High-precision attitude maneuver control method for flexible spacecraft

Abstract

The invention discloses a high-precision attitude maneuver control method for a flexible spacecraft, and the method comprises the steps: considering the fault and saturation conditions of an execution mechanism for a large-inertia spacecraft containing a flexible accessory, firstly building a rigid-flexible coupling dynamic model of the spacecraft, and obtaining the first three-order modal frequency and damping ratio of the spacecraft; secondly, designing a fast robust input shaper according to modal and damping ratio information, and taking a result obtained by convolution of the fast robust input shaper and reference input as control input; and then considering uncertainty such as inertia and external interference of the spacecraft, designing a self-adaptive sliding mode controller, and approaching the uncertainty of the system by adopting a Chebyshev inequality, thereby realizing high-precision attitude control of the spacecraft in finite time. According to the method, the stability of the spacecraft in the attitude maneuver process can be improved, meanwhile, vibration of the flexible component is restrained, and the control performance of the system is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of spacecraft attitude control, and in particular relates to an attitude control method for a flexible spacecraft. Background Technique

[0002] With the continuous development of space technology and the increasing complexity of space missions, the structure of a single spacecraft can no longer meet the increasingly complex mission requirements. A spacecraft needs to carry certain flexible components such as solar panels and antennas. Considering the limitations of its launch cost and carrying capacity, the flexible structure of the spacecraft becomes larger and larger. However, there is a strong rigid-flexible coupling effect between these flexible attachments and the central rigid body of the spacecraft. Especially during the on-orbit operation phase, it is extremely easy to cause vibrations of the flexible attachments. Considering the aging factors of the actuator structure and uncertain factors such as external disturbances, the required torque of the controller cannot be fully output, which will further affect the attitude control accuracy of the spacecraft. Therefore, studying the spacecraft attitude control under the above related problems provides a certain theoretical basis for improving the on-orbit operation ability of the spacecraft.

[0003] The existing spacecraft attitude control has the following deficiencies:

[0004] (1) During the spacecraft attitude control process, a disturbance observer and an attitude tracking control are designed separately. Although the stability of the spacecraft closed-loop system can be ensured, the control accuracy is not high.

[0005] (2) During the spacecraft attitude control process, there is a certain coupling between the central rigid body and the flexible attachments of the spacecraft, and there is a certain deviation between the dynamic model and the actual dynamic model.

[0006] (3) Due to the uncertainties of the moment of inertia and external disturbances and the faults and saturation factors of the actuators, the control accuracy of the spacecraft is not good. Summary of the Invention

[0007] Object of the Invention: The object of the present invention is to provide a high-precision attitude control method for a flexible spacecraft to solve the problem of spacecraft attitude maneuver under flexible vibration, uncertain moment of inertia and external disturbances, and actuator faults and saturation factors.

[0008] Technical solution: To achieve the above object, the present invention discloses a high-precision attitude maneuver control method for a flexible spacecraft. For a large-inertia spacecraft with flexible appendages, considering the faults and saturation of actuators, first, a rigid-flexible coupling dynamic model of the spacecraft is established to obtain the first three modal frequencies and damping ratios of the spacecraft; secondly, a fast robust input shaper is designed according to the modal and damping ratio information, and the result obtained by convolving with the reference input is used as the control input; then, considering the uncertainties such as the inertia of the spacecraft and external disturbances, an adaptive sliding mode controller is designed, and the Chebyshev inequality is used to approximate the system uncertainties, thereby achieving high-precision attitude control of the spacecraft within a finite time. The present invention can improve the stability during the attitude maneuver of the spacecraft, suppress the vibration of flexible components at the same time, and improve the control performance of the system. It includes the following steps:

[0009] (1) Establish the dynamic model of the flexible spacecraft: Considering uncertain factors such as flexible vibration, uncertain moment of inertia, actuator faults and saturation, and external disturbances, establish the nonlinear kinematic model and dynamic model of the spacecraft, providing a basis for further realizing the rigid-flexible coupling spacecraft attitude control theory;

