Flexible spacecraft attitude adaptive dynamic surface control method

Abstract

The invention discloses a flexible spacecraft attitude adaptive dynamic surface control method. The method comprises the following steps: establishing a flexible spacecraft system attitude kinematics model and a dynamic model; a self-adaptive robust nonlinear attitude controller and a self-adaptive nonlinear active vibration suppression controller are designed, the robust attitude controller adopts a dynamic surface control technology, complex differential operation is avoided, unknown inertial parameters and a system disturbance upper bound are adaptively estimated by combining self-adaptive control and sliding-mode control, and the self-adaptive nonlinear active vibration suppression control is realized. System disturbance is controlled, and a vibration suppression controller performs self-adaptive processing on unknown parameters of a nonlinear suppression algorithm by utilizing self-adaptive control to realize active vibration control; and carrying out flexible spacecraft attitude adaptive dynamic surface control through the controller. The feasibility of the control scheme is proved through Lyapunov stability analysis, and the simulation result shows that the provided control method can complete high-quality attitude control and vibration suppression performance and has good adaptability.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft control, and particularly to a method for attitude adaptive dynamic surface control of a flexible spacecraft. Background Art

[0002] The attitude control system of a flexible spacecraft is an important guarantee for the spacecraft to complete different tasks. Modern space missions put forward higher requirements for the stability and accuracy of the spacecraft's attitude control system. Considering system model uncertainties, external disturbances, and vibration effects caused by flexible appendages, etc., the control problem of the spacecraft's nonlinear attitude system becomes more difficult and complex. Therefore, in order to meet the system control requirements, high-performance attitude control and vibration suppression of flexible spacecraft are difficult problems that need to be deeply studied.

[0003] In the past few decades, the control of attitude systems has attracted the attention of a large number of researchers. To solve the control problem of the spacecraft's attitude system, some control schemes have been proposed, such as observer-based methods, optimal control strategies, sliding mode control strategies, adaptive schemes, backstepping methods, fuzzy control, model predictive control, and other attitude system control methods. At the same time, the vibration of the flexible appendages attached to the spacecraft will affect the control of the attitude system. For the vibration problem of the flexible appendages of the spacecraft, various vibration suppression schemes have been used to solve the vibration control of the flexible appendages.

[0004] For the control design problem of nonlinear systems, the backstepping method is a very effective systematic control design method. As a recursive design scheme, it has systematicness for the control design of systems with a cascaded form, and ensures that the system has a certain performance through the design of virtual control laws. However, for the mathematical model of the nonlinear attitude motion of a spacecraft represented by modified Rodrigues parameters, due to the complexity of the coefficient matrix of the system equation, if the backstepping method is applied, differential calculations need to be performed on the coefficient matrix in the model, which will bring the "differential explosion" problem of the attitude control algorithm, making the control algorithm very complex. Fortunately, the dynamic surface control strategy can solve the problems caused by the backstepping control scheme. The dynamic surface control is a systematic method similar to the backstepping method. The difference is that in order to avoid the differential expansion problem, a low-pass filter is introduced into the system, avoiding the direct derivation of the virtual control quantity. Compared with the backstepping method, since the convergence of the filtering error needs to be processed, the system stability analysis is an important issue in dynamic surface control technology. At the same time, in actual situations, the inertial parameters and disturbance upper bounds of the attitude control system are not always accurately known, and some control methods are difficult to apply, bringing difficulties to the control design of the system. If the control design is simplified, the system performance will be reduced. In summary, for the strongly coupled nonlinear complex flexible spacecraft attitude system, it is of great significance to study more adaptable attitude control strategies and active vibration suppression methods under unknown disturbances and system parameters. Summary of the Invention

[0005] The object of the present invention is to provide a flexible spacecraft attitude adaptive dynamic surface control method, which actively suppresses the vibration of the flexible appendages of the spacecraft and can achieve high-performance attitude control under the condition that the inertial parameters and disturbance upper bounds of the system are unknown.

