High-precision time-determined attitude tracking control method for flexible spacecraft subject to multiple disturbances

Abstract

The present invention discloses a high-precision predetermined time attitude tracking control method for a flexible spacecraft subject to multiple disturbances, the method comprising the following steps: step one, establishing a mathematical model of the flexible spacecraft based on a rotation matrix; step two, establishing an error kinematics and dynamics model of the flexible spacecraft; step three, based on the good nonlinear approximation capability of a radial basis neural network RBFNN, approximate estimation and compensation of lumped disturbances including external disturbances, parameter uncertainty, actuator failure and structural vibration; step four, designing a controller based on predetermined time theory and sliding mode control theory, so that the maximum convergence time of the system is independent of its initial state. The beneficial results of the present invention are: the lumped disturbance can be compensated by using a neural network under the condition of unknown prior information, wherein actuator failure and saturation problems are also considered; the system stabilization time can be preset; and the accuracy and stability of the attitude tracking control system of the flexible spacecraft are improved.

Description

Technical Field

[0001] The invention belongs to the field of aerospace technology, and in particular relates to a high-precision predetermined time attitude tracking control method for a flexible spacecraft subject to multiple disturbances. Background Art

[0002] Attitude control is of great significance to the successful execution of space missions. Attitude control systems need to be highly accurate, stable, and robust to cope with complex space environments and diverse mission requirements. However, designing a suitable controller for a spacecraft to meet performance requirements is still a challenging task, mainly due to the existence of unknown inertial parameters, complex space environment interference, actuator failure and saturation, and elastic deformation and coupling effects caused by flexible attachments on the spacecraft, which will reduce the accuracy of attitude control. In addition, since many space applications have strict requirements on the stabilization time of the attitude system, it is difficult to accurately estimate the upper bound of the convergence time of a finite-time control system under the condition of unknown initial state; the upper bound of the convergence time of a fixed-time control system depends on a complex function containing multiple parameters, so it is difficult to determine the maximum convergence time by adjusting the parameters. Therefore, it is necessary to design a predetermined time attitude tracking control strategy for flexible spacecraft under multiple disturbances, so that the maximum convergence time of the system can be explicitly represented by the system parameters and can be pre-set to achieve high-precision and high-robustness attitude control. Summary of the invention

[0003] In order to solve the problems existing in the prior art, the present invention proposes a high-precision predetermined time attitude tracking control method for flexible spacecraft subject to multiple disturbances. Based on the good nonlinear approximation ability of RBFNN, the lumped disturbances of the flexible spacecraft system including external disturbances, inertial parameter uncertainty, actuator failure and structural vibration are approximated and compensated in real time. Then, based on the predetermined time stability theorem, an adaptive sliding mode controller is designed so that the maximum convergence time of the system is independent of its initial state, and the attitude tracking of the spacecraft is achieved within the predetermined time.

[0004] A high-precision predetermined time attitude tracking control method for a flexible spacecraft subjected to multiple disturbances of the present invention comprises the following steps:

[0005] Step 1: Establish a mathematical model of the flexible spacecraft based on the rotation matrix, including inertial parameter uncertainty, external disturbance, actuator saturation and failure, and structural vibration;

[0006] Step 2: Given the expected attitude and the expected angular velocity, the error mathematical model of the flexible spacecraft is obtained according to the mathematical model of the flexible spacecraft, and the error kinematics and dynamics models of the flexible spacecraft are established using equivalent error variables;

[0007] Step 3: Design the sliding surface, combine it with step 2 to obtain the lumped disturbance term including external environmental disturbance, inertial parameter uncertainty, actuator failure and structural vibration, and perform approximate estimation and compensation for the lumped disturbance term based on the RBFNN network;

[0008] Step 4: Use the output of RBFNN to the lumped disturbance as the compensation signal of the uncertainty in the controller. Based on the predetermined time stability theorem, design an adaptive sliding mode controller so that the maximum convergence time of the system is independent of its initial state and the attitude tracking error of the spacecraft can be converged within the predetermined time.

