Large-aperture space telescope flexible load vibration suppression method and device based on preset performance control

Abstract

The invention discloses a large-aperture space telescope flexible load vibration suppression method and device based on preset performance control. The method comprises the following steps: establishing a three-inertia system dynamic model for describing a large-aperture space telescope; converting the three-inertia system dynamic model into a three-inertia system state space equation; converting the three-inertia system state-space equation into a three-inertia generalized full-drive system model by adopting a full-drive system theory; adopting a pole assignment method to improve the amplitude margin and the phase angle margin of the three-inertia generalized full-drive system model; fitting response output of the three-inertia generalized full-drive system model after the amplitude margin and the phase angle margin are improved by adopting a BP neural network, and designing a preset performance function of a three-inertia system; the preset performance function is used as a tracking error boundary of the three-inertia system, proportional differential is used as a nonlinear controller for preset performance control, closed-loop control over the three-inertia system is achieved, and then vibration suppression of the flexible load of the large-aperture space telescope is indirectly achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of large-aperture space telescope control, and particularly relates to a method and device for suppressing the vibration of a flexible load of a large-aperture space telescope based on preset performance control. Background Art

[0002] With the rapid development of aerospace technologies in various countries, the number of space debris in orbit has increased sharply, which poses a serious threat to the safe flight of on-orbit spacecraft. Currently, the monitoring of space debris mainly relies on ground-based astronomical observation equipment and space-based observation equipment. Among them, space telescopes are widely used in multiple fields such as space debris monitoring, Earth-Moon asteroid exploration, etc. because they can effectively overcome limitations such as the atmosphere, weather, and geography. In order to obtain more specific characteristics of the observed target, astronomical observation equipment needs to have the capabilities of "large field of view, high imaging resolution, high precision, and stable tracking", which has promoted the development of space telescopes towards larger sizes. At the same time, for large-aperture space telescopes, designing a control algorithm with stable tracking and high-precision pointing is one of the key technologies for effective detection, which is of great significance for ensuring the continuous detection of targets by space observation equipment.

[0003] In the deployment of space telescopes, they are usually placed on a spaceborne two-dimensional space tracking and pointing mechanism with an azimuth axis and an elevation axis, and tasks such as all-sky and all-direction target acquisition and detection, and stable tracking are achieved through the drive of an azimuth motor and an elevation motor. The lightweight design of large-aperture space telescopes is crucial for the precise orbit injection of satellites. Therefore, various lightweight technologies have been widely used in recent years. However, lightweight designs, such as the lightweighting of the primary mirror, the lightweighting of the turntable structure, and the use of large-volume flexible sunshades, have made space telescopes develop towards larger apertures, lighter weights, and more flexibility, and their natural frequencies have been continuously reduced, posing a serious threat to the performance of the control system. Flexible attachments and lightweight designs are extremely likely to cause electromechanical resonance and vibration phenomena in the control system. At the same time, due to structural limitations, a large number of sensors cannot be deployed on the flexible load sunshade of a large-aperture telescope, resulting in great challenges for the system to handle vibrations and presenting the characteristics of a partially underactuated system. In addition, nonlinear friction, model uncertainty, and environmental factor interference will also occur during the actual operation of the system, making the system exhibit strong nonlinear characteristics.

[0004] In the prior art, for the dynamic model of a servo motor driving a flexible load, most descriptions adopt a two-inertia system. This method results in a fixed resonance point in the system, and most studies are based on the two-inertia system to solve the resonance problem. Common control algorithms include PI control with pole placement, sliding mode control, notch filters, and the design of observers, etc. However, for systems such as large-aperture space telescopes, since the end of the load driven by the motor is a flexible structural member, the two-inertia system cannot accurately describe its dynamic behavior. For such systems, the prior art mostly uses the method of adding elements and reducing order to transform the system into a generalized first-order system, and then conducts state controllability and observability analysis, and further designs a controller. However, this method is difficult to improve the amplitude margin and phase margin of the system, and ignores the generalized fully actuated characteristics of the system itself. In terms of preset performance control, the prior art mostly realizes the constraint on system error based on the response constraint of the existing first-order inertial system. However, this method does not consider the characteristics of the system itself, making the constraint on system error may not be optimal. That is to say, the two-inertia system cannot accurately describe the dynamic behavior of a large-aperture space telescope because the end of the load of the large-aperture telescope is a flexible structural member. The method of adding elements and reducing order is difficult to improve the amplitude margin and phase margin of the system, and ignores the fully actuated characteristics of the system itself, which may lead to poor control effects. The preset performance function does not consider the characteristics of the system itself, making the constraint on system error not optimal. Summary of the Invention

[0005] Aiming at the problems existing in the prior art, the present invention provides a method and device for suppressing the vibration of a flexible load of a large-aperture space telescope based on preset performance control, which solves the problems of end vibration and electromechanical resonance of a large-aperture space telescope.

