Flexible solar wing and double-shaft driving mechanism combined control method
By using segmented stepped curve control and multibody dynamics simulation model optimization, the problem of rigid-flexible coupling between the flexible solar array and the dual-axis drive mechanism was solved, achieving stable tracking control of the solar array and improving control accuracy and adaptability.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- BEIJING INST OF SPACECRAFT SYST ENG
- Filing Date
- 2025-12-10
- Publication Date
- 2026-04-21
AI Technical Summary
The combined operation of the flexible solar array and the dual-axis drive mechanism leads to complex rigid-flexible coupling problems, resulting in unpredictable vibration modes that affect control accuracy.
A segmented stepped curve control strategy is adopted. By combining speed gradient control, vibration decay waiting time and dual-solar-wing reverse control with a multibody dynamics simulation model, the joint control strategy is optimized, the rotation path and parameters are designed, and vibration modes are suppressed.
It effectively suppressed transient vibrations of the solar array, improved control accuracy and robustness, reduced interference with spacecraft attitude control, and adapted to complex environmental changes.
Smart Images
Figure CN121900153A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a combined control method for a flexible solar array and a dual-axis drive mechanism, belonging to the overall technical field of aircraft design. Background Technology
[0002] In recent years, the complexity of spacecraft missions has continued to increase. On the one hand, the requirements for energy system efficiency and lightweight structures have grown exponentially. Spacecraft in orbit need to continuously provide stable power to support complex payloads, while the overall mass constraints of spacecraft have forced solar array systems to develop towards higher specific strength and higher power density. This contradiction has given rise to new solar array configurations such as circular folding and roll-up types, which significantly improve the surface-to-mass ratio by optimizing deployment efficiency and structural compactness. However, the flexibility brought about by the new structures has significantly reduced the fundamental frequency of the solar array.
[0003] On the other hand, with the continuous expansion of spacecraft functions, attitude control requirements are showing a trend towards multidimensional development. Traditional single-degree-of-freedom drive mechanisms can only achieve rotational control around a single axis, which is insufficient to meet the dynamic requirements of solar array tracking under complex attitude conditions. The dual-degree-of-freedom solar panel control mechanism, by introducing two mutually perpendicular rotational axes and cooperating with high-precision servo motors, achieves flexible positioning of the solar array in a three-dimensional spatial coordinate system. This ensures that the solar incidence angle remains within the optimal energy reception range under special conditions such as orbital rendezvous and attitude maneuvers. This multi-degree-of-freedom control scheme significantly improves the energy utilization efficiency of spacecraft, providing reliable power support for complex spacecraft such as deep space exploration and high-orbit remote sensing.
[0004] However, the combined operation of the flexible solar array and the dual-axis drive mechanism presents challenges to control. When the drive mechanism adjusts the solar array, the coupling effect between the flexible structure and the rigid drive system triggers complex dynamic responses, resulting in unpredictable vibration modes. This rigid-flexible coupling problem is particularly prominent in dual-axis drive systems. Traditional single-axis drive systems achieve attitude adjustment through a single rotational axis, while dual-axis drives require controlling two interrelated rotational degrees of freedom. When the solar array is in the deployed state and its angle is adjusted, the torque input of the drive mechanism generates multi-degree-of-freedom coupled vibrations through the structural flexibility, forming a complex rigid-flexible coupled nonlinear dynamic system. This coupling effect leads to multi-mode oscillations on the solar array surface, amplifying the solar array's amplitude and severely limiting control accuracy. Summary of the Invention
[0005] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose a joint control method for flexible solar array and dual-axis drive mechanism to achieve stable tracking control of solar array under complex dynamic environment.
[0006] The technical solution of this invention is:
[0007] A method for joint control of a flexible solar array and a dual-axis drive mechanism includes:
[0008] Design a joint control strategy for flexible solar array and dual-axis drive mechanism, including setting speed gradient control during the start-stop phase of dual-axis drive mechanism, adding vibration attenuation waiting time between the two degrees of freedom control actions of dual-axis drive mechanism, and planning rotation path based on the reverse control of dual solar array.
[0009] A multibody dynamics simulation model with rigid-flexible coupling characteristics is constructed. Based on the solar array drive control mission, the rotation path is designed first, and then the vibration decay waiting time and speed gradient parameters are set. The joint control strategy is simulated and verified based on the multibody dynamics simulation model to obtain the total rotation time and spacecraft angular velocity of the drive process. The compliance is confirmed by comparing with the set constraint requirements. If it does not comply, the vibration decay waiting time and speed gradient parameters are adjusted, and the iteration is carried out until the constraint requirements are met.
