An underactuated spacecraft attitude control method and system

Abstract

The application discloses a kind of underactuated spacecraft attitude control method and system, method includes: establishing underactuated spacecraft attitude control model;According to the averaging theorem and homogeneous system theory, the underactuated spacecraft attitude control model is simplified, and the simplified attitude control model is obtained;The derivative of the simplified attitude control model is obtained, and the high-order full-drive model is obtained;Based on the full-drive characteristics of the high-order full-drive model, the controller of the simplified attitude control model is obtained, and the linear constant closed-loop system is obtained in combination with the simplified attitude control model;According to the eigenvalue of the linear constant closed-loop system, the complete parameterized controller is obtained, and the stable linear constant closed-loop system is obtained.The underactuated spacecraft attitude control method and system disclosed by the application ultimately obtain linear closed-loop average system, and nonlinearity is not retained, so that the system performance is easier to analyze.

Description

Technical Field

[0001] This invention relates to the field of spacecraft attitude control technology, specifically to an underactuated spacecraft attitude control method and system. Background Technology

[0002] Spacecraft operating in the space environment face numerous uncertainties and disturbances, such as component failures and sensor malfunctions. If a spacecraft's controller, actuators, or sensors fail, effective and timely control methods are needed to maintain the required performance characteristics. When an actuator in one direction completely fails, and the number of degrees of freedom exceeds the control input dimension, the spacecraft enters an underactuated state. Fully actuated spacecraft attitude control methods become unsuitable, requiring a rethinking of control approaches to ensure system stability. Design limitations can also lead to underactuated states, particularly for microsatellites, where weight and size constraints limit the amount of control torque they can provide. Attitude control methods for underactuated spacecraft can improve system reliability and have significant practical application value.

[0003] Previous attitude control methods for underactuated spacecraft were designed using first-order state-space methods, which preserve the system's nonlinearity and are advantageous for state acquisition. However, these methods are not control-oriented models, making controller design difficult and resulting in complex control methods. Higher-order fully driven system methods, on the other hand, are control-oriented and facilitate controller design. By leveraging the characteristics of the model, the design is transformed into a higher-order model, resulting in a linear time-invariant closed-loop system with configurable characteristic structures, allowing for performance optimization.

[0004] In existing technologies, Panagiotis Tsiotras et al. published "Control of Spacecraft Subjectto Actuator Failures: State-of-the-Art and Open Problems," which used the averaging theorem to solve the attitude stabilization problem of underactuated spacecraft. However, the controller structure is too complex and may encounter singularities. Furthermore, most control methods use Euler angles, quaternions, etc., to describe the attitude of underactuated spacecraft, resulting in redundant parameters and potential singularities that limit the range of spacecraft attitude variations. Summary of the Invention

[0005] The technical problem to be solved by this invention is to address the issue that existing underactuated spacecraft attitude control methods retain nonlinearity, leading to difficulties in controller design and complex forms.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] An attitude control method for an underactuated spacecraft includes the following steps:

[0008] S100, Establish an attitude control model for an underactuated spacecraft;

[0009] S200, based on the averaging theorem and homogeneous system theory, the attitude control model of the underactuated spacecraft is simplified to obtain a simplified attitude control model.

[0010] S300, Differentiate the simplified attitude control model to obtain a higher-order all-wheel drive model;

[0011] S400, based on the all-drive characteristics of the high-order all-drive model, obtain the controller of the simplified attitude control model, and combine the simplified attitude control model to obtain a linear time-invariant closed-loop system.

[0012] S500: Based on the characteristic values ​​of the linear time-invariant closed-loop system, obtain a complete parameterized controller and a stable linear time-invariant closed-loop system.

[0013] Advantages: This method employs a high-order all-drive model, simplifying the design process. After averaging, the final closed-loop system is linear, preserving no nonlinearity. The underactuated spacecraft attitude control model is described using (w,z) parameters, simplified by homogeneous system theory. Compared to Euler angles, (w,z) parameters avoid singularities; compared to quaternions, they avoid parameter redundancy. The controller structure is simple. The high-order all-drive model is obtained using the averaging theorem and homogeneous system theory. Compared to current high-order all-drive system methods, this method avoids significant nonlinearity, simplifies the controller parameterization design process, provides degrees of freedom for further system performance optimization, and introduces auxiliary control variables to construct the controller, preventing the occurrence of higher-order derivatives.

