Vibration control method of distributed spacecraft solar panels considering adjacent control forces

Abstract

A distributed spacecraft solar panel vibration control method considering adjacent control forces relates to the field of aerospace control systems, and solves the problem that when the existing centralized control system is performing vibration suppression on large flexible components, a single controller cannot meet the control requirements, resulting in a long vibration suppression time. The present invention divides the solar panel into sub-modules according to the installation position of the actuator sensor on the solar panel. The actuator sensor and its control circuit of each sub-module constitute a control node, and a vibration equation of the sub-module is established. According to the vibration equation, the influence of the installation position of the actuator and the sensor on the control effect is considered, the coupling relationship between the sub-modules is analyzed, and the coupling influence of the output force of the adjacent control node is considered, and a distributed adaptive controller is used. The present invention has a shorter vibration suppression time and effectively improves the anti-interference ability.

Description

Technical Field

[0001] The present invention relates to the field of aerospace control systems, and in particular to a distributed spacecraft solar panel vibration control method considering adjacent control forces. Background Art

[0002] In order to ensure the stability of the spacecraft's on-orbit operating environment and effectively suppress the vibration of the spacecraft's large flexible components caused by the external environment and its own attitude adjustment, the designed control system is divided into two categories, one is the traditional centralized control system, and the other is the distributed control system. In the traditional centralized control system, when performing vibration suppression control, all the vibration information of the sailboard is collected by the sensor as the input of the system, and the control rate is output by the onboard computer. This centralized control system has a certain control effect, but because the output of the control rate requires the calculation of the overall information of the sailboard, the control time is slightly longer, especially for the vibration suppression of large flexible sailboards, the control effect will be reduced. Moreover, solar sailboards, as the main power energy guarantee components of satellite spacecraft, are currently developing in the direction of large-scale and flexible. When the distributed control system performs vibration suppression control, due to the existence of independent control nodes, a single control node collects partial structural vibration information of the large flexible solar sailboard as input, and the control node has independent calculation ability to obtain local control laws.

[0003] The advantages of the distributed control method are lower vibration amplitude and shorter transition time after vibration suppression; it has certain robustness to different node failures and different communication topologies; and it does not require high real-time computing power of computers. However, the existing distributed control method does not consider the coupling effect of the output force of adjacent control nodes and the influence of the actuator position on the control effect, resulting in a long vibration suppression time for strong external impact interference, which affects the stable operation of the spacecraft on orbit. Therefore, it is of great significance to design a new distributed control method. Summary of the invention

[0004] The present invention aims to solve the problem that when a centralized control system is performing vibration suppression on a large flexible component, a single controller cannot meet the control requirements, resulting in a long vibration suppression time; and the problem that the current distributed control method does not consider the coupling effect of the output force of adjacent control nodes and the influence of the actuator position on the control effect. A distributed spacecraft solar panel vibration control method considering adjacent control forces is provided.

[0005] A distributed spacecraft solar panel vibration control method considering adjacent control forces is implemented by the following steps:

[0006] Step 1: Divide the solar panel into sub-modules of equal area, so that each sub-module is equipped with a set of actuators and sensor pairs; calculate the damping matrix of Rayleigh damping according to the mass and stiffness matrix of the sub-module, and establish the vibration equation of the solar panel sub-module, as well as the modal form actuator and sensor equation of the entire panel;

[0007] Step 2: According to the modal form actuator and sensor equations of the solar panel established in step 1, based on Lyapunov stability theory, determine the analytical solution of the controllable observability Gram matrix, and then obtain the controllable observability actuator and sensor position optimization criteria;

[0008] The optimization criteria are used to calculate and obtain the optimal installation position of the actuator and the sensor in the submodule, and the actuator and the sensor and the control circuit constitute a control node;

[0009] Step 3: Considering the coupling effect of the output control force of the adjacent control nodes and the vibration coupling effect of the adjacent submodules, the distributed controller of each control node is designed according to the mass, stiffness matrix, damping matrix of the submodule of the solar panel in step 1 and the vibration equation of the submodule of the solar panel; the details are as follows:

[0010] f ai =B iu u i

[0011] f ai =[f i1 (t),f i2 (t),…,f iN (t)] T

[0012]

[0013] In the formula, f ai is the control rate of the local controller, B iu is the position matrix of the actuator, u i ∈R N×1 is the control input, i is the submodule number, t is the time; q ij is the j-th vibration mode coordinate of submodule i;

[0014] Where α=-R≤0, β<C ij ,j=1,2,…,N;C ij is the jth diagonal element of the damping matrix of submodule i; R is any positive constant, and n k is the submodule number adjacent to submodule i, k is the number of submodules adjacent to submodule i; and are the coefficients of the modal coordinate term and the control force coupling term in the controller.