[0006] The technical solution to achieve the object of the present invention is as follows:

[0007] A flexible spacecraft attitude adaptive dynamic surface control method, comprising:

[0008] Establish the attitude kinematic model and dynamic model of the flexible spacecraft system;

[0009] Based on the kinematic model and dynamic model, assuming that the vibration of the coupled flexible appendages and the change in the vibration velocity are bounded, and the unknown external disturbance torque is a finite value, an adaptive robust nonlinear attitude controller is designed by integrating adaptive control, dynamic surface control and sliding mode control. Using the adaptive control technology, the unknown parameters of the nonlinear vibration suppression algorithm are adaptively processed to design a vibration suppression controller;

[0010] Perform flexible spacecraft attitude adaptive dynamic surface control through the adaptive robust nonlinear attitude controller and the vibration suppression controller.

[0011] Further, the attitude kinematic model is:

[0012]

[0013] where the vector p = [p 1 p 2 p 3 T represents the modified Rodrigues parameters of the spacecraft attitude relative to the inertial coordinate system, p× represents the × operation acting on the vector p to form a skew-symmetric matrix, the vector ω = [ω x ω y ω z T represents the angular velocity of the spacecraft in the body coordinate system, I represents the identity matrix, is the function corresponding to the simplified transformation.

[0014] Further, the vector p is:

[0015] p = n tan(ψ / 4)

[0016] where n represents the Euler principal axis vector and ψ represents the Euler angle.

[0017] Further, the dynamic model is: ​​

[0018]

[0019] Among them, the diagonal matrix J = diag[J x J y J z represents the moments of inertia of the spacecraft about the x, y, and z axes, the matrix δ ∈ R 4 ×3 is the parameter for coupling the rigid model and the flexible model of the spacecraft, the modal vector η ∈ R 4 is the displacement coordinate of the flexible appendage, the vector u = [T x T y T z T represents the control torque, which can be generated by the attitude control execution part, the vector d(t) = [d 1 d 2 d 3 T represents the external disturbance, u p is the control voltage of the piezoelectric part, the vector δ 1 ∈ R 4 is the coupling parameter between the flexible dynamic part and the piezoelectric actuator part of the spacecraft; the matrix represents the damping parameter, the matrix represents the stiffness parameter, where χ is the number of flexible modes considered, ω ni is the natural frequency, and the parameter represents the corresponding system damping;

[0020] Integrating the dynamic model gives:

[0021]

[0022] In the formula, represents the disturbance of the integrated hybrid system.

[0023] Further, designing an adaptive robust nonlinear attitude controller specifically includes:

[0024] Designing an attitude tracking system equation based on the attitude kinematic model and the dynamic model;

[0025] Designing an adaptive robust nonlinear attitude controller based on the attitude tracking system equation.

[0026] Further, the attitude tracking system equation is:

[0027]

[0028] Among them, the vector z 1 = p - x d , ​​When the attitude kinematic model is transformed The corresponding function, vector x d = p d = [p 1d p 2d p 3d T represents the desired attitude, vector x 2 = [ω x ω y ω z T , z 2 = x 2 -α, α = [α 1 α 2 α 3 T represents the virtual control quantity, y 2 is the filtering error of the filter, θ = [J x J y J z T , L is a linear operator, The diagonal matrix τ = diag[τ 1 τ 2 τ 3 is the filter time constant, τ i is the filter time constant component, where i = 1, 2, 3, F(t) represents the hybrid system disturbance, J = diag[J x J y J z represents the moment of inertia of the spacecraft about the x, y, and z axes.

[0029] Furthermore, the adaptive robust nonlinear attitude controller is:

[0030]

[0031] where P 2 is a diagonal positive definite matrix, sgn(·) represents the sign function, M, N are diagonal positive definite matrices, represents the estimator of the inertia parameter θ, represents the upper bound of the total hybrid system disturbance F(t), is the upper bound of the adaptive estimated value.

[0032] Furthermore, the vibration suppression controller is:

[0033]

[0034] ​​​​where h is the positive gain of the controller, is the bounded control parameter, represents the upper bound of h, represents the estimated value of, q is a positive constant, and ε is a small positive number.