[0006] In order to solve the above technical problems, the present invention is realized through the following technical solutions:

[0007] According to the first aspect of the present invention, there is provided a method for suppressing the vibration of a flexible load of a large-aperture space telescope based on preset performance control, including:

[0008] Establish a dynamic model of a three-inertia system for describing a large-aperture space telescope;

[0009] Convert the dynamic model of the three-inertia system into a state space equation of the three-inertia system;

[0010] Adopt the theory of fully actuated systems to transform the state space equation of the three-inertia system into a three-inertia generalized fully actuated system model;

[0011] Adopt the pole placement method to improve the amplitude margin and phase margin of the three-inertia generalized fully actuated system model;

[0012] Use a BP neural network to fit the response output of the three-inertia generalized fully actuated system model with improved amplitude margin and phase margin, and design a preset performance function for the three-inertia system;

[0013] Use the preset performance function as the tracking error boundary of the three-inertia system, and use proportional derivative as the non-linear controller of the preset performance control to achieve the closed-loop control of the three-inertia system, and then indirectly achieve the vibration suppression of the flexible load of the large-aperture space telescope.

[0014] In a possible implementation manner of the first aspect, the dynamic model of the three-inertia system for describing the large-aperture space telescope is specifically:

[0015]

[0016] where J m is the equivalent inertia of the drive motor of the large-aperture space telescope; θ m is the rotation angle of the drive motor of the large-aperture space telescope; T e is the output torque of the drive motor of the large-aperture space telescope; T S1 is the torsional torque of the equivalent elastic system between the drive motor and the load of the large-aperture space telescope; K 1 is the stiffness coefficient of the equivalent elastic system between the drive motor and the load of the large-aperture space telescope; θ L1 is the rotation angle of the load end of the large-aperture space telescope; C 1 is the damping coefficient of the equivalent elastic system between the drive motor and the load of the large-aperture space telescope; J L1 is the equivalent inertia of the load of the large-aperture space telescope; T L is the torque acting on the load end of the large-aperture space telescope; T S2 is the torsional torque of the equivalent elastic system between the load and the sunshade of the large-aperture space telescope; K 2 is the stiffness coefficient of the equivalent elastic system between the load and the sunshade of the large-aperture space telescope; θ L2 is the rotation angle of the sunshade of the large-aperture space telescope; C 2 is the damping coefficient of the equivalent elastic system between the load and the sunshade of the large-aperture space telescope; J L2 is the equivalent inertia of the sunshade of the large-aperture space telescope; ω m is the rotational angular velocity of the drive motor of the large-aperture space telescope; ω L1 is the rotational angular velocity of the load end of the large-aperture space telescope; ω L2 is the rotational angular velocity of the sunshade of the large-aperture space telescope.

[0017] In a possible implementation manner of the first aspect, the conversion of the dynamic model of the three-inertia system into the state space equation of the three-inertia system includes:

[0018] Using the modern control theory method, the dynamic model of the three-inertia system is converted into the state-space equation of the three-inertia system, specifically as follows:

[0019] Select the state of the three-inertia system x = [θ m ω m θ L1 ω L1 θ L2 ω L2 , then the state-space equation of the three-inertia system can be established as follows:

[0020]

[0021] In the formula, u is the control input of the three-inertia system; y is the control output of the three-inertia system.

[0022] In a possible implementation manner of the first aspect, the state-space equation of the three-inertia system is transformed into a three-inertia generalized fully actuated system model by adopting the fully actuated system theory, specifically as follows:

[0023] Based on the state-space equation of the three-inertia system, the characteristic polynomial of the three-inertia system is obtained as:

[0024] det(sI - A) = s 6 + α 5 s 5 + … α 1 s + α 0

[0025] In the formula, det(sI - A) is the determinant of sI - A; s is the Laplace operator; I is the 6x6 identity matrix; A is the characteristic matrix of the three-inertia system; α 0 , α 1 , …, α 5 are constants;

[0026] The non-singular transformation of the state-space equation of the three-inertia system is realized by constructing a non-singular transformation matrix P:

[0027]

[0028] In the formula, Q c is the controllability matrix of the three-inertia system;

[0029] Perform a linear non-singular transformation on the state-space equation of the three-inertia system so that the state-space equation of the three-inertia system is transformed into the second controllable canonical form of Luenberger:

[0030]

[0031] where: A c = P -1 AP,B c = P -1 B,C c = CP, D c = D; A c is the characteristic matrix of the generalized fully actuated system; B c is the input matrix of the generalized fully actuated system; C c is the output matrix of the generalized fully actuated system; D c is the transfer matrix of the generalized fully actuated system;

[0032] Furthermore, the state - space equation of the three - inertia system is converted into a three - inertia generalized fully actuated system model:

[0033] z (6) = -α 0 z - α 1 z (1) -α 2 z (2) -α 3 z (3) -α 4 z (4) -α 5 z (5) + u

[0034] In the equation, z (i) is the i - th derivative of the state of the three - inertia system after non - singular transformation, i = 0, 1, …, 6.

