A space ring-cylinder antenna satellite distributed active cable vibration control method

Abstract

The application discloses a kind of space ring column antenna satellite distributed active cable vibration control method, it belongs to space large ring column antenna satellite control technical field.The application solves the problem of poor robustness of the existing space large ring column antenna satellite vibration control method.The application ensures that the system can accurately adjust the pretightening force of cable to respond to external disturbance through controllability analysis.Based on model predictive control technology, a distributed model predictive control strategy is designed to predict and control the vibration response at future time. An objective optimization function is established to optimize the cable pretightening force adjustment strategy in the rolling time domain, real-time response to the dynamic changes of the structure. The distributed active cable vibration control method optimizes the vibration suppression process, improves the robustness of the system, and effectively ensures the performance of the antenna and the quality of signal reception. The application can be applied to the control of space large ring column antenna satellite.

Description

Technical Field

[0001] This invention belongs to the field of space large ring-pillar antenna satellite control technology, specifically relating to a distributed active cable vibration control method for space ring-pillar antenna satellites. Background Technology

[0002] Large space-based ring-pillar antenna satellites play an irreplaceable role as crucial space-based equipment in space remote sensing, electronic reconnaissance, and deep space exploration. With ever-increasing demands for signal reception frequency and detection accuracy, space antenna structural designs are evolving towards larger apertures and higher gains. This presents greater challenges to vibration control systems. Due to the complexity of the space environment, large space-based ring-pillar antenna satellites are prone to structural vibration under on-orbit conditions. Therefore, vibration control is one of the key technologies for realizing on-orbit missions of large space structures, and the effectiveness of vibration control directly affects the antenna signal quality.

[0003] However, under external disturbances, the robustness of existing vibration control methods for large space-based ring-pillar antenna satellites is still poor. Therefore, it is essential to propose a new vibration control method to ensure the performance and signal reception quality of large space-based ring-pillar antenna satellites. Summary of the Invention

[0004] The purpose of this invention is to address the problem of poor robustness of existing vibration control methods for large space ring-pillar antenna satellites under external disturbances, and to propose a distributed active cable vibration control method for space ring-pillar antenna satellites.

[0005] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a method for distributed active cable vibration control of a space ring-pillar antenna satellite, the method specifically including the following steps:

[0006] Step 1: Establish a finite element model of the flexible space ring-pillar antenna satellite system, then abstract the structure of the flexible space ring-pillar antenna satellite system into various rod elements, beam elements and plate elements, and construct a dynamic model of the flexible space ring-pillar antenna satellite system based on the finite element model and the abstract results.

[0007] Step 2: Perform modal decomposition on the inertia matrix, damping matrix, and stiffness matrix in the dynamic model, and obtain the model after modal coordinate transformation based on the dynamic model and the modal decomposition results;

[0008] Step 3: Establish state variables based on the model after modal coordinate transformation, and construct a modal space model of the flexible satellite system with a space ring-shaped antenna based on the state variables;

[0009] Step 4: Iteratively optimize the control node positions of the space ring-shaped antenna satellite flexible system based on the modal space model, and arrange distributed active cables based on the optimization results of the control node positions;

[0010] Step 5: Vibration control of the distributed active cables of the flexible system of the space ring-pillar antenna satellite is carried out using model predictive control algorithms.

[0011] Furthermore, the dynamic model of the space ring-shaped antenna satellite flexible system is as follows:

[0012]

[0013] In the formula, M, C′, and K are the inertial matrix, damping matrix, and stiffness matrix of the flexible system of the space ring-shaped antenna satellite, respectively; B′ is the actuator arrangement matrix; and F... c Let x be the control force vector for the cable, and let x represent the vector composed of the coordinates of each control node. Denotes the first derivative of x. Let x represent the second derivative.

[0014] Furthermore, the model after the modal coordinate transformation is as follows:

[0015] x=Φη (2)

[0016] In the formula, η is the n-dimensional modal coordinate vector of the flexible system of the space ring-pillar antenna satellite, and Φ is the first n-order regular mode matrix.