[0009] Furthermore, the step 1 includes:

[0010] The kinematic and dynamic models of flexible spacecraft are described based on the rotation matrix:

[0011] ,

[0012] ;

[0013] Where: is the rotation matrix that transforms the spacecraft from the body coordinate system to the inertial coordinate system; is the actual inertia matrix of the spacecraft, where Nominal inertia matrix, is the uncertain inertia parameter;

[0014] is a flexible mode, Represents the coupling coefficient matrix between the rigid body and the flexible structure, and is expressed as Indicates The flexible mode, , is the modal damping matrix, the stiffness matrix express, is the damping ratio, is the natural frequency;

[0015] d represents the external disturbance, and the angular velocity of the spacecraft in the body coordinate system is ,and ;

[0016] Consider the control input with gain fault and additive fault as:

[0017] ;

[0018] Where: u is the control input, represents the nonlinear saturation characteristic of the actuator, ; Set the maximum control input value of the actuator to ,Will Defined as:

[0019] ;

[0020] ;

[0021] in, represents the actuator failure coefficient, , ,in It is an unknown normal number used to indicate whether the actuator is working properly;

[0022] For additional faults, ,in is an unknown positive scalar.

[0023] Furthermore, in step 2, the error kinematics and dynamics models of the flexible spacecraft are established as follows:

[0024] Attitude Error of Flexible Spacecraft and angular velocity error Defined by:

[0025] ;

[0026] ;

[0027] In the formula, and represents the desired attitude and desired angular velocity;

[0028] Selecting the Error Vector Error kinematics model describing flexible spacecraft:

[0029] ;

[0030] ;

[0031] is the attitude error function; E is the intermediate variable;

[0032] The error dynamics model of the flexible spacecraft is:

[0033] ;

[0034] ;

[0035] ;

[0036] F and G are intermediate variables.

[0037] Furthermore, the step three is specifically as follows:

[0038] S31 Design of sliding surface with predetermined time:

[0039] Predetermined Time Lemma: For Nonlinear Systems , if there exists a positive definite continuous Lyapunov function , so that the inequality:

[0040] ;

[0041] Established, , , , is a constant value, satisfy and ; then the equilibrium point of the nonlinear system is stable for a predetermined time, is the predetermined upper bound of the convergence time;

[0042] According to the time lemma, the form of the predetermined time sliding surface is:

[0043] ;

[0044] is defined as follows:

[0045] { Φ 1 = π 2 p 1 T c 1 λ 1 λ 2 [ λ 1 V 1 − p 1 2 + λ 2 2 p 1 2 V 1 + p 1 2 ] E -1 e R ˜ V = 1 2 e R ˜ T e R ˜ ;

[0046] Combined with the scheduled time lemma, , , is an adjustable parameter for posture tracking error Satisfy the predetermined time convergence, and its variation range satisfies , , and It can be preset Upper limit of convergence time;

[0047] S32 substitutes the predetermined time sliding mode surface into the error dynamics model of the flexible spacecraft to obtain:

[0048] ;

[0049] In the formula, is the nominal dynamics part of the spacecraft, It is the uncertain dynamic part that includes external environmental disturbances, inertial parameter uncertainties, actuator failures, and structural vibrations:

[0050] ;

[0051] ;

[0052] The RBFNN network is used to compensate and approximate the lumped disturbance including external environmental disturbance, inertial parameter uncertainty, actuator failure and structural vibration:

[0053] ;

[0054] In the formula is the optimal weight matrix, is the output of the hidden layer of the neural network, is the estimation error, and Bounded, .

[0055] Furthermore, the design of the adaptive sliding mode controller described in step 4 is divided into two steps: first, the nominal controller is designed ; Then use the adaptive rate to design a passive fault-tolerant controller , to handle actuator saturation and failure, the control input is .

[0056] Furthermore, the nominal controller is in the form of:

[0057] ;

[0058] is the output of the RBFNN as a lumped perturbation The compensation signal is in the form of , is the actual weight of RBFNN, which is updated using the following adaptive rate:

[0059] ;

[0060] in, , is an adjustable parameter; the input vector of the RBFNN network is selected as ; Assume that RBFNN has neurons, then The output of a neuron is:

[0061] ;

[0062] , is the hidden layer The coordinate vector of the center point of the Gaussian basis function of each neuron, It is The width of the Gaussian basis function of each neuron;

[0063] The form is as follows:

[0064] ;

[0065] Combined with the scheduled time lemma, , , is an adjustable parameter whose range satisfies , , and is the predetermined time sliding surface The upper bound of the convergence time is ;

[0066] Considering the handling of actuator failures, passive fault-tolerant control is achieved using adaptive rate:

[0067] ;

[0068] Adaptive Rate Decide, , , is an adjustable parameter of the adaptation rate.