[0035] In a possible implementation of the first aspect, the pole - placement method is used to improve the amplitude margin and phase - angle margin of the three - inertia generalized fully actuated system model, specifically:

[0036] By constructing the control input of the three - inertia system u = -[φ 5 z (5) + φ 4 z (4) + φ 3 z (3) + φ 2 z (2) + φ 1 z (1) + φ 0 z (0) + -α 0 z - α 1 z (1) -α 2 z (2) -α 3 z (3) -α 4 z (4) -α 5 z(5) -v], the characteristic polynomial of the closed-loop system can be obtained:

[0037]

[0038] The control problem of the three-inertia generalized fully actuated system model is essentially equivalent to finding a set of coefficients such that the characteristic polynomial of the closed-loop system has the desired characteristic structure;

[0039] To find this set of coefficients The characteristic polynomial of the closed-loop system is rewritten as the state-space equation of the following closed-loop system:

[0040]

[0041] For the state-space equation of the closed-loop system, finding the coefficients is equivalent to the pole-placement problem of the following open-loop system: By constructing the control law u 1 =-Kx + u, select to improve the amplitude margin and phase margin of the three-inertia generalized fully actuated system model:

[0042]

[0043] where v is the reference input.

[0044] In a possible implementation of the first aspect, the structure of the BP neural network includes: 1 input layer, 7 hidden layers, 1 output layer, the output layer uses linear activation, and the activation function uses the sigmoid function; during training, the number of training times is 10,000, and the learning rate is 0.01.

[0045] In a possible implementation of the first aspect, using the preset performance function as the tracking error boundary of the three-inertia system, and using proportional differentiation as the nonlinear controller of the preset performance control to achieve the closed-loop control of the three-inertia system, specifically:

[0046] To ensure that the dynamic characteristics of the system controller are as expected, the preset performance function is used to constrain the tracking error e(t) of the three-inertia system, and the dynamic performance of the three-inertia system is improved. Its design steps usually include the following three steps:

[0047] Step1: Use the preset performance function to constrain the three-inertia system error:

[0048]

[0049] where: e is the tracking error variable of the three-inertia system; H (t) is the upper boundary of the tracking error; is the lower boundary of the tracking error; t is the time;

[0050] The upper and lower boundaries depend on the design of the preset performance function. Therefore, the boundary function is designed according to the preset performance function:

[0051]

[0052] where: e 0 is the initial error of the three-inertia system; δ∈(0,1] is the constraint on the overshoot of the three-inertia system; ρ(t) is the preset performance function;

[0053] Step2: Perform a spatial equivalent mapping on the three-inertia system using homeomorphic mapping

[0054] Define the normalized tracking error of the three-inertia system according to the constraint on the error of the three-inertia system by the preset performance function:

[0055]

[0056] Convert the constraint on the error of the three-inertia system to:

[0057] {e * ∈R, -δ < e * < 1} if e 0 ≥0

[0058] {e * ∈R, -1 < e * < δ} else e 0 ≤0

[0059] where, e * is the normalized tracking error of the three-inertia system; R is the set of real numbers;

[0060] Use the following function to achieve the bijective transformation of the normalized tracking error of the three-inertia system:

[0061]

[0062] where, α is the normalized tracking error of the three-inertia system after the bijective transformation;

[0063] Step3: Design of the non-linear controller

[0064] Use a PD controller as the non-linear controller to realize the discussion of the preset performance control:

[0065]

[0066] where, K p is the proportional constant; K d is the differential constant.

[0067] According to a second aspect of the present invention, there is provided a flexible load vibration suppression device for a large-aperture space telescope based on preset performance control, including:

[0068] A modeling module, configured to establish a three-inertia system dynamics model for describing the large-aperture space telescope;

[0069] A first conversion module, configured to convert the three-inertia system dynamics model into a three-inertia system state space equation;

[0070] A second conversion module, configured to convert the three-inertia system state space equation into a three-inertia generalized fully actuated system model by using the fully actuated system theory;

[0071] A configuration module, configured to improve the amplitude margin and phase margin of the three-inertia generalized fully actuated system model by using the pole placement method;

[0072] A fitting module, configured to fit the response output of the three-inertia generalized fully actuated system model with improved amplitude margin and phase margin by using a BP neural network, and design a preset performance function for the three-inertia system;

[0073] A control module, configured to use the preset performance function as the tracking error boundary of the three-inertia system, and use proportional derivative as a non-linear controller for preset performance control to implement closed-loop control of the three-inertia system, thereby indirectly realizing flexible load vibration suppression of the large-aperture space telescope.

