A ring-column deployable antenna beam pointing micro-vibration control method

Abstract

The present invention belongs to the field of antenna micro-vibration control technology, and specifically discloses a ring-column deployable antenna beam pointing micro-vibration control method, comprising the following steps: installing a voice coil actuator, a force sensor and a vibration response sensor on the antenna structure to obtain the axial force of the actuator cable and the vibration response information of the antenna structure; using the cable unit and beam unit of the antenna structure to establish a finite element model, performing dynamic analysis to obtain the frequency response data, modal vibration shape and damping ratio of the antenna, and selecting a control modal target; designing a beam pointing vibration controller to calculate the modal control force; converting the modal control force into a control signal, inputting the control force into an actuator to generate the control force, and realizing effective control of the vibration of the antenna beam pointing. The present invention solves the problem that the low-frequency micro-vibration problem encountered by the ring-column deployable antenna in space applications will significantly reduce the pointing stability of the antenna beam, and improves the pointing stability of the antenna beam.

Description

Technical Field

[0001] The invention belongs to the technical field of antenna micro-vibration control, and in particular relates to the design of a ring-column deployable antenna beam pointing micro-vibration control method. Background Art

[0002] Large-scale space cable net antennas play a key role in satellite microwave communications, remote sensing, deep space exploration and other fields. The ring-column deployable antenna is applied to a variety of ultra-large space cable net antenna structures with its advantages of high shrinkage ratio, light weight and high reliability. In order to complete tasks such as communication or remote sensing observation, it is necessary to ensure the precise beam pointing of the ring-column deployable antenna to the target under maneuvering or jet interference. Therefore, the antenna beam must have extremely high on-orbit pointing stability to ensure the accuracy and efficiency of signal transmission.

[0003] However, the ring-column deployable antenna that is deployed and locked in orbit has greater structural flexibility, lower stiffness and weaker damping due to its light weight and large size. These characteristics cause the antenna to exhibit low-frequency and dense spectrum characteristics at its natural frequency. When the antenna is subjected to internal and external interference such as thermal flutter, jet attitude adjustment, and motor jitter, multimodal vibration will inevitably occur. Multimodal vibration will significantly reduce the directional qualitativeness of the antenna beam and may even cause damage to the antenna structure.

[0004] To address this issue, traditional PID Although control can produce a certain control effect on multiple modes to a certain extent, it cannot achieve precise control of specific modes. However, in the multi-modal vibration of the ring-column deployable antenna, there are usually some main modes that have a significant impact on the pointing stability of the beam. If the vibration of these modes cannot be effectively controlled, the stability performance of the antenna will be directly reduced. Therefore, developing a method that can accurately control the micro-vibration of the key modes of the ring-column deployable antenna has important application value and theoretical significance. Summary of the invention

[0005] The purpose of the present invention is to solve the problem of low-frequency micro-vibration encountered by a ring-column deployable antenna in space applications, which will significantly reduce the pointing stability of the antenna beam. A method for controlling the micro-vibration of the beam pointing of a ring-column deployable antenna is proposed.

[0006] The technical solution of the present invention is: a ring-column deployable antenna beam pointing micro-vibration control method, comprising the following steps:

[0007] S1. Use multiple antenna support cables symmetrical about the center of the column as actuating cables, and install voice coil actuators, force sensors, and vibration response sensors to obtain the axial force of the actuating cables and the vibration response information of the antenna structure;

[0008] S2. Based on the axial force of the actuating cable, the antenna structural parameters and the basic characteristics of its components, a finite element model is established using the cable unit and beam unit of the antenna structure, and a dynamic analysis is performed based on the finite element model to obtain the frequency response data, modal vibration shape and damping ratio of the antenna;

[0009] S3. Selecting a control mode target according to the antenna mode shape;

[0010] S4. According to the vibration response information of the antenna structure, the frequency response data of the antenna, the damping ratio of the antenna and the control mode target, a beam pointing vibration controller is designed based on the independent modal space control theory, and the modal control force is calculated;

[0011] S5. The modal control force is converted into a control signal using the modal superposition principle, and the control signal is input into the voice coil actuator to generate a physical control force, thereby achieving effective control of the vibration of the antenna beam pointing.

[0012] The beneficial effects of the present invention are:

[0013] 1. The present invention adopts independent modal space control theory to effectively achieve decoupling between modes, thereby simplifying the control design process. This decoupling capability enables more precise and targeted control of key vibration modes that affect beam pointing performance.