[0035] Furthermore, h satisfies:

[0036] Furthermore, ε = 0.0005.

[0037] Compared with the prior art, in order to solve the problems of flexible spacecraft attitude tracking control and coupled flexible appendage vibration suppression under the conditions of unknown inertial parameters and system disturbance upper bounds, a nonlinear adaptive dynamic surface sliding mode attitude control algorithm and an adaptive nonlinear vibration suppression control method are respectively proposed. Their significant advantages are as follows:

[0038] 1) The attitude tracking control scheme adopts a method that combines adaptive control, dynamic surface control technology and sliding mode control, avoiding the differential problem of complex matrices in the system. Using the adaptive control method, the unknown system inertial parameters and the upper bound of the hybrid system disturbance are adaptively estimated respectively to achieve robust adaptive attitude control of the system;

[0039] 2) The vibration suppression method has the characteristics of adaptive nonlinear control, and can adaptively suppress the vibration of the coupled flexible appendage during the attitude tracking control process to achieve active vibration control;

[0040] 3) The simulation results show that under the conditions of unknown upper bounds of system disturbances and inertial parameters, the adaptive attitude control method can complete the attitude tracking process within 30 s, the maximum attitude control torque is less than 8 Nm, the maximum vibration suppression control input is less than 0.3 V. After 30 s, the amplitude of the modal displacement change caused by the attitude movement decays rapidly; the proposed control strategy can achieve high-quality flexible spacecraft attitude tracking control effects and good active vibration suppression performance;

[0041] 4) The designed adaptive robust control scheme is applicable to the control design of complex systems with strong coupling and nonlinearity. Under the conditions of less system parameter information and unknown external disturbances, it provides an effective solution for the active vibration suppression and attitude system control of spacecraft with coupled flexible appendages, and has a wide range of applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is the simulation diagram of attitude angle tracking control.

[0043] Figure 2 is the simulation diagram of attitude angular velocity.

[0044] Figure 3 is the simulation diagram of system control input.

[0045] Figure 4 It is the control simulation diagram of modal displacement. Specific implementation mode

[0046] This embodiment provides a method for attitude adaptive dynamic surface control of a flexible spacecraft, which specifically includes:

[0047] (1) Mathematical model of the attitude system of a flexible spacecraft

[0048] 1. Kinematic model of the attitude system

[0049] The attitude kinematic model of a flexible spacecraft represented by the modified Rodrigues parameters can be described as

[0050]

[0051] Among them, the vector p = [p 1 p 2 p 3 T represents the modified Rodrigues parameters of the spacecraft attitude relative to the inertial coordinate system, and its form is expressed by Equation (2)

[0052] p = ntan(ψ / 4) (2)

[0053] Among them, n represents the Euler principal axis vector. According to the principal axis rotation theorem, ψ represents the Euler angle, and the symbol p× represents the × operation acting on the vector p to form a skew-symmetric matrix, as shown below

[0054]

[0055] The vector ω = [ω x ω y ω z T represents the angular velocity of the spacecraft in the body coordinate system.

[0056] 2. Dynamic model of the flexible spacecraft system

[0057] Considering the coupled flexible appendages, the spacecraft attitude dynamics description can be expressed as the following equation

[0058]

[0059] Among them, the diagonal matrix J = diag[J x J y J z represents the moment of inertia of the spacecraft, the matrix δ ∈ R 4×3 is the parameter for coupling the rigid model and the flexible model of the spacecraft, and the modal vector η ∈ R4 are the displacement coordinates of the flexible appendage, and the vector u = [T x T y T z T represents the control moment, which can be generated by the attitude control execution part. The vector d(t) = [d 1 d 2 d 3 T represents the external disturbance, u p is the control voltage of the piezoelectric part, and the vector δ 1 ∈R 4 is the coupling parameter between the flexible dynamic part and the piezoelectric actuator part of the spacecraft. In addition, the matrix represents the damping parameter, and the matrix represents the stiffness parameter, where x is the number of flexible modes considered, ω ni is the natural frequency, and the parameter represents the corresponding system damping.

