finally, a method based on... The adaptive learning observer estimation of the function is based on the comprehensive uncertainty consisting of actuator failure, external disturbances, and observer estimation errors. Finally, an active fault-tolerant controller is designed based on the estimated comprehensive uncertainty; this controller is a second-order adaptive non-singular terminal sliding mode controller with a specified time. This method ensures the stability of the attitude system when the flexible spacecraft experiences failure, external disturbances, and flexible vibrations without angular velocity measurement information, meeting the accuracy requirements of practical control systems and exhibiting strong fault tolerance and robustness to external disturbances and vibrations. The specific method is implemented through the following steps:

[0021] Step 1: Provide the attitude kinematics and dynamics equations of the flexible spacecraft, as well as the actuator fault modeling equations:

[0022] The kinematic equations for the attitude of a flexible spacecraft are as follows:

[0023] (1)

[0024] in, This represents the scalar part of the quaternion representing the spacecraft's attitude unit. The vector part of the spacecraft attitude quaternion is represented, and it satisfies the normalization constraint. ; This represents the attitude angular velocity vector of the spacecraft relative to the inertial coordinate system in its body coordinate system. yes The identity matrix; ; It is a vector The skew-symmetric matrix has the following specific form:

[0025] (2)

[0026] The attitude dynamics equations (3) for the flexible spacecraft and the dynamics equations (4) for the flexible appendages are established respectively:

[0027] (3)

[0028] (4)

[0029] in, It is the overall inertia matrix of the flexible spacecraft. It is the rigid part of the total inertia. It is the inertial effect caused by the flexible attachments of the spacecraft. This indicates the coupling effect of flexible attachments on rigid dynamics. for The derivative, yes The skew-symmetric matrix is ​​of the following form: , This represents the vibration coordinate vector of the fourth mode of flexibility. It is the total torque acting on the flexible spacecraft. For external disturbance torque. Diagonal matrix. and These are the damping matrix and the stiffness matrix, respectively. The vibration mode damping ratio, These are the vibrational modal frequencies. (Definition) ,in ,in, Given the designed flexible vibration vector, the attitude dynamics equations of the flexible spacecraft can be rewritten as:

[0030] (5)

[0031] in, This indicates the dynamic characteristics associated with flexible attachments.

[0032] This invention uses a reaction flywheel as the actuator, and the actuator fault modeling equation is as follows:

[0033] (6)

[0034] in, This indicates that the actuator efficiency has decreased. This refers to the command torque of the actuator. For additive bias faults, This represents the total failure effect, including actuator efficiency reduction and additive bias fault. Substituting the actuator fault modeling equation (6) into (5), we can obtain the flexible spacecraft fault attitude dynamics equation:

[0035] (7)

[0036] in, This indicates a lumped failure effect that combines actuator malfunctions with external interference.

[0037] Step 2: Based on the dynamic equations of the flexible spacecraft's fault attitude, a second-order nonlinear state-space model of the spacecraft is derived. A fixed-time sliding mode observer based on a cosine nonsingular sliding mode function is designed to estimate the attitude derivatives. Then, the estimated attitude angular velocity is calculated using a one-step method. A flexible vibration observer is designed to estimate the flexible modes. The dynamic equations are rewritten based on the estimates obtained from both observers.

[0038] The fault attitude dynamics equations of the flexible spacecraft are rewritten as a second-order nonlinear state-space model of the spacecraft as follows:

[0039] (8)

[0040] in, , and Is with The relevant functions are as follows: , ; To account for overall uncertainty;

[0041] The fixed-time sliding mode observer based on the cosine nonsingular sliding mode function is designed as follows:

[0042] (9)

[0043] in, It is a positive number. and It is a positive constant to be designed; and ,in, They are The estimated value; It is a novel nonlinear sliding mode function; To and The relevant functions to be designed, and To and The relevant functions, among which, , and The specific form is:

[0044] (10)

[0045] (11)

[0046] (12)

[0047] in, Let be discrete variables, each taking values ​​in the range {1, 2, 3}, representing the function . , and Three-dimensional component representation; positive constants satisfy: and ; positive numbers satisfy ,in, This is a positive constant. After obtaining the estimated value of the attitude derivative through the above observations, based on... An estimate of the angular velocity can be calculated, where, and They are and The estimated value.