[0069] Beneficial effects of the present invention:

[0070] The present invention takes into account practical engineering applications, combines RBFNN with adaptive sliding mode control, and estimates and compensates for the lumped disturbances of flexible spacecraft including external disturbances, inertial parameter uncertainties, actuator failures and structural vibrations in real time in the absence of multiple disturbance prior information, and realizes attitude tracking control of the flexible spacecraft within a predetermined time, ensuring that the upper limit of the system convergence time can be arbitrarily configured by setting parameters, can be explicitly represented in the controller and is not limited by the initial value of the system. The method has strong robustness and high convergence accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 It is a system block diagram of a method for high-precision predetermined time attitude tracking control of a flexible spacecraft subjected to multiple disturbances in the present application;

[0072] FIG2(a) is an attitude error curve of a high-precision predetermined time attitude tracking control method for a flexible spacecraft subjected to multiple disturbances of the present application, and FIG2(b) is an enlarged view of the attitude error after an actuator failure occurs;

[0073] FIG3(a) is an angular velocity error curve of a high-precision predetermined time attitude tracking control method for a flexible spacecraft subjected to multiple disturbances of the present application, and FIG3(b) is an amplified diagram of the angular velocity error after an actuator failure occurs;

[0074] FIG4(a) is a sliding mode surface of a high-precision predetermined time attitude tracking control method for a flexible spacecraft subjected to multiple disturbances of the present application, and FIG4(b) is an enlarged view of the sliding mode surface after an actuator failure occurs;

[0075] Figure 5 It is the control input of a high-precision predetermined time attitude tracking control method of a flexible spacecraft subject to multiple disturbances in the present application;

[0076] Figure 6 It is a flexible mode of a high-precision predetermined time attitude tracking control method for a flexible spacecraft subject to multiple disturbances in the present application. DETAILED DESCRIPTION

[0077] like Figure 1 As shown, the present application provides a high-precision predetermined time attitude tracking control method for a flexible spacecraft subject to multiple disturbances, and the specific steps include:

[0078] Step 1: In order to avoid unwinding in attitude description, a mathematical model of the flexible spacecraft including inertial parameter uncertainty, external disturbance, actuator saturation and failure, and structural vibration is established based on the rotation matrix;

[0079] Step 2: Given the desired attitude and desired angular velocity, the error mathematical model of the flexible spacecraft is obtained. At the same time, in order to simplify the design of the controller, the error kinematics and dynamics models of the flexible spacecraft are established using equivalent error variables;

[0080] Step 3: Design the sliding surface of the predetermined time, and combine it with step 2 to obtain the lumped disturbance term including external disturbance, parameter uncertainty, actuator failure and structural vibration. Based on the good nonlinear approximation ability of RBFNN, the lumped disturbance term is approximately estimated and compensated;

[0081] Step 4: Use the output of RBFNN to the lumped disturbance as the compensation signal of the uncertainty in the controller. Based on the predetermined time stability theorem, design an adaptive sliding mode controller so that the maximum convergence time of the system is independent of its initial state and the attitude tracking error of the spacecraft can be converged within the predetermined time.

[0082] In step 1, the kinematic and dynamic models of the flexible spacecraft are established based on the rotation matrix

[0083] ;

[0084] ;

[0085] Where: is the rotation matrix that transforms the spacecraft from the body coordinate system to the inertial coordinate system. is the actual inertia matrix of the spacecraft. Among them, is the nominal inertia matrix, is an uncertain inertia parameter. is a flexible mode, Represents the coupling coefficient matrix between the rigid body and the flexible structure. Indicates The flexible mode, , , is the modal damping matrix, is the damping ratio, is the natural frequency. The stiffness matrix is express. represents the external disturbance, and the angular velocity of the spacecraft in the body coordinate system is ,and .

[0086] Consider the control input with gain fault and additive fault as:

[0087] ;

[0088] Where: is the control input, , Represents the nonlinear saturation characteristic of the actuator. The maximum control input value of the actuator is , It can be defined as:

[0089] ;

[0090] ;

[0091] represents the actuator failure coefficient, ,in is an unknown positive constant. Indicates that the actuator is working normally. Indicates An actuator part has failed. For additional faults, ,in is an unknown positive scalar.

[0092] In step 2, the error kinematics and dynamics models of the flexible spacecraft are established. The attitude error and angular velocity error are defined by the following equations:

[0093] ;

[0094] ;

[0095] In the formula, and represents the desired attitude and the desired angular velocity. Due to the complexity of the rotation matrix, the above error model is generally not directly used to design the controller. Select the following error vector Error kinematics model describing flexible spacecraft:

[0096] ;

[0097] ;

[0098] is the attitude error function. In addition, the error dynamics model of the flexible spacecraft is:

[0099] ;

[0100] ;

[0101] .

