Dynamic modeling and energy optimization control method for flexible annular space antenna

Abstract

The invention discloses a dynamic modeling and energy optimization control method for a flexible annular space antenna, and belongs to the technical field of space antennas. According to the method, the problem that an existing control method is difficult to give consideration to high-precision pointing control, energy optimization and vibration suppression in a complicated flexible structure and a changeable operation environment is solved. Aiming at a space antenna system of a complex flexible structure, a dynamic model of the complex flexible structure is simplified by adopting a modal simplification technology, and then a control method capable of dynamically switching a control strategy is designed through an energy optimization switching model prediction control method, so that energy consumption is optimized during task switching, and the task switching efficiency is improved. And by effectively suppressing vibration, accurate pointing and stable operation of the antenna system are ensured, dynamic balance between accurate pointing control and vibration suppression can be realized, and energy consumption is optimized. The method can be applied to the technical field of space antennas.

Description

Technical Field

[0001] The invention belongs to the technical field of space antennas, and in particular relates to a method for dynamic modeling and energy optimization control of a flexible annular space antenna. Background Art

[0002] With the development of modern space technology, space antenna systems play an increasingly important role in fields such as earth observation, deep space communication, and astronomical research. These space antennas are usually large in size, light in weight, and flexible in structure, which makes them face many challenges during launch, deployment, and on-orbit operation. Especially during task switching, the antenna needs to adjust its direction quickly and accurately, while avoiding the vibration of the flexible structure that affects the performance and stability of the system.

[0003] Traditional space antenna control methods mainly rely on classical methods such as proportional-derivative (PD) control. Although these methods are simple and easy to use, they often have difficulty in taking into account control accuracy, system stability, and energy efficiency at the same time when faced with flexible structures with complex dynamic characteristics. In addition, the high-order vibration modes and nonlinear characteristics of flexible antenna systems further increase the difficulty of control strategy design, making traditional methods incapable of coping with complex space environments and multi-task switching.

[0004] In recent years, model predictive control (MPC), as an advanced control method, has been gradually applied to the control of complex space systems due to its optimization control capabilities under multiple constraints. However, when facing the energy optimization and vibration suppression problems of flexible structures, the existing MPC methods still have problems such as high model complexity, insufficient real-time performance, and sensitivity to parameter changes.

[0005] In the face of the above challenges, there is an urgent need for an advanced control method that can take into account pointing control accuracy, energy efficiency and vibration suppression for the operation of space antenna systems. Although the existing proportional-derivative (PD) control method has a simple structure, it is difficult to maintain efficient control performance in complex flexible structures and changing operating environments. As an advanced control strategy, model predictive control (MPC) has certain optimization capabilities, but its application in the control of complex flexible structures still faces the problems of high model complexity, insufficient real-time performance and high parameter sensitivity. Summary of the invention

[0006] The purpose of the present invention is to solve the problem that the existing control methods are difficult to achieve high-precision pointing control, energy optimization and vibration suppression under complex flexible structures and changeable operating environments, and propose a flexible annular space antenna dynamics modeling and energy optimization control method.

[0007] The technical solution adopted by the present invention to solve the above technical problems is: a method for dynamic modeling and energy optimization control of a flexible annular space antenna, the method specifically comprising the following steps:

[0008] Step 1, respectively establish the dynamic model of each flexible component in the annular space antenna satellite system;

[0009] Step 2: Based on the topological structure of the annular space antenna satellite system, a recursive format flexible body kinematic equation is constructed;

[0010] Step 3: Based on the kinematic equation constructed in step 2, the kinetic energy and potential energy of the annular space antenna satellite system are obtained, and then the dynamic equation of the flexible body is assembled according to the kinetic energy and potential energy to obtain the explicit dynamic equation of the entire annular space antenna satellite system;

[0011] Step 4, performing order reduction processing on the explicit dynamic equation of the annular space antenna satellite system to obtain the dynamic equation after order reduction processing;

[0012] Step 5, designing an energy optimization switching model predictive control method that meets the constraint conditions, wherein the energy optimization switching model predictive control method includes a prediction model, a first MPC controller and a second MPC controller; determining the control target of the annular space antenna satellite system, and then designing a cost function of the energy optimization switching model predictive control method according to the control target, and establishing a prediction model of the energy optimization switching model predictive control method according to the dynamic equation after order reduction processing;

[0013] Calculate the prediction model output corresponding to the minimum cost function value J1 of the first MPC controller and the prediction model output corresponding to the minimum cost function value J2 of the second MPC controller; then compare the energy consumption of the first MPC controller and the second MPC controller;

[0014] If the energy consumption of the first MPC controller is less than that of the second MPC controller, the first MPC controller is selected to control the annular space antenna, and the prediction model output corresponding to the minimum cost value J1 is used as the control input of the first MPC controller;

[0015] If the energy consumption of the second MPC controller is smaller than that of the first MPC controller, the second MPC controller is selected to control the annular space antenna, and the prediction model output corresponding to the minimum cost value J2 is used as the control input of the second MPC controller.