[0014] 2. The sliding mode controller used in the present invention is insensitive to changes in system parameters and external disturbances. This controller does not require online identification, can quickly respond to changes in system states, and exhibits strong stability.

[0015] 3. The control method of the present invention shortens the transition time of the antenna beam pointing and improves the pointing stability of the antenna beam, thereby providing a strong guarantee for the smooth implementation of high-precision remote sensing and communication tasks.

[0016] Preferably, in step S1, the voice coil actuator is located on a side of the actuating cable close to the annular frame beam, and the force sensor is connected in series with the voice coil actuator;

[0017] The force sensor is located at the connection between the actuating cable and the annular frame beam;

[0018] The vibration response information is vibration displacement, vibration velocity or vibration acceleration.

[0019] The beneficial effects of the above preferred solution are:

[0020] Installing a voice coil actuator as an actuator in the antenna structure, and installing a force sensor and a force sensor to respectively measure the axial force of the actuator cable and the vibration response of the antenna structure under external disturbance and control, will help to accurately analyze the antenna structure and enable more precise and targeted control of those key vibration modes that affect the beam pointing performance.

[0021] Preferably, the step S4 specifically comprises the following steps:

[0022] S41. Designing a modal filter according to the control modal target and the frequency response data of the antenna;

[0023] S42. Extracting modal information from the vibration response information of the antenna structure using a modal filter;

[0024] S43. Design a state observer, and use the state observer to extract modal displacement and modal velocity from modal information based on the damping ratio and the natural circular frequency of the system;

[0025] S44. Design a modal controller based on the modal displacement and modal velocity, complete the design of the beam pointing vibration controller, and obtain the modal control force.

[0026] The beneficial effects of the above preferred solution are:

[0027] The precise conversion from physical information to modal information is achieved through modal filters and state observers, and the modal control force is determined from the modal information using a sliding mode controller, thus simplifying the control process.

[0028] Preferably, the step S41 specifically includes the following steps:

[0029] S411. For the control mode target, the antenna's first Dynamic equations of the first-order mode;

[0030] S412. According to the antenna The vibration response information of each mode is obtained by calculating the dynamic equation of the mode and the vibration response information;

[0031] S413. According to each order modal vibration response information, the modal filter decoupling matrix is ​​calculated to complete the modal filter design for controlling the modal target.

[0032] As a preference, the antenna in step S411 The dynamic equation of the first mode is:

[0033] in, Indicates The acceleration of the first mode, Indicates The damping ratio of the first mode, Indicates the antenna structure The natural circular frequency of the order mode, Indicates The velocity of the first mode, Indicates The first modal displacement, Indicates Order mode excitation;

[0034] The calculation formula of the vibration response information of each mode in step S412 is:

[0035]

[0036] in, represents the node acceleration vector, represents the node velocity vector, represents the node displacement vector, represents the modal filter decoupling matrix Column vector, i.e. order mode filter vector;

[0037] The calculation relationship of the modal filter decoupling matrix in step S413 is:

[0038]

[0039] in, represents the modal coordinate vector, represents the modal filter decoupling matrix, the superscript represents the transpose of a matrix, represents the number of degrees of freedom measured by the vibration response sensor, Represents the node displacement vector No. vector, that is, the antenna is displacement in degrees of freedom.

[0040] Preferably, the calculation formula for the modal displacement and modal velocity from the modal information using the state observer in step S43 is:

[0041]

[0042] in, represents the state observer The state vector of order, represents the state observer Order state vector The first derivative of represents the state matrix, , Indicates The damping ratio of the first mode, Indicates the antenna structure The natural circular frequency of the order mode, represents the input matrix, , Indicates The modal control force, represents the output error feedback matrix of the observer, represents the state observer The output vector of order, represents the system to be observed The actual output vector of order.

[0043] Preferably, the mode controller in step S44 is connected to the sliding mode controller via PD The controller is designed in parallel, specifically: The first-order mode is selected, the tracking error, switching function and switching control are selected, and the saturation function is used for control design to obtain the modal control force under the sliding mode controller; PD The controller is connected in parallel with the sliding mode controller to obtain a modal controller; and the modal control force is obtained according to the modal controller.