[0014] In one embodiment of the present invention, obtaining a simplified attitude control model includes the following steps:

[0015] The attitude control model of the underactuated spacecraft is established using (w,z) parameters, and the angular velocities of the spacecraft on the X and Y axes are used as inputs to the attitude control model. The averaged attitude control model of the underactuated spacecraft is obtained using the averaging theorem. The attitude control model of the underactuated spacecraft is simplified by the homogeneous system theory and an expansion operator is introduced to obtain the simplified attitude control model.

[0016] In one embodiment of the present invention, the simplified attitude control model is obtained by the following formula:

[0017]

[0018]

[0019]

[0020]

[0021] In the formula, w1 and w2 represent the angle-related variables from the intermediate coordinate system to the body coordinate system during the second rotation under the (w,z) parameters. and They are respectively represented as and The first derivative, and Let w1 and w2 be the averaged variables, and z be the angle from the reference coordinate system to the intermediate coordinate system during the first rotation with parameters (w, z). Represented as The first derivative, Let z be the variable after z-average. Represented as ω z The averaged variable, ω z Expressed as the angular velocity of the spacecraft along the Z-axis in the body coordinate system. Represented as The first derivative of c3 represents the degree to which the spacecraft approaches axisymmetry, and v, v1, and v2 represent auxiliary control variables.

[0022] In one embodiment of the present invention, obtaining the linear time-invariant closed-loop system includes the following steps:

[0023] right Take the derivative again to obtain the higher-order all-drive model; based on the higher-order all-drive system method, obtain the controller of the simplified attitude control model; and substitute the controller of the simplified attitude control model into the simplified attitude control model to obtain the linear time-invariant closed-loop system.

[0024] In one embodiment of the present invention, the controller of the simplified attitude control model is obtained by the following formula:

[0025]

[0026] In the formula, k1, k2 and k3 represent controller parameters.

[0027] In one embodiment of the present invention, the linear time-invariant closed-loop system is obtained by the following formula:

[0028]

[0029] In the formula, A represents a matrix;

[0030] Then the eigenvalues ​​of matrix A are: Let the eigenvalues ​​of matrix A be s1, s2, s3, and s4, and s1 = s2, then:

[0031]

[0032]

[0033]

[0034] Based on the eigenvalues ​​of matrix A, the controller parameters k1, k2, and k3 are obtained. Then, the parameterized controller is input into the simplified attitude control model to obtain the stable linear time-invariant closed-loop system. Therefore, the final complete controller for the underactuated spacecraft attitude control system is:

[0035] ω x =v1+|v| 1 / 2 cos(t / e),ω y =v2+sgn(v)|v| 1 / 2 cos(t / e);

[0036] In the formula, ω x ,ω y Let ω represent the angular velocities on the X and Y axes of the spacecraft in the body coordinate system, e represent the design parameters, and the range is 0 < e < < 1. cos represents the cosine function, sgn represents the sign function, and the corresponding variables in v1, v2, v are replaced with the variables before averaging.

[0037] The present invention also provides a system for an underactuated spacecraft attitude control method, comprising:

[0038] The model building module is used to build an attitude control model for underactuated spacecraft.

[0039] The simplification module is used to simplify the attitude control model of the underactuated spacecraft according to the averaging theorem and the theory of homogeneous systems, so as to obtain a simplified attitude control model.

[0040] The high-order all-wheel drive model module is used to differentiate the simplified attitude control model to obtain the high-order all-wheel drive model.

[0041] A linear steady-loop closed-loop system module is used to obtain the controller of the simplified attitude control model based on the all-drive characteristics of the high-order all-drive model, and to obtain a linear steady-loop closed-loop system by combining the simplified attitude control model.

[0042] The stabilization module is used to obtain a complete parameterized controller and a stable linear time-invariant closed-loop system based on the characteristic values ​​of the linear time-invariant closed-loop system.