[0016] Furthermore, the flexible components in the annular space antenna system include solar panels and antennas, and a dynamic model of each flexible component is established respectively. The dynamic model is specifically as follows:

[0017]

[0018] Among them, M II,i and M IZ,i is the mass matrix of the internal node of the i-th flexible body, M ZI,i and M ZZ,i is the mass matrix of the ith flexible body interface node, K II,i and K IZ,i is the stiffness matrix of the internal nodes of the i-th flexible body, K ZI,i and K ZZ,i is the stiffness matrix of the i-th flexible body interface node;

[0019] x i ′=[x′ I,i T x′ Z,i T ] T (2)

[0020] Among them, x′ I,i is the displacement vector of the ith flexible body interface node, x′ Z,i is the displacement vector of the internal node of the i-th flexible body, x i ′ is the displacement vector of the i-th flexible body, and the superscript T represents the transpose. is x I ' ,i The second-order derivative of is x′ Z,i The second derivative of .

[0021] Furthermore, the displacement vector x of the i-th flexible body i ′Use the modal reduction vector η i It is expressed as:

[0022]

[0023] in, is the modal matrix of the first D modes of the ith flexible body, is the constraint mode matrix of the i-th flexible body. The superscript -1 represents the inverse of the matrix. η D,i is the displacement vector of the first D modes of the i-th flexible body, η Z,i is the displacement vector of the constrained mode, Φ i is the intermediate variable, I Z is the identity matrix of the constraint mode of the ith flexible body.

[0024] Furthermore, the modal reduction vector η i The mass matrix and stiffness matrix are:

[0025]

[0026] Among them, m i is the modal reduction vector η i The mass matrix, k i is the modal reduction vector η i The stiffness matrix, M i is the mass matrix of the i-th flexible body without modal reduction, K i is the stiffness matrix of the i-th flexible body without modal reduction, I D,i is the identity matrix of the first D modes of the i-th flexible body, m DZ,i is the mass coupling matrix of the interaction between the i-th flexible body modes, m ZD,i is m DZ,i The transposed matrix, m ZZ,i is the mass matrix of the ith flexible body interface node, k DD,i is the stiffness matrix of the i-th flexible body mode, k ZZ,i is the stiffness matrix of the ith flexible body interface node.

[0027] Furthermore, the specific process of step 2 is as follows:

[0028] The connection relationship between adjacent flexible bodies in the annular space antenna system is:

[0029]

[0030] in, is η Z,i The first derivative of i is the rotation axis selection matrix of the i-th individual; q i is the joint rotation angle array of the i-th individual; Yes i The first derivative of i-1 is the coordinate transformation matrix of the position and posture before and after the joint rotation of the i-1th individual; S i-1 is the coordinate installation matrix of the front and rear interface nodes of the i-1th individual; is the modal matrix of the first D modes of the i-1th flexible body; η D,i-1 is the displacement vector of the first D modes of the i-1th flexible body, is η D,i-1 The first derivative of ;

[0031] Through the recursive relationship of kinematics, the kinematic equation of each flexible body is obtained:

[0032]

[0033] Among them, q j is the joint rotation angle array of the jth individual, Yesj The first derivative of j-1 is the coordinate transformation matrix of the position and posture before and after the joint rotation of the j-1th individual; S j-1 is the coordinate installation matrix of the front and rear interface nodes of the j-1th individual; C k-1 is the coordinate transformation matrix of the position and posture before and after the joint rotation of the k-1th individual; q k is the joint rotation angle array of the kth individual, Yes k The first derivative of k-1 is the coordinate installation matrix of the front and rear interface nodes of the k-1th individual; β j is the rotation axis selection matrix of the jth individual; q k-1 is the joint rotation angle array of the k-1th individual, Yes k-1 The first derivative of q j+1 is the joint rotation angle array of the j+1th individual; C j is the coordinate transformation matrix of the position and posture before and after the joint rotation of the jth individual; is the modal matrix of the first D modes of the j-th flexible body; is the modal matrix of the first D modes of the i-1th flexible body; C i-1 is the coordinate transformation matrix of the position and posture before and after the joint rotation of the i-1th individual; q i-1 is the joint rotation angle array of the i-1th individual, Yes i-1 The first derivative of ; Represents the kinematic information of the initial body.

[0034] Furthermore, the specific process of step three is:

[0035] Step 3: Based on the kinematic equations constructed in step 2 and the modal reduction vector η i The mass matrix and stiffness matrix of the annular space antenna system are used to obtain the kinetic energy T and potential energy V:

[0036]

[0037] Among them, R represents the rigid body set, F represents the flexible body set, v0 is the velocity of the satellite in the donut-shaped space antenna system, ω0 is the angular velocity of the satellite in the donut-shaped space antenna satellite system, is the joint angle array, n represents the number of bodies, I′ is the total number of flexible bodies, is η DThe first derivative of , M(q) is the total mass matrix of the annular space antenna satellite system, and K is the total stiffness matrix;

[0038] Step 32: Establish the Lagrangian equation according to the kinetic energy and potential energy of the annular space antenna satellite system, assemble the dynamic equation of the flexible body according to the Lagrangian equation, and obtain the explicit dynamic equation of the entire annular space antenna satellite system.