[0010] (2) Add pulse excitation to obtain angular velocity vibration data, and give the first three modal frequencies and damping of the spacecraft under unconstrained conditions by the identification algorithm. The flexible parameters of the spacecraft are identified from the telemetry data under the actual operating state of the spacecraft;

[0011] (3) On the basis of step (2), obtain the modal frequencies and damping ratios, and design a corresponding fast robust input shaper. The shaper is convolved with the desired reference input to obtain the actual control input acting on the controller;

[0012] (4) Rewrite the dynamic model of the spacecraft, analyze the deterministic part and the uncertain part of the spacecraft respectively, and design their controllers. The nominal controller is implemented by a sliding mode controller, and a terminal function sliding mode surface is designed;

[0013] (5) For the deterministic part of the dynamics, design an adaptive integral sliding mode controller based on the terminal function sliding mode surface. For the uncertain part, considering the faults and saturation factors of the actuators, design an interference observer based on the Chebyshev inequality, and then estimate the comprehensive uncertain part for compensation to ensure that the spacecraft can achieve high-precision attitude control within a finite time.

[0014] Furthermore, in step (3): In the input shaper design stage, considering the problem of the contradiction between the action time and robustness existing in the existing ZV shaper and ZVD shaper, design an FR shaper. The principle of the shaper is to consider that there is a certain delay in the action time. The specific form of the input shaper in the Laplace time domain is:

[0015]

[0016] Wherein: is the Laplace expression of the ZV input shaper;

[0017] is the Laplace expression of the ZV input shaper affected by interference; ε > 0; A1 represents the pulse amplitude at the initial moment;

[0018] A2 represents the pulse amplitude at the moment of τ d moment.

[0019] Furthermore, the pulse sequence of the input shaper is obtained as:

[0020]

[0021] Wherein, V tol The maximum allowable residual vibration ratio is 0.05.

[0022] Furthermore, in the step (4), the design of the terminal sliding surface is as follows: According to the attitude quaternion and angular velocity of the dynamic model of the flexible spacecraft, the terminal function sliding surface is designed to achieve the rapid convergence of the attitude quaternion and angular velocity after reaching the terminal sliding surface. The specific expression form of the function surface is:

[0023] S = ω e + K1q ev + K2S c

[0024] Wherein, S = [S1, S2, S3] T is the designed sliding surface, ω e is the attitude error angular velocity, q ev is the vector part of the attitude error quaternion, and the positive constants K1 > 0, K2 > 0.

[0025]

[0026] Wherein, i = 1, 2, 3; the constants l1 and l2 are both positive numbers;

[0027] If the system selects appropriate parameters and control inputs, the system will surely converge to the sliding surface within a finite time, that is When reaching the stable state, it satisfies the conditions of q e4 = 1, q ev = 0, ω e = 0.

[0028] Further, in step (5), the Chebyshev inequality is used to estimate the uncertainty of the system, and the Chebyshev polynomial uses the angular velocity ω and the derivative of the angular velocity as input variables to estimate the uncertainty N1 of the system. The optimal weight matrix and the error boundary function are used to approximate the uncertainty of the system;

[0029]

[0030] Chebyshev polynomial is recursively approximated to the fourth order, and its specific form is:

[0031]

[0032] The optimal weight matrix is:

[0033]

[0034] Further, in step (5), an adaptive sliding mode controller is designed, and its specific form is:

[0035] u = u N + u A

[0036]

[0037] where u A (t) is an adaptive compensation controller, which is zero in the case of no fault, no saturation, no uncertainty, and no interference, and is non-zero in other cases; is the estimated value of ρ i , and its adaptive law is:

[0038]

[0039] where w i is the average value of sgn(S i ) obtained through a low-pass filter, α 1i > 0, l oi > 0, υ i > 0, i = 1, 2, 3, l oi = l i (t max ), is bounded above and below;

[0040]

[0041] where M = [M1, M2, M3] T = -B0ω × J0ω + E(ω), N = [N1, N2, N3] T= B0(E - (I3 - D)u),

[0042] The advantages of the present invention are as follows:

[0043] 1. By adopting the fast robust input shaper method, the vibration of flexible appendages is actively suppressed.