[0060] For the convenience of designing the control algorithm, the attitude dynamics description of the flexible spacecraft is integrated to obtain the following representation

[0061]

[0062] where represents the total hybrid system disturbance after integration.

[0063] (2) Control Scheme Design

[0064] For the above model, in the design of the control scheme, the following reasonable assumptions are required:

[0065] 1) The vibration of the coupled flexible appendage and the change in the vibration velocity are bounded. In other words, under the application of the control signal u p , ||η|| and are bounded quantities during the entire attitude tracking control process;

[0066] 2) The unknown external disturbance torque d(t) is a finite value.

[0067] According to the above assumptions 1) and 2), there exist bounded constant variables D i , i = 1, 2, 3, such that the total hybrid system disturbance after integration satisfies

[0068] f i ≤D i (6)

[0069] 1. Design of Adaptive Robust Nonlinear Attitude Controller

[0070] ​​Based on the systematic dynamic surface control strategy, assuming that the system inertia matrix J and the upper bound of the hybrid system disturbance are both unknown, an adaptive robust dynamic surface sliding mode nonlinear attitude control algorithm is designed. Define the vector x d = p d = [p 1d p 2d p 3d T which represents the desired attitude, and the vector Let the vector z 1 = p - x d , and the vector x 2 = [ω x ω y ω z T . Through transformation, the attitude kinematic equation (1) of the flexible spacecraft can be described as the following equation

[0071]

[0072] The attitude tracking equation of the flexible spacecraft system can be expressed as

[0073]

[0074] A system Lyapunov function is selected as

[0075]

[0076] Taking the derivative of equation (9) gives

[0077]

[0078] Define

[0079] z 2 = x 2 - α. In equation (11), α represents the virtual control quantity.

[0080] Equation (11) is substituted into equation (10) to obtain

[0081]

[0082] If the backstepping control technique is used, α is selected in the following form

[0083]

[0084] where P 1 is a diagonal positive definite matrix. However, for the backstepping control scheme, calculating will cause the "differential explosion" problem.

[0085] ​​Therefore, to solve the problems caused by the backstepping method using the dynamic surface control method, define

[0086]

[0087] To avoid the "differential explosion" problem caused by the backstepping method, use a first-order filter to process That is

[0088]

[0089] where the diagonal matrix τ = diag[τ 1 τ 2 τ 3 is the filter time constant, τ i is the filter time constant component, where i = 1, 2, 3. Through transformation, we can get Define y 2 as the filtering error of the filter,

[0090] Then the attitude tracking system equation (8) can be expressed as

[0091]

[0092] In the design of the control algorithm, combined with the adaptive control method, an adaptive method is used to estimate the inertia parameters of the flexible spacecraft system. To estimate these inertia parameters J x 、J y 、J z , design a linear operator L: R 3 →R 3 ×R 3 , the vector b = [b 1 b 2 b 3 T Using the operator, we can get

[0093]

[0094] Let θ = [J x J y J z T , and we can get Jb = L(b)θ. Therefore, we get

[0095]

[0096] where

[0097] The system attitude tracking equation (16) can be expressed in the following form

[0098] ​​

[0099] Let represent the estimator of the inertia parameter θ, and use to denote the estimation error of the inertia parameter. Use to represent the upper bound of the total hybrid system disturbance F(t), and define as the upper bound of the adaptive estimated value, and define as the adaptive estimation error. Construct a Lyapunov function for the system in Equation (19) as follows

[0100]

[0101] where M and N are positive definite diagonal matrices.