[0043] In one embodiment of the present invention, the simplified attitude control model is obtained by the following formula:

[0044]

[0045]

[0046]

[0047]

[0048] In the formula, w1 and w2 represent the angle-related variables from the intermediate coordinate system to the body coordinate system during the second rotation under the (w,z) parameters. and They are respectively represented as and The first derivative, and Let w1 and w2 be the averaged variables, and z be the angle from the reference coordinate system to the intermediate coordinate system during the first rotation with parameters (w, z). Represented as The first derivative, Let z be the variable after z-average. Represented as ω z The averaged variable, ω z Expressed as the angular velocity of the spacecraft along the Z-axis in the body coordinate system. Represented as The first derivative of c3 represents the degree to which the spacecraft approaches axisymmetry, and v, v1, and v2 represent auxiliary control variables.

[0049] In one embodiment of the present invention, the controller of the simplified attitude control model is obtained by the following formula:

[0050]

[0051] In the formula, k1, k2 and k3 represent controller parameters.

[0052] In one embodiment of the present invention, the linear time-invariant closed-loop system is obtained by the following formula:

[0053]

[0054] In the formula, A represents a matrix;

[0055] Then the eigenvalues ​​of matrix A are: Let the eigenvalues ​​of matrix A be s1, s2, s3, and s4, and s1 = s2, then:

[0056]

[0057] Based on the eigenvalues ​​of matrix A, the controller parameters k1, k2, and k3 are obtained. Then, the parameterized controller is input into the simplified attitude control model to obtain the stable linear time-invariant closed-loop system. Therefore, the final complete controller for the underactuated spacecraft attitude control system is:

[0058] ω x =v1+|v| 1 / 2 cos(t / e),ω y =v2+sgn(v)|v| 1 / 2 cos(t / e);

[0059] In the formula, ω x ,ω y Let ω represent the angular velocities on the X and Y axes of the spacecraft in the body coordinate system, e represent the design parameters, and the range is 0 < e < < 1. cos represents the cosine function, sgn represents the sign function, and the corresponding variables in v1, v2, v are replaced with the variables before averaging.

[0060] Compared with existing technologies, the advantages of this invention are: It is based on a high-order all-drive model, making control easier; the closed-loop system is a linear time-invariant system, using (w,z) parameters to describe the kinematic equations; combined with the averaging theorem, and utilizing the system's good homogeneity, the model is reasonably simplified through homogeneity theory; the designed controller is simple in form, avoiding singularities. This invention introduces auxiliary control quantities to increase the input dimension, thus constructing a high-order all-drive model and avoiding the occurrence of higher-order derivatives. Attached Figure Description

[0061] Figure 1 This is a flowchart of an underactuated spacecraft attitude control method according to an embodiment of the present invention.

[0062] Figure 2 This is a graph showing the attitude change of an underactuated spacecraft according to an embodiment of the present invention.

[0063] Figure 3 This is a graph showing the variation of angular velocity and control quantity of an underactuated spacecraft according to an embodiment of the present invention.

[0064] Figure 4 This is a block diagram of an underactuated spacecraft attitude control system according to an embodiment of the present invention. Detailed Implementation

[0065] To facilitate understanding of the technical solution of the present invention by those skilled in the art, the technical solution of the present invention will now be further described in conjunction with the accompanying drawings.

[0066] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0067] Please see Figure 1 As shown, the present invention provides an underactuated spacecraft attitude control method, comprising the following steps:

[0068] S100, establish an attitude control model for underactuated spacecraft.

[0069] S200, based on the averaging theorem and homogeneous system theory, the attitude control model of the underactuated spacecraft is simplified to obtain a simplified attitude control model.

[0070] S300, differentiate the simplified attitude control model to obtain the higher-order all-drive model.

[0071] S400, based on the all-drive characteristics of the high-order all-drive model, obtain the controller of the simplified attitude control model, and combine the simplified attitude control model to obtain a linear time-invariant closed-loop system.

[0072] S500: Based on the characteristic values ​​of the linear time-invariant closed-loop system, obtain a complete parameterized controller and a stable linear time-invariant closed-loop system.