[0044] Preferably, the calculation formula of the modal control force in step S4 is:

[0045]

[0046] in, represents the modal control force, represents the modal displacement tracking error The first derivative of represents the switching function of the sliding mode controller in the modal controller, , represents the coefficient of the first-order term in the switching function, represents the modal controller connected in parallel with the sliding mode controller PD The controller's derivative gain, express PD The proportional gain in the controller, represents the modal coordinate vector of the controlled mode, The modal coordinate vector representing the controlled mode The first derivative of The modal coordinate vector representing the controlled mode The second-order derivative of The modal coordinate vector representing the controlled mode The third-order derivative of represents the modal damping ratio of the controlled mode; represents the natural circular frequency of the controlled mode; It represents the speed at which the moving point of the system approaches the sliding surface; represents the saturation function; Represents the coefficient of the exponential reaching term in the exponential reaching law adopted by the sliding mode controller.

[0047] The beneficial effects of the above preferred solution are:

[0048] The sliding mode controller is used to determine the modal control force from the modal information and PD The controller is connected in parallel with the sliding mode controller, which optimizes the control effect and can effectively suppress the structural vibration phenomenon that may be caused by the sliding mode controller.

[0049] Preferably, the calculation formula of the control force in step S5 is:

[0050]

[0051] in, Indicates physical control. Indicates the modal truncation before The transposed matrix of the order mode matrix, Represents the mounting position matrix of the voice coil actuator, represents the modal control force vector, Indicates The control force output by each voice coil actuator is Indicates The control signal of each voice coil actuator is the input current. and Represents the inherent properties of discrete electromagnetic voice coil actuators, Indicates the total number of voice coil actuators.

[0052] The beneficial effects of the above preferred solution are:

[0053] The modal control force is converted into the physical control force required for each voice coil motor, which enables effective control of the vibration of the antenna beam pointing. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 Shown is a flow chart of a ring-column deployable antenna beam pointing micro-vibration control method.

[0055] Figure 2 The figure shows the installation position diagram of each sensor and voice coil actuator when the number of sensors installed on the annular frame is 4.

[0056] Figure 3The figure shows a side view of the installation positions of each sensor and the voice coil actuator when the number of sensors installed on the annular frame is 4.

[0057] Figure 4 The figure shows a schematic diagram of a three-dimensional model of the installation positions of each sensor and the voice coil actuator when the number of sensors installed on the annular frame is 4.

[0058] Figure 5 The figure shows a schematic diagram of the second-order modal vibration shape analysis of the control object, where the dotted line represents the initial state of the antenna and the solid line represents the second-order modal vibration shape.

[0059] Among them: 1. Ring-column antenna structure; 2. Sensing and actuating device; 11. Ring frame; 12. Antenna supporting inclined cable; 13. Center column; 21. Voice coil actuator; 22. Force sensor; 23. Vibration response sensor. DETAILED DESCRIPTION

[0060] Now, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. It should be understood that the embodiments shown and described in the accompanying drawings are only exemplary and are intended to explain the principles and spirit of the present invention, rather than to limit the scope of the present invention.

[0061] Embodiment 1, as Figure 1 As shown, a ring-column expandable antenna beam pointing micro-vibration control method comprises the following steps:

[0062] S1. A plurality of antenna supporting inclined cables 12 are symmetrical about the center of the column as the actuating cables, and a voice coil actuator 21, a force sensor 22 and a vibration response sensor 23 are installed to obtain the axial force of the actuating cable and the vibration response information of the antenna structure;

[0063] S2. Based on the axial force of the actuating cable, the antenna structural parameters and the basic characteristics of its components, a finite element model is established using the cable unit and beam unit of the antenna structure, and a dynamic analysis is performed based on the finite element model to obtain the frequency response data, modal vibration shape and damping ratio of the antenna;

[0064] S3. According to the modal vibration shape of the antenna, select the mode that has a significant impact on the beam pointing stability as the control mode target;

[0065] S4. According to the vibration response information of the antenna structure, the frequency response data of the antenna, the damping ratio of the antenna and the control mode target, a beam pointing vibration controller is designed based on the independent modal space control theory, and the modal control force is calculated;

[0066] S5. The modal control force is converted into a control signal using the modal superposition principle, and the control signal is input into the voice coil actuator 21 to generate a physical control force, thereby achieving effective control of the vibration of the antenna beam pointing direction.