[0102] Take the derivative of the function V and obtain it considering the attitude system in Equation (19)

[0103]

[0104] To apply the sliding mode control strategy, the form of the sliding surface is constructed as z 2 , and design the adaptive robust nonlinear attitude control algorithm as follows

[0105]

[0106] where P 2 is a positive definite diagonal matrix, and sgn(·) represents the sign function. The vector z 2 = [z 21 z 22 z 23 T ,

[0107]

[0108] Substitute Equation (22) into Equation (21) to obtain

[0109]

[0110] The maximum value of all elements in the set {τ 1 τ 2 τ 3} is denoted by the symbol τ max . At the same time, noting that the relationship holds, thus it can be obtained

[0111]

[0112] Considering the variable it can be obtained ​

[0113]

[0114] Considering that Obtain

[0115]

[0116] Considering Equation (22), it is possible to obtain

[0117]

[0118] Since

[0119]

[0120] Therefore, it can be obtained

[0121]

[0122] Deriving Equation (30), it can be obtained

[0123]

[0124] When the relational expression holds, the following proves through calculation and analysis that the variable is bounded.

[0125] Rearranging Equation (14), it can be obtained

[0126]

[0127] Differentiating the relational expression (32), it can be obtained

[0128]

[0129] Since The relational expression (33) shows that the variable is a function of the state parameters z 1 , x d , v d , z 2 , y 2 , Therefore, when the parameters z 1 , x d , v d , z 2 , y 2 , are bounded variables, the variable is bounded. Therefore,[[]] is bounded.

[0130] Let β represent the upper bound of . Therefore, according to Equation (31), it can be obtained

[0131]

[0132] According to Young's inequality, it is possible to obtain

[0133]

[0134] Considering Equation (35), Equation (34) can be used to obtain

[0135]

[0136] Let k 1 and k 2 represent the minimum values of the elements on the diagonals of the coefficient matrices P 1 and P 2 respectively. Therefore, we get

[0137]

[0138] Select parameters such that

[0139]

[0140] Therefore, it can be obtained that

[0141]

[0142] Select So, we get

[0143]

[0144] From the above Lyapunov stability analysis, it can be seen that the adaptive robust nonlinear control algorithm designed in this part can achieve the stability of the attitude tracking control of the flexible spacecraft system. Therefore, all the states of the closed-loop control are semi-globally uniformly bounded with respect to the system set Θ = {z 1 , z 2 , y 2}. By appropriately adjusting the values of the parameters k 1 , k 2 , τ max , M, and N in the designed control algorithm, the set Θ = {z 1 , z 2 , y 2} can be made to become smaller moderately, that is to say, the tracking error of the attitude control can be reduced. Since the tracking error z 1 of the attitude can be reduced moderately, if the desired velocity v d is bounded, the attitude angular velocity vector x 2 can be controlled to approach a bounded vector

[0145] 2. Design of Vibration Suppression Controller

[0146] For a flexible spacecraft with a piezoelectric actuator, an adaptive nonlinear active vibration control algorithm for modal motion is designed in this section to achieve active vibration suppression of flexible appendages.

[0147] In the scheme, the process of attitude tracking control is such that when t → ∞, p → x d , ω → 0, and at the same time This control will result in bounded elastic modal vibrations. For Equation (4), the dynamic equation of the elastic motion coupled with the angular velocity is

[0148]

[0149] For the dynamic Equation (41), considering Assumption 1) and Assumption 2), the of the system is bounded. Assume that there exists a bounded control parameter h such that

[0150]

[0151] where h is the positive gain of the controller, |·| represents the absolute value, and I is the identity matrix.

[0152] Let represent the upper bound of h, and let represent the estimated value of . Define the estimation error To suppress the elastic modal vibrations, an adaptive nonlinear active vibration control algorithm of the following form is designed

[0153]

[0154] where q is a positive constant.