[0073] Please see Figure 1 As shown, in one embodiment of the present invention, in step S100, the underactuated spacecraft attitude control model is established using (w,z) parameters:

[0074]

[0075] In the formula, w1 and w2 represent the angle-related variables of the second rotation from the intermediate coordinate system to the body coordinate system under the (w,z) parameters, and z represents the angle of the first rotation from the reference coordinate system to the intermediate coordinate system under the (w,z) parameters. and Let w1 and w2 be the first derivatives, respectively. Let ω be the first derivative of z. x ,ω y ,ω z This is expressed as the three-axis angular velocity of the spacecraft in the body coordinate system.

[0076] The (w,z) parameter, i.e., the w-z parameterization, has the fewest parameters. It only needs to avoid w1 and w2 tending to infinity to avoid singularity. In addition, it can achieve decoupling of underdriven axes. Moreover, this description method has good homogeneous properties, and the model can be reasonably simplified by using homogeneous system theory to reduce system complexity.

[0077] Please see Figure 1 As shown, in one embodiment of the present invention, before obtaining the simplified attitude control model in step S200, the characteristics of the underactuated spacecraft attitude control model are first analyzed.

[0078] The establishment of spacecraft dynamics models mainly relies on the theorem of angular momentum relative to the center of mass: when a system of particles is subjected to an external force, the rate of change of its total angular momentum with time is equal to the torque caused by the external force. Specifically, this is expressed as:

[0079]

[0080] In the formula, H represents the total angular momentum, u represents the torque caused by the external force, and t represents time. The total angular momentum H can be written as the following formula:

[0081] H = h x i+h y j+h z k;

[0082] In the formula, i, j, and k are unit vectors representing coordinates, and h x h y and h z It is expressed as the components of the total angular momentum H in each direction of the coordinate system.

[0083] Differentiating the total angular momentum H, it can be expressed as:

[0084]

[0085] In the formula, ω=[ω x ω y ω z ] T ∈R 3 R is expressed as the three-axis angular velocity of the spacecraft in its body coordinate system. 3 It is represented as a three-dimensional real number space.

[0086] Considering H = Jω, the spacecraft dynamics model can be expressed as:

[0087]

[0088] In the formula, Let J ∈ R be the first derivative of ω. 3×3Represented as the moment of inertia matrix, R 3×3 Represented as a 3×3 dimensional real space, ω × Represented as an antisymmetric matrix of angular velocity vectors; u = [u x u y u z ] T ∈R 3 , where u x u x and u z These represent the three-axis control torques of the spacecraft. An underactuated spacecraft lacks control torque in one direction; for simplicity, we'll take the lack of control torque in the Z-axis direction as an example. The spacecraft dynamics model can then be simplified to...

[0089]

[0090] In the formula, and Let τ be the first derivative of the three-axis angular velocities of the spacecraft in its body coordinate system. a and τ b c1 and c2 represent the simplified control torques of the spacecraft's X and Y axes, respectively, while c3 represents the degree to which the spacecraft is nearly axisymmetric. The closer c3 is to 0, the closer the spacecraft is to axisymmetric. When c3 is 0, the underactuated axis angular velocity is completely uncontrollable.

[0091] angular velocity ω x and ω y The derivative of ω is the control torque. x and ω y It is used as input to the attitude control model of the underactuated spacecraft.

[0092] Underactuated spacecraft are a special type of system that cannot achieve system stability through continuous smooth state feedback. A time variable t can be introduced, so the controller is no longer a state feedback mechanism. Therefore, the input can be expressed as:

[0093] ω x =v1+|v| 1 / 2 cos(t / e),ω y =v2+sgn(v)|v| 1 / 2 cos(t / e);

[0094] In the formula, v1, v2, v represent auxiliary control variables, and ω x and ω y The parameters include v1, v2, v, and e, which are selected within the range of 0 < e << 1. cos represents the cosine function, and sgn represents the sign function.

[0095] The set input is fed into the underactuated spacecraft attitude control model, and the averaged underactuated spacecraft attitude control model is obtained by using the averaging theorem.