[0017] Furthermore, the modal space model of the space ring-shaped antenna satellite flexible system is as follows:

[0018]

[0019] y=CX (4)

[0020] In the formula, the state variable It is the first derivative of η. is the first derivative of X, u represents the system control quantity, and y represents the system output;

[0021] The state space matrices A, B, and C are in the following forms:

[0022]

[0023] In the formula, I represents the identity matrix, the superscript T denotes the transpose of the matrix, and the frequency matrix... Damping coefficient matrix B c Represents the distributed cable control matrix. Let denot η as the second derivative, and F as the modal space force.

[0024] Furthermore, the distributed active cable includes an inner ring distributed active cable and an outer ring distributed active cable.

[0025] Furthermore, the control node of the inner ring distributed active cable is located on the antenna surface of the space ring-pillar antenna satellite flexible system;

[0026] The entire antenna profile is divided into N equal parts along the circumference, and a control node is set on the corresponding truss in each part.

[0027] Furthermore, the control node of the outer ring distributed active cable is located on the ring hoop of the space ring-pillar antenna satellite flexible system;

[0028] The ring is divided into N equal parts along the circumference, and a control node is set in each part.

[0029] Furthermore, the iterative optimization of the control node positions of the flexible space ring-shaped antenna satellite system based on the modal space model is specifically performed as follows:

[0030] Step 4.1: Initialize the number of iterations l = 1;

[0031] Step 4.2: Within the antenna profile range of the i-th control node of the inner ring distributed active cable, randomly initialize the position (x) of the i-th control node in the l-th iteration. l,i ,y l,i ,z l,i );

[0032] Step 4.3: Adjust the control force u at both ends of the cable. s The components in the three-axis directions are represented as follows:

[0033] u s =[T ax1 T ay1 T az1 T ax2 T ay2 T az2 (12)

[0034] In the formula:

[0035]

[0036] Then the distributed cable control matrix B c for:

[0037]

[0038] Where, φ x1 φ y1 φ z1 φ x2 φ y2 φ z2 φ xn φ yn and φzn All are elements in matrix Φ;

[0039] Then the diagonal element corresponding to the i-th control node of the inner ring distributed active cable in the Grammian matrix is:

[0040]

[0041] Step 4: Calculate the diagonal element w corresponding to the l-th iteration. l,ci The mean of i = 1, 2, ..., n;

[0042] Steps four and five: Determine if the number of iterations satisfies l = L, where L represents the maximum number of iterations set.

[0043] If l = L is satisfied, then compare the mean values ​​calculated in step 44 for each iteration, and take the control node position corresponding to the largest mean value as the control node position of the optimized inner circle distributed active cable.

[0044] If l = L is not satisfied, then let l = l + 1 and return to step four two.

[0045] Furthermore, the specific process of step five is as follows:

[0046] Step 51: Initialize time k = 1;

[0047] Step 5.2, the state-space equation for the vibration control of the space ring-shaped antenna is:

[0048] X(k+1|k+1)=F(k)X(k|k)+G(k)u(k) (18)

[0049] Where F(k) and G(k) are the discrete state matrices at time k, X(k|k) represents the measured value of the state variable at time k, X(k+1|k+1) represents the measured value of the state variable at time k+1, and u(k) represents the control quantity at time k.

[0050] F(k) = I + AT s G(k) = BT s (19)

[0051] In the formula, T s Sampling time;

[0052] Predicting time domain N p The state variable X(k+N) within p |k) is:

[0053]

[0054] In the formula, N p For prediction in the time domain; X(k+N)p |k) represents the state at time k for k+N p The predicted state at time k; u(k+j|k) is the predicted value of the control quantity at time k+j at time k;

[0055] Equation (20) can be rewritten in matrix form as follows:

[0056] E(k+1)=Ψ(k)X(k|k)+Θ(k)U(k) (21)

[0057] Γ(k+1)=H(k)E(k+1) (22)

[0058] In the formula, the expressions for E(k+1), Ψ(k), Θ(k), Γ(k+1), H(k), and U(k) are as follows:

[0059]

[0060]

[0061] Wherein, η(k+N) p |k) represents the condition at time k, for k+N p Predicted values ​​of the n-dimensional modal coordinate vectors of a time-space loop-pillar antenna satellite flexible system;

[0062] Step 53: Construct the objective function J(k) as follows:

[0063] J(k)=(Γ(k+1)-Γ r (k+1)) T Q(Γ r (k+1)-Γ r (k+1))+U(k) T RU(k) (29)

[0064] In the formula, Q represents the curve tracking weight matrix, and Γ r (k+1) represents the reference trajectory matrix, and R represents the constraint weight matrix.