[0067] In this embodiment, the voice coil actuator in step S1 is located on the side of the actuating cable close to the beam of the annular frame 11, and the force sensor 22 is connected in series with the voice coil actuator 21;

[0068] The vibration response sensor 23 is located at the connection between the actuating cable and the beam of the annular frame 11;

[0069] The vibration response information is vibration displacement, vibration velocity or vibration acceleration.

[0070] like Figure 2 , Figure 3 and Figure 4 As shown, in this embodiment, the number of sensors installed on the annular frame 11 of the ring-column antenna structure 1 is 4, and the sensing and actuating device 2 is symmetrically installed on the beam of the annular frame 11 about the central column 13. The sensing and actuating device 2 includes a plurality of vibration response sensors 23 for measuring the vibration response of the structure. According to the task requirements, the vibration response sensor 23 can be a displacement sensor or a velocity sensor or an acceleration sensor, but the sensor specifications are required to be consistent. The voice coil actuator 21 and the force sensor 22 are connected in series on the two antenna supporting inclined cables 12 adjacent to the vibration response sensor 23 to apply control force and measure the axial force of the cable.

[0071] In this embodiment, the control mode target selects the second mode vibration shape, such as Figure 5 As shown, in this mode, the entire antenna structure swings around the fixed end, causing a large deflection in the plane where the beam of the annular frame 11 is located, thereby causing a large-angle deflection of the beam pointing.

[0072] In this embodiment, step S4 specifically includes the following steps:

[0073] S41. Designing a modal filter according to the control modal target and the frequency response data of the antenna;

[0074] S42. Extracting modal information from the vibration response information of the antenna structure using a modal filter;

[0075] S43. Design a state observer, and use the state observer to extract modal displacement and modal velocity from modal information based on the damping ratio and the natural circular frequency of the system;

[0076] S44. Design a modal controller based on the modal displacement and modal velocity, complete the design of the beam pointing vibration controller, and obtain the modal control force.

[0077] In this embodiment, step S41 specifically includes the following steps:

[0078] S411. For the control mode target, the antenna's first Dynamic equations of the first-order mode;

[0079] S412. According to the antenna The vibration response information of each mode is obtained by calculating the dynamic equation of the mode and the vibration response information;

[0080] S413. According to each order modal vibration response information, the modal filter decoupling matrix is ​​calculated to complete the modal filter design for controlling the modal target.

[0081] In this embodiment, without considering the rigid-flexible coupling effect between the spacecraft body and the flexible antenna, the dynamic equation of the antenna is:

[0082]

[0083] in, They are the node displacement vector, velocity vector and acceleration vector respectively; They are the mass matrix, damping matrix and stiffness matrix of the whole antenna structure respectively; They are the control force vector generated by the actuator and the external interference force vector on the structure; is the actuator installation position matrix, , , and Represent sets of real numbers of different dimensions;

[0084] According to the basic assumption of the mode superposition method that the displacement is linearly related to the natural mode, that is:

[0085]

[0086] in, is the mode matrix, is the natural frequency of the structure The corresponding natural vibration mode; Indicates The first modal displacement, Represents the modal coordinate vector , is the modal number.

[0087] Get the antenna The dynamic equation of the first mode is:

[0088]

[0089] in, Indicates The acceleration of the first mode, Indicates The damping ratio of the first mode, Indicates the antenna structure The natural frequency of the order mode, Indicates The velocity of the first mode, Indicates The first modal displacement, Indicates Order mode excitation;

[0090] The calculation formula of the acceleration, velocity or displacement of each mode in step S412 is:

[0091]

[0092] in, represents the node acceleration vector, represents the node velocity vector, represents the node displacement vector, represents the modal filter decoupling matrix Column vector, i.e. order mode filter vector;

[0093] The calculation relationship of the modal filter decoupling matrix in step S413 is:

[0094]

[0095] in, represents the modal coordinate vector, represents the modal filter decoupling matrix, the superscript represents the transpose of a matrix, represents the number of degrees of freedom measured by the vibration response sensor, Represents the node displacement vector No. vector, that is, the antenna is displacement in degrees of freedom.

