Modularized hierarchical attitude control method for space solar power station

Abstract

The invention relates to a modular hierarchical attitude control method for a space solar power station, and the method comprises the following steps: S1, carrying out the kinematics description of the space solar power station according to the characteristics of the space solar power station; s2, establishing an in-orbit multi-flexible-body attitude dynamic model of the space solar power station based on a Lagrange equation; and S3, designing a modular hierarchical control system scheme of the space solar power station. According to the invention, the three components of the battery sub-array, the central truss structure and the microwave transmitting antenna are independently controlled, so that the purposes of pointing to the ground of the antenna and pointing to the sun of the battery sub-array are achieved, and the requirements of pointing to the ground and pointing to the sun can be met on the premise of ensuring the attitude control precision.

Description

Technical Field

[0001] The present invention relates to the technical field of space solar power stations, and in particular to a modular hierarchical attitude control method for space solar power stations. Background Art

[0002] Space solar power stations convert solar energy into electricity in Earth orbit and transmit it wirelessly to users on Earth. They provide sustainable, clean energy that is unaffected by seasonal fluctuations, weather patterns, or daytime, and are crucial for addressing future energy challenges. They are currently the largest feasible space systems. Their exceptional size and low structural frequency significantly differentiate them from existing spacecraft, presenting new problems and challenges in the fields of dynamics and control.

[0003] Since the concept of space solar power stations was proposed, countries around the world have proposed various types of space solar power station configurations. These configurations have significant design differences, resulting in different control methods. Among them, non-concentrating heliodirectional space solar power stations consist of three components with different stiffnesses: a central truss structure, a microwave transmitting antenna, and a solar cell subarray. The central truss structure has the lowest fundamental frequency in the entire structure and is therefore a flexible body. The existing traditional "central rigid body + flexible attachment" spacecraft dynamics model is not applicable to space solar power stations. Its dynamic modeling problem falls within the scope of multi-flexible body system dynamics.

[0004] Previous research on attitude control for space solar power plants has used only PD controllers for simulation analysis. These controllers are simplistic in design and lack analysis of control performance and robustness. The large size and extremely low structural frequency of space solar power plants require high control output actuators and potential control / structure interaction issues. Therefore, while ensuring attitude control accuracy, it is necessary to rationally design attitude control systems to reduce actuator output requirements and avoid dynamic instabilities caused by control / structure interaction. This approach will provide valuable insights for future research on the dynamics and control of space solar power plants in my country. Summary of the Invention

[0005] To address the technical problems existing in the above-mentioned prior art, the present invention aims to provide a modular hierarchical attitude control method for a space solar power station, establish an attitude dynamics model of a space solar power station in the form of multiple flexible bodies, and adopt a modular hierarchical control design for the attitude control system. The three components, namely the battery sub-array, the central truss structure and the microwave transmitting antenna, are independently controlled to achieve the purpose of pointing the antenna toward the ground and the battery sub-array toward the sun.

[0006] To achieve the above-mentioned object, the present invention provides a modular hierarchical attitude control method for a space solar power station, comprising the following steps:

[0007] Step S1: Based on the characteristics of the space solar power station, a kinematic description is performed;

[0008] Step S2: establishing an on-orbit multi-flexible body attitude dynamics model of a space solar power station based on the Lagrange equation;

[0009] Step S3: Design a modular hierarchical control system for a space solar power station.

[0010] According to a technical solution of the present invention, in step S1, it specifically includes:

[0011] Step S11: modularizing the space solar power station according to its characteristics;

[0012] Step S12: Propose the assumptions of the dynamic model based on the configuration modularization results;

[0013] Step S13, establishing a coordinate system of the dynamic model;

[0014] Step S14: establishing a kinematic relationship according to the coordinate system.

[0015] According to a technical solution of the present invention, the modular configuration includes:

[0016] According to the structure of the space solar power station, it is modularized into a central truss structure, a microwave transmitting antenna and a battery subarray. The microwave transmitting antenna can rotate freely relative to the central truss structure, and the battery subarray can rotate around the central truss structure. The ground pointing accuracy requirements of the microwave transmitting antenna and the sun pointing accuracy requirements of the battery subarray are different.

[0017] According to a technical solution of the present invention, in step S12, the following steps are specifically included:

[0018] The space solar power station is regarded as a multi-flexible body system, and its dynamic model is established according to the following three assumptions:

[0019] a. The structural deformation is much smaller than the characteristic size of the structure;

[0020] b. The influence of orbital motion on attitude motion and structural vibration can be ignored;

[0021] c. The effects of structural deformation on gravity gradient, solar pressure and microwave reaction force can be ignored.