[0065] Considering the output characteristic constraints of the cable, the objective function J(k) is transformed into solving a quadratic programming problem:

[0066]

[0067] In the formula, U represents the optimal control sequence to be solved. max This indicates the maximum control amount of the cable;

[0068] The optimal output sequence u(k) of the cable is then:

[0069]

[0070] Step 54: Let k = k + 1, then return to step 52.

[0071] The beneficial effects of this invention are:

[0072] 1. By actively adjusting the preload of the distributed cables, the vibration amplitude of the antenna can be effectively reduced, achieving high-precision vibration suppression for large space-based ring-shaped antenna satellites, ensuring antenna stability and signal reception quality. Furthermore, the system has a simple structure and is lightweight, making it suitable for use in space environments, reducing the burden on the antenna and improving system reliability and maintainability.

[0073] 2. Enhanced design flexibility and scalability. It can be adjusted according to different mission requirements and space environments, adapting to antenna systems of varying scales and complexities. Through flexible design with distributed control and cable preload adjustment, it can be easily expanded to larger-scale antenna systems or different types of space missions, meeting future demands for higher precision and larger scale.

[0074] 3. Optimized control strategy and vibration suppression efficiency. By combining model predictive control algorithms, the vibration response of the antenna system is predicted and adjusted in real time, making the control input more precise and efficient. Furthermore, the optimized control strategy not only improves vibration suppression but also effectively enhances vibration control efficiency.

[0075] 4. Effectively suppresses vibration and improves system reliability. This invention can effectively suppress the vibration of the antenna system, reduce mechanical stress and fatigue, significantly improve the long-term reliability and safety of the system, and is suitable for mission execution in complex space environments.

[0076] 5. Enhanced system robustness and adaptability. Through distributed control, the system can respond to external disturbances and dynamic changes in real time, ensuring accurate antenna pointing and vibration control in complex environments. Attached Figure Description

[0077] Figure 1 This is a schematic diagram of the large-scale space-based ring-shaped antenna satellite system of the present invention;

[0078] In the diagram, 1 represents the antenna profile, and 2 represents the ring.

[0079] Figure 2a This is the first-order mode shape diagram of the ring-shaped antenna;

[0080] Figure 2b This is the second-order mode shape diagram of the ring-shaped antenna;

[0081] Figure 2c This is the third-order mode shape diagram of the ring-shaped antenna;

[0082] Figure 2dThis is the fourth-order mode shape diagram of the ring-shaped antenna;

[0083] Figure 2e This is the fifth-order mode shape diagram of the ring-shaped antenna;

[0084] Figure 2f This is the sixth-order mode shape diagram of the ring-shaped antenna;

[0085] Figure 3 This is a schematic diagram of the force analysis of a single cable in the method of the present invention;

[0086] Figure 4a This is the result of a quantitative analysis of the controllability of the inner ring distributed active cables;

[0087] Figure 4b This is the result of a quantitative analysis of the controllability of the outer ring distributed active cables;

[0088] Figure 5 This is a flowchart of the distributed active cable model predictive vibration control strategy of the present invention;

[0089] Figure 6a The distributed vibration first-order mode coordinate control results and cable output force are obtained by the method of this invention.

[0090] Figure 6b The distributed vibration second-order modal coordinate control results and cable output force are derived from the method of this invention.

[0091] Figure 6c The distributed vibration third-order modal coordinate control results and cable output force are derived from the method of this invention.

[0092] Figure 6d The distributed vibration fourth-order modal coordinate control results and cable output force are derived from the method of this invention.

[0093] Figure 6e The distributed vibration fifth-order modal coordinate control results and cable output force are obtained by the method of this invention.