[0039] Furthermore, in step 32, the dynamic equations of the flexible body are assembled according to the Lagrange equations to obtain the explicit dynamic equations of the entire annular space antenna satellite system, which are specifically:

[0040]

[0041] in, is the first-order derivative of M(q), is the first-order derivative of κ, M 1～6 are the first six rows of the mass matrix M(q), τ is the force generated by the torque on each revolute joint, F D It is the force generated by the piezoelectric material on each rotating joint. F0 represents the three-axis thrust of the satellite, and T0 represents the three-axis torque of the satellite. The antisymmetric matrix representing the satellite angular velocity ω0, The antisymmetric matrix representing the satellite velocity v0.

[0042] Furthermore, the process of establishing the prediction model is specifically as follows:

[0043] The reduced-order dynamic equation of the annular space antenna satellite system is expressed as follows through local linearization:

[0044]

[0045] in, and is the Jacobian matrix of the state space variables x(t), and is the Jacobian matrix of the control input u(t), is the first derivative of x(t), and y(t) is the output of the donut-shaped space antenna satellite system;

[0046] The prediction model is:

[0047]

[0048] Where X is the stacked vector of the predicted state for the next N steps; x k+i″is the predicted state of the k+i″th step in the future, i″=1,2,…,N; U is the stacked vector of control inputs for the next N steps, u k+i″ is the control input for the future k+i″ step, x k is the current state, Φ and Γ are both intermediate variable matrices;

[0049]

[0050] Among them, A d represent The discretized state matrix, B d Represents the input matrix after discretization of the system.

[0051] Furthermore, the cost function is specifically:

[0052]

[0053] Where J is the cost function, is the tracking error cost, y k+i″ represents the output variable of the annular space antenna satellite system at the k+i″ step, r k+i″ represents the value of the k+i″th step in the reference trajectory r, Q represents the state error weight matrix, is the cost of the control input change, and R represents the control input weight matrix.

[0054] Furthermore, the cost function is solved as follows:

[0055]

[0056] Among them, y min is the minimum value of the output variable of the annular space antenna satellite system, y max is the maximum value of the output variable of the annular space antenna satellite system, y k+i″ is the output variable of the annular space antenna satellite system in the future k+i″ step, u min is the lower limit of the control input, u max is the upper limit of the control input, C d is the discretized output matrix of the annular space antenna satellite system.

[0057] The beneficial effects of the present invention are:

[0058] For the space antenna system with complex flexible structure, the present invention uses modal simplification technology to simplify the dynamic model of the complex flexible structure, and then designs a control method that can dynamically switch the control strategy through the energy optimization switching model predictive control method to optimize energy consumption during task switching, and ensure the precise pointing and stable operation of the antenna system by effectively suppressing vibration. It can achieve a dynamic balance between precise pointing control and vibration suppression, and optimize energy consumption.

[0059] The present invention has the following advantages:

[0060] 1. Improve system control accuracy and stability. The present invention adopts the energy optimized switching model predictive control (EOS-MPC) method to dynamically adjust the control strategy under different operating conditions, effectively improve the control accuracy and stability of the system, and ensure that the antenna always maintains accurate pointing during the target switching process.

[0061] 2. Significantly reduce energy consumption. The present invention minimizes system energy consumption by optimizing the control algorithm and reasonably allocating controller resources. Compared with traditional control methods, the present invention can significantly reduce energy consumption during operation and extend the operating life of the satellite.

[0062] 3. Effectively suppress vibration and improve system reliability. While achieving precise control, the present 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.

[0063] 4. Improve computational efficiency and achieve real-time control. By introducing modal simplification and order reduction processing, the present invention significantly improves computational efficiency while ensuring the integrity of the system's dynamic characteristics, making real-time control of complex flexible structures possible and adapting to rapidly changing task requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 It is a schematic diagram of the structure of the annular space antenna system of the method of the present invention;

[0065] Figure 2 is a modal frequency diagram of the antenna of the method of the present invention;

[0066] Figure 3 It is a block diagram of the energy optimization switching model predictive control of the method of the present invention;

[0067] Figure 4a is a graph showing the change of the joint angle q3 over time under PD control and EOS-MPC control in the method of the present invention;

[0068] For the graphs containing two curves, the curves connecting circles represent the results of the PD algorithm, and the curves connecting squares represent the results of the EOS-MPC algorithm;

[0069] Figure 4b is a graph showing the angle error of the joint angle q3 changing with time under PD control and EOS-MPC control in the method of the present invention;

[0070] Figure 4c is a graph showing the change of joint torque τ3 with time under PD control in the method of the present invention;

[0071] Figure 4d is a graph showing the change of joint torque τ3 over time under EOS-MPC control in the method of the present invention;

[0072] Figure 4e is a graph showing the change of the joint angle q4 with time under PD control and EOS-MPC control in the method of the present invention;

[0073] Figure 4f is a graph showing the angle error of the joint angle q4 changing with time under PD control and EOS-MPC control in the method of the present invention;

[0074] Figure 4g is a graph showing the change of joint torque τ4 with time under PD control in the method of the present invention;

[0075] Figure 4h is a graph showing the change of joint torque τ4 over time under EOS-MPC control in the method of the present invention;

[0076] Figure 4i is a graph showing the change of the joint angle q5 with time under PD control and EOS-MPC control in the method of the present invention;

[0077] Figure 4j is a graph showing the angle error of the joint angle q5 changing with time under PD control and EOS-MPC control in the method of the present invention;

[0078] Figure 4k is a graph showing the change of joint torque τ5 with time under PD control in the method of the present invention;