[0015] Beneficial effects of the present invention:

[0016] The present invention divides the solar panel into submodules according to the installation position of the actuator sensor on the solar panel. The actuator sensor and its control circuit of each submodule constitute a control node, and the vibration equation of the submodule is established. According to the vibration equation, the influence of the installation position of the actuator and the sensor on the control effect is considered, the coupling relationship between the submodules is analyzed, the coupling influence of the output force of the adjacent control node is considered, and a complete distributed adaptive controller is designed based on the Lyapunov theory. The distributed control method designed by the present invention that considers the influence of the control force of the adjacent control node has a shorter vibration suppression time, effectively improves the anti-interference ability, has better robustness for the situation of strong impact interference at a certain point of the solar panel, greatly reduces the vibration influence on the adjacent control node, and makes it easier for the solar panel to remain stable.

[0017] The distributed collaborative control method proposed in the present invention can effectively realize the vibration suppression of the satellite's large flexible sailboard when it is working in orbit; compared with the traditional centralized control method, under the same external interference and the external interference of a single strong impact, it has a shorter stable convergence time and a better stable control effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 A schematic diagram of the positional relationship of each submodule in the distributed spacecraft solar panel vibration control method considering adjacent control forces according to the present invention;

[0019] Figure 2 It is the schematic diagram of the coupling influence relationship between each sub-module;

[0020] Figure 3 This is the distributed control schematic diagram;

[0021] Figure 4 Schematic diagram of optimized positions for actuators and sensors;

[0022] Figure 5 This is a diagram showing the vibration suppression convergence effect of submodule 1 under continuous external interference.

[0023] Figure 6 This is a diagram showing the vibration suppression convergence effect of submodule 1 when a single strong impact interference is added while the external interference continues. DETAILED DESCRIPTION

[0024] Combination Figures 1 to 6 The present embodiment describes a distributed spacecraft solar panel vibration control method considering adjacent control forces, which is implemented by the following steps:

[0025] Step 1: According to the mass and stiffness matrix of the solar panel submodule, calculate the damping matrix of Rayleigh damping, establish the vibration equation of the solar panel submodule, and the modal form actuator and sensor equation of the whole panel.

[0026]

[0027] Among them, q i ∈R N×1 is the vibration modal coordinate of submodule i; M i ∈R N×N and K i ∈R N×N is the generalized mass matrix and stiffness matrix of submodule i; C i ∈R N×N is the damping matrix, and is Rayleigh damping, that is, C i =k m M i +k k K i ; B iu is the position matrix of the actuator; u i ∈R N×1 It is the control input, which is generated by the piezoelectric ceramic actuator after applying voltage;

[0028] The modal form of the actuator and sensor equations of the entire windsurfing board are:

[0029]

[0030]

[0031] Among them, η c ∈R m×1 is the first m-order master mode, is m×n c dimensional master mode matrix, ω i is the i-th order natural frequency, ξ i is the i-th order modal damping ratio, is the measurement vector, They are the output matrices of acceleration, velocity, and displacement sensors, is the control force vector generated by the actuator, Φ c is an n×m dimensional matrix composed of the m-order main control mode vibration shapes;

[0032] Step 2: Based on Lyapunov stability theory, determine the analytical solution of the controllable observability Gram matrix, and then derive the optimization criteria for the controllable observability actuator sensor position of the system. Obtain the optimal installation position of the actuator / sensor pair, divide the windsurfing board into sub-modules, so that the actuator / sensor is located at the geometric center point of the sub-module and forms a control node with the control circuit:

[0033] The optimization configuration criteria for the actuator are:

[0034]

[0035] The optimal configuration criteria for sensors are:

[0036]

[0037] Where m is the number of master modes, σ ci is the controllability Gram matrix W c The singular values ​​of σ oi is the observability Gram matrix W o The singular values ​​of .