[0044] The present invention uses a fast robust input shaper to actively suppress the vibration of flexible appendages, solves the contradiction between the action time of the input shaper and the system robustness, and when using this method, the robustness is 0.5 when the system residual vibration ratio is 0.05. Compared with the ZV and ZVD shapers, the robustness of the system is greatly improved.

[0045] 2. By using the Chebyshev inequality to estimate the uncertainty of the system, the observation accuracy of the system is improved.

[0046] The present invention uses the Chebyshev inequality to estimate the uncertainty of the system. Compared with the traditional least squares method and Kalman filtering method for estimating the uncertainty of the system, the neural network estimates the uncertainty of the system with higher accuracy and does not require many parameters. Description of the Drawings

[0047] Figure 1 is the attitude control block diagram of the flexible spacecraft of the present invention;

[0048] Figure 2 is the sensitivity curve of the fast robust inputter of the present invention;

[0049] Figure 3 is the attitude convergence curve under the action of the system controller;

[0050] Figure 4 is the vibration curve of the flexible component without the input shaper in the system;

[0051] Figure 5 is the vibration curve of the flexible appendage with the input shaper in the system. Detailed Embodiment

[0052] To make the purpose, technical solution and effect of the present invention clearer and more definite, the following examples are listed to further elaborate on the present invention in detail. It should be noted that the specific implementation described here is only used to explain the present invention and is not used to limit the present invention.

[0053] As Figure 1 shown, the high-precision attitude control method block diagram of the flexible spacecraft of the present invention includes the following steps:

[0054] (1) Establish the dynamic model of a flexible spacecraft: Considering uncertain factors such as flexible vibration, uncertain moment of inertia, actuator faults and saturation, and external disturbances, establish the nonlinear kinematic model and dynamic model of the spacecraft, providing a basis for further realizing the attitude control theory of rigid-flexible coupled spacecraft.

[0055]

[0056] (2) According to the problem of the contradiction between the action time and robustness existing in the existing ZV shaper and ZVD shaper, design the FR shaper. The principle of the shaper is to consider that there is a certain delay in the action time. The specific form of the input shaper in the Laplace time domain is:

[0057]

[0058] Where: is the Laplace expression of the ZV input shaper;

[0059] is the Laplace expression of the ZV input shaper affected by interference;

[0060] ε > 0; A1 represents the pulse amplitude at the initial moment;

[0061] A2 represents the pulse amplitude at the moment of τ d moment.

[0062] Then the sequence of the FR input shaper is:

[0063]

[0064] Where, V tol The maximum allowable residual vibration ratio is 0.05.

[0065] (3) Design the terminal function sliding mode surface according to the attitude quaternion and angular velocity of the dynamic model of the flexible spacecraft, and realize the rapid convergence of the attitude quaternion and angular velocity after reaching the terminal sliding mode surface. The specific expression form of the function surface is:

[0066] S = ω e + K1q ev + K2S c

[0067] Where, S = [S1, S2, S3] T is the designed sliding mode surface, ω e is the attitude error angular velocity, q ev is the vector part of the attitude error quaternion, and the positive constants K1 > 0, K2 > 0.

[0068]

[0069] Among them, i = 1, 2, 3. The constants l1 and l2 are both positive. If the system selects appropriate parameters and control inputs, the system will surely converge to the sliding surface within a finite time, that is When reaching the stable state, it satisfies q e4 = 1, q ev = 0, ω e = 0 conditions.

[0070] (4) Use the Chebyshev inequality to estimate the uncertainty of the system. The Chebyshev polynomial takes the angular velocity ω and the derivative of the angular velocity as input quantities to estimate the uncertainty N1 of the system. Use the optimal weight matrix and the error boundary function to approximate the uncertainty of the system.