[0079] Figure 4l It is a curve diagram of the change of joint torque τ5 with time under EOS-MPC control in the method of the present invention. DETAILED DESCRIPTION

[0080] Specific implementation method 1: A method for dynamic modeling and energy optimization control of a flexible annular space antenna described in this implementation method specifically includes the following steps:

[0081] Step 1: Establish the dynamic model of each flexible component in the annular space antenna satellite system to ensure that the dynamic model can accurately reflect the inherent dynamic characteristics of the flexible body. The schematic diagram of the annular space antenna satellite system is shown in Figure 1 As shown;

[0082] Step 2: Based on the topological structure of the annular space antenna satellite system, a recursive format flexible body kinematic equation is constructed to ensure that the motion state of all flexible components can be accurately captured;

[0083] Step 3: Based on the kinematic equation constructed in step 2, the kinetic energy and potential energy of the annular space antenna satellite system are obtained, and then the dynamic equations of the flexible body are assembled according to the kinetic energy and potential energy to obtain the explicit dynamic equations of the entire annular space antenna satellite system. The explicit dynamic equations of the system can accurately describe the dynamic response of the system under different working conditions and have high computational efficiency.

[0084] Step 4: using a modal simplification method to reduce the order of the explicit dynamic equations of the annular space antenna satellite system to obtain the dynamic equations after the reduction process;

[0085] Due to the complex structure of the ring column antenna, in order to improve the calculation efficiency and facilitate real-time control, the dynamic equations of the system are simplified by selecting important modes and discarding high-order modes with less influence, while retaining the key dynamic characteristics of the system.

[0086] Step 5: Design an energy-optimized switching model predictive control method (EOS-MPC) that satisfies the constraints (including the maximum allowable displacement, angle change rate, and actuator force and torque limits), such as Figure 3 As shown, the energy optimization switching model predictive control method includes a predictive model, a first MPC controller and a second MPC controller; determining the control target of the annular space antenna satellite system (the control target is to maintain the precise pointing of the antenna and suppress vibration during the target switching period), and then designing the cost function of the energy optimization switching model predictive control method (EOS-MPC) according to the control target, and establishing the predictive model of the energy optimization switching model predictive control method according to the dynamic equation after the order reduction processing;

[0087] Calculate the prediction model output corresponding to the minimum cost function value J1 of the first MPC controller and the prediction model output corresponding to the minimum cost function value J2 of the second MPC controller;

[0088] Then, the energy consumption of the first MPC controller and the second MPC controller are compared according to the calculation results (because the cost function designed in the present invention includes an energy consumption term, the energy consumption for subsequent comparison is obtained in the process of calculating the minimum cost function value);

[0089] If the energy consumption of the first MPC controller is less than that of the second MPC controller, the first MPC controller is selected to control the annular space antenna, and the prediction model output corresponding to the minimum cost value J1 is used as the control input of the first MPC controller;

[0090] If the energy consumption of the second MPC controller is smaller than that of the first MPC controller, the second MPC controller is selected to control the annular space antenna, and the prediction model output corresponding to the minimum cost value J2 is used as the control input of the second MPC controller.

[0091] Due to the complex dynamic characteristics of the ring-column space antenna system, the control method of the present invention is selected to optimize energy consumption under dynamic conditions and maintain the stability of the system.

[0092] Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that the flexible components in the annular space antenna system include solar wings and antennas, and a dynamic model of each flexible component is established respectively. The dynamic model is specifically:

[0093]

[0094] Among them, M II,i and M IZ,i is the mass matrix of the internal node of the i-th flexible body, M ZI,i and M ZZ,i is the mass matrix of the ith flexible body interface node (the connection points on the flexible body are defined as interface nodes, and the other nodes are internal nodes), K II,i and K IZ,i is the stiffness matrix of the internal nodes of the i-th flexible body, K ZI,i and K ZZ,i is the stiffness matrix of the i-th flexible body interface node;

[0095] x i ′=[x I ' ,i T x′ Z,i T ] T (2)

[0096] Among them, x I ' ,i is the displacement vector of the ith flexible body interface node, x′ Z,i is the displacement vector of the internal node of the ith flexible body, x i ′ is the displacement vector of the i-th flexible body, and the superscript T represents the transpose. is x I ',i The second-order derivative of is x′ Z,i The second derivative of .

[0097] The other steps and parameters are the same as those in the first embodiment.

[0098] Specific implementation method 3: This implementation method is different from specific implementation method 1 or 2 in that the displacement vector x of the i-th flexible body i ′Use the modal reduction vector η i It is expressed as:

[0099]

[0100] in, is the modal matrix of the first D modes of the ith flexible body (D<<I, I is the total number of modes of the ith flexible body), is the constraint mode matrix of the ith flexible body, The superscript -1 represents the inverse of the matrix, η D,i is the displacement vector of the first D modes of the ith flexible body, η Z,i is the displacement vector of the constrained mode, Z is the number of constrained modes, Φ i is the intermediate variable, I Z is the identity matrix of the constraint mode of the ith flexible body.

[0101] The other steps and parameters are the same as those in the first or second embodiment.