[0094] Figure 6f The results of the distributed vibration sixth-order modal coordinate control method of the present invention and the cable output force are shown. Detailed Implementation

[0095] Specific Implementation Method 1: The distributed active cable vibration control method for a space ring-pillar antenna satellite described in this implementation method specifically includes the following steps:

[0096] Step 1: Establish a finite element model of the flexible space ring-pillar antenna satellite system, then abstract the structure of the flexible space ring-pillar antenna satellite system into various rod elements, beam elements and plate elements, and construct a dynamic model of the flexible space ring-pillar antenna satellite system based on the finite element model and the abstract results.

[0097] Step 2: Perform modal decomposition on the inertia matrix, damping matrix, and stiffness matrix in the dynamic model, and obtain the model after modal coordinate transformation based on the dynamic model and the modal decomposition results;

[0098] Step 3: Establish state variables based on the model after modal coordinate transformation, and construct a modal space model of the flexible satellite system with a space ring-shaped antenna based on the state variables;

[0099] Step 4: Iteratively optimize the control node positions of the space ring-shaped antenna satellite flexible system based on the modal space model, and arrange distributed active cables based on the optimization results of the control node positions;

[0100] Step 5: Vibration control of the distributed active cables of the flexible system of the space ring-pillar antenna satellite is carried out using the Model Predictive Control (MPC) algorithm.

[0101] Distributed vibration control schemes are renowned for their reliability and flexibility. Through local control and information sharing at each control node, the system can withstand faults when local problems occur, ensuring stable operation. Furthermore, distributed control schemes can adapt to different environmental changes, enabling real-time vibration adjustment and providing strong technical support for efficient vibration control in space missions.

[0102] Due to the lightweight design and reliability requirements of flexible space structures, the active cable vibration scheme offers a novel solution for vibration suppression of large space ring-shaped antenna satellites. Active cable control uses distributed control nodes and sensors to monitor antenna vibration in real time, solve for structural modal parameters in real time, and dynamically adjust the control strategy based on the vibration data. By analyzing the antenna's vibration modes, the system can accurately identify the main vibration modes and adjust the cable tension according to the mode shape information to reduce structural vibration, thus achieving vibration suppression of the space ring-shaped antenna structure.

[0103] Structural vibration problems often involve complex constraints such as actuator saturation and maximum structural deformation. This invention addresses this issue by designing a distributed model predictive control (MPC) strategy using MPC technology. A state-space model for the vibration control of a large spatial ring-shaped antenna is established, along with an objective optimization function. The strategy for adjusting the cable preload in the rolling time domain is optimized to predict and control the vibration response at future moments. This invention employs MPC, which embeds constraints into the optimization problem. By solving the constrained optimization problem, optimal control that satisfies the constraints in the prediction time domain is achieved. Furthermore, model predictive feedback correction enables highly robust vibration control under external disturbances.

[0104] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the dynamic model of the space ring-shaped antenna satellite flexible system is as follows:

[0105]

[0106] In the formula, M, C′, and K are the inertial matrix, damping matrix, and stiffness matrix of the flexible system of the space ring-shaped antenna satellite, respectively; B′ is the actuator arrangement matrix (the actuator arrangement matrix contains only elements 0 and 1; when there is an actuator at a corresponding position, the corresponding element is 1, otherwise the corresponding element is 0); F c Let x be the control force vector for the cable, and let x represent the vector composed of the coordinates of each control node. Denotes the first derivative of x. Let x represent the second derivative.

[0107] The other steps and parameters are the same as in Specific Implementation Method 1.

[0108] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that it analyzes the natural frequencies of the large space antenna structure and the main influencing mode shapes to ensure that the selected low-order modes can accurately reflect the inherent dynamic characteristics of the large space ring-shaped antenna; the model after the mode coordinate transformation is as follows:

[0109] x=Φη (2)

[0110] In the formula, η is the n-dimensional modal coordinate vector of the flexible system of the space ring-pillar antenna satellite, and Φ is the first n-order canonical mode matrix. The analysis yields the first six mode shapes of the ring-pillar antenna satellite as follows: Figures 2a to 2f As shown.

[0111] Other steps and parameters are the same as in specific implementation method one or two.