[0155] For the dynamic Equation (41) of the elastic motion, the Lyapunov - like function of the system is designed as

[0156]

[0157] Differentiate the Lyapunov function V f According to the dynamic Equation (41), the derivative can be obtained as

[0158]

[0159] Substitute the control algorithm Equation (43) into the expression (45), and we can get

[0160]

[0161] Considering the absolute value of the number and It can be obtained that

[0162]

[0163] Considering that It is obtained that

[0164]

[0165] Considering Equation (42), it can be obtained that

[0166]

[0167] Through the above stability analysis, the designed adaptive nonlinear active vibration suppression control algorithm can ensure the stability of the modal motion. Therefore, during the attitude tracking control process, under the action of the vibration suppression controller, when t→∞, the stability of the flexible appendage motion can reduce the influence on the attitude control. Under the combined control of the attitude tracking control scheme and the vibration suppression controller, the stability of the entire system can be achieved.

[0168] (III) Simulation verification

[0169] To demonstrate the effectiveness of the proposed control scheme, simulation analysis and verification are carried out.

[0170] 1. System parameters

[0171] The parameters of the flexible spacecraft system are selected as the following form, and the parameter coupling matrix is selected as

[0172]

[0173] The four natural frequencies of the flexible appendage modes are taken as ω n1 = 0.7681 rad / s, ω n2 = 1.1038 rad / s, ω n3 = 1.8733 rad / s, ω n4 = 2.5496 rad / s, and the system damping parameter is selected as Considering external disturbances, it is assumed to be

[0174] d(t) = [0.29cos(0.1t) + 0.09 0.14sin(0.1t) + 0.29cos(0.1t) 0.29sin(0.1t) + 0.09] T Nm(50)

[0175] The initial attitude of the modified Rodrigues parameters of the flexible spacecraft is selected as p(0) = [0 0 0] TAssume that the spacecraft completes the transition from an initial static motion to another desired static attitude, and set the terminal spacecraft attitude to p f = [-0.22425 0.67278 -0.44852] T Assume that the inertia parameters of the spacecraft are J x = 350 kgm 2 , J y = 280 kgm 2 , J z = 190 kgm 2 The initial angular velocity value of the attitude is taken as ω x (0) = 0° / s, ω y (0) = 0° / s, ω z (0) = 0° / s. The initial flexible modes and the derivative values of the modes are taken as For the adaptive robust nonlinear sliding mode control algorithm, the initial estimated value of the spacecraft inertia parameters is taken as In the simulation, the filtering time constant is set to τ i = 0.01 s, i = 1, 2, 3. To deal with the chattering phenomenon of the nonlinear control in the proposed scheme, the sign function sgn(s) in the designed control strategy is replaced by the following saturation function

[0176]

[0177] In the function, Δ represents the "boundary layer". For the adaptive robust nonlinear sliding mode control algorithm, Δ = 0.02 is selected, and for the vibration suppression controller, Δ = 1.5 is selected. In the simulation analysis, in order to make the attitude system have better tracking performance, the adjustable parameters of the nonlinear control algorithm and the adaptive control gain are selected to be appropriate sizes. Among them, the control parameter matrix P 1 = diag[140 142 140], the matrix P 2 = diag[162 163 162], the adaptive estimation control parameter matrix of the inertia parameter θ is set as M = diag[205 310 290], and the upper bound of F(t) The adaptive estimation control parameter matrix is selected as N = diag[200 300 300], and the parameter q = 5000 in the active vibration control algorithm.

[0178] Because the absolute value |z 2 | of the components of z 2i | (i = 1, 2, 3) will not accurately become 0, in order to avoid the continuous growth of the adaptive control parameters, the following dead zone control method is adopted in the control algorithm

[0179]

[0180] In the formula, is a vector The i-th component in the elements, N i is the i-th component in the diagonal elements of matrix N, N = diag[N 1 N 2 N 3 , μ i is a relatively small positive number, i = 1, 2, 3, select μ 1 = 0.006, μ 2 = 0.05, μ 3 = 0.05. Since is very difficult to be exactly 0, the adaptive control method in the active vibration control algorithm for modal motion utilizes the following dead zone control technology

[0181]

[0182] In the formula, ε is a small positive number, select ε = 0.0005.

[0183] 2. Simulation analysis

[0184] In order to verify the feasibility and adaptability of the proposed control strategy, the designed adaptive control scheme is compared and verified through simulation with the attitude control algorithm and vibration suppression control method designed under the condition that the parameters are known.