[0102] Specific implementation method 4: This implementation method is different from any one of the specific implementation methods 1 to 3 in that the modal reduction vector η i The mass matrix and stiffness matrix are:

[0103]

[0104] Among them, m i is the modal reduction vector η i The mass matrix, k i is the modal reduction vector η i The stiffness matrix, M i is the mass matrix of the i-th flexible body without modal reduction, K i is the stiffness matrix of the i-th flexible body without modal reduction, I D,i is the identity matrix of the first D modes of the i-th flexible body, m DZ,i is the mass coupling matrix of the interaction between the i-th flexible body modes, m ZD,i is m DZ,i The transposed matrix, m ZZ,iis the mass matrix of the ith flexible body interface node, k DD,i is the stiffness matrix of the i-th flexible body mode, k ZZ,i is the stiffness matrix of the ith flexible body interface node,

[0105] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0106] Specific implementation method 5: This implementation method is different from the specific implementation methods 1 to 4 in that the specific process of step 2 is as follows:

[0107] The connection relationship between adjacent flexible bodies in the annular space antenna system is:

[0108]

[0109] in, is η Z,i The first derivative of i is the rotation axis selection matrix of the i-th body (rigid body or flexible body), q i is the joint rotation angle array of the i-th body (rigid body or flexible body), Yes i The first derivative of i-1 is the coordinate transformation matrix of the position and posture before and after the joint rotation of the i-1th individual (rigid body or flexible body), S i-1 is the coordinate installation matrix of the front and rear interface nodes of the i-1th body (rigid body or flexible body) (indicates the next body B i The movement of the previous body B i-1 The rigid motion, rotation at the interface point and flexible vibration at the interface point are composed of. When the previous one is a rigid body, This item is 0), is the modal matrix of the first D modes of the i-1th flexible body; η D,i-1 is the displacement vector of the first D modes of the i-1th flexible body, is η D,i-1 The first derivative of ;

[0110]

[0111] Among them, the x-axis, y-axis, and z-axis are the three coordinate axes of the joint coordinate system, and the directions of the coordinate axes are consistent with the directions of the coordinate axes of the i-1th individual coordinate system;

[0112]

[0113] Among them, Ri-1 The rotation matrix of the i-1th body (rigid body or flexible body) is used to describe the rotation angle array q at the joint i Rotation of the coordinate system, I is the unit matrix, r is the displacement vector from the previous body to the next body, is the antisymmetric matrix of r;

[0114] Through the recursive relationship of kinematics, the kinematic equation of each flexible body is obtained:

[0115]

[0116] Among them, q j is the joint rotation angle array of the jth individual (rigid body or flexible body), Yes j The first derivative of j-1 is the coordinate transformation matrix of the position and posture before and after the joint rotation of the j-1th individual (rigid body or flexible body); S j-1 is the coordinate installation matrix of the front and rear interface nodes of the j-1th body (rigid body or flexible body); C k-1 is the coordinate transformation matrix of the position and posture before and after the joint rotation of the k-1th individual (rigid body or flexible body); q k is the joint rotation angle array of the kth individual (rigid body or flexible body), Yes k The first derivative of k-1 is the coordinate installation matrix of the front and rear interface nodes of the k-1th individual (rigid body or flexible body); β j is the rotation axis selection matrix of the jth individual (rigid body or flexible body); q k-1 is the joint rotation angle array of the k-1th individual (rigid body or flexible body), Yes k-1 The first derivative of q j+1 is the joint rotation angle array of the j+1th individual (rigid body or flexible body); C j is the coordinate transformation matrix of the position and posture before and after the joint rotation of the jth individual (rigid body or flexible body); is the modal matrix of the first D modes of the j-th flexible body; is the modal matrix of the first D modes of the i-1th flexible body; C i-1 is the coordinate transformation matrix of the position and posture before and after the joint rotation of the i-1th individual (rigid body or flexible body); q i-1 is the joint rotation angle array of the i-1th individual (rigid body or flexible body), Yes i-1 The first derivative of ; Represents the kinematic information of the initial body (including velocity and angular velocity, etc.).

[0117] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0118] Specific implementation method 6: This implementation method is different from the specific implementation methods 1 to 5 in that the specific process of step 3 is as follows:

[0119] Step 3: Based on the kinematic equations constructed in step 2 and the modal reduction vector η i The mass matrix and stiffness matrix of the annular space antenna system are used to obtain the kinetic energy T and potential energy V:

[0120]

[0121] Among them, R represents the rigid body set, F represents the flexible body set, v0 is the velocity of the satellite in the donut-shaped space antenna system, ω0 is the angular velocity of the satellite in the donut-shaped space antenna satellite system, is the joint angle array, n represents the number of bodies, I′ is the total number of flexible bodies, is η D The first derivative of , M(q) is the total mass matrix of the annular space antenna satellite system, and K is the total stiffness matrix;

[0122] Step 32: Establish the Lagrangian equation according to the kinetic energy and potential energy of the annular space antenna satellite system, assemble the dynamic equation of the flexible body according to the Lagrangian equation, and obtain the explicit dynamic equation of the entire annular space antenna satellite system.

[0123] The other steps and parameters are the same as those in Specific Implementation Methods 1 to 5.