[0071]

[0072] The Chebyshev polynomial is recursively approximated to the 4th order, and its specific form is:

[0073]

[0074] The optimal weight matrix is:

[0075] (5) Design an adaptive sliding mode controller, and its specific form is:

[0076] u = u N + u A

[0077]

[0078] Among them, u A (t) is an adaptive compensation controller, which is zero in the case of no fault, no saturation, no uncertainty, and no interference, and is non-zero in other cases. is the estimated value of ρ i , and its adaptation law is:

[0079]

[0080] Among them, w i is the average value of sgn(S i ) obtained through a low-pass filter, α 1i > 0, l oi > 0, υ i > 0, i = 1, 2, 3, l oi = l i (tmax ) has upper and lower bounds;

[0081]

[0082] where M = [M1, M2, M3] T = -B0ω × J0ω + E(ω), N = [N1, N2, N3] T = B0(E - (I3 - D)u),

[0083]

[0084] (6) Verify the effectiveness of this method by performing simulation verification in MATLAB / Simulink. The specific simulation parameters are as follows:

[0085]

[0086] The sequence of the FR input shaper is:

[0087] The fault model of the actuator is:

[0088]

[0089] The frequencies of the first three vibration modes of the spacecraft are Ω1 = 0.768 rad / s, Ω2 = 1.1038 rad / s, Ω3 = 1.8733 rad / s, and the damping ratios are ξ1 = 0.0056, ξ2 = 0.0086, ξ3 = 0.0013 respectively. The external uncertain disturbance is given by a sine function, d = [0.1sin(t), 0.1cos(t), 0.1sin(t)] T N·m. The initial attitude quaternion and initial angular velocity of the spacecraft are q(0) = [0.8832 0.3 -0.2 -0.3] T , ω(0) = [0, 0, 0] T rad / s, and the desired attitude quaternion q d = [1 0 0 0] T , and the desired angular velocity ω d = [0 0 0] T rad / s. The parameters of the controller are set as σ1 = 100, σ2 = 0.1, τ = 0.1, λ = 0.6, γ = 0.35.

[0090] Figure 2 is the sensitivity curve of the FR input shaper. Assume that the natural frequency and damping of the system satisfy Ω nThe sensitivity curves of the ZV, ZVD, and FR shapers are plotted respectively when the natural frequency ωn = 20π and the damping ratio ξ = 0.1. It can be seen from the figure that when the ratio of residual vibration is less than 0.05, the ratio of the actual frequency to the natural frequency of the ZV shaper is 0.97 - 1.03, that is, the robustness range is 0.06; the frequency ratio of the ZVD input shaper is 0.855 - 1.145, that is, the robustness range is 0.29; while for the FR shaper, it is 0.94 - 1.44, that is, the robustness range is 0.5. Obviously, the FR shaper has a better robustness range and its action time is relatively shorter than that of the ZVD shaper.

[0091] Figures 3 to 5 are the system simulation results. Among them Figure 3 describes the convergence curve of the attitude quaternion. It can be Figure 3 seen that in the case of actuator failures, uncertain moments of inertia, and external disturbances, the spacecraft system can still converge quickly within a finite time under the action of the adaptive sliding mode controller, and the convergence accuracy reaches 5×10 -3 degrees or less. While achieving attitude stabilization, the vibration of the flexible appendages is also suppressed, and the suppression effect reaches 70%.

[0092] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, several improvements can be made without departing from the principle of the present invention, and these improvements should also be regarded as the protection scope of the present invention.