[0185] Under the same conditions, the compared attitude control algorithm with known parameters is designed as

[0186]

[0187] Among them, P 2 is a positive definite diagonal matrix, the parameter matrix λ = diag[λ 1 λ 2 λ 3 , the component element λ 1 ≥ D 1 , λ 2 ≥ D 2 , λ 3 ≥ D 3 .

[0188] Adopt modal velocity feedback (MVF) control as the vibration suppression control method for comparison, and the system measurement equation is assumed to be

[0189]

[0190] In order to suppress elastic modal vibration, design the compared feedback control method

[0191] u p = F p y(56) where F p is a positive bounded constant.

[0192] For the control algorithm designed under the condition of known parameters, the parameters are selected as λ = diag[1513 1514 1513], P 1 = diag[15 12 14], P 2 = diag[12 13 15] and F p = 280.

[0193] This part uses the joint simulation of the adaptive robust spacecraft attitude tracking nonlinear control algorithm and the adaptive nonlinear active vibration control algorithm of modal motion, and compares it with the control algorithm with known parameters. It can be seen from Figures 1-4 that the designed adaptive control method can achieve a control effect similar to that of the control algorithm under the condition of known parameters. Figure 1 Shows the tracking control effect of the adaptive robust attitude nonlinear control algorithm on attitude parameters. It can be seen from the figure that the attitude tracking control has a good transient response, and the attitude tracking process is completed in less than 30 s. The designed algorithm enables the actual attitude parameters to track the desired command attitude parameters more ideally, and there is no obvious overshoot of attitude parameter control throughout the attitude control process. After the dynamic process, the flexible spacecraft maintains the required attitude parameters, reflecting high-quality attitude tracking control. The angular velocity change curve is as Figure 2 shown. Since the sign function in the control algorithm is replaced by a saturation function, there is no angular velocity chattering phenomenon in the transient process. It can be found that the attitude angular velocity tends to 0 according to the control requirements after the transient process. Figure 3 Displays the control input of the system. It can be seen from the figure that the required attitude control input values are not large throughout the attitude tracking control process. Among them, the attitude control torque T y is the largest, less than 8 Nm, and the maximum vibration suppression control input is less than 0.3 V. As time t → ∞, the active vibration suppression algorithm control input u p also becomes a smaller quantity, indicating that the designed control method requires less control energy during the attitude tracking process, and the energy consumption performance of the attitude control system is excellent. The change of modal displacement is as Figure 4As shown, the designed vibration suppression control algorithm realizes the system stability of the flexible appendage motion, and the vibration of the flexible appendage of the spacecraft is actively suppressed. After 30 s, the amplitude of the modal displacement change caused by the attitude motion rapidly decays, indicating that the control method has good active vibration suppression ability. Through the simulation comparison results, it is concluded that the designed adaptive robust nonlinear attitude control strategy and vibration controller can better adapt to the flexible spacecraft system in the presence of unknown system disturbances and inertial parameters, providing an ideal active vibration suppression and attitude tracking control effect for the coupled flexible appendages.

[0194] The above are only the preferred embodiments of the present invention, and do not limit the patent scope of the present invention. Any equivalent desired attitude design made by using the specification and drawings of the present invention under the inventive concept of the present invention, or direct / indirect application in other related technical fields, is included in the patent protection scope of the present invention.

Claims

1. A method for controlling a flexible spacecraft attitude adaptive dynamic surface, characterized in that: include: Establish the attitude kinematics model and dynamics model of the flexible spacecraft system; Based on the kinematic model and the dynamic model, assuming that the vibration of the coupled flexible attachment and the speed variation of the vibration are bounded, and the unknown external disturbance torque is a finite value, an adaptive robust nonlinear attitude controller is designed by integrating adaptive control, dynamic surface control and sliding mode control. Adaptive control technology is used to adaptively process the unknown parameters of the nonlinear vibration suppression algorithm and design a vibration suppression controller. Adaptive dynamic surface control of flexible spacecraft attitude via adaptive robust nonlinear attitude controller and vibration suppression controller.