[0048] In this embodiment, the flexible vibration observer is designed as follows:

[0049] (13)

[0050] in, They are The estimated value. After obtaining the estimated value of the flexible mode by estimating the flexible vibration observer, the estimated value of the flexible mode is substituted into (7) to obtain:

[0051] (14)

[0052] in,

[0053] and ; and These are angular velocities. , , and The estimation error; It is the derivative of the angular velocity estimation error; It is about skew-symmetric matrix; To account for the uncertainty, it includes actuator failure, external disturbances, and observer estimation errors.

[0054] Step 3: Design based on The adaptive learning observer estimate of the function incorporates comprehensive uncertainty, which includes actuator failure, external disturbances, and observer estimation errors.

[0055] (15)

[0056] in yes The estimated value, This represents the angular velocity estimation error of the observer. It is a comprehensive uncertainty The estimated value, yes The value before time T. Parameter It is the adaptive gain to be designed. It is a normal number. It is designed function, where, It is the sliding mode function to be designed. It is Hadamaji. and The specific form is as follows:

[0057] (16)

[0058] (17)

[0059] (18)

[0060] in and It is a positive constant and an adaptive parameter. There is an upper realm . To comprehensively address uncertainties The estimated value before time T.

[0061] Step 4: Using the comprehensive uncertainty estimate obtained from the observer, establish a second-order spacecraft dynamics system design controller; the controller combines specified time theory and second-order non-singular terminal sliding mode, and uses an adaptive law to offset the influence of observer estimation errors:

[0062] The controller design is as follows:

[0063] (19)

[0064] (20)

[0065] (twenty one)

[0066] (twenty two)

[0067] in, This is an equivalent control law. The compensation control law is used to compensate for overall uncertainty and flexural vibration.

[0068] An adaptive law is used to compensate for the estimation error of the observer. . .

[0069] Gain and Selected as:

[0070] ;

[0071] A matrix is ​​defined as:

[0072] Gain and Selected as:

[0073] ,

[0074] .

[0075] Gain and Selected as:

[0076] .

[0077] in, and It is a positive number. It is a predefined time constant. Sliding surface and The format is as follows:

[0078] ,

[0079] .

[0080] The method described in this embodiment can estimate the unmeasurable angular velocity, the estimated value of the flexible mode, and the estimated value of the comprehensive uncertainty through three observers, and compensate for the influence of the comprehensive uncertainty on the attitude maneuver of the flexible spacecraft through a fault-tolerant controller.

[0081] The active fault-tolerant attitude control method for flexible spacecraft that does not require angular velocity measurement, as described in this embodiment, is applied to a flexible spacecraft with the following moment of inertia: The first natural frequency of the mode is The damping ratio of the mode is set to

[0082] The rigid-flexible coupling matrix is:

[0083]

[0084] External disturbances to flexible spacecraft are described as follows .

[0085] Control system block diagram as follows Figure 1As shown. Based on the above steps, an observer-based controller is designed. Simulation results are shown below. Figure 2-4 The observer estimation results are shown in the diagram. Using the effective information obtained from the observer, simulations are performed to obtain... Figure 5-6 Response plots of attitude and attitude angular velocity estimates, and response plots of modal displacement and modal velocity.

[0086] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0087] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for active fault-tolerant attitude control of flexible spacecraft without the need for angular velocity measurement, characterized by: This method is implemented by the following steps: Step 1: Define the attitude kinematics and attitude dynamics equations of the flexible spacecraft and the actuator fault modeling equations. Based on the actuator fault modeling equations and the flexible spacecraft attitude dynamics equations, obtain the flexible spacecraft fault attitude dynamics equations. Step 2: Based on the flexible spacecraft fault attitude dynamics equation described in Step 1, determine the second-order nonlinear state-space model of the spacecraft. Design a fixed-time sliding mode observer based on a cosine nonsingular sliding mode function to obtain the estimated value of the attitude derivative, and then obtain the estimated value of the attitude angular velocity. Design a flexible vibration observer to estimate the flexible modes, and rewrite the flexible spacecraft fault attitude dynamics equation based on the estimated values ​​obtained by the fixed-time sliding mode observer and the flexible vibration observer. Step 3: Design based on The adaptive learning observer estimates the comprehensive uncertainty of the function, which includes actuator failure, external disturbances, and observer estimation error; Step 4: Using the comprehensive uncertainty estimate obtained by the observer described in Step 3, establish a second-order spacecraft dynamics system design controller; and implement active fault-tolerant control of the flexible spacecraft's attitude based on the controller.