[0010] Furthermore, a speed step curve is designed to perform speed gradient control during the start-stop phase of the dual-axis drive mechanism;
[0011] The speed step curve includes a control start section and a control stop section, and the speed gradient parameters include:
[0012] The number of steps 2n-1 indicates that the rotational speed changes 2n-1 times; steps 1 to n are the starting section, and the rotational speed reaches its maximum on step n; steps n+1 to 2n-2 are the stopping section, and the rotational speed drops to 0 on step 2n-2.
[0013] Rotational speed w1~w 2n-2 Rotational speed w i This indicates that during the duration of the i-th step, the dual-axis drive mechanism moves at an angular velocity w i Perform rotation drive control;
[0014] Step duration t1~t 2n-2 : Step duration t i This represents the duration of the rotational speed at the i-th step.
[0015] Furthermore, the duration of the step is t1~t n-1 For design parameters, the step duration t n The total rotation angle W, the rotation speed and duration of the previous step, and the w of the nth step. n Determine, satisfy the following relations:
[0016]
[0017] Step duration t n+1 ~t 2n-2 Based on the duration of the step t1~t n-1It is determined that the values are symmetrically taken with the nth step as the center.
[0018] Furthermore, the speed gradually increases during the starting phase and gradually decreases during the stopping phase, with the speed w n+1 ~w 2n-2 According to w n-1 ~w1 takes values sequentially.
[0019] Furthermore, a multibody dynamics simulation model incorporating rigid-flexible coupling characteristics is constructed: the solar array assembly is modeled as a flexible body, the dual-axis drive mechanism achieves dual-degree-of-freedom motion through a series of single-degree-of-freedom rotary pairs, and the spacecraft body is characterized using a rigid body dynamics model; based on the spacecraft's moment of inertia, the flexible dynamic parameters of the solar array, the stiffness of the drive mechanism, the designed rotation path, vibration decay waiting time, and speed gradient parameters, the joint control strategy is simulated and verified using the multibody dynamics simulation model.
[0020] Furthermore, the analytical dynamic model of the spacecraft is established as follows:
[0021] Equations of motion for the center of mass of a spacecraft system during translation:
[0022]
[0023] The equations of motion for the spacecraft system about its center of mass are as follows:
[0024]
[0025] Solar wing vibration equation:
[0026]
[0027] In the formula, ω s For the angular velocity array of the spacecraft's central body, Let M be an antisymmetric array of angular velocity arrays, and I be the total mass array of the spacecraft. s For the spacecraft's relative system center of mass inertial array, P s For the array of external forces acting on the spacecraft, T s T is the array of external moments acting on the spacecraft; u The torque exerted on the spacecraft by the rotation of the solar panels. I u For the inertia array in the solar wing system, ω u The stepped curve formed by the speed gradient parameters of the designed drive mechanism. The transformation matrix from the solar array body system to the spacecraft body system; Ω a1 Ω a2 These are the diagonal arrays of mode frequencies for the left and right solar panels, respectively, η a1 η a2 These are the modal coordinate matrices for the left and right solar panels, respectively, ζ.a1 ζ a2 These are the modal damping coefficients for the left and right solar panels, respectively; F ta1 F ta2 F represents the flexible coupling coefficient matrix of the vibration of the left and right solar arrays on the translational motion of the spacecraft's central body. sa1 F sa2 These are the flexible coupling coefficient matrices of the vibration of the left and right solar panels on the rotation of the spacecraft's central body.
[0028] Furthermore, the connection topology of the multibody dynamics simulation model is as follows: the two orthogonal rotational degrees of freedom of the dual-axis drive mechanism are denoted as the A-axis and the B-axis. The rotation direction of the A-axis of the dual-axis drive mechanism is fixed relative to the spacecraft, while the rotation direction of the B-axis changes with the rotation of the A-axis. The dual-axis drive mechanism is a variable stiffness system during the rotation of the solar array. The A-axis of the dual-axis drive mechanism is regarded as an independent substructure, which, together with the B-axis and the solar array at different angles, forms a new flexible accessory.
[0029] Furthermore, based on the solar array drive control mission, a rotation path was designed, and a reverse rotation method was adopted to reduce the change in the spacecraft's rotational inertia.