[0096]

[0097] In the formula, and They are respectively represented as and The first derivative, and Let w1 and w2 be the averaged variables. Represented as The first derivative, Let z be the variable after z-average. This is expressed as the averaged angular velocity along the Z-axis of the spacecraft. Represented as The first derivative.

[0098] By rationally designing v1, v2, and v, the average underactuated spacecraft attitude control model becomes stable. By the averaging theorem, the corresponding underactuated spacecraft attitude control model also becomes stable. The average underactuated spacecraft attitude control model exhibits good homogeneity. Using homogeneous system theory, the average underactuated spacecraft attitude control model is simplified by introducing an expansion operator to obtain the simplified attitude control model. The introduced expansion operator is δ. λ :

[0099]

[0100] In the formula, λ represents a parameter in homogeneous system theory, used to calculate the degree of the homogeneous system. The average underactuated spacecraft attitude control model then has the following expression:

[0101]

[0102] in,

[0103] In the formula, f1~f4 and g1~g4 are merely concise expressions and have no other meaning. The above formula is then processed by adding an expansion operator:

[0104]

[0105] Then we have:

[0106]

[0107] In the formula, lim represents the limit. According to the theory of homogeneous systems, g1 to g4 can be neglected, thus obtaining the simplified attitude control system model:

[0108]

[0109]

[0110]

[0111]

[0112] According to the theory of homogeneous systems and the averaging theorem, we only need to design v1, v2, v reasonably to make the average underactuated spacecraft attitude control model stable. By the averaging theorem, the corresponding underactuated spacecraft attitude control system will also be stable, thus realizing the attitude control of the underactuated spacecraft.

[0113] Please see Figure 1 As shown, in one embodiment of the present invention, in steps S300 and S400, for Taking the first derivative, we obtain the higher-order all-drive model:

[0114]

[0115] in,

[0116] In the formula, Represented as The second derivatives Φ and B are merely simplified representations without further meaning. In this case, the dimension of the control input of the higher-order all-drive model is equal to the number of states, matrix B is a constant matrix, completely invertible, and meets the all-drive condition. Based on the higher-order all-drive system method, a simplified attitude control model controller is obtained:

[0117]

[0118] In the formula, k1, k2, and k3 represent controller parameters, all of which are greater than 0. Substituting the controller from the simplified attitude control model into the simplified attitude control system model yields the linear time-invariant closed-loop system:

[0119]

[0120] By appropriately designing the values ​​of k1, k2, and k3, the eigenvalues ​​of the linear time-invariant closed-loop system can be guaranteed to be negative, ensuring system stability. The characteristic structure of the linear time-invariant closed-loop system can be modified using k1, k2, and k3 to optimize its performance. The final controller is:

[0121] ω x =v1+|v| 1 / 2 cos(t / e),ω y =v2+sgn(v)|v|1 / 2 cos(t / e);

[0122] In this case, the corresponding variables in v1, v2, and v are replaced with the variables before averaging, that is:

[0123] v1 = -k1w1

[0124] v2 = -k1w2

[0125]

[0126] Please see Figure 1 As shown, in one embodiment of the present invention, in step S500, after the simplified attitude control system model is added to the controller, a linear time-invariant closed-loop system is finally obtained:

[0127]

[0128]

[0129] Then the eigenvalues ​​of matrix A are Let the eigenvalues ​​of matrix A be s1, s2, s3, and s4, and s1 = s2, then we have the following equation:

[0130]

[0131] Based on the eigenvalues ​​of matrix A, the controller parameters k1, k2, and k3 are obtained. Then, the parameterized controller is input into a simplified attitude control model to obtain the stable linear time-invariant closed-loop system, thus achieving underactuated spacecraft attitude control. By rationally designing the characteristic structure of the linear time-invariant closed-loop system, system performance can be optimized.

[0132] Please see Figures 1 to 3 As shown, in one embodiment of the present invention, by setting controller parameters, the eigenvalues ​​of the linear time-invariant closed-loop system can be changed. The performance of the linear time-invariant closed-loop system is only related to the eigenvalues, thus giving the linear time-invariant closed-loop system a desired characteristic structure and optimizing its performance. The effectiveness of this embodiment will be demonstrated below with a specific system model.