[0124] Specific implementation method 7: This implementation method is different from specific implementation methods 1 to 6 in that, in step 32, the dynamic equations of the flexible body are assembled according to the Lagrange equation to obtain the explicit dynamic equations of the entire annular space antenna satellite system, which are specifically:

[0125]

[0126] in, It includes the motion state of the satellite, the speed of each joint and the modal coordinates of the flexible body. is the first-order derivative of M(q), is the first-order derivative of κ, M 1～6 are the first six rows of the mass matrix M(q), τ is the force generated by the torque on each revolute joint, F DIt is the force generated by the piezoelectric material on each rotating joint. F0 represents the three-axis thrust of the satellite, and T0 represents the three-axis torque of the satellite. The antisymmetric matrix representing the satellite angular velocity ω0, The antisymmetric matrix representing the satellite velocity v0.

[0127] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0128] Specific implementation eight: This implementation differs from any one of specific implementations one to seven in that the process of establishing the prediction model is as follows:

[0129] The reduced-order dynamic equation of the annular space antenna satellite system is expressed as follows through local linearization:

[0130]

[0131] in, and is the Jacobian matrix of the state space variable x(t) obtained by transforming the dynamic equation into the state space equation, and is the Jacobian matrix of the control input u(t), is the first derivative of x(t), and y(t) is the output of the donut-shaped space antenna satellite system;

[0132] The prediction model is:

[0133]

[0134] Where X is the stacked vector of the predicted state for the next N steps; x k+i″ is the predicted state of the k+i″th step in the future, i″=1,2,…,N; U is the stacked vector of control inputs for the next N steps, u k+i″ is the control input for the future k+i″ step, x k is the current state, Φ and Γ are both intermediate variable matrices;

[0135] The matrices Φ and Γ respectively describe the impact of state transition and control input on future states, in the following form:

[0136]

[0137] Among them, A d represent The discretized state matrix, B d Represents the input matrix after discretization of the system.

[0138] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0139] The prediction model of the present invention should be able to accurately predict the state changes of the system in the future, and adapt to the nonlinear changes that may occur in the system during operation, and be used to calculate the optimal control input in real time.

[0140] Specific implementation method 9: This implementation method is different from any one of specific implementation methods 1 to 8 in that the cost function is specifically:

[0141]

[0142] Where J is the cost function, is the tracking error cost, y k+i″ represents the output variable of the annular space antenna satellite system at the k+i″ step, r k+i″ represents the value of the k+i″th step in the reference trajectory r, Q represents the state error weight matrix, is the cost of the control input change, which is used to measure the output variable y of the annular space antenna satellite system k+i″ and the reference trajectory r k+i″ The error cost between them, R represents the control input weight matrix, which is used to measure the control input u k+i″ The cost.

[0143] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0144] Specific implementation method 10: This implementation method is different from the specific implementation methods 1 to 9 in that the method for solving the cost function is:

[0145] Assuming that the state is available at each time step t, the following optimization problem can be solved at time step t by minimizing J and satisfying the following constraints:

[0146]

[0147] Among them, y min is the minimum value of the output variable (the physical quantity controlled and monitored) of the annular space antenna satellite system, y max is the maximum value of the output variable (the physical quantity controlled and monitored) of the annular space antenna satellite system, y k+i″ is the output variable of the annular space antenna satellite system in the next k+i″ step, u min is the lower limit of the control input, u max is the upper limit of the control input, C d is the discretized output matrix of the annular space antenna satellite system.

[0148] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0149] The cost function of the present invention includes a tracking error part and a control input change part. The tracking error part is used to measure the difference between the system output and the reference trajectory, and the control input change part is used to ensure the stability and energy saving in the control process to minimize the control input. By optimizing the cost function, the optimal control strategy that meets the operating requirements can be obtained to achieve energy optimization.

[0150] At each sampling moment, the optimization problem is solved to obtain the optimal control input. To improve system efficiency, the controller can be dynamically switched according to the operation requirements, that is, the controller corresponding to the small cost function value is selected to ensure that the global optimal control is achieved at every moment. The EOS-MPC method takes advantage of the advantages of two MPC controllers, such as Figure 3 As shown. During the target switching operation, the system characteristics change dynamically and different control strategies must be adopted to obtain the best performance. The EOS-MPC method ensures the use of the predictive controller with the lowest energy consumption by dynamically selecting between these MPC controllers. The first MPC controller is used for precise angle adjustment, and its weight matrix is ​​designed to prioritize accurate tracking of key state variables and control efforts; the second MPC2 controller is used for effective vibration suppression, and its weight matrix is ​​set to minimize vibration while maintaining overall control stability.

[0151] Experimental Section

[0152] In order to verify the effectiveness of the proposed dynamic modeling and energy optimization control method for the space ring antenna system, the algorithm was tested and evaluated in detail in a simulation environment. The experiment is mainly divided into two parts: model verification and control performance evaluation.

[0153] First, in order to verify the accuracy of the dynamic model, the antenna system was modeled using standard dynamic simulation software, and the simulation results were compared with the response of the actual physical model. Figure 2 The modal frequency distribution of the system under different control methods is demonstrated, and the results show that the method of the present invention can effectively reduce the occurrence of repeated modes and improve the calculation efficiency.