[0096] In this embodiment, the modal displacement and modal velocity are obtained from the modal information using a state observer, specifically:

[0097] By antenna The dynamic equation of the first-order mode obtains the antenna structure First-order modal control force Under the action of The modal equation is:

[0098]

[0099] in, Indicates The acceleration of the first mode, Indicates The damping ratio of the first mode, Indicates the antenna structure The natural frequency of the order mode, Indicates The velocity of the first mode, Indicates The first modal displacement, Indicates The first-order mode excitation of the antenna structure The first-order modal equation is transformed into the state space equation:

[0100]

[0101] in, represents the state matrix, , The antenna structure The state vector of order, , Indicates the antenna structure The first-order derivative of the state vector, represents the input matrix, , is the output matrix of the corresponding dimension, Represents the modal control force vector, which can be sensed by the force sensor and the cable axial force get;

[0102] Then, the calculation formula of modal displacement and modal velocity from modal information using state observer is obtained as follows:

[0103]

[0104] in, represents the state observer The state vector of order, represents the state observer Order state vector The first derivative of represents the state matrix, , Indicates The damping ratio of the first mode, Indicates the antenna structure The natural circular frequency of the order mode, represents the input matrix, , represents the output error feedback matrix of the observer, represents the state observer The output vector of order, represents the system to be observed The actual output vector of order.

[0105] In this embodiment, the mode controller in step S44 is connected to the sliding mode controller via PD The controller is designed in parallel, specifically: The first-order mode is selected, the tracking error, switching function and switching control are selected, and the saturation function is used for control design to obtain the modal control force under the sliding mode controller; PD The controller is connected in parallel with the sliding mode controller to obtain the modal control force.

[0106] For order mode, rewrite the antenna structure The first-order modal dynamic equation is:

[0107]

[0108] in, represents the modal coordinate vector of the controlled mode, The modal coordinate vector representing the controlled mode The first derivative of The modal coordinate vector representing the controlled mode The second-order derivative of represents the modal damping ratio of the controlled mode; represents the natural circular frequency of the controlled mode, represents the modal control force, Indicates external interference, represents the modal coordinate vector, Represents the modal coordinate vector The first derivative of A state vector representing the antenna structure;

[0109] The first derivative of the switching function of the sliding mode controller in the modal controller:

[0110]

[0111] in, It represents the speed at which the moving point of the system approaches the sliding surface. For added interference, and there is an upper limit on interference , is the preset threshold;

[0112] Set the tracking error to:

[0113]

[0114] in, represents the tracking error, Represents the modal coordinate vector target value. Since the control purpose is to suppress vibration, is the zero vector, represents the modal coordinate vector;

[0115] Select the switch function for:

[0116]

[0117] in, represents the modal displacement tracking error The first derivative of represents the switching function of the sliding mode controller in the modal controller, Represents the coefficient of the first-order term in the switching function;

[0118] Let the first-order derivative of the switching function of the sliding mode controller in the modal controller be , the equivalent controller is calculated :

[0119] ;

[0120] In order to ensure that the state of the system does not leave the sliding surface after reaching the sliding surface, a switching control is designed. :

[0121]

[0122] in, represents the symbolic function, represents the switching control term coefficient, that is, the rate at which the system's moving point approaches the sliding surface, represents the coefficient of the exponential reaching term in the exponential reaching law adopted by the sliding mode controller, . Then the sliding mode control law expression is obtained:

[0123]

[0124] Considering the model uncertainty and potential large disturbances, in order to ensure the stability of the system, the control term coefficient is switched It needs to be set larger. However, this may lead to aggravated vibration. To avoid this, a saturation function is used. Replace symbol function Conduct control design, namely:

[0125]

[0126] in, and Indicates the preset threshold value;

[0127] This leads to the sliding mode control law:

[0128] ;

[0129] Will PD The controller and the sliding mode controller are connected in parallel to obtain the final modal control force:

[0130]

[0131] in, represents the modal control force, represents the modal displacement tracking error The first derivative of represents the switching function of the sliding mode controller in the modal controller, , represents the coefficient of the first-order term in the switching function, represents the modal controller connected in parallel with the sliding mode controller PD The controller's derivative gain, express PD The proportional gain in the controller, represents the modal coordinate vector of the controlled mode, The modal coordinate vector representing the controlled mode The first derivative of The modal coordinate vector representing the controlled mode The second-order derivative of The modal coordinate vector representing the controlled mode The third-order derivative of represents the modal damping ratio of the controlled mode; represents the natural circular frequency of the controlled mode; It represents the speed at which the moving point of the system approaches the sliding surface; represents the saturation function; Represents the coefficient of the exponential reaching term in the exponential reaching law adopted by the sliding mode controller.