[0022] According to a technical solution of the present invention, in step S13, the following steps are specifically included:

[0023] Definition: B c For the central truss structure, B i is the i-th battery sub-array, N is the total number of battery sub-arrays, B a is the antenna, coordinate system n is the geocentric inertial system, coordinate system o is the orbital coordinate system, coordinate system b is the c is the fixed connection system of the central truss structure, coordinate system b i is the fixed connection system of the ith battery subarray, coordinate system b ci is the coordinate system b attached to the hinge point between the i-th battery subarray and the central truss structure and its three-axis directions are not deformed with the central truss structure c The three axes of the coordinate system are parallel, coordinate system b a is the fixed connection of the antenna, then the position vectors of the central truss structure, the i-th battery subarray and any point on the antenna can be expressed as

[0024]

[0025] Where, From the origin of coordinate system n to coordinate system b c The position vector of the origin, R c The origin of the coordinate system n points to the central truss structure B before the spatial solar power station is deformed. c The position vector of the mass element on the c The space solar power station is deformed by the coordinate system b c The origin points to the center of the truss structure B c The position vector of the mass element on c is the position vector of the mass element of the central truss structure after deformation relative to the position vector before deformation of the spatial solar power station, R i The origin of the coordinate system n points to the i-th cell array B before the spatial solar power station is deformed. i The position vector of the mass element on the i The space solar power station is deformed by the coordinate system b i The origin points to the i-th battery subarray B i The position vector of the mass element on i is the position vector of the mass element of the i-th cell array after the deformation of the spatial solar power station relative to the position vector before the deformation, r ci The coordinate system b is the space solar power station before deformation c The origin points to coordinate system b ci The position vector of the origin, u ci is the coordinate system b ciThe origin of the solar power station in the space is the position vector after deformation relative to the position vector before deformation; R a The space solar power station is deformed so that the origin of the coordinate system n points to the antenna B. a The position vector of the mass element on the a The coordinate system b is the space solar power station before deformation a The origin points to the antenna B a The position vector of the mass element on a is the position vector of the mass element of the antenna after deformation relative to the position vector before deformation of the spatial solar power station, r ca The coordinate system b is the space solar power station before deformation a The origin of the position vector points to the hinge point between the antenna and the central truss structure, u ca is the position vector of the hinge point between the antenna and the central truss structure at the spatial solar power station after deformation relative to before deformation;

[0026] The velocities of the central truss structure, the ith battery subarray, and any point on the antenna can be expressed in the Earth-centered inertial system as follows:

[0027]

[0028] Where, is the coordinate system b c The angular velocity relative to the coordinate system n, and In coordinate system b c Down measurement; is the coordinate system b i Relative to coordinate system b ci The angular velocity of In coordinate system b i Down measurement; is the coordinate system b a The angular velocity relative to the coordinate system n, and In coordinate system b a Lower metric; q c represents the modal coordinates of the central truss structure, q i represents the modal coordinates of the ith battery subarray, q a represents the modal coordinates of the antenna; and denote the vibration modes of the central truss structure, the i-th battery subarray and the antenna, respectively, ci and are the vibration mode and vibration mode slope at the hinge point between the central truss structure and the i-th battery subarray, respectively, ca represents the vibration mode at the hinge point between the central truss structure and the antenna, n c 、n i and na are the number of modes intercepted by the central truss structure, the i-th battery subarray and the antenna respectively;

[0029] The posture is described by Euler angles, where the posture of the central truss structure is described by three Euler angles (θ1 c ,θ2 c ,θ3 c ) describes the posture of the i-th battery array using an Euler angle θ i The antenna attitude is described using three Euler angles (θ1 a ,θ2 a ,θ3 a ) description, then the coordinate transformation matrix A cn 、A ci and A an Can be expressed as:

[0030]

[0031] Where:

[0032] According to a technical solution of the present invention, in step S14, the dynamic relationship of the space solar power station is expressed as:

[0033]

[0034] According to a technical solution of the present invention, in step S2, the on-orbit attitude dynamics model of the space solar power station is:

[0035]

[0036]

[0037] Where, T represents the total kinetic energy of the space solar power station; T c represents the control torque of the torque actuator acting on the central truss structure; T i represents the control torque acting on the motor of the i-th battery subarray; T a represents the control torque of the torque actuator acting on the antenna;

[0038] Δ c , Δ i and Δ c is the proportional damping matrix of the central truss structure, the i-th battery subarray and the antenna, and there exists:

[0039]

[0040] in, represents the damping ratio of the kth mode of the central truss structure, represents the damping ratio of the j-th mode of the i-th battery subarray, represents the damping ratio of the mth-order mode of the antenna;

[0041] The remaining coefficient matrix expressions in the on-orbit attitude dynamics model of the space solar power station are as follows:

[0042]

[0043] m ci ≈A ci J i E

[0044] m ca ≈0

[0045]

[0046] m cie ≈r ci× A ci P i +A ci H i

[0047] m cae ≈r ca× A ca P a

[0048] in, E=

[010] T ,

[0049] According to a technical solution of the present invention, the modular hierarchical control system design of the space solar power station includes the control design of the central truss structure and the battery subarray and the antenna pointing control design.