[0038] Set the controllability Gram matrix W c The parsed form is:

[0039]

[0040] in, W cpq W c The two-row and two-column block matrix form of ; Take the actuator sensor equation When is the state variable, the pth row of the state equation B matrix;

[0041] Observability Gram matrix W o The parsed form is:

[0042]

[0043] in W opq W o The two-row and two-column block matrix form of c rp For the actuator and sensor equations When it is a state variable, the sensor is the pth column of the output equation C matrix of the speed sensor;

[0044] The J obtained from equations 4 and 5 above is c and J o The orders of magnitude need to be unified to obtain the optimal configuration criteria J′ for actuators and sensors of the same order of magnitude c and J′ o.

[0045] Since the actuator sensor is installed in alignment to avoid control overflow, the two criterion coefficients of the same order of magnitude are combined into a comprehensive optimization criterion of controllability and observability:

[0046]

[0047] Step 3: Consider the coupling effect of the output control force of adjacent control nodes and the vibration coupling effect of adjacent submodules, and design the distributed controller of each control node. The distributed controller is:

[0048] f ai =B iu u i

[0049] f ai =[f i1 (t),f i2 (t),…,f iN (t)] T (9)

[0050]

[0051] where f ai is the control rate of the local controller, t is the time, B iu is the position matrix of the actuator, u i ∈R N×1 is the control input, and i is the submodule number. ij is the j-th vibration mode coordinate of submodule i.

[0052] Where α=-R≤0, β<C ij ,j=1,2,…,N。C ij is the jth diagonal element of the damping matrix of submodule i. R is any positive constant, and n k is the submodule number adjacent to submodule i, n k The k is adjacent to the submodule i. and are the coefficients of the modal coordinate term and the control force coupling term in the controller.

[0053] The method described in this embodiment abandons the global optimum to achieve the local optimum of the sub-module, so that the sub-module closest to the central rigid body and having the greatest influence on it is stabilized, thereby ensuring that the flexible component system has the least effect on the overall vibration of the spacecraft.

[0054] Specific implementation method 2: Combination Figures 1 to 6This embodiment is described as an example of a distributed spacecraft solar panel vibration control method considering adjacent control forces described in the first embodiment.

[0055] The distributed spacecraft solar panel vibration control method considering adjacent control forces designed in this embodiment is applied to the vibration suppression control of a large flexible solar panel, ignoring the torsion of the panel in the x oy plane and only considering the vibration of the panel in the z-axis direction. The actuator is installed on the panel and outputs control force to act on the panel according to control requirements, so that the panel can achieve active vibration suppression. The actuators are arranged in two rows along the x-axis direction of the panel coordinate system, as shown in FIG. Figure 1 The solar panel is 10m long, 3m wide, 0.05m thick, with an elastic modulus of 70.3GPa, a Poisson's ratio of 0.3, and a density of 2700kg / m 3 The coupling influence relationship between the windsurfing submodules is as follows: Figure 2 As shown, the vibration of a submodule will have a coupling effect on the adjacent submodules, which is expressed as a coefficient multiplied by the modal coordinate form of the vibration. Taking submodule 1 as an example, the adjacent submodules are submodule 2 and submodule i+1, and the coupling effect on the two is and At the same time, the coupling effect of the two on it is and Among them, C 12 and C 1,i+1 is the vibration coupling influence coefficient of submodule 1 on the two, C 21 and C i+1,1 is the vibration coupling influence coefficient of the two. The actuator uses a piezoelectric ceramic actuator, which is installed on the surface of the large flexible solar panel. In order to avoid the control overflow phenomenon when using piezoelectric elements, the sensor and the actuator are installed in a positional manner. The positions of the actuator and the sensor are optimized according to the parameters of the panel, and the following is obtained: Figure 4 The results shown in Figure 4 In the example, the left midpoint of the sailboard is used as the origin of the coordinate system. According to the size of the sailboard in this embodiment, the edge line of the sailboard is drawn. The coordinate position after optimization is represented by a black square, and its coordinates are marked. Then the sub-modules are divided according to this. Then the distributed controllers of each sub-module are designed. The controllers are designed according to Figure 3 Considering the coupling effect of adjacent submodules, take two adjacent submodules i and j as an example, that is, considering the vibration coupling of adjacent submodules The coupling effect of the output control force k i f ai k j f aj . Among them, C ij and k i are the vibration coupling influence coefficient and control force coupling influence coefficient of submodule i on submodule j respectively; C jiand k j are the vibration coupling influence coefficient and control force coupling influence coefficient of submodule j on submodule i respectively; is the modal coordinate of vibration, f ai f aj To control the force output.