[0030] Furthermore, vibration decay waiting time and rotational speed gradient parameters were set, and simulation verification was performed based on a multibody dynamics simulation model. In this model, the duration of each step was set to avoid coupling with the solar array fundamental frequency, and the duration of each step was initially set to be the same.
[0031] Furthermore, the constraints are the solar array vibration amplitude characteristics and control accuracy indicators, including the total rotation time of the solar array, the root load of the solar array, the amplitude constraint of the solar array, or the overload constraint of the solar array center of mass.
[0032] The advantages of this invention compared to the prior art are:
[0033] (1) This invention creatively adopts a segmented step curve control strategy. By decomposing the drive command into multiple gradient stages, the solar array undergoes gradual deformation at different stages, effectively suppressing transient vibration. At the same time, by introducing system-level strategies such as waiting time and dual solar array reverse control between the two degrees of freedom alternating control, control interference is further reduced.
[0034] (2) In order to ensure the optimal configuration of parameters under the constraint of finite drive control time, this invention constructs a joint simulation including structural dynamics model, control algorithm model and environmental disturbance model, and determines the combination of control strategy parameters through multiple rounds of iterative optimization. Attached Figure Description
[0035] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:
[0036] Figure 1 This is a speed step control curve diagram according to an embodiment of the present invention;
[0037] Figure 2 This is a connection topology diagram of the multibody dynamics simulation model according to an embodiment of the present invention;
[0038] Figure 3 This is a flowchart of the joint control method of the flexible solar array and the dual-axis drive mechanism according to an embodiment of the present invention. Detailed Implementation
[0039] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
[0040] This invention proposes a joint control method for a flexible solar array and a dual-axis drive mechanism, comprising:
[0041] 1) Design of control strategy optimization scheme
[0042] This invention innovatively proposes three optimized joint control strategies:
[0043] Firstly, a phased acceleration and deceleration strategy is adopted, and speed gradient control is set during the start-up and shutdown phases of the drive mechanism to effectively suppress structural coupling vibration by reducing the rotational acceleration of the solar array.
[0044] Speed step control curve design as follows Figure 1 As shown, this includes control steps for starting and stopping. To simplify the design, the starting and stopping steps are typically designed symmetrically. The design of the step curve should include the following parameters:
[0045] The speed step curve includes a control start section and a control stop section, and the speed gradient parameters include:
[0046] The number of steps 2n-1 indicates that the rotational speed changes 2n-1 times; steps 1 to n are the starting section, and the rotational speed reaches its maximum on step n; steps n+1 to 2n-2 are the stopping section, and the rotational speed drops to 0 on step 2n-2.
[0047] Rotational speed w1~w 2n-2Rotational speed w i This indicates that during the duration of the i-th step, the dual-axis drive mechanism moves at an angular velocity w i Rotational drive control should be implemented; the speed should gradually increase during startup and gradually decrease during shutdown to avoid exciting additional vibrations. Simultaneously, the intervals between speeds should be as uniform as possible.
[0048] Step duration t1~t 2n-2 : Step duration t i This represents the duration of the rotational speed at the i-th step.
[0049] The duration of the step is t1~t n-1 For design parameters, the step duration t n The total rotation angle W, the rotation speed and duration of the previous step, and the w of the nth step. n Determine, satisfy the following relations:
[0050]
[0051] Step duration t n+1 ~t 2n-2 Based on the duration of the step t1~t n-1 It is determined that the values are symmetrically taken with the nth step as the center.
[0052] To reduce strategy complexity, we can initially set t1 = t2 = ... = t 2n-2 With increased understanding of the system's modalities, further design of the timing can be achieved.
[0053] Secondly, a dual-degree-of-freedom control timing interval mechanism is introduced into the dual-axis sail control mechanism, setting a vibration attenuation waiting time t between the two degree-of-freedom control actions. d To ensure that the preceding vibrations are fully dissipated before subsequent control is executed, it is necessary to avoid the situation where vibrations in the A direction are excited and then vibrations in the B direction are excited again, resulting in vibration superposition, which would further cause interference and reduce control accuracy.
[0054] Third, implement counter-clockwise cooperative control of the two solar arrays. By optimizing trajectory planning, the two solar arrays can rotate synchronously in opposite directions, effectively suppressing abrupt changes in the spacecraft's inertial parameters and thus reducing the system's coupled vibration response. For example, rotating the two solar arrays in opposite directions (one clockwise and one counterclockwise) reduces the impact on the spacecraft's rotational angular velocity, thereby reducing disturbances and improving control accuracy.