[0050] According to a technical solution of the present invention, the control design of the central truss structure and the battery sub-array is as follows:

[0051] The central truss structure and battery subarray of the space solar power station adopt a two-loop control strategy with low control bandwidth. The inner loop adopts a control design of feedforward control + feedback linearization; the outer loop adopts a control design of low-bandwidth PD control + disturbance observer.

[0052] Then the dynamic model of the central truss structure and battery sub-array can be expressed as

[0053]

[0054] Where,

[0055] p=[θcT ,θ sT ] T ,θ s =[θ 1 ,θ 2 ,...,θ N ] T , T s =[T 1 ,T 2 ,...,T N ] T , M ss =diag(J2 1 ,J2 2 ,...,J2 N ), M cs =[J2 1 E,J2 2 E,...,J2 N E],

[0056] The control output of the inner loop is

[0057] T=M0a+C0-g0-d0

[0058] Where a is the outer loop control output, M0, C0, g0 and d0 are the design values ​​of M, C, g and d; Based on the above control rate, the dynamic model of the central truss structure and battery subarray can be re-expressed as

[0059]

[0060] Where f = M -1 M0a-aM -1 (C-C0)+M -1 (g-g0)+M -1 (d-d0) is the uncertainty caused by modeling error;

[0061] The control output of the outer loop can be expressed as

[0062]

[0063] Where r=[0,-ω o t,0,ω o t,...,ω o t] T is the reference input signal, K P and K D is the parameter of the PD controller, and its value is as follows:

[0064]

[0065] is the estimated value of the disturbance observer, Q(s) is a low-pass filter, and there exists:

[0066]

[0067] According to a technical solution of the present invention, the antenna pointing control is designed as follows:

[0068] The antenna pointing control system adopts a high-bandwidth control design strategy compared to the central truss structure and battery subarray control design, which can be expressed as:

[0069]

[0070] Where,

[0071] p a =[θ aT ,q aT ] T ,

[0072] and are the torque output and position vector of the g-th control torque gyro group respectively.

[0073] Compared with the prior art, the present invention has the following beneficial effects:

[0074] The present invention proposes a modular hierarchical attitude control method, electronic equipment and storage medium for space solar power stations. Based on the configuration of a non-concentrating heliocentric space solar power station and targeting its multi-flexible body characteristics, a multi-flexible body attitude dynamics model of the space solar power station is developed, taking into account the mutual coupling between attitude / vibration, and used for attitude control design and nonlinear numerical simulation verification.

[0075] The present invention proposes a modular hierarchical attitude control method to control components with different precision requirements separately. The central truss and battery sub-array control adopts a two-loop nonlinear control strategy, which reduces the control system bandwidth as much as possible to avoid possible interaction between control and structure while ensuring that the pointing accuracy requirements are met. The antenna adopts high-bandwidth linear control to ensure its ability to quickly redirect, while being able to meet the requirements of ground pointing accuracy and sun pointing accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be derived from these drawings without inventive effort.

[0077] Figure 1 A flowchart of a modular hierarchical attitude control method for a space solar power station provided in accordance with one embodiment of the present invention is schematically shown;

[0078] Figure 2 Schematically showing the structure of a space solar power station provided in one embodiment of the present invention;

[0079] Figure 3 Schematically showing an on-orbit modeling diagram provided in accordance with one embodiment of the present invention;

[0080] Figure 4 Schematically shows a block diagram of a posture control system provided according to one embodiment of the present invention;

[0081] Figure 5 Schematically showing a low-bandwidth two-loop control design diagram provided in accordance with one embodiment of the present invention;

[0082] Figure 6 Schematic diagram of outer loop control design provided in one embodiment of the present invention. DETAILED DESCRIPTION

[0083] The description of the embodiments in this specification should be combined with the corresponding drawings, which should be considered a complete part of this specification. In the drawings, the shapes and thicknesses of the embodiments may be exaggerated and indicated for simplicity or convenience. Furthermore, the various structural components in the drawings will be described separately. It is worth noting that components not shown in the drawings or not described in words are known to those of ordinary skill in the art.