2. The flexible spacecraft attitude adaptive dynamic surface control method according to claim 1, characterized in that: The posture kinematics model is: Where, vector p = [p1 p2 p3] T represents the modified Rodrigues parameter of the spacecraft attitude relative to the inertial coordinate system, p× represents the × operation acting on the vector p to form a skew-symmetric matrix, and the vector ω=[ω x ω y ω z ] T represents the angular velocity of the spacecraft in the body coordinate system, I represents the unit matrix, To simplify the function corresponding to the transformation.

3. The method for controlling the attitude adaptive dynamic surface of a flexible spacecraft according to claim 2, characterized in that: The vector p is: p=ntan(ψ / 4) Where n represents the Euler principal axis vector and ψ represents the Euler rotation angle.

4. The flexible spacecraft attitude adaptive dynamic surface control method according to claim 1, characterized in that: The kinetic model is: Among them, the diagonal matrix J = diag[J x J y J z ] represents the moment of inertia of the spacecraft on the x, y and z axes, and the matrix δ∈R 4×3 is the parameter of the coupling between the rigid model and the flexible model of the spacecraft, the modal vector η∈R 4 is the displacement coordinate of the flexible attachment, vector u=[T x T y T z ] T Represents the control torque, which can be generated by the attitude control execution part, vector d(t) = [d1 d2 d3] T represents external interference, u p is the control voltage of the piezoelectric part, vector δ1∈R 4 is the coupling parameter of the flexible dynamic part and the piezoelectric actuator part of the spacecraft; the matrix represents the damping parameter, the matrix represents the stiffness parameter, where χ is the number of flexural modes considered, ω ni is the natural frequency, parameter represents the corresponding system damping; The kinetic model is integrated to obtain: In the formula, represents the integrated mixed system disturbance.

5. The method for controlling the attitude adaptive dynamic surface of a flexible spacecraft according to claim 1, characterized in that: Designing an adaptive robust nonlinear attitude controller specifically involves: Design the posture tracking system equations based on the posture kinematics model and dynamics model; Based on the attitude tracking system equation, an adaptive robust nonlinear attitude controller is designed.

6. The method for controlling the attitude adaptive dynamic surface of a flexible spacecraft according to claim 5, characterized in that: The posture tracking system equation is: Among them, vector z1 = px d , When the posture kinematics model is transformed The corresponding function, vector x d =p d =[p 1d p 2d p 3d ] T Represents the desired posture, vector x2=[ω x ω y ω z ] T , z2=x2-α, α=[α1 α2 α3] T represents the virtual control quantity, y2 is the filtering error of the filter, θ=[J x J y J z ] T , L is a linear operator, The diagonal matrix τ = diag[τ1 τ2 τ3] is the filter time constant, τ i is the filter time constant component, where i = 1, 2, 3, F(t) represents the mixed system disturbance, J = diag[J x J y J z ] represents the spacecraft's moment of inertia about the x, y, and z axes.

7. The method for controlling the attitude adaptive dynamic surface of a flexible spacecraft according to claim 6, characterized in that: The adaptive robust nonlinear attitude controller is: Where P2 is a diagonal positive definite matrix, sgn(·) represents the sign function, M and N are diagonal positive definite matrices, represents the estimate of the inertia parameter θ, represents the upper bound of the total hybrid system disturbance F(t), Upper bound Adaptive estimate of .

8. The method for controlling the attitude adaptive dynamic surface of a flexible spacecraft according to claim 4, characterized in that: The vibration suppression controller is: Where h is the positive gain of the controller and is a bounded control parameter. represents the upper bound of h, express An estimate of , q is a positive constant, and ε is a positive number.

9. The method for controlling the attitude adaptive dynamic surface of a flexible spacecraft according to claim 8, characterized in that: h satisfies:

10. The method for controlling the attitude adaptive dynamic surface of a flexible spacecraft according to claim 8, characterized in that: ε=0.0005.

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