[0074] According to a third aspect of the present invention, there is provided a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, where when the processor executes the computer program, the method for suppressing flexible load vibration of a large-aperture space telescope based on preset performance control as described above is implemented.

[0075] According to a fourth aspect of the present invention, there is provided a computer-readable storage medium storing a computer program, where when the computer program is executed by a processor, the method for suppressing flexible load vibration of a large-aperture space telescope based on preset performance control as described above is implemented.

[0076] Compared with the prior art, the present invention has at least the following beneficial effects:

[0077] A method for suppressing the vibration of a flexible load of a large-aperture space telescope based on preset performance control. By establishing a three-inertia system dynamics model for describing the large-aperture space telescope, it can more accurately reflect the actual dynamic behavior of the large-aperture space telescope. Compared with the traditional two-inertia system model, the three-inertia system model can better describe the flexible load characteristics of the telescope. Using the full-drive system theory to transform the state-space equation of the three-inertia system, a three-inertia generalized full-drive system model is obtained. Through the pole-placement method, the amplitude margin and phase margin of the three-inertia generalized full-drive system model can be directly improved, thereby significantly enhancing the stability of the system. Compared with the method of adding elements and reducing order, the present invention avoids the problem of poor control effect caused by ignoring the full-drive characteristics of the system. Combining the BP neural network to fit the response output of the three-inertia generalized full-drive system model with improved amplitude margin and phase margin as the preset performance function of the three-inertia system. This design enables the preset performance function to be more closely combined with the dynamic characteristics of the system, achieving a better constraint on the system error. Compared with the traditional first-order inertial system response constraint, the preset performance function of the present invention can significantly reduce the occurrence probability of system vibration. Adopting the preset performance control strategy can ensure the dynamic and steady-state performance of the three-inertia system during the tracking process. By using the preset performance function as the boundary of the system tracking error and combining it with a proportional-derivative nonlinear controller, the closed-loop control of the system is realized. It can not only suppress the vibration of the flexible load of the large-aperture space telescope, but also ensure the stability of the system during the tracking process.

[0078] To make the above objects, features, and advantages of the present invention more obvious and understandable, the following specifically enumerates preferred embodiments and, in conjunction with the accompanying drawings, provides a detailed description as follows. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] To more clearly illustrate the technical solutions in the specific embodiments of the present invention, the following will briefly introduce the drawings required for use in the description of the specific embodiments. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0080] Figure 1 It is a flowchart of a method for suppressing the vibration of a flexible load of a large-aperture space telescope based on preset performance control according to the present invention;

[0081] Figure 2 It is a schematic diagram of the structure of a large-aperture space telescope;

[0082] Figure 3 It is a dynamics model of a three-inertia system;

[0083] Figure 4 It is a structure diagram of a BP neural network;

[0084] Figure 5 It is a block diagram of the preset performance control structure for a three-inertia system;

[0085] Figure 6 It is the Bode diagram of the three-inertia system, where (a) is the amplitude and (b) is the phase angle;

[0086] Figure 7 It is the Bode diagram of the three-inertia system after pole placement, where (a) is the amplitude and (b) is the phase angle;

[0087] Figure 8 It is the design of the preset performance function;

[0088] Figure 9 It is the comparison of step responses, where (a) is the motor angle output and (b) is the load side angle output.

[0089] In the figure: 1 - light shield; 2 - optical load; 3 - azimuth axis + encoder; 4 - U-shaped frame; 5 - elevation axis + encoder. Specific embodiments

[0090] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention.

[0091] Combined with Figure 1 and Figure 5 as shown, the embodiments of the present invention provide a method for suppressing the vibration of a flexible load of a large-aperture space telescope based on preset performance control, which specifically includes the following steps:

[0092] S1. Establish a dynamic model of a three-inertia system for describing a large-aperture space telescope.

[0093] Specifically, combined with Figure 2 and Figure 3 as shown, the large-aperture space telescope is abstracted into a dynamic model of a three-inertia system. The equivalent inertia J m of the driving motor of the large-aperture space telescope and the equivalent inertia J L1 of the load of the large-aperture space telescope are connected by an elastic system with a stiffness coefficient of K 1 for the equivalent elastic system between the driving motor and the load of the large-aperture space telescope and a damping coefficient of C 1 for the equivalent elastic system between the driving motor and the load of the large-aperture space telescope. The equivalent inertia J L1Equivalent inertia J of the baffle of a large-aperture space telescope L2 The stiffness coefficient of the equivalent elastic system of a large-aperture space telescope load and the baffle is K 2 and the damping coefficient of the equivalent elastic system of the large-aperture space telescope load and the baffle is C 2 Connected by an elastic system, under the action of the output torque T e of the driving motor of the large-aperture space telescope, the rotation angles of the driving motor of the large-aperture space telescope, the rotation angle of the load end of the large-aperture space telescope, and the rotation angle of the baffle of the large-aperture space telescope are θ m , θ L1 and θ L2 .