[0132] In this embodiment, the calculation formula of the control force in step S5 is:

[0133]

[0134] in, Indicates physical control. Indicates the modal truncation before The transposed matrix of the order mode matrix, Represents the mounting position matrix of the voice coil actuator, represents the modal control force vector, Indicates The control force output by each voice coil actuator is Indicates The control signal of each voice coil actuator is the input current. and Represents the inherent properties of discrete electromagnetic voice coil actuators, Indicates the total number of voice coil actuators.

[0135] In Embodiment 2, the vibration response sensor 23 is an acceleration sensor, and the obtained vibration response information is vibration acceleration. The design steps of the modal filter are specifically as follows:

[0136] By antenna The dynamic equation of the first-order mode and the conversion relationship between the modal control force and the physical control force of the actuator:

[0137]

[0138] in, represents the modal control force vector, Indicates the modal truncation before The transposed matrix of the order mode matrix, Indicates physical control. represents the installation position matrix of the voice coil actuator; the first Frequency response function of the ring-column antenna structure when the control force is applied to the degree of freedom :

[0139]

[0140] in, For the system Order natural vibration mode, corresponding to the modal truncation vibration mode matrix No. column vector; For the system The first degree of freedom Order mode parameters, corresponding to the modal cutoff mode matrix No. Line The elements of the column, Indicates The damping ratio of the first mode, Indicates the antenna structure The natural circular frequency of the order mode, represents the natural circular frequency of the controlled mode, represents the order of the mode matrix, Represents an imaginary unit.

[0141] Frequency response function of the ring-column antenna structure Left multiplication Order mode filter vector , and considering the orthogonality and normalization characteristics of the modes, we can get the solution The calculation relationship is:

[0142]

[0143] in, , is the unknown column vector, select the appropriate observation point frequency Get the frequency response data at different selected frequencies and value, thus we can establish a is a set of equations with unknown variables to achieve Therefore, each modal acceleration can be calculated through the physical measurement value of the physical acceleration.

[0144] In this embodiment, the modal displacement and modal velocity are extracted from the modal acceleration, and the design steps of the state observer are specifically as follows:

[0145] Introduction Luenberger The state observer extracts the modal displacement and modal velocity, and the calculation formula is:

[0146]

[0147] in, represents the state observer The state vector of order, represents the state observer Order state vector The first derivative of represents the state matrix, , Indicates The damping ratio of the first mode, Indicates the antenna structure The natural circular frequency of the order mode, represents the input matrix, , Indicates The modal control force, represents the output error feedback matrix of the observer, represents the state observer The output vector of order, represents the system to be observed The actual output vector of order, represents the matrix of corresponding dimension, , , define the state error vector :

[0148]

[0149] in, Indicates the antenna structure The state vector of order, , Indicates The velocity of the first mode, Indicates The first modal displacement;

[0150] The state error equation is obtained:

[0151]

[0152] in, represents the state error vector The first derivative of represents the identity matrix of the corresponding dimension;

[0153] The solution is:

[0154]

[0155] in, express The state error vector at time , express The state error vector at the moment can be obtained by selecting a suitable error feedback matrix , so that With enough negative real parts, the observation error can be made to approach zero exponentially, resulting in the observed mode being as close to the true mode as possible.

[0156] Embodiment 3, the vibration response sensor 23 is a velocity sensor, and the obtained vibration response information is the vibration velocity. The design steps of the modal filter are specifically as follows:

[0157] By antenna The dynamic equation of the first mode and the conversion relationship between the modal control force and the physical control force of the actuator are obtained. The frequency response function of the ring-column antenna structure when the control force is applied to the degree of freedom is:

[0158]

[0159] in, For the system Order natural vibration mode, corresponding to the modal truncation vibration mode matrix No. column vector; For the system The first degree of freedom Order mode parameters, corresponding to the modal cutoff mode matrix No. Line The elements of the column, Indicates The damping ratio of the first mode, Indicates the antenna structure The natural circular frequency of the order mode, represents the natural circular frequency of the controlled mode, represents the order of the mode matrix, Represents an imaginary unit.