[0112] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the modal space model of the space ring-shaped antenna satellite flexible system is as follows:

[0113]

[0114] y=CX (4)

[0115] In the formula, the state variable It is the first derivative of η. is the first derivative of X, u represents the system control quantity, and y represents the system output;

[0116] The state space matrices A, B, and C are in the following forms:

[0117]

[0118]

[0119] In the formula, I represents the identity matrix, the superscript T denotes the transpose of the matrix, and the frequency matrix... Damping coefficient matrix B c Represents the distributed cable control matrix. Let denot η as the second derivative, and F as the modal space force.

[0120] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0121] The vibration state of the system is represented as state variables, including modal coordinates and the rate of change of these coordinates. Its dynamic behavior is described by state-space equations. These equations consider the coupling effects of different modes and the influence of external disturbances, accurately describing the vibration response of the space ring-shaped antenna under various operating conditions. By solving these state-space equations, the vibration characteristics of large space ring-shaped antenna satellites can be analyzed, providing a basis for control strategy design and system stability analysis.

[0122] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the distributed active cable includes an inner ring distributed active cable and an outer ring distributed active cable.

[0123] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0124] The distributed active cable control scheme of the present invention achieves real-time and efficient structural vibration suppression by actively adjusting the cable preload, and improves the stability of large-scale space-based ring-shaped antenna satellites.

[0125] Specific Implementation Method Six: Combination Figure 1 This embodiment is described below. The difference between this embodiment and one of the specific embodiments one to five is that the control node of the inner ring distributed active cable is located on the antenna surface 1 of the space ring-pillar antenna satellite flexible system;

[0126] The entire antenna profile 1 is divided into N equal parts along the circumference, and a control node is set on the corresponding truss in each part.

[0127] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0128] This invention optimizes the specific truss location where the control node is situated.

[0129] Specific implementation method seven: Combining Figure 1This embodiment is described below. The difference between this embodiment and one of the specific embodiments one through six is ​​that the control node of the outer ring distributed active cable is located on the ring 2 of the space ring-pillar antenna satellite flexible system;

[0130] The ring 2 is divided into N equal parts along the circumference, and a control node is set in each part.

[0131] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0132] This invention optimizes the specific location of the control node in the ring 2.

[0133] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One through Seven in that the iterative optimization of the control node positions of the space ring-shaped antenna satellite flexible system based on the modal space model is performed as follows:

[0134] The Grammian factor is introduced to analyze the state space matrices A, B, and C: by calculating the Grammian matrix (controllable Grammian matrix), the control effect of installing the active cable mechanism at different positions is judged, ensuring that the system can be effectively adjusted under limited control resources and achieve the expected vibration control effect.

[0135] The controllability Grammian matrix is ​​defined as follows:

[0136]

[0137] Where τ represents the integration variable, W c (t) represents the Grammian matrix;

[0138] Equation (7) can be rewritten in the form of a differential equation as follows:

[0139]

[0140] In the formula, W c For a time-varying parameter, the controllable Grammian matrix W is... c The derivative with respect to time is 0.

[0141] Equation (8) can be rewritten as:

[0142] AW c +W c A T +BB T =0 (9)

[0143] Under weakly damped conditions, the Grammian matrix is ​​diagonally dominant. In modal coordinates, the controllable Grammian matrix satisfies:

[0144]

[0145] In the formula, w ci >0 is the controllable Grammian factor of the i-th mode. The diagonal elements of the controllable Grammian matrix of the i-th mode satisfy:

[0146]

[0147] In the formula,

[0148] To determine the controllable Grammian factor of the active cables of a large space antenna satellite, a stress analysis of a single cable is considered, such as... Figure 3 As shown, taking the inner ring distributed active cable as an example, the optimization process for the control node position is as follows:

[0149] Step 4: 1. Initialize the number of iterations l = 1;

[0150] Step 4.2: Within the range of antenna profile 1 where the i-th control node of the inner ring distributed active cable is located, randomly initialize the position (x) of the i-th control node during the l-th iteration. l,i ,y l,i ,z l,i );

[0151] Step 4.3: Adjust the control force u at both ends of the cable. s The components in the three-axis directions are represented as follows:

[0152] u s =[T ax1 T ay1 T az1 T ax2 T ay2 T az2 (12)

[0153] In the formula:

[0154]

[0155] Then, according to equation (5), the distributed cable control matrix B is obtained. c for:

[0156]

[0157] Where, φ x1 φ y1 φ z1 φ x2 φ y2 φ z2 φ xn φ yn and φzn All are elements in matrix Φ;

[0158] Then the diagonal element corresponding to the i-th control node of the inner ring distributed active cable in the Grammian matrix is:

[0159]

[0160] Step 4: Calculate the diagonal element w corresponding to the l-th iteration. l,ci The mean of i = 1, 2, ..., n;

[0161] Steps four and five: Determine if the number of iterations satisfies l = L, where L represents the maximum number of iterations set.