[0056] This embodiment is compared with the traditional centralized control method. Set the continuous external interference condition and perform simulation to obtain the following Figure 5 The vibration suppression convergence image is shown in Figure 2. The condition of adding a single strong impact disturbance while continuing the external disturbance is set, and the simulation results are as follows Figure 6 Vibration suppression convergence image shown.

[0057] The technical features of the above-described embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0058] The above-mentioned embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for ordinary technicians in this field, several variations and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the attached claims.

Claims

1. A distributed spacecraft solar panel vibration control method considering adjacent control forces, characterized by: The method comprises the following steps: Step 1: Divide the solar panel into sub-modules of equal area, so that each sub-module is equipped with a set of actuators and sensor pairs; calculate the damping matrix of Rayleigh damping according to the mass and stiffness matrix of the sub-module, and establish the vibration equation of the solar panel sub-module, as well as the modal form actuator and sensor equation of the entire panel; Step 2: According to the modal form actuator and sensor equations of the solar panel established in step 1, based on Lyapunov stability theory, determine the analytical solution of the controllable observability Gram matrix, and then obtain the controllable observability actuator and sensor position optimization criteria; The optimization criteria are used to calculate and obtain the optimal installation position of the actuator and the sensor in the submodule, and the actuator and the sensor and the control circuit constitute a control node; Step 3: Considering the coupling effect of the output control force of the adjacent control nodes and the vibration coupling effect of the adjacent submodules, the distributed controller of each control node is designed according to the mass, stiffness matrix, damping matrix of the submodule of the solar panel in step 1 and the vibration equation of the submodule of the solar panel; the details are as follows: f ai =B iu u i f ai =[f i1 (t),f i2 (t),…,f iN (t)] T In the formula, f ai is the control rate of the local controller, B iu is the position matrix of the actuator, u i ∈R N×1 is the control input, i is the submodule number, t is the time; q ij is the j-th vibration mode coordinate of submodule i; Where α=-R≤0, β<C ij ,j=1,2,…,N;C ij is the jth diagonal element of the damping matrix of submodule i; R is any positive constant, and n k is the submodule number adjacent to submodule i, k is the number of submodules adjacent to submodule i; and are the coefficients of the modal coordinate term and the control force coupling term in the controller.

2. The distributed spacecraft solar panel vibration control method considering adjacent control forces according to claim 1 is characterized in that: In the step 1, the vibration equation of the solar panel submodule is: Among them, q i ∈R N×1 is the vibration modal coordinate of submodule i; M i ∈R N×N and K i ∈R N×N is the generalized mass matrix and stiffness matrix of submodule i; C i ∈R N×N is the damping matrix, and is Rayleigh damping, that is, C i =k m M i +k k K i , where the coefficient f1 and f2 are the upper and lower frequency limits of the sailboard, and ξ is the modal damping ratio; The modal form of the actuator and sensor equations of the entire windsurfing board are: Among them, η c ∈R m×1 is the first m-order master mode, is m×n c dimensional master mode matrix, ω l is the lth order natural frequency, ξ l is the l-th order modal damping ratio, is the measurement vector, They are the output matrices of acceleration, velocity, and displacement sensors, is the control force vector generated by the actuator, Φ c It is an n×m dimensional matrix composed of the m-order main mode vibration shapes.

3. The distributed spacecraft solar panel vibration control method considering adjacent control forces according to claim 1, characterized in that: In the step 2, the controllable and observable actuator and sensor position optimization criteria are obtained, and the actuator optimization configuration criteria are: The sensor optimization configuration criteria are: Among them, i is the number of the sailboard submodule, m is the number of the main control mode, σ ci is the controllability Gram matrix W c The singular value of represents the controllability of all the main control modes; σ oi is the controllability Gram matrix W o The singular values ​​of .

4. The distributed spacecraft solar panel vibration control method considering adjacent control forces according to claim 3 is characterized in that: Controllability Gram matrix W c The parsed form is: in, W cpq W c The two-row and two-column block matrix form of ; Take the actuator sensor equation When is the state variable, the pth row of the state equation B matrix; Observability Gram matrix W o The parsed form is: in W opq W o The two-row and two-column block matrix form of c rp For the actuator and sensor equations When it is a state variable, the sensor is the pth column of the output equation C matrix of the speed sensor; The actuator and sensor are installed in alignment, and two criterion coefficients of the same order of magnitude are combined into a comprehensive optimization criterion for controllability and observability: In the formula, J' c and J' o For J c and J o Unify the optimization configuration criteria for actuators and sensors of the same order of magnitude.

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