[0084] The description of the embodiments herein and any references to directions and orientations are for ease of description only and are not to be construed as limiting the scope of the present invention. The following description of the preferred embodiments may involve combinations of features, which may exist independently or in combination. The present invention is not specifically limited to the preferred embodiments. The scope of the present invention is defined by the claims.

[0085] like Figure 1 As shown, the modular hierarchical attitude control method for a space solar power station of the present invention includes the following steps:

[0086] Step S1: Based on the characteristics of the space solar power station, a kinematic description is performed.

[0087] In the step S1, it specifically includes:

[0088] Step S11: modularizing the space solar power station according to its characteristics;

[0089] The space solar power station in this embodiment of the present invention consists of three components of varying rigidity: a central truss structure, a microwave transmitting antenna, and a solar cell array. Based on the relative motion relationships between these components, the system is modularized into a "three-body" structure: the central truss structure, the microwave transmitting antenna, and the solar cell array. The antenna can rotate freely relative to the central truss structure, and the solar cell array can rotate around it. The antenna's pointing accuracy toward the Earth and the solar cell array must be different.

[0090] Step S12: Propose the assumptions of the dynamic model based on the configuration modularization results;

[0091] The central truss structure is the component with the lowest fundamental frequency in the entire space solar power station structure. Therefore, the central truss structure is a flexible body. Considering the embodiment as a multi-flexible body system, the following three assumptions are followed when establishing its on-orbit attitude dynamics model based on the Lagrange equation:

[0092] (1) The structural deformation is much smaller than the characteristic size of the structure;

[0093] (2) The influence of orbital motion on attitude motion and structural vibration can be ignored;

[0094] (3) The effects of structural deformation on gravity gradient, solar pressure, and microwave reaction force can be neglected;

[0095] Assumption (1) indicates that the structural dynamics problem being addressed is a linear problem, and the structural deformation can be described using the assumed modal method.

[0096] Assumption (2) indicates that the influence of the track will not be considered in the derivation of the formula of this application. This is mainly because the origin of the fixed connection system of the central truss structure is taken as the center of mass of the embodiment, and the attitude-track coupling is minimized.

[0097] Assumption (3) corresponds to the small deformation assumption of assumption (1), indicating that the generalized forces corresponding to the gravity gradient, solar pressure, and microwave reaction force are independent of the deformation of the structure.

[0098] Step S13, establishing a coordinate system of the dynamic model;

[0099] like Figure 3 As shown, where B c For the central truss structure, Bi is the i-th battery subarray (assuming there are N battery subarrays), B a is the antenna, coordinate system n is the geocentric inertial system, coordinate system o is the orbital coordinate system, coordinate system b is the c is the fixed connection system of the central truss structure, coordinate system b i is the fixed connection system of the ith battery subarray, coordinate system b ci is the coordinate system b attached to the hinge point between the i-th battery subarray and the central truss structure and the three-axis direction and the central truss structure are not deformed c The three axes of the coordinate system are parallel, coordinate system b a is the fixed connection of the antenna, and the position vectors of the central truss structure, the i-th battery subarray and any point on the antenna can be expressed as

[0100]

[0101] Where A nc is the coordinate system b c The coordinate transformation matrix to coordinate system n. The rest of A with different subscripts are defined similarly. From the origin of coordinate system n to coordinate system b c The position vector of the origin, R c The origin of the coordinate system n points to the central truss structure B before the spatial solar power station is deformed. c The position vector of the mass element on the c The space solar power station is deformed by the coordinate system b c The origin points to the center of the truss structure B c The position vector of the mass element on c is the position vector of the mass element of the central truss structure after deformation relative to the position vector before deformation of the spatial solar power station, R i The origin of the coordinate system n points to the i-th cell array B before the spatial solar power station is deformed. i The position vector of the mass element on the i The space solar power station is deformed by the coordinate system b i The origin points to the i-th battery subarray B i The position vector of the mass element on i is the position vector of the mass element of the i-th cell array after the deformation of the spatial solar power station relative to the position vector before the deformation, r ci The coordinate system b is the space solar power station before deformation c The origin points to coordinate system b ci The position vector of the origin, u ci is the coordinate system b ciThe origin of the solar power station in the space is the position vector after deformation relative to the position vector before deformation; R a The space solar power station is deformed so that the origin of the coordinate system n points to the antenna B. a The position vector of the mass element on the a The coordinate system b is the space solar power station before deformation a The origin points to the antenna B a The position vector of the mass element on a is the position vector of the mass element of the antenna after deformation relative to the position vector before deformation of the spatial solar power station, r ca The coordinate system b is the space solar power station before deformation a The origin of the position vector points to the hinge point between the antenna and the central truss structure, u ca It is the position vector of the hinge point between the antenna and the central truss structure at the spatial solar power station after deformation relative to the position vector before deformation.