[0162] If l = L is satisfied, then compare the mean values ​​calculated in step 44 for each iteration, and take the control node position corresponding to the largest mean value as the control node position of the optimized inner circle distributed active cable.

[0163] If l = L is not satisfied, then let l = l + 1 and return to step four two.

[0164] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0165] By introducing a Grammian factor to analyze the state-space equations, the controllability of the system can be evaluated. Calculating the Grammian matrix allows for the quantitative analysis of the control effect of installing active cable mechanisms at different locations. Iterative optimization of the distributed cable arrangement ensures the optimal distribution of each control node, guaranteeing effective system adjustment with limited control resources and achieving the desired vibration control effect, thereby maximizing system controllability and stability. Similarly, the control node positions of the outer ring distributed active cables can be optimized. For example... Figure 4a and Figure 4b As shown, two rings of distributed active cables are arranged in the inner and outer rings according to the optimized position to achieve the suppression of the first six modes of vibration.

[0166] This invention determines the effectiveness of the solution through controllability analysis, ensuring that the system can accurately adjust the preload of the cable to cope with external disturbances.

[0167] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One to Eight in that the specific process of step five is as follows:

[0168] This invention requires vibration control for each control node of the inner and outer ring distributed active cables. The control principle of each control node is the same, the only difference being the position of the control node. The different positions of the control nodes will directly affect the distributed cable control matrix B. cThe difference lies in the distributed cable control matrix B. c Directly related to the state space matrix B, different control node positions will result in different state space matrices in equation (19). Using the method of this embodiment, the control quantity for each control node can be calculated separately. For example... Figure 5 As shown, after calculating the control quantity of each control node, it is equivalent to obtaining the hoop cable controller and the profile cable controller. Subsequent conventional control can be performed based on the obtained controllers.

[0169] Step 51: Initialize time k = 1;

[0170] Step 5.2, the state-space equation for the vibration control of the space ring-shaped antenna is:

[0171] X(k+1|k+1)=F(k)X(k|k)+G(k)u(k) (18)

[0172] Where F(k) and G(k) are the discrete state matrices at time k, X(k|k) represents the measured value of the state variable at time k, X(k+1|k+1) represents the measured value of the state variable at time k+1, and u(k) represents the control quantity at time k.

[0173] F(k) = I + AT s G(k) = BT s (19)

[0174] In the formula, T s Sampling time;

[0175] Predicting time domain N p The state variable X(k+N) within p |k) is:

[0176]

[0177] In the formula, N p For prediction in the time domain; X(k+N) p |k) represents the state at time k for k+N p The predicted state at time k; u(k+j|k) is the predicted value of the control quantity at time k+j at time k;

[0178] Equation (20) can be rewritten in matrix form as follows:

[0179] E(k+1)=Ψ(k)X(k|k)+Θ(k)U(k) (21)

[0180] Γ(k+1)=H(k)E(k+1) (22)

[0181] In the formula, the expressions for E(k+1), Ψ(k), Θ(k), Γ(k+1), H(k), and U(k) are as follows:

[0182]

[0183] Wherein, η(k+N) p |k) represents the condition at time k, for k+N p Predicted values ​​of the n-dimensional modal coordinate vectors of a time-space loop-pillar antenna satellite flexible system;

[0184] It needs to be explained that F(k) = F(k+1) = ... = F(k+N) p -1), G(k)=G(k+1)=…=G(k+N p -1);

[0185] Step 53: To achieve the optimal control effect of the system in the prediction time domain, the objective function J(k) is constructed as follows:

[0186]

[0187] Rewrite the objective function in matrix form:

[0188] J(k)=(Γ(k+1)-Γ r (k+1)) T Q(Γ r (k+1)-Γ r (k+1))+U(k) T RU(k) (29)

[0189] In the formula, Q represents the curve tracking weight matrix, and Γ r (k+1) represents the reference trajectory matrix, and R represents the constraint weight matrix.