[0055] 2) Multi-body co-simulation verification
[0056] A multibody dynamics simulation model incorporating rigid-flexible coupling characteristics is constructed: the solar array assembly is modeled as a flexible body, the dual-axis drive mechanism achieves two-degree-of-freedom motion through a series of single-degree-of-freedom rotary pairs, and the spacecraft body is characterized using a rigid body dynamics model, forming a complete system dynamics simulation model to verify and analyze the design control strategy.
[0057] The simulation model connection topology diagram is as follows: Figure 2 As shown. The two orthogonal rotational degrees of freedom of the dual-axis drive mechanism are denoted as the A-axis and the B-axis. Since the rotation direction of the A-axis of the dual-axis drive mechanism is fixed relative to the spacecraft, while the rotation direction of the B-axis changes with the rotation of the A-axis, the dual-axis drive mechanism is a variable stiffness system during the rotation of the solar array. Taking the A-axis of the dual-axis drive mechanism as an independent substructure, it forms a new flexible accessory with the B-axis and the solar array at different angles. The analytical dynamic model of the spacecraft is established as follows:
[0058]
[0059]
[0060] Equation (1) is the equation of translational motion of the spacecraft system's center of mass, equation (2) is the equation of rotational motion of the spacecraft system around its center of mass, and equation (3) is the equation of vibration of the solar array. Where:
[0061] ω s --The angular velocity array of the spacecraft's central body, measured within the spacecraft's intrinsic system, ∈3×1;
[0062] --An antisymmetric matrix of angular velocity arrays, ∈3×3;
[0063] M -- Total mass array of spacecraft, ∈3×3;
[0064] I s --The spacecraft's relative system center of mass inertia matrix, measured within the spacecraft's own system, ∈3×3;
[0065] P s --The array of external forces acting on the spacecraft, measured within the spacecraft's own system, ∈3×1;
[0066] T u --The torque exerted on the spacecraft by the rotation of the solar panels I u For the inertia array in the solar wing system, ω u The drive mechanism rotation speed step curve is designed according to the strategy of this invention. The transformation matrix from the solar array body system to the spacecraft body system;
[0067] T s--The matrix of external moments acting on the spacecraft, measured within the spacecraft's own system, ∈3×1;
[0068] Ω a1 Ω a2 --These are the diagonal arrays of modal frequencies for the left and right solar panels, respectively, ∈m×m;
[0069] η a1 η a2 -- is the modal coordinate matrix of the left and right solar panels, ∈m×1;
[0070] ζ a1 ζ a2 -- represents the modal damping coefficients of the left and right solar panels;
[0071] F ta1 F ta2 -- is the flexible coupling coefficient matrix of the vibration of the left and right solar panels on the translation of the spacecraft's central body, ∈3×m;
[0072] F sa1 F sa2 -- is the flexible coupling coefficient matrix of the vibration of the left and right solar panels on the rotation of the spacecraft's central body, ∈3×m;
[0073] m -- Modal order.
[0074] 3) Iterative optimization method for control parameters
[0075] Establish a parameter optimization closed loop based on the joint simulation results: If the vibration amplitude characteristics and control accuracy indicators of the solar array determined by the joint simulation results do not meet the design constraints, the parameter iterative optimization process is initiated. Performance optimization is achieved by adjusting key parameters in the control strategy (such as speed gradient coefficient, timing interval, etc.) until the engineering constraints are met.
[0076] 1) Iteration constraints
[0077] Since the solar array provides energy to the entire spacecraft, the spacecraft usually cannot generate electricity during the rotation of the solar array, and the total rotation time usually needs to be constrained.
[0078] To reduce interference during solar array control and its impact on control accuracy, it is usually necessary to constrain the spacecraft's angular velocity caused by solar array rotation.
[0079] To reduce the torque required for driving and decrease the weight requirements of the drive mechanism, it is usually necessary to constrain the load at the root.
[0080] Other constraints can be added depending on the specific task, such as adding constraints on solar array amplitude and solar array center of mass overload.
[0081] 2) Iterative design quantity
[0082] Iterative design quantities include the number of steps n, rotational speeds w1 to w2, and so on. n The duration of the step is t1~t n Two-degree-of-freedom control interval time t d .
[0083] 3) Iterative design process
[0084] Iterative design process as follows Figure 3 As shown.