[0154] Subsequently, the performance of the control algorithm of the present invention was evaluated. In the experiment, the energy optimization and controller switching parts in the energy optimized switching model predictive control method (EOS-MPC) were ablated respectively and trained with the same simulation parameters. Figures 4a to 4lThe energy and time loss comparison of the energy optimization switching model predictive control and PD control method is presented. The results show that the control method of the present invention significantly reduces the energy and time consumption while ensuring the smooth completion of the target switching task. In contrast, the scheme that only uses energy optimization or controller switching performs poorly in terms of energy and time consumption, while the baseline method without any optimization is difficult to ensure the stability of the system and the successful completion of the task.

[0155] Experimental results show that the method of the present invention can not only achieve high-precision pointing and stable vibration suppression of the antenna system, but also significantly improve the energy utilization efficiency and reduce the task completion time. It has high practical value and promotion prospects.

[0156] By testing and verifying the control strategy designed by the present invention in a simulation environment, the controller parameters are adjusted to meet actual needs. The focus is on the performance under different working conditions, such as the control accuracy and energy consumption in different target switching tasks. Through repeated iterations and optimization, it is ensured that the control strategy has good robustness and reliability in practical applications.

[0157] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. Flexible annular space antenna dynamics modeling and energy optimization control method, characterized in that: The method specifically comprises the following steps: Step 1, respectively establish the dynamic model of each flexible component in the annular space antenna satellite system; Step 2: Based on the topological structure of the annular space antenna satellite system, a recursive format flexible body kinematic equation is constructed; Step 3: Based on the kinematic equation constructed in step 2, the kinetic energy and potential energy of the annular space antenna satellite system are obtained, and then the dynamic equation of the flexible body is assembled according to the kinetic energy and potential energy to obtain the explicit dynamic equation of the entire annular space antenna satellite system; Step 4, performing order reduction processing on the explicit dynamic equation of the annular space antenna satellite system to obtain the dynamic equation after order reduction processing; Step 5, designing an energy optimization switching model predictive control method that meets the constraint conditions, wherein the energy optimization switching model predictive control method includes a prediction model, a first MPC controller and a second MPC controller; determining the control target of the annular space antenna satellite system, and then designing a cost function of the energy optimization switching model predictive control method according to the control target, and establishing a prediction model of the energy optimization switching model predictive control method according to the dynamic equation after order reduction processing; Calculate the prediction model output corresponding to the minimum cost function value J1 of the first MPC controller and the prediction model output corresponding to the minimum cost function value J2 of the second MPC controller; then compare the energy consumption of the first MPC controller and the second MPC controller; If the energy consumption of the first MPC controller is less than that of the second MPC controller, the first MPC controller is selected to control the annular space antenna, and the prediction model output corresponding to the minimum cost value J1 is used as the control input of the first MPC controller; If the energy consumption of the second MPC controller is less than that of the first MPC controller, the second MPC controller is selected to control the annular space antenna, and the prediction model output corresponding to the minimum cost value J2 is used as the control input of the second MPC controller.

2. The method for dynamic modeling and energy optimization control of a flexible annular space antenna according to claim 1 is characterized in that: The flexible components in the annular space antenna system include solar panels and antennas. A dynamic model of each flexible component is established respectively. The dynamic model is specifically as follows: Among them, M II,i and M IZ,i is the mass matrix of the internal node of the i-th flexible body, M ZI,i and M ZZ,i is the mass matrix of the ith flexible body interface node, K II,i and K IZ,i is the stiffness matrix of the internal nodes of the i-th flexible body, K ZI,i and K ZZ,i is the stiffness matrix of the i-th flexible body interface node; Among them, x′ I,i is the displacement vector of the ith flexible body interface node, x′ Z,i is the displacement vector of the internal node of the ith flexible body, x′ i is the displacement vector of the i-th flexible body, the superscript T represents the transpose, is x′ I,i The second-order derivative of is x′ Z,i The second derivative of .

3. The method for dynamic modeling and energy optimization control of a flexible annular space antenna according to claim 2 is characterized in that: The displacement vector x of the i-th flexible body i ′Use the modal reduction vector η i It is expressed as: in, is the modal matrix of the first D modes of the ith flexible body, is the constraint mode matrix of the i-th flexible body. The superscript -1 represents the inverse of the matrix. η D,i is the displacement vector of the first D modes of the i-th flexible body, η Z,i is the displacement vector of the constrained mode, Φ i is the intermediate variable, I Z is the identity matrix of the constraint mode of the ith flexible body.

4. The method for dynamic modeling and energy optimization control of a flexible annular space antenna according to claim 3 is characterized in that: The modal reduction vector η i The mass matrix and stiffness matrix are: Among them, m i is the modal reduction vector η i The mass matrix, k i is the modal reduction vector η i The stiffness matrix, M i is the mass matrix of the i-th flexible body without modal reduction, K i is the stiffness matrix of the i-th flexible body without modal reduction, I D,i is the identity matrix of the first D modes of the i-th flexible body, m DZ,i is the mass coupling matrix of the interaction between the i-th flexible body modes, m ZD,i is m DZ,i The transposed matrix, m ZZ,i is the mass matrix of the ith flexible body interface node, k DD,i is the stiffness matrix of the i-th flexible body mode, k ZZ,i is the stiffness matrix of the ith flexible body interface node.