[0102] Then, the velocities of the central truss structure, the i-th battery subarray, and any point on the antenna can be expressed in the inertial system as

[0103]

[0104] Where, is the coordinate system b c The angular velocity relative to coordinate system n, and in coordinate system b c Next measurement. is the coordinate system b i Relative to coordinate system b ci The angular velocity of the coordinate system b i Measure down, is the coordinate system b a The angular velocity relative to coordinate system n, and in coordinate system b a Next metric. q c represents the modal coordinates of the central truss structure, q i represents the modal coordinates of the ith battery subarray, q a represents the modal coordinates of the antenna, and denote the vibration modes of the central truss structure, the i-th battery subarray and the antenna, respectively, ci and are the vibration mode and vibration mode slope of the central truss structure at the hinge point with the i-th battery array, φ ca represents the vibration mode at the hinge point between the central truss structure and the antenna, n c 、n i and n aare the numbers of modes intercepted by the central truss structure, the i-th battery subarray and the antenna, respectively.

[0105] Step S14: establishing a kinematic relationship according to the coordinate system.

[0106] Since the center of mass of the space solar power station remains unchanged when it is not deformed, and the battery array is symmetrical about the hinge point, the coordinate system b can be c The origin of the coordinate system b is taken as the center of mass of the MRJ-SPS when it is not deformed. i The origin of the coordinate system b is taken as the center of mass of the battery array when it is not deformed. a The origin of is taken as the center of mass of the antenna when it is not deformed, then the following conditions hold

[0107]

[0108] The concept of Euler angle is used to describe the posture motion of the space solar power station. The posture of the central truss structure is described by three Euler angles (θ1 c ,θ2 c ,θ3 c ) describes the posture of the i-th battery array using an Euler angle θ i The antenna attitude is described using three Euler angles (θ1 a ,θ2 a ,θ3 a ) description, based on the order of "231", the coordinate transformation matrix A cn A ci and A an It can be expressed as

[0109]

[0110] Where, oi=1, 2 or 3.

[0111] Then the kinematic relationship of the space solar power station is:

[0112]

[0113]

[0114] Step S2: establishing an on-orbit multi-flexible body attitude dynamics model of a space solar power station based on assumption (1) and the Lagrange equation;

[0115] The resulting kinetic model is:

[0116]

[0117] Where, T represents the total kinetic energy of the space solar power station; Tc represents the control torque of the torque actuator (such as a control torque gyro or a large-diameter momentum wheel based on space assembly) acting on the central truss structure; T i represents the control torque of the motor acting on the i-th battery subarray, which is the interaction torque; T a It represents the control torque of the torque actuator (such as the control torque gyro or the large-diameter momentum wheel based on space assembly) acting on the antenna.

[0118] Δ c , Δ i and Δ c is the proportional damping matrix of the central truss structure, the i-th battery subarray and the antenna, and there exists:

[0119]

[0120] in, represents the damping ratio of the kth mode of the central truss structure, represents the damping ratio of the j-th mode of the i-th battery subarray, It represents the damping ratio of the m-th mode of the antenna.

[0121] The expressions of the remaining coefficient matrices in the on-orbit attitude dynamics model of the space solar power station are as follows:

[0122]

[0123] m ci ≈A ci J i E

[0124] m ca ≈0

[0125]

[0126] m cie ≈r ci× A ci P i +A ci H i

[0127] m cae ≈r ca× A ca P a

[0128] in, E=[0 1 0] T ,

[0129] Step S3: Design a modular hierarchical control system for a space solar power station;

[0130] The modular hierarchical control system design scheme of the space solar power station includes the control design of the central truss structure and the battery sub-array and the antenna pointing control design.

[0131] like Figure 4 The following is a block diagram of the attitude control system of an embodiment of the present invention. The central truss structure's ground pointing control is primarily achieved through a control moment gyro assembly, supplemented by electric thrusters to offset the effects of microwave reaction forces and prevent saturation of the control moment gyros. The central truss structure's attitude sensor and attitude angular velocity sensor, including components such as a star sensor and rate gyros, provide attitude angle and angular velocity information for ground pointing. The control moment gyro assembly, attitude sensor, and attitude angular velocity sensor are all located on the central support cylinder, and their positions should be as close as possible. The solar pointing control of the battery subarray is achieved through a motor, and the rotation angle of the battery subarray is measured by an angular position sensor and angular velocity sensor located at the motor. The antenna's ground pointing control is achieved through a co-located control moment gyro assembly, attitude sensor, and attitude angular velocity sensor on the antenna. Electric thrusters are also used to offset the effects of the constant gravity gradient torque and microwave reaction forces to prevent saturation of the control moment gyros.