[0085] Based on the solar array drive control mission, the rotation control path is designed first, and methods such as reverse rotation are used as much as possible to reduce the change in spacecraft rotational inertia. For example, when performing incident angle offset control, the two solar arrays rotate in opposite clockwise / counterclockwise directions. Based on the designed rotation path, the waiting interval between the two degrees of freedom rotations is determined. According to the flexible state of the solar array, the lower the fundamental frequency, the lower the damping, and the longer the waiting time. The speed step is further designed to complete the control strategy design.
[0086] The inputs required to establish a joint simulation model include determining parameters such as the spacecraft's moment of inertia, the flexible dynamic parameters of the solar array, and the stiffness of the drive mechanism.
[0087] The control strategy design was verified using a co-simulation model to obtain parameters such as the total rotation time of the driving process and the spacecraft's angular velocity. These parameters were then compared with the constraints to confirm compliance. If they did not comply, the parameters in the control strategy were adjusted, and the process was iterated until the requirements were met.
[0088] 4) Iterative Reference
[0089] The relationship between each control parameter and constraint is given to facilitate iterative design.
[0090] Number of steps n: The more steps there are, the longer the total rotation time, the lower the spacecraft interference force, and the lower the root load.
[0091] Rotational speed w1~w n The lower the rotational speed, the longer the total rotation time, the lower the spacecraft interference force, and the lower the root load.
[0092] Step duration t1~t n The step duration is related to the solar array's fundamental frequency, and the design of the step duration should avoid coupling with the solar array's fundamental frequency.
[0093] Two-degree-of-freedom control interval time t d The longer the interval, the longer the total rotation time, the lower the spacecraft interference force, and the lower the root load.
[0094] This invention presents an innovative solution that integrates mechanism characteristics and control strategies, providing a reliable technical path for high-precision control of future large-scale flexible solar array systems. Its beneficial effects are as follows:
[0095] (1) This invention has high control precision and strong adaptability, significantly reducing the vibration amplitude during the rotation of the solar array. While improving the control precision of the solar array itself, it can also reduce interference with the attitude control of the spacecraft. The co-simulation and multi-model optimization mechanism can adapt to complex environmental disturbances and structural characteristic changes, and improve the robustness of the control strategy under multiple operating conditions.
[0096] (2) The present invention has high scalability. The proposed mechanism-control fusion design provides a reusable technical framework for future large-scale flexible structures, such as larger-scale solar arrays and large deployable antennas.
[0097] (3) This invention is easy to operate and the algorithm is simple to implement. It can be programmed and controlled using a motor-driven FPGA or computer application software, without the need for additional or modified hardware products. It is suitable for various missions such as deep space exploration and high-orbit remote sensing.
[0098] (4) The present invention has high engineering feasibility. The parameter configuration based on simulation optimization and iteration avoids the high cost and long cycle of large-scale ground tests, thus improving the efficiency of technology implementation.
[0099] The embodiments described above are merely preferred embodiments of the present invention. Ordinary variations and substitutions made by those skilled in the art within the scope of the technical solution of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for joint control of a flexible solar array and a dual-axis drive mechanism, characterized in that, include: Design a joint control strategy for flexible solar array and dual-axis drive mechanism, including setting speed gradient control during the start-stop phase of dual-axis drive mechanism, adding vibration attenuation waiting time between the two degrees of freedom control actions of dual-axis drive mechanism, and planning rotation path based on the reverse control of dual solar array. A multibody dynamics simulation model with rigid-flexible coupling characteristics is constructed. Based on the solar array drive control mission, the rotation path is designed first, and then the vibration decay waiting time and speed gradient parameters are set. The joint control strategy is simulated and verified based on the multibody dynamics simulation model to obtain the total rotation time and spacecraft angular velocity of the drive process. The compliance is confirmed by comparing with the set constraint requirements. If it does not comply, the vibration decay waiting time and speed gradient parameters are adjusted, and the iteration is carried out until the constraint requirements are met.
2. The method for joint control of a flexible solar array and a dual-axis drive mechanism according to claim 1, characterized in that, Design a speed step curve to perform speed gradient control during the start-stop phase of the dual-shaft drive mechanism; The speed step curve includes a control start section and a control stop section, and the speed gradient parameters include: The number of steps 2n-1 indicates that the rotational speed changes 2n-1 times; steps 1 to n are the starting section, and the rotational speed reaches its maximum on step n; steps n+1 to 2n-2 are the stopping section, and the rotational speed drops to 0 on step 2n-2. Rotational speed w1~w 2n-2 Rotational speed w i This indicates that during the duration of the i-th step, the dual-axis drive mechanism moves at an angular velocity w i Perform rotation drive control; Step duration t1~t 2n-2 : Step duration t i This represents the duration of the rotational speed at the i-th step.