[0094] According to Figure 3 a differential equation system of the three-inertia system can be established, that is, a dynamic model of the three-inertia system of the large-aperture space telescope is described, specifically as follows:

[0095]

[0096] In the formula, J m is the equivalent inertia of the driving motor of the large-aperture space telescope; θ m is the rotation angle of the driving motor of the large-aperture space telescope; T e is the output torque of the driving motor of the large-aperture space telescope; T S1 is the torsional torque of the equivalent elastic system between the driving motor and the load of the large-aperture space telescope; K 1 is the stiffness coefficient of the equivalent elastic system of the driving motor and the load of the large-aperture space telescope; θ L1 is the rotation angle of the load end of the large-aperture space telescope; C 1 is the damping coefficient of the equivalent elastic system of the driving motor and the load of the large-aperture space telescope; J L1 is the equivalent inertia of the load of the large-aperture space telescope; T L is the torque acting on the load end of the large-aperture space telescope; T S2 is the torsional torque of the equivalent elastic system between the load and the baffle of the large-aperture space telescope; K 2 is the stiffness coefficient of the equivalent elastic system of the load and the baffle of the large-aperture space telescope; θ L2 is the rotation angle of the baffle of the large-aperture space telescope; C 2 is the damping coefficient of the equivalent elastic system of the load and the baffle of the large-aperture space telescope; J L2 is the equivalent inertia of the baffle of the large-aperture space telescope; ω m is the rotational angular velocity of the driving motor of the large-aperture space telescope; ω L1 is the rotational angular velocity of the load end of the large-aperture space telescope; ωL2 is the rotational angular velocity of the baffle of the large-aperture space telescope.

[0097] S2. Convert the dynamic model of the three-inertia system into the state-space equation of the three-inertia system, specifically as follows:

[0098] Select the state of the three-inertia system \(x = [\theta\) m \(\omega\) m \(\theta\) L1 \(\omega\) L1 \(\theta\) L2 \(\omega\) L2 , then the state-space equation of the three-inertia system can be established as follows:

[0099]

[0100] In the formula, \(u\) is the control input of the three-inertia system; \(y\) is the control output of the three-inertia system.

[0101] S3. Use the full-drive system theory to transform the state-space equation of the three-inertia system into the generalized full-drive system model of the three-inertia system, specifically as follows:

[0102] It can be easily obtained from the state-space equation of the three-inertia system that the three-inertia system belongs to a typical underactuated system. To make the three-inertia system have the desired closed-loop characteristics, the state-space equation of the three-inertia system is transformed using the full-drive system theory.

[0103] Based on the state-space equation of the three-inertia system, the characteristic polynomial of the three-inertia system is obtained as:

[0104] \(\det(sI - A)=s\) 6 +\(\alpha\) 5 \(s\) 5 +\(\cdots\alpha\) 1 \(s+\alpha\) 0

[0105] In the formula, \(\det(sI - A)\) is the determinant of \(sI - A\); \(s\) is the Laplace operator; \(I\) is the \(6\times6\) identity matrix; \(A\) is the characteristic matrix of the three-inertia system; \(\alpha\) 0 , \(\alpha\) 1 , \(\cdots\), \(\alpha\) 5 are constants;

[0106] Theorem: The necessary and sufficient condition for the controllability of the state-space equation of the three-inertia system is the existence of a transformation:

[0107]

[0108] where the non-singular transformation matrix \(P\in R\) 6×6 is an invertible matrix, such that under this transformation, the state-space equation of the three-inertia system is equivalent to the standard high-order full-drive system:

[0109] z (6) +α 5 z (5) +…+α 1 z (1) +α 0 z = u

[0110] It can be seen from the theorem that the transformation of the fully actuated system can be realized by constructing a non - singular transformation matrix P. Therefore, the non - singular transformation of the state - space equation of the three - inertia system is realized by constructing the non - singular transformation matrix P:

[0111]

[0112] where Q c is the controllability matrix of the three - inertia system;

[0113] Perform a linear non - singular transformation on the state - space equation of the three - inertia system so that the state - space equation of the three - inertia system is transformed into the second controllable canonical form of Luenberger:

[0114]

[0115] where: A c = P -1 AP, B c = P -1 B, C c = CP, D c = D; A c is the characteristic matrix of the generalized fully actuated system; B c is the input matrix of the generalized fully actuated system; C c is the output matrix of the generalized fully actuated system; D c is the transfer matrix of the generalized fully actuated system;

[0116] Furthermore, the state - space equation of the three - inertia system is transformed into the model of the three - inertia generalized fully actuated system:

[0117] z (6) = -α 0 z - α 1 z (1) -α 2 z (2) -α 3 z (3) -α 4 z (4) -α 5 z (5) + u

[0118] where z (i) is the i - th derivative of the state of the three - inertia system after non - singular transformation, i = 0, 1, …, 6.