5. The method for dynamic modeling and energy optimization control of a flexible annular space antenna according to claim 4 is characterized in that: The specific process of step 2 is as follows: The connection relationship between adjacent flexible bodies in the annular space antenna system is: in, is η Z,i The first derivative of i is the rotation axis selection matrix of the i-th individual; q i is the joint rotation angle array of the i-th individual; Yes i The first derivative of i-1 is the coordinate transformation matrix of the position and posture before and after the joint rotation of the i-1th individual; S i-1 is the coordinate installation matrix of the front and rear interface nodes of the i-1th individual; is the modal matrix of the first D modes of the i-1th flexible body; η D,i-1 is the displacement vector of the first D modes of the i-1th flexible body, is η D,i-1 The first derivative of ; Through the recursive relationship of kinematics, the kinematic equation of each flexible body is obtained: Among them, q j is the joint rotation angle array of the jth individual, Yes j The first derivative of j-1 is the coordinate transformation matrix of the position and posture before and after the joint rotation of the j-1th individual; S j-1 is the coordinate installation matrix of the front and rear interface nodes of the j-1th individual; C k-1 is the coordinate transformation matrix of the position and posture before and after the joint rotation of the k-1th individual; q k is the joint rotation angle array of the kth individual, Yes k The first derivative of k-1 is the coordinate installation matrix of the front and rear interface nodes of the k-1th individual; β j is the rotation axis selection matrix of the jth individual; q k-1 is the joint rotation angle array of the k-1th individual, Yes k-1 The first derivative of q j+1 is the joint rotation angle array of the j+1th individual; C j is the coordinate transformation matrix of the position and posture before and after the joint rotation of the jth individual; is the modal matrix of the first D modes of the j-th flexible body; is the modal matrix of the first D modes of the i-1th flexible body; C i-1 is the coordinate transformation matrix of the position and posture before and after the joint rotation of the i-1th individual; q i-1 is the joint rotation angle array of the i-1th individual, Yes i-1 The first derivative of ; Represents the kinematic information of the initial body.

6. The method for dynamic modeling and energy optimization control of a flexible annular space antenna according to claim 5 is characterized in that: The specific process of step three is: Step 3: Based on the kinematic equations constructed in step 2 and the modal reduction vector η i The mass matrix and stiffness matrix of the annular space antenna system are used to obtain the kinetic energy T and potential energy V: Among them, R represents the rigid body set, F represents the flexible body set, v0 is the velocity of the satellite in the donut-shaped space antenna system, ω0 is the angular velocity of the satellite in the donut-shaped space antenna satellite system, is the joint angle array, n represents the number of bodies, I′ is the total number of flexible bodies, is η D The first derivative of , M(q) is the total mass matrix of the annular space antenna satellite system, and K is the total stiffness matrix; Step 32: Establish the Lagrangian equation according to the kinetic energy and potential energy of the annular space antenna satellite system, assemble the dynamic equation of the flexible body according to the Lagrangian equation, and obtain the explicit dynamic equation of the entire annular space antenna satellite system.

7. The method for dynamic modeling and energy optimization control of a flexible annular space antenna according to claim 6 is characterized in that: In step 32, the dynamic equations of the flexible body are assembled according to the Lagrange equations to obtain the explicit dynamic equations of the entire annular space antenna satellite system, which are specifically: in, is the first-order derivative of M(q), is the first-order derivative of κ, M 1～6 are the first six rows of the mass matrix M(q), τ is the force generated by the torque on each revolute joint, F D It is the force generated by the piezoelectric material on each rotating joint. F0 represents the three-axis thrust of the satellite, and T0 represents the three-axis torque of the satellite. The antisymmetric matrix representing the satellite angular velocity ω0, The antisymmetric matrix representing the satellite velocity v0.

8. The method for dynamic modeling and energy optimization control of a flexible annular space antenna according to claim 7 is characterized in that: The process of establishing the prediction model is specifically as follows: The reduced-order dynamic equation of the annular space antenna satellite system is expressed as follows through local linearization: in, and is the Jacobian matrix of the state space variables x(t), and is the Jacobian matrix of the control input u(t), is the first derivative of x(t), and y(t) is the output of the donut-shaped space antenna satellite system; The prediction model is: Where X is the stacked vector of the predicted state for the next N steps; x k+i″ is the predicted state of the k+i″th step in the future, i″=1,2,…,N; U is the stacked vector of control inputs for the next N steps, u k+i″ is the control input for the future k+i″ step, x k is the current state, Φ and Γ are both intermediate variable matrices; Among them, A d represent The discretized state matrix, B d Represents the input matrix after discretization of the system.

9. The method for dynamic modeling and energy optimization control of a flexible annular space antenna according to claim 8, characterized in that: The cost function is specifically: Where J is the cost function, is the tracking error cost, y k+i″ represents the output variable of the annular space antenna satellite system at the k+i″ step, r k+i″ represents the value of the k+i″th step in the reference trajectory r, Q represents the state error weight matrix, is the cost of the control input change, and R represents the control input weight matrix.

10. The method for dynamic modeling and energy optimization control of a flexible annular space antenna according to claim 9, characterized in that: The solution method of the cost function is: Among them, y min is the minimum value of the output variable of the annular space antenna satellite system, y max is the maximum value of the output variable of the annular space antenna satellite system, y k+i″ is the output variable of the annular space antenna satellite system in the future k+i″ step, u min is the lower limit of the control input, u max is the upper limit of the control input, C d is the discretized output matrix of the annular space antenna satellite system.

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