[0160] Frequency response function of the ring-column antenna structure Left multiplication Order mode filter vector , and considering the orthogonality and normalization characteristics of the modes, we can get the solution The calculation relationship is:

[0161]

[0162] in, , is the unknown column vector, select the appropriate observation point frequency Get the frequency response data at different selected frequencies and value, thus we can establish a is a set of equations with unknown variables to achieve Therefore, each modal velocity can be calculated through the physical measurement value of the physical velocity.

[0163] In this embodiment, the modal displacement is extracted from the modal velocity, and the design steps of the state observer are specifically as follows:

[0164]

[0165] Among them, among them, represents the state observer The state vector of order, represents the state observer Order state vector The first derivative of represents the state matrix, , Indicates The damping ratio of the first mode, Indicates the antenna structure The natural circular frequency of the order mode, represents the input matrix, , Indicates The modal control force, represents the output error feedback matrix of the observer, represents the state observer The output vector of order, represents the system to be observed The actual output vector of order, represents the matrix of corresponding dimension, , , Indicates the antenna structure The state vector of order, , Indicates The velocity of the first mode, Indicates The first-order mode displacement; the state error equation is obtained:

[0166]

[0167] in, represents the state error vector The first derivative of ;

[0168] The solution is:

[0169]

[0170] in, express The state error vector at time , express The state error vector at the moment can be obtained by selecting a suitable error feedback matrix , so that With enough negative real parts, the observation error can be made to approach zero exponentially, resulting in the observed mode being as close to the true mode as possible.

[0171] Embodiment 4: the vibration response sensor 23 is a displacement sensor, and the obtained vibration response information is vibration displacement. The design steps of the modal filter are specifically as follows:

[0172] By antenna The dynamic equation of the first mode and the conversion relationship between the modal control force and the physical control force of the actuator are obtained. The frequency response function of the ring-column antenna structure when the control force is applied to the degree of freedom is:

[0173]

[0174] in, For the system Order natural vibration mode, corresponding to the modal truncation vibration mode matrix No. column vector; For the system The first degree of freedom Order mode parameters, corresponding to the modal cutoff mode matrix No. Line The elements of the column, Indicates The damping ratio of the first mode, Indicates the antenna structure The natural circular frequency of the order mode, represents the natural circular frequency of the controlled mode, represents the order of the mode matrix, Represents an imaginary unit.

[0175] Frequency response function of the ring-column antenna structure Left multiplication Order mode filter vector , and considering the orthogonality and normalization characteristics of the modes, we can get the solution The calculation relationship is:

[0176]

[0177] in, , is the unknown column vector, select the appropriate observation point frequency Get the frequency response data at different selected frequencies and value, thus we can establish a is a set of equations with unknown variables to achieve Therefore, each modal displacement can be calculated through the physical measurement value of the physical displacement.

[0178] In this embodiment, the modal velocity is extracted from the modal displacement, , , represents the matrix of corresponding dimension, represents the system to be observed The actual output vector of order, Indicates the antenna structure The state vector of order, , Indicates The velocity of the first mode, Indicates The modal displacement.

[0179] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A ring-column deployable antenna beam pointing micro-vibration control method, characterized in that: The following steps are involved: S1. Using multiple antenna support inclined cables (12) symmetrical about the center of the column as actuating cables, and installing a voice coil actuator (21), a force sensor (22) and a vibration response sensor (23) to obtain axial force of the actuating cable and vibration response information of the antenna structure; S2. Based on the axial force of the actuating cable, the antenna structural parameters and the basic characteristics of its components, a finite element model is established using the cable unit and beam unit of the antenna structure, and a dynamic analysis is performed based on the finite element model to obtain the frequency response data, modal vibration shape and damping ratio of the antenna; S3. Selecting a control mode target according to the antenna mode shape; S4. According to the vibration response information of the antenna structure, the frequency response data of the antenna, the damping ratio of the antenna and the control mode target, a beam pointing vibration controller is designed based on the independent modal space control theory, and the modal control force is calculated, which specifically includes the following steps: S41. Designing a modal filter according to the control modal target and the frequency response data of the antenna; S42. Extracting modal information from the vibration response information of the antenna structure using a modal filter; S43. Design a state observer, and use the state observer to extract modal displacement and modal velocity from modal information based on the damping ratio and the natural circular frequency of the system; S44. Design a modal controller according to the modal displacement and modal velocity, complete the design of the beam pointing vibration controller, and obtain the modal control force; The calculation formula of the modal control force is: in, represents the modal control force, represents the modal displacement tracking error The first derivative of represents the switching function of the sliding mode controller in the modal controller, , represents the coefficient of the first-order term in the switching function, represents the modal controller connected in parallel with the sliding mode controller PD The controller's derivative gain, express PD The proportional gain in the controller, represents the modal coordinate vector of the controlled mode, The modal coordinate vector representing the controlled mode The first derivative of The modal coordinate vector representing the controlled mode The second-order derivative of The modal coordinate vector representing the controlled mode The third-order derivative of represents the modal damping ratio of the controlled mode; represents the natural circular frequency of the controlled mode; It represents the speed at which the moving point of the system approaches the sliding surface; represents the saturation function; represents the coefficient of the exponential reaching term in the exponential reaching law adopted by the sliding mode controller; S5. The modal control force is converted into a control signal by using the modal superposition principle, and the control signal is input into the voice coil actuator (21) to generate a physical control force, thereby achieving effective control of the vibration of the antenna beam pointing.