[0119] S4. Use the pole placement method to improve the amplitude margin and phase margin of the three-inertia generalized fully actuated system model, specifically:

[0120] By constructing the control input u of the three-inertia system as u = -[φ 5 z (5) + φ 4 z (4) + φ 3 z (3) + φ 2 z (2) + φ 1 z (1) + φ 0 z (0) + -α 0 z - α 1 z (1) - α 2 z (2) - α 3 z (3) - α 4 z (4) - α 5 z (5) - v], the characteristic polynomial of the closed-loop system can be obtained:

[0121]

[0122] For the control problem of the three-inertia generalized fully actuated system model, it is essentially equivalent to finding a set of coefficients such that the characteristic polynomial of the closed-loop system has the desired characteristic structure;

[0123] To find this set of coefficients rewrite the characteristic polynomial of the closed-loop system as the following state-space equation of the closed-loop system:

[0124]

[0125] For the state-space equation of the closed-loop system, finding the coefficients is equivalent to solving the pole placement problem for the following open-loop system: By constructing the control law u 1 = -Kx + u, select to improve the amplitude margin and phase margin of the three-inertia generalized fully actuated system model:

[0126]

[0127] where v is the reference input.

[0128] S5. Use a BP neural network to fit the response output of the three-inertia generalized fully actuated system model with improved amplitude margin and phase margin, and design the preset performance function of the three-inertia system.

[0129] In an implementable manner, in order to design the preset performance function by using the stable output curve formed after pole configuration, a BP neural network is used to fit it, and its structure is as Figure 4 shown. The training set of the BP neural network is the response output of the three-inertia generalized fully actuated system model with improved amplitude margin and phase margin. The number of training times is 10,000, and the learning rate is 0.01. The structure of the BP neural network is 1 input layer, 7 hidden layers, and 1 output layer. The activation function uses the sigmoid function, and the output layer uses linear activation.

[0130] More specifically, discuss the training parameters and define the loss function:

[0131]

[0132] From the forward propagation of the data of the neural network, we can get:

[0133] q i = Wx + b, i = 1,..., 7

[0134] h i = f(q i ), i = 1,..., 7

[0135] q 8 = Vx + g

[0136] Y = q 8

[0137] The above formula shows the forward propagation process of the data. The training of the neural network parameters is achieved through backpropagation. That is, by taking the derivative of the loss function, the change amount of each connection parameter can be obtained, so as to realize the process of parameter training.

[0138]

[0139] S6. Use the preset performance function as the tracking error boundary of the three-inertia system, and use proportional differential as the nonlinear controller of the preset performance control to realize the closed-loop control of the three-inertia system, and then indirectly realize the vibration suppression of the flexible load of the large-aperture space telescope.

[0140] Specifically, to ensure that the dynamic characteristics of the system controller are as expected, the preset performance function is used to constrain the tracking error e(t) of the three-inertia system, and the dynamic performance of the three-inertia system is improved. Its design steps include the following three steps:

[0141] Step1: Constrain the three-inertia system error using a preset performance function:

[0142]

[0143] where: e is the tracking error variable of the three-inertia system; H (t) is the upper bound of the tracking error; is the lower bound of the tracking error; t is time;

[0144] The upper and lower bounds depend on the design of the preset performance function. Therefore, design a boundary function according to the preset performance function:

[0145]

[0146] where: e 0 is the initial error of the three-inertia system; δ ∈ (0, 1] is the constraint on the overshoot of the three-inertia system; ρ(t) is the preset performance function;

[0147] Step2: Perform a spatial equivalence mapping on the three-inertia system using homeomorphic mapping

[0148] It can be seen from the three-inertia system error constraint that introducing the preset performance function makes the three-inertia system a constrained system, which is not conducive to the design of the control law of the three-inertia system. Therefore, to simplify the design of the control law, convert the inequality constraint (three-inertia system error constraint) of the system into an equality constraint through homeomorphic mapping. Define the normalized tracking error of the three-inertia system according to the constraint of the preset performance function on the three-inertia system error:

[0149]

[0150] Convert the constraint of the three-inertia system error to:

[0151] {e * ∈ R, -δ < e * < 1} if e 0 ≥ 0

[0152] {e * ∈ R, -1 < e * < δ} else e 0 ≤ 0

[0153] where, e * is the normalized tracking error of the three-inertia system; R is the set of real numbers;

[0154] Use the following function to achieve the bijective transformation of the normalized tracking error of the three-inertia system:

[0155]

[0156] where α is the normalized tracking error of the three-inertia system after the conversion bijective mapping;

[0157] Step3: Design of the non-linear controller

[0158] For the non-linear controller of the preset performance control, the method is arbitrary. Here, the widely used PD controller is mainly adopted as the non-linear controller to realize the discussion of the preset performance control:

[0159]

[0160] where K p is the proportional constant; K d is the differential constant.