2. The active fault-tolerant attitude control method for flexible spacecraft without angular velocity measurement according to claim 1, characterized in that: In step two, a fixed-time sliding mode observer based on a cosine nonsingular sliding mode function is designed as follows: ； In the formula, For positive integers, and All are positive constants to be designed; and , They are respectively The estimated value, It is a nonlinear sliding mode function. and Is with The relevant functions, To and The relevant functions to be designed, and To and The relevant function obtains the estimated value of the attitude angular velocity after obtaining the estimated value of the attitude derivative through the observer.

3. The active fault-tolerant attitude control method for flexible spacecraft without angular velocity measurement according to claim 2, characterized in that: In step two, the flexible vibration observer is designed as follows: ； In the formula, They are respectively The estimated value, The vibration coordinate vector of the fourth mode of the flexible structure. For the designed flexible vibration vector, This refers to the coupling effect of flexible attachments on rigid dynamics. and These are the damping matrix and the stiffness matrix, respectively. The attitude angular velocity estimate is the attitude angular velocity. The estimated value.

4. The active fault-tolerant attitude control method for flexible spacecraft without angular velocity measurement according to claim 3, characterized in that: Based on the estimates obtained from the fixed-time sliding mode observer and the flexible vibration observer using the cosine nonsingular sliding mode function, the dynamic equations of the flexible spacecraft's fault attitude are rewritten as follows: ； In the formula, The rigid component of the total inertia. For attitude angular velocity estimation The derivative, For attitude angular velocity estimation A skew-symmetric matrix, For the actuator's command torque, These are estimates of the dynamic characteristics associated with flexible attachments. To account for overall uncertainty.

5. The active fault-tolerant attitude control method for flexible spacecraft without angular velocity measurement according to claim 4, characterized in that: In step three, the design is based on The adaptive learning observer estimates the overall uncertainty of the function, as shown in the following formula: ； In the formula, For attitude angular velocity estimation The estimated value, To account for the angular velocity estimation error of the self-adaptive learning observer, for A skew-symmetric matrix, To comprehensively address uncertainties The estimated value, for The value before time T, For the adaptive gain to be designed, It is a positive number; For design function, For the sliding mode function to be designed, For the Hadamard product, sgn() is the sign function.

6. The active fault-tolerant attitude control method for flexible spacecraft without angular velocity measurement according to claim 5, characterized in that: The function is represented as: ,in: and The format is as follows: ； ； ； In the formula, and All are positive numbers, and are adaptive parameters. There is an upper realm , To comprehensively address uncertainties The estimated value before time T.

7. The active fault-tolerant attitude control method for flexible spacecraft without angular velocity measurement according to claim 6, characterized in that: In step four, the controller is designed as follows: ； in, ; ； In the formula, This is an equivalent control law. The control law is used to compensate for overall uncertainty and flexible vibration. , It is the identity matrix; For vectors A skew-symmetric matrix, For the vector part of the spacecraft attitude quaternion, For the scalar part of the spacecraft attitude unit quaternion, , , and All are gain. and For a matrix, , , R is the total torque acting on the flexible spacecraft, a normal number. and All are sliding surfaces. An adaptive law is used to compensate for the estimation error of the observer.

8. The active fault-tolerant attitude control method for flexible spacecraft without angular velocity measurement according to claim 7, characterized in that: Used to compensate for the estimation error of the observer Represented as: ； In the formula, and All are gain. It is a positive number; Sliding surface and The format is as follows: ； 。

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