3. The method for joint control of a flexible solar array and a dual-axis drive mechanism according to claim 2, characterized in that, Step duration t1~t n-1 For design parameters, the step duration t n The total rotation angle W, the rotation speed and duration of the previous step, and the w of the nth step. n Determine, satisfy the following relations: Step duration t n+1 ~t 2n-2 Based on the duration of the step t1~t n-1 It is determined that the values are symmetrically taken with the nth step as the center.
4. The method for joint control of a flexible solar array and a dual-axis drive mechanism according to claim 2, characterized in that, During the starting phase, the speed gradually increases, and during the stopping phase, the speed gradually decreases. (Speed w) n+1 ~w 2n-2 According to w n-1 ~w1 takes values sequentially.
5. The method for joint control of a flexible solar array and a dual-axis drive mechanism according to claim 1, characterized in that, A multibody dynamics simulation model incorporating rigid-flexible coupling characteristics is constructed: the solar array assembly is modeled as a flexible body, the dual-axis drive mechanism achieves dual-degree-of-freedom motion through a series of single-degree-of-freedom rotary pairs, and the spacecraft body is characterized by a rigid body dynamics model; based on the spacecraft's moment of inertia, the flexible dynamic parameters of the solar array, the stiffness of the drive mechanism, the designed rotation path, vibration decay waiting time, and speed gradient parameters, the joint control strategy is simulated and verified using the multibody dynamics simulation model.
6. The method for joint control of a flexible solar array and a dual-axis drive mechanism according to claim 5, characterized in that, The analytical dynamic model of the spacecraft is established as follows: Equations of motion for the center of mass of a spacecraft system during translation: The equations of motion for the spacecraft system about its center of mass are as follows: Solar wing vibration equation: In the formula, ω s For the angular velocity array of the spacecraft's central body, Let M be an antisymmetric array of angular velocity arrays, and I be the total mass array of the spacecraft. s For the spacecraft's relative system center of mass inertial array, P s For the array of external forces acting on the spacecraft, T s T is the array of external moments acting on the spacecraft; u The torque exerted on the spacecraft by the rotation of the solar panels. I u For the inertia array in the solar wing system, ω u The stepped curve formed by the speed gradient parameters of the designed drive mechanism. The transformation matrix from the solar array body system to the spacecraft body system; Ω a1 Ω a2 These are the diagonal arrays of mode frequencies for the left and right solar panels, respectively, η a1 η a2 These are the modal coordinate matrices for the left and right solar panels, respectively, ζ. a1 ζ a2 These are the modal damping coefficients for the left and right solar panels, respectively; F ta1 F ta2 F represents the flexible coupling coefficient matrix of the vibration of the left and right solar arrays on the translational motion of the spacecraft's central body. sa1 F sa2 These are the flexible coupling coefficient matrices of the vibration of the left and right solar panels on the rotation of the spacecraft's central body.
7. The method for joint control of a flexible solar array and a dual-axis drive mechanism according to claim 5, characterized in that, The multibody dynamics simulation model connection topology is as follows: the two orthogonal rotational degrees of freedom of the dual-axis drive mechanism are denoted as axis A and axis B. The rotation direction of axis A of the dual-axis drive mechanism is fixed relative to the spacecraft, while the rotation direction of axis B changes with the rotation of axis A. The dual-axis drive mechanism is a variable stiffness system during the rotation of the solar array. The axis A of the dual-axis drive mechanism is regarded as an independent substructure, which, together with axis B and the solar array at different angles, forms a new flexible accessory.
8. The method for joint control of a flexible solar array and a dual-axis drive mechanism according to claim 1, characterized in that, Based on the solar array drive control mission, a rotation path was designed, and a reverse rotation method was adopted to reduce the change in the spacecraft's rotational inertia.
9. The method for joint control of a flexible solar array and a dual-axis drive mechanism according to claim 2, characterized in that, Vibration decay waiting time and rotational speed gradient parameters were set, and simulation verification was performed based on a multibody dynamics simulation model. The duration of each step was set to avoid coupling with the solar array fundamental frequency, and the duration of each step was initially set to be the same.
10. The method for joint control of a flexible solar array and a dual-axis drive mechanism according to claim 1, characterized in that, The constraints are the solar array vibration amplitude characteristics and control accuracy indicators, including the total rotation time of the solar array, the root load of the solar array, the amplitude constraint of the solar array or the overload constraint of the solar array center of mass.