[0161] This embodiment is implemented on the premise of the technical solution of the present invention, and the detailed implementation manners and specific operation processes are given, but the protection scope of the present invention is not limited to the following embodiments.

[0162] The parameters and simulation steps adopted in this embodiment are mainly as follows:

[0163] Design step 1: Establish the dynamic model of the three-inertia system, and the model parameters are selected as: C 1 = 0.052 N·m·s / rad, C 2 = 0.002 N·m·s / rad, K 1 = 572958 N·m / rad, K 2 = 4996 N·m / rad, J m = 15 kg·m 2 , J L1 = 10 kg·m 2 , J L2 = 1.25 kg·m 2 , and then analyze the frequency characteristics of the three-inertia system to obtain the Bode diagram as shown in Figure 6 It can be seen that the amplitude margin and phase margin of the three-inertia system are -194 dB and -4.17x10 -11 deg, respectively.

[0164] Design step 2: Make the three-inertia underactuated system be converted into a generalized fully actuated system by constructing a non-singular transformation matrix P.

[0165] Design step 3: The desired poles are respectively configured at [-12 + 12i, -12 - 12i, -10, -11, -12 - 13i, -12 + 13i], and then the system is as shown in Figure 7As shown, it can be seen that after pole placement, the amplitude margin and phase margin of the three-inertia system are 5.28 dB and 170 deg respectively, and the amplitude margin and phase margin of the three-inertia generalized fully actuated system model are significantly improved.

[0166] Design step 3: Use a BP neural network to fit the response of the three-inertia system after pole placement. The network parameters are selected as the input layer with 1 layer, the hidden layer with 7 layers, the output layer with 1 layer, the number of iterations with 3000, and the learning rate with 0.01. By designing the output of the fitted three-inertia system as a preset performance function as Figure 8 shown.

[0167] Design step 4: Select the nonlinear controller parameters K p = 3.3, K d = 7.5. The simulation experiment results are as Figure 9 shown.

[0168] From Figure 9 it can be seen that the PID fails to effectively suppress the vibration problems at the motor end and the load end, resulting in vibrations at both the motor end and the load end. However, the method for suppressing the vibration of the flexible load of the large-aperture space telescope based on preset performance control of the present invention achieves obvious effects. At the same time, obvious overshoot will occur when using the classical PID controller, while the method for suppressing the vibration of the flexible load of the large-aperture space telescope based on preset performance control of the present invention can ensure the dynamic performance of the controller.

[0169] An embodiment of the present invention provides a device for suppressing the vibration of the flexible load of a large-aperture space telescope based on preset performance control, which is used to implement the foregoing method for suppressing the vibration of the flexible load of a large-aperture space telescope based on preset performance control, and specifically includes the following modules:

[0170] A building module, which is used to build a three-inertia system dynamic model for describing a large-aperture space telescope.

[0171] A first conversion module, which is used to convert the three-inertia system dynamic model into a three-inertia system state space equation.

[0172] A second conversion module, which is used to convert the three-inertia system state space equation into a three-inertia generalized fully actuated system model by using the fully actuated system theory.

[0173] A configuration module, which is used to improve the amplitude margin and phase margin of the three-inertia generalized fully actuated system model by using the pole placement method.

[0174] A fitting module, which is used to fit the response output of the three-inertia generalized fully actuated system model with improved amplitude margin and phase margin by using a BP neural network, and design a preset performance function of the three-inertia system.

[0175] A control module, which is configured to use the preset performance function as the tracking error boundary of the three-inertia system, and use proportional differential as the non-linear controller of the preset performance control to achieve the closed-loop control of the three-inertia system, and indirectly achieve the vibration suppression of the flexible load of the large-aperture space telescope.

[0176] All relevant contents of each step involved in the embodiment of the foregoing method for suppressing the vibration of the flexible load of a large-aperture space telescope based on preset performance control can be cited in the function description of the corresponding functional modules of the device for suppressing the vibration of the flexible load of a large-aperture space telescope based on preset performance control in the embodiments of the present invention, and will not be repeated here. The division of modules in the embodiments of the present invention is illustrative, and is only a logical function division. In actual implementation, there may be other division methods. In addition, in each embodiment of the present invention, the functional modules may be integrated in one processor, or may exist separately physically, or two or more modules may be integrated in one module. The above integrated modules may be implemented in the form of hardware or in the form of software functional modules.

[0177] In another embodiment of the present invention, a computer device is provided. The computer device includes a processor and a memory. The memory is used to store a computer program. The computer program includes program instructions. The processor is used to execute the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or may also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, and is suitable for implementing one or more instructions. Specifically, it is suitable for loading and executing one or more instructions in the computer storage medium to achieve the corresponding method flow or corresponding function. The processor described in the embodiments of the present invention can be used for the operation of a method for suppressing the vibration of the flexible load of a large-aperture space telescope based on preset performance control.