[0132] Taking into account the decoupling of the central truss structure and the antenna in attitude motion, the sun-facing and ground-facing pointing control systems can be designed independently.

[0133] When designing the control system for the central truss structure and battery subarrays, a two-loop control strategy with low control bandwidth was adopted, taking into account the large size and low structural frequency of the space solar power station. Furthermore, due to the low control accuracy requirements, the control bandwidth can be further reduced. This helps reduce actuator output and avoids undesirable control-structure interactions.

[0134] like Figure 5 As shown in the figure, the inner loop adopts the control design of feedforward control + feedback linearization to offset the influence of external environmental interference and nonlinear terms in the dynamic model; the outer loop adopts the control design of low-bandwidth PD control + disturbance observer to achieve the attitude control accuracy requirements and offset the nonlinear disturbance caused by modeling uncertainty.

[0135] According to equations (7) to (12), the dynamic model of the central truss structure, antenna, and battery subarray can be expressed as:

[0136]

[0137] Where,

[0138] p=[θ cT ,θ sT ]T ,θ s =[θ 1 ,θ 2 ,...,θ N ] T ,

[0139] T s =[T 1 ,T 2 ,...,T N ] T , M ss =diag(J2 1 ,J2 2 ,...,J2 N ),

[0140] M cs =[J2 1 E,J2 2 E,...,J2 N E],

[0141] The control output of the inner loop is

[0142] T=M0a+C0-g0-d0

[0143] Where a is the outer loop control output, M0, C0, g0, and d0 are the design values ​​of M, C, g, and d, and the differences between them are mainly caused by modeling errors.

[0144] Based on the above control rate, the kinetic model can be reformulated as

[0145]

[0146] Where f = M -1 M0a-aM -1 (C-C0)+M -1 (g-g0)+M -1 (d-d0) is the uncertainty caused by modeling error.

[0147] like Figure 6 As shown, the control output of the outer loop can be expressed as

[0148]

[0149] Where r=[0,-ω o t,0,ω o t,...,ω o t] T is the reference input signal, KP and K D is the parameter of the PD controller, and its value is as follows:

[0150]

[0151] is the estimated value of the disturbance observer, and Q(s) is the low-pass filter.

[0152] This means that within the low-pass filter's low-frequency band (Q(jω)≈1), The influence of f can be well estimated.

[0153] When designing the antenna pointing control system, taking into account the need for high-precision control, the antenna pointing control system adopts a high-bandwidth (compared to the central truss / battery subarray control design) control design strategy.

[0154] In the present invention, four groups of control moment gyroscopes and attitude / attitude angular velocity sensors co-located on the antenna back truss structure are used to achieve stable control of the antenna attitude.

[0155] In order to take into account the influence of the arrangement of the control moment gyro group on the vibration of the antenna structure, the antenna pointing control design adopts the dynamic model obtained by linearizing equations (9) and (12):

[0156]

[0157] The model can be further expressed as follows

[0158]

[0159] Where,

[0160] p a =[θ aT ,q aT ] T ,

[0161] Among them, T i a and are the torque output and position vector of the i-th control torque gyro group respectively.

[0162] The outputs of the 4 groups of attitude / attitude angular velocity sensors are

[0163]

[0164] The output feedback controller is designed as follows

[0165] T a=-K1y1-K2y2

[0166] Where K1 and K2 are symmetric positive definite feedback gain matrices. Based on the above control rate, the closed-loop system is

[0167]

[0168] The antenna attitude control design should not excite the vibration of the structure as much as possible. For the selection of K1 and K2, only the following rigid body dynamics model can be considered

[0169]

[0170]

[0171] Based on the previous control rate, the closed-loop system of antenna pointing control is obtained as

[0172]

[0173] Then K1 and K2 can be given by the following formula

[0174] K1=L ar + K r (L ar T ) +

[0175] K2=L ar + D r (L ar T ) +

[0176] Where, and is the desired damping matrix and stiffness matrix, L ar + For L ar Moore-Penrose inverse.

[0177] The position optimization of the four control moment gyros can be considered as the following disturbed closed-loop system:

[0178]

[0179] Where w is Gaussian white noise, the covariance matrix is ​​W, L w Determined by the noise input position. The system is re-expressed in the following state space form:

[0180]

[0181] The control torque of the closed-loop system for antenna pointing control is expressed as

[0182] T a =Cx

[0183] The optimization criterion of the actuator is defined as follows

[0184]

[0185] Where E(·) represents the expectation operator, and P is the solution of the following Lyapunov equation:

[0186] AP+PA T +BWB T =0.