[0102] Step three includes:

[0103] The sliding surface with predetermined time is designed and combined with the error mathematical model of flexible spacecraft to obtain the uncertain dynamics including lumped disturbance.

[0104] The sliding surface is in the form of:

[0105] ;

[0106] ;

[0107] In the formula, , , , , , It is a sliding surface that can be pre-set The upper bound of the convergence time. yes The estimated value of Defined by the adaptation rate:

[0108] ;

[0109] In the formula, , .besides, Designed for:

[0110] .

[0111] Combined with step 2, the sliding surface is substituted into the error dynamics equation of the spacecraft to obtain:

[0112] ;

[0113] is the nominal dynamics part of the spacecraft, is the uncertain dynamic part including the lumped perturbation:

[0114] ;

[0115] .

[0116] RBFNN is used to compensate and approximate the lumped disturbance:

[0117] ;

[0118] In the formula is the optimal weight matrix, is the estimation error, and Bounded, The input vector of RBFNN is selected as .

[0119] Step 4 further includes: calculating the control rate of the flexible spacecraft according to the following formula:

[0120] ;

[0121] is a nominal controller of the form:

[0122] ;

[0123] In the formula, is the output of the RBFNN as a lumped perturbation The compensation signal uses the adaptive rate to update the weights of the neural network:

[0124] ;

[0125] in, , .

[0126] ;

[0127] in, , , , , ;

[0128] Considering the handling of actuator failures, passive fault-tolerant control is achieved using adaptive rate:

[0129] ;

[0130] Adaptive Rate Determine, , , .

[0131] Next, verify that the designed controller meets the predetermined time stability. The selected Lyapunov function is:

[0132] ;

[0133] The weight error of the neural network is defined as ; Related to the actuator failure coefficient, , , yes Estimated value; Derivative of the Lyapunov function:

[0134] ;

[0135] Substitute the control input The expression of Scale to:

[0136] ;

[0137] According to Lemma 1, the following inequality holds:

[0138] ;

[0139] ;

[0140] at this time Converts to:

[0141] ;

[0142] Since the following equation holds:

[0143] ;

[0144] Using Lemma 2, the following inequality holds:

[0145] ;

[0146] ;

[0147] Also because ,make , so there exists a normal number , so that . Thus Simplified to:

[0148] ;

[0149] In the formula .

[0150] In summary, , , Within the scheduled time Converges to a region containing zeros :

[0151] .

[0152] Select the following Lyapunov function:

[0153] ;

[0154] right The derivative is:

[0155] ;

[0156] There is a positive constant , so that , thus Simplified to:

[0157] ;

[0158] In the formula, ;

[0159] By the scheduled time theorem, and At the scheduled time Converges to a region containing zeros :

[0160] .

[0161] In order to illustrate the effectiveness of the proposed scheduled time controller, a numerical simulation is carried out taking a certain spacecraft as an example, and the basic sampling time is 0.01s.

[0162] The simulation parameters of the flexible spacecraft are selected as follows:

[0163] The initial angular velocity is , modal initial value , , the initial value of the posture is

[0164] The uncertain moment of inertia matrix is

[0165] , the nominal moment of inertia matrix is .

[0166] The damping ratio, natural frequency and coupling matrix are:

[0167] , , , , , , ;

[0168] , the external disturbance is , The initial value of the desired posture is set to , the expected angular velocity is

[0169] The actuator fault signal is as follows:

[0170] ,

[0171] .

[0172] Parameters of the flexible spacecraft scheduled time attitude tracking controller based on RBFNN: , , , , , , , , , , , , , The input of RBFNN is , the range of the input vector is , ,

[0173] , The parameter for the adaptive rate used to update the neural network weights is , .