Claims

1. A high-precision attitude maneuver control method for flexible spacecraft, characterized in that, The described control method includes the following steps: (1) Establish the dynamic model of the flexible spacecraft: Considering flexible vibration, uncertain moment of inertia, actuator faults and saturation, and uncertain external disturbances, establish the nonlinear kinematic model and dynamic model of the spacecraft, providing a basis for further realizing the rigid-flexible coupling spacecraft attitude control theory; (2) Add pulse excitation to obtain angular velocity vibration data, and use the identification algorithm to give the first three modal frequencies and damping under the unconstrained conditions of the spacecraft. The flexible parameters of the spacecraft are identified from the telemetry data under the actual operating conditions of the spacecraft; (3) Based on step (2), obtain the modal frequency and damping ratio, and design the corresponding fast robust input shaper. The shaper is convolved with the desired reference input to obtain the actual control input acting on the controller; (4) Rewrite the dynamic model of the spacecraft, analyze the deterministic part and the uncertain part of the spacecraft respectively, and design their controllers. The nominal controller is implemented using a sliding mode controller, and the terminal function sliding mode surface is designed; (5) For the deterministic part of the dynamics, design an adaptive integral sliding mode controller based on the terminal function sliding mode surface. For the uncertain part, considering the actuator faults and saturation factors, design an interference observer based on the Chebyshev inequality, and then estimate the comprehensive uncertain part for compensation to ensure that the spacecraft can achieve high-precision attitude control within a finite time.

2. The high-precision attitude maneuver control method for a flexible spacecraft according to claim 1, characterized in that, In step (3) described above: In the input shaper design stage, design the FR shaper. The principle of the shaper is to consider that there is a certain delay in the action time. The specific form of the input shaper in the Laplace time domain is: Wherein: is the Laplace expression of the ZV input shaper; is the Laplace expression of the disturbed ZV input shaper; ε > 0; A1 represents the pulse amplitude at the initial moment; A2 represents the pulse amplitude at time τ d instant. Furthermore, the pulse sequence of the input shaper is obtained as: Among them V tol The maximum allowable residual vibration ratio is 0.

05.

3. A high-precision attitude maneuver control method for a flexible spacecraft according to claim 1, characterized in that In step (4) described above, the design of the terminal sliding mode surface is: Design the terminal function sliding mode surface according to the attitude quaternion and angular velocity of the dynamic model of the flexible spacecraft to achieve rapid convergence of the attitude quaternion and angular velocity after reaching the terminal sliding mode surface. The specific expression form of the function surface is: S = ω e + K1q ev + K2S c where \(S = [S_1, S_2, S_3]\) T is the designed sliding mode surface, \(\omega\) e is the angular velocity of attitude error, \(q\) ev is the vector part of the attitude error quaternion, and the positive constants \(K_1>0\), \(K_2>0\); wherein, i = 1, 2, 3; the constants l1 and l2 are both positive numbers; If the system selects appropriate parameters and control inputs, the system will surely converge to the sliding surface within a finite time, that is When reaching the steady state, it satisfies q e4 = 1, q ev = 0, ω e = 0 condition.

4. A high-precision attitude maneuver control method for a flexible spacecraft according to claim 1, characterized in that, In step (5) described above, the Chebyshev inequality is used to estimate the uncertainty of the system. The Chebyshev polynomial takes the angular velocity ω and the derivative of the angular velocity as input quantities to estimate the uncertainty N1 of the system. Use the optimal weight matrix and the error boundary function to approximate the uncertainty of the system; Chebyshev polynomial Recursively approximated to the fourth order, and its specific form is as follows: The optimal weight matrix is W: Where: σ1 and σ2 are the designed optimal parameters.

5. A high-precision attitude maneuver control method for a flexible spacecraft according to claim 4, characterized in that, In step (5), design the adaptive sliding mode controller, and its specific form is: u = u N + u A where, u N (t) is the nominal controller, and u A (t) is the adaptive compensation controller, which is zero in the case of no fault, no saturation, no uncertainty, and no disturbance, and is non-zero in other cases; is the estimated value of ρ i and its adaptation law is: where, w i is the average value of sgn(S i ) obtained after passing through a low-pass filter, α 1i > 0, l oi > 0, υ i > 0, i = 1, 2, 3, l oi = l i (t max ), is bounded above and below; where M = [M1, M2, M3] T = -B0ω × J0ω + E(ω), N = [N1, N2, N3] T = B0(E - (I3 - D)u),

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