[0187] As the criterion defines, J measures the magnitude of the average control torque in steady state. Current control designs aim only to achieve attitude control while minimizing the impact on the structure, which also implies minimizing the control torque. Therefore, optimizing the control torque gyro position is essentially finding the optimal position that minimizes J.

[0188] It should be noted that the above is a preferred embodiment of the present invention. It should be noted that although the preferred embodiment of the present invention has been described, it is clear that those skilled in the art, once they understand the basic inventive concept of the present invention, can make various improvements and modifications without departing from the principles of the present invention. Such improvements and modifications should also be considered as within the scope of protection of the present invention. Therefore, the appended claims are intended to be interpreted as including the preferred embodiment and all changes and modifications that fall within the scope of the embodiments of the present invention.

Claims

1. A modular hierarchical attitude control method for a space solar power station, characterized in that: The following steps are involved: Step S1: Based on the characteristics of the space solar power station, a kinematic description is performed; Step S2: establishing an on-orbit multi-flexible body attitude dynamics model of a space solar power station based on the Lagrange equation; Step S3: Design a modular hierarchical control system for a space solar power station.

2. The modular hierarchical attitude control method for a space solar power station according to claim 1, characterized in that: In the step S1, it specifically includes: Step S11: modularizing the space solar power station according to its characteristics; Step S12: Propose the assumptions of the dynamic model based on the configuration modularization results; Step S13, establishing a coordinate system of the dynamic model; Step S14: establishing a kinematic relationship according to the coordinate system.

3. The modular hierarchical attitude control method for a space solar power station according to claim 2, characterized in that: The modular configuration includes: According to the structure of the space solar power station, it is modularized into a central truss structure, a microwave transmitting antenna and a battery subarray. The microwave transmitting antenna can rotate freely relative to the central truss structure, and the battery subarray can rotate around the central truss structure. The ground pointing accuracy requirements of the microwave transmitting antenna and the sun pointing accuracy requirements of the battery subarray are different.

4. The modular hierarchical attitude control method for a space solar power station according to claim 3, characterized in that: In the step S12, it specifically includes: The space solar power station is regarded as a multi-flexible body system, and its dynamic model is established according to the following three assumptions: a. The structural deformation is much smaller than the characteristic size of the structure; b. The influence of orbital motion on attitude motion and structural vibration can be ignored; c. The effects of structural deformation on gravity gradient, solar pressure and microwave reaction force can be ignored.

5. The modular hierarchical attitude control method for a space solar power station according to claim 4, characterized in that: In the step S13, it specifically includes: Definition: B c For the central truss structure, B i is the i-th battery sub-array, N is the total number of battery sub-arrays, B a is the antenna, coordinate system n is the geocentric inertial system, coordinate system o is the orbital coordinate system, coordinate system b is the c is the fixed connection system of the central truss structure, coordinate system b i is the fixed connection system of the ith battery subarray, coordinate system b ci is the coordinate system b attached to the hinge point between the i-th battery subarray and the central truss structure and its three-axis directions are not deformed with the central truss structure c The three axes of the coordinate system are parallel, coordinate system b a is the fixed connection of the antenna, then the position vectors of the central truss structure, the i-th battery subarray and any point on the antenna can be expressed as Where, From the origin of coordinate system n to coordinate system b c The position vector of the origin, R c The origin of the coordinate system n points to the central truss structure B before the spatial solar power station is deformed. c The position vector of the mass element on the c The space solar power station is deformed by the coordinate system b c The origin points to the center of the truss structure B c The position vector of the mass element on c is the position vector of the mass element of the central truss structure after deformation relative to the position vector before deformation of the spatial solar power station, R i The origin of the coordinate system n points to the i-th cell array B before the spatial solar power station is deformed. i The position vector of the mass element on the i The space solar power station is deformed by the coordinate system b i The origin points to the i-th battery subarray B i The position vector of the mass element on i is the position vector of the mass element of the i-th cell array after the deformation of the spatial solar power station relative to the position vector before the deformation, r ci The coordinate system b is the space solar power station before deformation c The origin points to coordinate system b ci The position vector of the origin, u ci is the coordinate system b ci The origin of the solar power station in the space is the position vector after deformation relative to the position vector before deformation; R a The space solar power station is deformed so that the origin of the coordinate system n points to the antenna B. a The position vector of the mass element on the a The coordinate system b is the space solar power station before deformation a The origin points to the antenna B a The position vector of the mass element on a is the position vector of the mass element of the antenna after deformation relative to the position vector before deformation of the spatial solar power station, r ca The coordinate system b is the space solar power station before deformation a The origin of the position vector points to the hinge point between the antenna and the central truss structure, u ca is the position vector of the hinge point between the antenna and the central truss structure at the spatial solar power station after deformation relative to before deformation; The velocities of the central truss structure, the ith battery subarray, and any point on the antenna can be expressed in the Earth-centered inertial system as follows: Where, is the coordinate system b c The angular velocity relative to the coordinate system n, and In coordinate system b c down measurement; is the coordinate system b i Relative to coordinate system b ci The angular velocity of In coordinate system b i Down measurement; is the coordinate system b a The angular velocity relative to the coordinate system n, and In coordinate system b a Lower metric; q c represents the modal coordinates of the central truss structure, q i represents the modal coordinates of the ith battery subarray, q a represents the modal coordinates of the antenna; and denote the vibration modes of the central truss structure, the i-th battery subarray and the antenna, respectively, ci and are the vibration mode and vibration mode slope at the hinge point between the central truss structure and the i-th battery subarray, respectively, ca represents the vibration mode at the hinge point between the central truss structure and the antenna, n c 、n i and n a are the number of modes intercepted by the central truss structure, the i-th battery subarray and the antenna respectively; The posture is described by Euler angles, where the posture of the central truss structure is described by three Euler angles (θ1 c ,θ2 c ,θ3 c ) describes the posture of the i-th battery array using an Euler angle θ i The antenna attitude is described using three Euler angles (θ1 a ,θ2 a ,θ3 a ) description, then the coordinate transformation matrix A cn 、A ci and A an Can be expressed as: Where:

6. The modular hierarchical attitude control method for a space solar power station according to claim 5, characterized in that: In step S14, the dynamic relationship of the space solar power station is expressed as:

7. The modular hierarchical attitude control method for a space solar power station according to claim 6, characterized in that: In step S2, the on-orbit attitude dynamics model of the space solar power station is: Where, T represents the total kinetic energy of the space solar power station; T c represents the control torque of the torque actuator acting on the central truss structure; T i represents the control torque acting on the motor of the i-th battery subarray; T a represents the control torque of the torque actuator acting on the antenna; Δ c , Δ i and Δ c is the proportional damping matrix of the central truss structure, the i-th battery subarray and the antenna, and there exists: in, represents the damping ratio of the kth mode of the central truss structure, represents the damping ratio of the j-th mode of the i-th battery subarray, represents the damping ratio of the mth-order mode of the antenna; The remaining coefficient matrix expressions in the on-orbit attitude dynamics model of the space solar power station are as follows: m ci ≈A ci J i HAVE BEEN m ca ≈0 m cie ≈r ci× A ci P i +A ci H i m cae ≈r ca× A ca P a in, E=[0 1 0] T , 8. The modular hierarchical attitude control method for a space solar power station according to claim 7, characterized in that: The modular hierarchical control system design scheme of the space solar power station includes the control design of the central truss structure and the battery sub-array and the antenna pointing control design.

9. The modular hierarchical attitude control method for a space solar power station according to claim 8, characterized in that: The control design of the central truss structure and the battery sub-array is as follows: The central truss structure and battery subarray of the space solar power station adopt a two-loop control strategy with low control bandwidth. The inner loop adopts a control design of feedforward control + feedback linearization; the outer loop adopts a control design of low-bandwidth PD control + disturbance observer. Then the dynamic model of the central truss structure and battery sub-array can be expressed as Where, p=[θ cT ,θ sT ] T ,θ s =[θ 1 ,θ 2 ,...,θ N ] T , T s =[T 1 ,T 2 ,...,T N ] T , M ss =diag(J2 1 ,J2 2 ,...,J2 N ),M cs =[J2 1 E,J2 2 E,...,J2 N [E], The control output of the inner loop is T=M0a+C0-g0-d0 Where a is the control output of the outer loop, M0, C0, g0 and d0 are the design values ​​of M, C, g and d; Based on the above control rate, the dynamic model of the central truss structure and the battery subarray can be reformulated as Where f = M -1 M0a-aM -1 (C-C0)+M -1 (g-g0)+M -1 (d-d0) is the uncertainty caused by modeling error; The control output of the outer loop can be expressed as Where r=[0,-ω o t,0,ω o t,...,ω o t] T is the reference input signal, K P and K D is the parameter of the PD controller, and its value is as follows: is the estimated value of the disturbance observer, Q(s) is a low-pass filter, and there exists:

10. The modular hierarchical attitude control method for a space solar power station according to claim 8, characterized in that: The antenna pointing control design is as follows: The antenna pointing control system adopts a high-bandwidth control design strategy compared to the central truss structure and battery subarray control design, which can be expressed as: Where, p a =[θ aT ,q aT ] T , and are the torque output and position vector of the g-th control torque gyro group respectively.

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