Claims

1. A high-precision predetermined time attitude tracking control method for a flexible spacecraft subject to multiple disturbances, characterized in that: The steps include: Step 1: Establish a mathematical model of the flexible spacecraft based on the rotation matrix, including inertial parameter uncertainty, external disturbance, actuator saturation and failure, and structural vibration; Step 2: Given the desired attitude and the desired angular velocity, the error mathematical model of the flexible spacecraft is obtained according to the mathematical model of the flexible spacecraft, and the error kinematics and dynamics models of the flexible spacecraft are established using equivalent error variables; the control input with gain fault and additional fault is designed as follows: ； Where: u is the control input, represents the nonlinear saturation characteristic of the actuator, ; Set the maximum control input value of the actuator to ,Will Defined as: ; ; in, represents the actuator failure coefficient, , ,in It is an unknown normal number used to indicate whether the actuator is working properly; For additional faults, ,in is an unknown positive scalar; Step 3: Design the sliding surface, combine step 2 to obtain the lumped disturbance term including external environmental disturbance, inertial parameter uncertainty, actuator failure and structural vibration, and approximate and compensate the lumped disturbance term based on the RBFNN network; the specific step 3 is: S31 Design of sliding surface with predetermined time: Predetermined Time Lemma: For Nonlinear Systems , if there exists a positive definite continuous Lyapunov function , so that the inequality: ； Established, , , , is a constant value, satisfy and ; then the equilibrium point of the nonlinear system is stable for a predetermined time, is the predetermined upper bound of the convergence time; According to the time lemma, the form of the predetermined time sliding surface is: ； is defined as follows: ； Combined with the scheduled time lemma, , , is an adjustable parameter for posture tracking error Satisfy the predetermined time convergence, and its variation range satisfies , , and It can be preset Upper limit of convergence time; S32 substitutes the predetermined time sliding mode surface into the error dynamics model of the flexible spacecraft to obtain: ； In the formula, is the nominal dynamics part of the spacecraft, It is the uncertain dynamic part that includes external environmental disturbances, inertial parameter uncertainties, actuator failures, and structural vibrations: ； ； The RBFNN network is used to compensate and approximate the lumped disturbance including external environmental disturbance, inertial parameter uncertainty, actuator failure and structural vibration: ； In the formula is the optimal weight matrix, is the output of the hidden layer of the neural network, is the estimation error, and Bounded, ; Step 4: Use the output of RBFNN to the lumped disturbance as the compensation signal of the uncertainty in the controller. Based on the predetermined time stability theorem, design an adaptive sliding mode controller so that the maximum convergence time of the system is independent of its initial state and the attitude tracking error of the spacecraft is converged within the predetermined time. The design of the adaptive sliding mode controller described in step 4 is divided into two steps: first, design the nominal controller ; Then use the adaptive rate to design a passive fault-tolerant controller , to handle actuator saturation and failure, the control input is ; The nominal controller is of the form: ； is the output of the RBFNN as a lumped perturbation The compensation signal is in the form of , is the actual weight of RBFNN, which is updated using the following adaptive rate: ； in, , is an adjustable parameter; the input vector of the RBFNN network is selected as ; Assume that RBFNN has neurons, then The output of a neuron is: ； , is the hidden layer The coordinate vector of the center point of the Gaussian basis function of each neuron, It is The width of the Gaussian basis function of each neuron; The form is as follows: ； Combined with the scheduled time lemma, , , is an adjustable parameter whose range satisfies , , and is the predetermined time sliding surface The upper bound of the convergence time is ; Considering the handling of actuator failures, passive fault-tolerant control is achieved using adaptive rate: ； Adaptive Rate Decide, , , is an adjustable parameter of the adaptation rate.

2. The method for high-precision predetermined time attitude tracking control of a flexible spacecraft subjected to multiple disturbances according to claim 1 is characterized in that: The step one comprises: The kinematic and dynamic models of flexible spacecraft are described based on the rotation matrix: ， ； Where: is the rotation matrix that transforms the spacecraft from the body coordinate system to the inertial coordinate system; is the actual inertia matrix of the spacecraft, where Nominal inertia matrix, is the uncertain inertia parameter; is a flexible mode, Represents the coupling coefficient matrix between the rigid body and the flexible structure, and is expressed as Indicates The flexible mode, , is the modal damping matrix, the stiffness matrix express, is the damping ratio, is the natural frequency; d represents the external disturbance, and the angular velocity of the spacecraft in the body coordinate system is ,and .

3. The method for high-precision predetermined time attitude tracking control of a flexible spacecraft subjected to multiple disturbances according to claim 2 is characterized in that: In step 2, the error kinematics and dynamics models of the flexible spacecraft are established as follows: Attitude Error of Flexible Spacecraft and angular velocity error Defined by: ； ； In the formula, and represents the desired attitude and desired angular velocity; Selecting the Error Vector Error kinematics model describing flexible spacecraft: ； ； is the attitude error function; E is the intermediate variable; The error dynamics model of the flexible spacecraft is: ； ； ； F and G are intermediate variables.

Images