[0133] The relevant parameters of the verification system are as follows, and the characteristic values ​​of the variable linear time-invariant closed-loop system are:

[0134] s1=s2=-1, s3=-0.5+0.866j, s4=-0.5-0.866j;

[0135] In the formula, j is the imaginary unit. According to the parametric design process, k1, k2, k3 can be calculated: k1 = 2, k2 = k3 = 1. Taking c3 = 0.2 and e = 0.1, the initial values ​​of the linear time-invariant closed-loop system are set as: [w1(0) w2(0) z(0) ω z [(0)] = [0.8 - 0.6 0.6 - 0.5].

[0136] Figure 2 The graph shows the attitude change of an underactuated spacecraft. The controller can ensure that the attitude of the underactuated spacecraft converges rapidly to near the origin. Since a cosine function is introduced into the controller, the attitude stabilization process of the underactuated spacecraft is an oscillation with gradually decreasing amplitude. Figure 3 This is a graph showing the changes in angular velocity and control inputs of an underactuated spacecraft, where ω x ,ω y The controller, designed based on the high-order all-drive system method, can achieve relatively smooth convergence of angular velocity. The controller does not need to cancel out too much nonlinearity, the control quantity will not change over a large range, and it can converge in a short time.

[0137] Please see Figure 4 As shown, the present invention also provides a system for an underactuated spacecraft attitude control method, including an underactuated model establishment module 10, a simplification module 20, a high-order full-drive model module 30, a linear time-invariant closed-loop system module 40, and a stabilization module 50. The underactuated model establishment module 10 is used to establish an underactuated spacecraft attitude control model. The simplification module 20 is used to simplify the underactuated spacecraft attitude control model according to the averaging theorem and homogeneous system theory to obtain a simplified attitude control model. The high-order full-drive model module 30 is used to differentiate the simplified attitude control model to obtain a high-order full-drive model. The linear time-invariant closed-loop system module 40 is used to obtain the controller of the simplified attitude control model based on the full-drive characteristics of the high-order full-drive model, and to obtain a linear time-invariant closed-loop system in combination with the simplified attitude control model. The stabilization module 50 is used to obtain a complete parameterized controller based on the eigenvalues ​​of the linear time-invariant closed-loop system, and to obtain a stable linear time-invariant closed-loop system. In the simplification module 20, the simplified attitude control model is obtained through the following formula:

[0138]

[0139]

[0140]

[0141]

[0142] In the formula, w1 and w2 represent the angle-related variables from the intermediate coordinate system to the body coordinate system during the second rotation under the (w,z) parameters. and They are respectively represented as and The first derivative, and Let w1 and w2 be the averaged variables, and z be the angle from the reference coordinate system to the intermediate coordinate system during the first rotation with parameters (w, z). Represented as The first derivative, Let z be the variable after z-average. Represented as ω z The averaged variable, ω z Expressed as the angular velocity of the spacecraft along the Z-axis in the body coordinate system. Represented as The first derivative of c3 represents the degree to which the spacecraft approaches axisymmetry, and v, v1, and v2 represent auxiliary control variables.

[0143] The controller of the simplified attitude control model is obtained through the following formula:

[0144]

[0145] In the formula, k1, k2 and k3 represent controller parameters.

[0146] The linear time-invariant closed-loop system is obtained through the following formula:

[0147]

[0148] In the formula, A represents a matrix;

[0149] Then the eigenvalues ​​of matrix A are: Let the eigenvalues ​​of matrix A be s1, s2, s3, and s4, and s1 = s2. Then:

[0150]

[0151]

[0152]

[0153] Based on the eigenvalues ​​of matrix A, the controller parameters k1, k2, and k3 are obtained. Then, the parameterized controller is input into the simplified attitude control model to obtain the stable linear time-invariant closed-loop system. Therefore, the final complete controller for the underactuated spacecraft attitude control system is:

[0154] ω x=v1+|v| 1 / 2 cos(t / e),ω y =v2+sgn(v)|v| 1 / 2 cos(t / e);

[0155] In the formula, ω x ,ω y Let ω represent the angular velocities on the X and Y axes of the spacecraft in the body coordinate system, e represent the design parameters, and the range is 0 < e < < 1. cos represents the cosine function, sgn represents the sign function, and the corresponding variables in v1, v2, v are replaced with the variables before averaging.