[0190] Considering the output characteristic constraints of the cable, the objective function J(k) is transformed into solving a quadratic programming problem, which can be expressed as:

[0191]

[0192] In the formula, U represents the optimal control sequence to be solved. max This indicates the maximum control amount of the cable;

[0193] The optimal output sequence u(k) of the cable is then:

[0194]

[0195] Step 54: Let k = k + 1, then return to step 52.

[0196] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0197] This embodiment employs model predictive control to design a cable preload adjustment strategy, optimizing the vibration suppression process and enabling real-time response to dynamic structural changes. Through a distributed active cable vibration control method, system robustness is improved, effectively ensuring antenna performance and signal reception quality. This invention first clarifies the main control objectives and constraints of the ring-column antenna system. Control objectives include suppressing key vibration modes and maintaining structural stability to achieve high-quality signal reception. Constraints include physical limitations of the cable mechanism, such as the maximum control preload of the cables and the requirement to generate control output in only one direction. By defining these objectives and constraints, the control strategy can be implemented efficiently and feasiblely while meeting performance requirements.

[0198] The prediction process of this invention considers the dynamic characteristics and disturbances of the system, providing real-time state estimation and dynamic adjustment for model predictive control. It also establishes an objective optimization function considering the system's constraints and control objectives, and achieves the optimal control strategy by minimizing this function, thus realizing efficient vibration suppression for large-scale space ring-pillar antennas. To verify the distributed active cable model predictive vibration control strategy for space ring-pillar antenna systems proposed in this invention, we conducted detailed tests and evaluations in a simulation environment, such as... Figures 6a to 6f As shown, the experimental results demonstrate that the control method proposed in this invention performs excellently in suppressing antenna vibration, effectively improving the stability and accuracy of the antenna, possessing high practicality, and having broad application prospects. In particular, it can significantly optimize system performance and reliability in high-precision space missions.

[0199] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for distributed active cable vibration control of a space ring-shaped antenna satellite, characterized in that, The method specifically includes the following steps: Step 1: Establish a finite element model of the flexible space ring-pillar antenna satellite system, then abstract the structure of the flexible space ring-pillar antenna satellite system into various rod elements, beam elements and plate elements, and construct a dynamic model of the flexible space ring-pillar antenna satellite system based on the finite element model and the abstract results. Step 2: Perform modal decomposition on the inertia matrix, damping matrix, and stiffness matrix in the dynamic model, and obtain the model after modal coordinate transformation based on the dynamic model and the modal decomposition results; Step 3: Establish state variables based on the model after modal coordinate transformation, and construct a modal space model of the flexible satellite system with a space ring-shaped antenna based on the state variables; Step 4: Iteratively optimize the control node positions of the space ring-shaped antenna satellite flexible system based on the modal space model, and arrange distributed active cables based on the optimization results of the control node positions; Step 5: Vibration control of the distributed active cables of the flexible system of the space ring-pillar antenna satellite is performed using model predictive control algorithms; The specific process of step five is as follows: Step 51: Initialization ; Step 5.2, the state-space equation for the vibration control of the space ring-shaped antenna is: (18) in, and for Discrete state matrix at time t, express The measured value of the state variable at time t. express The measured value of the state variable at time t. express The amount of control at any given moment; (19) In the formula, Sampling time; Prediction Time Domain Internal state variables for: (20) In the formula, For prediction in the time domain; In order to be in At any time, for The predictive quantity of the state at any given time; In order to be in At any time, for Predicted values ​​of control quantities at specific times; Rewriting equation (20) yields , Indicates in At any time, for The predicted values ​​of the n-dimensional modal coordinate vectors of the time-space ring-shaped antenna satellite flexible system are obtained, and the objective function is constructed.