2. The ring-column deployable antenna beam pointing micro-vibration control method according to claim 1, characterized in that: In step S1, the voice coil actuator (21) is located on a side of the actuating cable close to the beam of the annular frame (11), and the force sensor (22) is connected in series with the voice coil actuator (21); The vibration response sensor (23) is located at the connection between the actuating cable and the beam of the annular frame (11); The vibration response information is vibration displacement, vibration velocity or vibration acceleration.

3. The ring-column deployable antenna beam pointing micro-vibration control method according to claim 1, characterized in that: The step S41 specifically includes the following steps: S411. For the control mode target, the antenna's first Dynamic equations of the first-order mode; S412. According to the antenna The vibration response information of each mode is obtained by calculating the dynamic equation of the mode and the vibration response information; S413. According to each order modal vibration response information, the modal filter decoupling matrix is ​​calculated to complete the modal filter design for controlling the modal target.

4. The ring-column deployable antenna beam pointing micro-vibration control method according to claim 3, characterized in that: In step S411, the antenna The dynamic equation of the first mode is: in, Indicates The acceleration of the first mode, Indicates The damping ratio of the first mode, Indicates the antenna structure The natural circular frequency of the order mode, Indicates The velocity of the first mode, Indicates The first modal displacement, Indicates Order mode excitation; The calculation formula of the vibration response information of each mode in step S412 is: in, represents the node acceleration vector, represents the node velocity vector, represents the node displacement vector, represents the modal filter decoupling matrix Column vector, i.e. order mode filter vector; The calculation relationship of the modal filter decoupling matrix in step S413 is: in, represents the modal coordinate vector, represents the modal filter decoupling matrix, the superscript represents the transpose of a matrix, represents the number of degrees of freedom measured by the vibration response sensor, Represents the node displacement vector No. vector, that is, the antenna is displacement in degrees of freedom.

5. The ring-column deployable antenna beam pointing micro-vibration control method according to claim 1, characterized in that: The calculation formula of the modal displacement and modal velocity from the modal information using the state observer in step S43 is: in, represents the state observer The state vector of order, represents the state observer Order state vector The first derivative of represents the state matrix, , Indicates The damping ratio of the order mode, Indicates the antenna structure The natural circular frequency of the order mode, represents the input matrix, , Indicates The modal control force, represents the output error feedback matrix of the observer, represents the state observer The output vector of order, represents the system to be observed The actual output vector of order.

6. The ring-column deployable antenna beam pointing micro-vibration control method according to claim 1, characterized in that: In step S44, the modal controller is connected to the PD The controller is designed in parallel, specifically: The first-order mode is selected, the tracking error, switching function and switching control are selected, and the saturation function is used for control design to obtain the modal control force under the sliding mode controller; PD The controller is connected in parallel with the sliding mode controller to obtain a modal controller; and the modal control force is obtained according to the modal controller.

7. The ring-column deployable antenna beam pointing micro-vibration control method according to claim 1, characterized in that: The calculation formula of the physical control force in step S5 is: in, Indicates physical control. Indicates the modal truncation before The transposed matrix of the order mode matrix, Represents the mounting position matrix of the voice coil actuator, represents the modal control force vector, Indicates The control force output by each voice coil actuator is Indicates The control signal of each voice coil actuator is the input current. and Represents the inherent properties of discrete electromagnetic voice coil actuators, Indicates the total number of voice coil actuators.

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