[0156] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention, and no reference numerals in the claims should be construed as limiting the scope of the claims.

[0157] The above embodiments are merely examples of implementation methods of the invention. The scope of protection of the present invention is not limited to the above embodiments. For those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. An underactuated spacecraft attitude control method, characterized by, Includes the following steps: S100, Establish an attitude control model for an underactuated spacecraft; S200, based on the averaging theorem and homogeneous system theory, the attitude control model of the underactuated spacecraft is simplified to obtain a simplified attitude control model, including: use The parameters establish the attitude control model of the underactuated spacecraft, and the angular velocities of the spacecraft on the X and Y axes are used as the inputs of the attitude control model of the underactuated spacecraft; the averaging theorem is used to obtain the average attitude control model of the underactuated spacecraft; the attitude control model of the underactuated spacecraft is simplified by the homogeneous system theory, and an expansion operator is introduced to obtain the simplified attitude control model. The simplified attitude control model is obtained through the following formula: ； In the formula, and Represented as The angle-related variables of the second rotation from the intermediate coordinate system to the body coordinate system under the parameters. and They are respectively represented as and The first derivative, and Represented as and The averaged variable Represented as The angle of the first rotation from the reference coordinate system to the intermediate coordinate system under the given parameters. Represented as The first derivative, Represented as z The averaged variable Represented as The averaged variable Expressed as the angular velocity of the spacecraft along the Z-axis in the body coordinate system. Represented as The first derivative, This indicates the degree to which a spacecraft approaches axisymmetry. , and Represented as auxiliary control quantity; S300, Differentiate the simplified attitude control model to obtain a higher-order all-wheel drive model; S400, based on the all-wheel drive characteristics of the high-order all-wheel drive model, obtains the controller of the simplified attitude control model, and combines the simplified attitude control model to obtain a linear time-invariant closed-loop system, including: To Secondly, the second derivative is obtained to get the high-order full-drive model; the controller of the simplified attitude control model is obtained based on the high-order full-drive system method; and the controller of the simplified attitude control model is brought into the simplified attitude control model to obtain the linear constant closed-loop system. The controller of the simplified attitude control model is obtained through the following formula: ； wherein k 1, k 2 and k 3 are expressed as controller parameters; The linear time-invariant closed-loop system is obtained through the following formula: ； In the formula, A represents a matrix; Then the eigenvalues of the matrix A are: ; set the eigenvalues of the matrix A as , , and , and , then: ； According to the eigenvalues of the matrix A , the controller parameters k 1, k 2 and k 3 are obtained, and the parameterized controller is brought into the simplified attitude control model to obtain a stable linear constant closed-loop system; and finally, the complete controller of the underactuated spacecraft attitude control system is obtained. ； In the formula, Expressed as the angular velocities along the X and Y axes of the spacecraft in the body coordinate system. Represented as design parameters, selection range , Represented as a cosine function, Represented as a symbolic function, Replace the corresponding variables in the equation with the variables before averaging. Represented as time; S500: Based on the characteristic values ​​of the linear time-invariant closed-loop system, obtain a complete parameterized controller and a stable linear time-invariant closed-loop system.

2. A system for the attitude control of an underactuated spacecraft according to the method of claim 1, characterized by include: The model building module is used to build an attitude control model for underactuated spacecraft. The simplification module is used to simplify the attitude control model of the underactuated spacecraft according to the averaging theorem and the theory of homogeneous systems, so as to obtain a simplified attitude control model. The high-order all-wheel drive model module is used to differentiate the simplified attitude control model to obtain the high-order all-wheel drive model. A linear steady-loop closed-loop system module is used to obtain the controller of the simplified attitude control model based on the all-drive characteristics of the high-order all-drive model, and to obtain a linear steady-loop closed-loop system by combining the simplified attitude control model. The stabilization module is used to obtain a complete parameterized controller and a stable linear time-invariant closed-loop system based on the characteristic values ​​of the linear time-invariant closed-loop system.

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