2. The method for distributed active cable vibration control of a space ring-shaped antenna satellite according to claim 1, characterized in that, The dynamic model of the space ring-shaped antenna satellite flexible system is as follows: (1) In the formula, M, K and K represent the inertial matrix, damping matrix, and stiffness matrix of the flexible system of the space ring-shaped antenna satellite, respectively. For the actuator arrangement matrix, F c The control force vector of the cable. This represents a vector composed of the coordinates of each control node. express The first derivative, express The second derivative of .

3. The method for distributed active cable vibration control of a space ring-shaped antenna satellite according to claim 2, characterized in that, The model after modal coordinate transformation is as follows: (2) In the formula, η is the n-dimensional modal coordinate vector of the flexible system of the space ring-pillar antenna satellite, and Φ is the first n-order regular mode matrix.

4. The method for distributed active cable vibration control of a space ring-shaped antenna satellite according to claim 3, characterized in that, The modal space model of the flexible satellite system with a space ring-shaped antenna is as follows: (3) (4) In the formula, the state variable , yes The first derivative, yes The first derivative, Indicates system control variables. Indicates system output; The state space matrices A, B, and C are in the following forms: (5) (6) In the formula, The identity matrix is ​​represented by the superscript T, which indicates the transpose of the matrix. The frequency matrix is ​​also mentioned. Damping coefficient matrix , , Represents the distributed cable control matrix. express The second derivative, This represents the modal space force.

5. The method for distributed active cable vibration control of a space ring-shaped antenna satellite according to claim 4, characterized in that, The distributed active cable system includes an inner ring of distributed active cables and an outer ring of distributed active cables.

6. The method for distributed active cable vibration control of a space ring-shaped antenna satellite according to claim 5, characterized in that, The control node of the inner ring distributed active cable is located on the antenna surface of the space ring column antenna satellite flexible system. The entire antenna profile is divided into N equal parts along the circumference, and a control node is set on the corresponding truss in each part.

7. The method for distributed active cable vibration control of a space ring-shaped antenna satellite according to claim 6, characterized in that, The control node of the outer ring distributed active cable is located on the ring hoop of the flexible system of the space ring column antenna satellite. The ring is divided into N equal parts along the circumference, and a control node is set in each part.

8. The method for distributed active cable vibration control of a space ring-shaped antenna satellite according to claim 7, characterized in that, The iterative optimization of the control node positions of the space ring-shaped antenna satellite flexible system based on the modal space model is as follows: Step 4.1 Initialize the number of iterations ; Step 42, the second step of the inner circle distributed active cable Within the antenna configuration range of the control node, randomly initialize the first... During the nth iteration Location of each control node ; Step 43: Control the force at both ends of the cable. The components in the three-axis directions are represented as follows: (12) In the formula: (13) (14) (15) Distributed cable control matrix for: (16) in, , , , , , , , and All are elements in matrix Φ; Then the inner circle distributed active cable's first The diagonal elements corresponding to each control node in the Grammian matrix are: (17) Step 4: Calculate the... The diagonal element corresponding to the next iteration The mean, ; Steps four and five: Determine if the number of iterations is satisfied. , This indicates the maximum number of iterations set. If satisfied Then compare the mean values ​​calculated in step 44 for each iteration, and take the control node position corresponding to the largest mean value as the control node position of each inner circle distributed active cable after optimization. If not satisfied Then let Return to step four two.

9. A method for distributed active cable vibration control of a space ring-shaped antenna satellite according to claim 8, characterized in that, The specific process of step five also includes: In step 52, equation (20) is rewritten in the following matrix form: (21) (22) In the formula, , , , , and The expression is as follows: (23) (24) (25) (26) (27) in, Indicates in At any time, for Predicted values ​​of the n-dimensional modal coordinate vectors of a time-space loop-pillar antenna satellite flexible system; Step 53: Construct the objective function as follows: (29) In the formula, This represents the curve tracking weight matrix. Represents the reference trajectory matrix. Represents the constraint weight matrix; Considering the output characteristic constraints of the cable, the objective function is... Transform it into a quadratic programming problem: (30) In the formula, This represents the optimal control sequence obtained from the solution. This indicates the maximum control amount of the cable; Then the optimal output sequence of the cable for: (31) Step 54, Order Return to step five two.

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