[0178] In another embodiment of the present invention, the present invention further provides a storage medium, specifically a computer-readable storage medium (Memory). The computer-readable storage medium is a memory device in a computer device and is used to store programs and data. It can be understood that the computer-readable storage medium here can include both the built-in storage medium in the computer device and, of course, the extended storage medium supported by the computer device. The computer-readable storage medium provides a storage space, and the operating system of the terminal is stored in this storage space. Moreover, one or more instructions suitable for being loaded and executed by the processor are also stored in this storage space, and these instructions can be one or more computer programs (including program codes). It should be noted that the computer-readable storage medium here can be a high-speed RAM memory or a non-volatile memory, such as at least one disk memory. One or more instructions stored in the computer-readable storage medium can be loaded and executed by the processor to implement the corresponding steps of the method for suppressing the vibration of a large-aperture space telescope flexible load based on preset performance control in the above embodiment.

[0179] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.) containing computer-usable program codes.

[0180] The present invention is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, and the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for implementing the specified functions in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0181] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured article including an instruction device, and the instruction device implements the functions in the flow Figure 1one or more processes and / or blocks Figure 1 the functions specified in one or more blocks.

[0182] These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process. Thus, the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one Figure 1 one or more processes and / or blocks Figure 1 or more processes and / or blocks.

[0183] The present invention also provides a computer program product, because the computer program product is used to execute any one of the above-mentioned methods for suppressing the vibration of a flexible load of a large-aperture space telescope based on preset performance. Since the computer program product provided by the present invention and the above-mentioned method for suppressing the vibration of a flexible load of a large-aperture space telescope based on preset performance belong to the same inventive concept, the computer program product provided by the present invention has all the advantages of the above-mentioned method for suppressing the vibration of a flexible load of a large-aperture space telescope based on preset performance. Therefore, the beneficial effects of the computer program product provided by the present invention will not be described in detail herein.

[0184] In the present invention, the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples", etc. mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0185] Finally, it should be noted that the above-described embodiments are only specific embodiments of the present invention, used to illustrate the technical solutions of the present invention, rather than limiting it. The protection scope of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that any person skilled in the art within the technical scope disclosed by the present invention can still modify the technical solutions described in the foregoing embodiments or can easily think of changes, or perform equivalent replacements on some of the technical features; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims described.

Claims

1. A method for suppressing vibration of flexible loads of a large-aperture space telescope based on preset performance control, characterized in that: include: Establish a three-inertia system dynamics model for describing large aperture space telescopes; Converting the three-inertia system dynamics model into a three-inertia system state space equation; The three-inertia system state space equation is converted into a three-inertia generalized full-drive system model by using the full-drive system theory; A pole placement method is used to improve the amplitude margin and phase margin of the three-inertia generalized full-drive system model; The BP neural network is used to fit the response output of the three-inertia generalized full-drive system model after the amplitude margin and phase margin are improved, and the preset performance function of the three-inertia system is designed. The preset performance function is used as the tracking error boundary of the three-inertia system, and the proportional differential is used as the nonlinear controller of the preset performance control to realize the closed-loop control of the three-inertia system, thereby indirectly realizing the vibration suppression of the flexible load of the large-aperture space telescope.

2. The method for suppressing vibration of flexible load of large aperture space telescope based on preset performance control according to claim 1, characterized in that: The three-inertia system dynamics model used to describe the large-aperture space telescope is specifically: In the formula, J m is the equivalent inertia of the driving motor of the large aperture space telescope; θ m is the rotation angle of the large aperture space telescope drive motor; T e is the output torque of the driving motor of the large aperture space telescope; T S1 is the torsional torque of the equivalent elastic system between the large-aperture space telescope drive motor and the load; K1 is the stiffness coefficient of the equivalent elastic system between the large-aperture space telescope drive motor and the load; θ L1 is the rotation angle of the load end of the large-aperture space telescope; C1 is the damping coefficient of the equivalent elastic system of the large-aperture space telescope drive motor and the load; J L1 is the equivalent inertia of the large aperture space telescope payload; T L is the torque acting on the load end of the large aperture space telescope; T S2 is the torsional moment of the equivalent elastic system between the large-aperture space telescope load and the light shield; K2 is the stiffness coefficient of the equivalent elastic system between the large-aperture space telescope load and the light shield; θ L2 is the rotation angle of the sunshade of the large-aperture space telescope; C2 is the damping coefficient of the equivalent elastic system of the large-aperture space telescope load and the sunshade; J L2 is the equivalent inertia of the large aperture space telescope shield; ω m is the angular velocity of the large-aperture space telescope drive motor; ω L1 is the angular velocity of the load end of the large-aperture space telescope; ω L2 is the angular velocity of the sunshade of a large-aperture space telescope.

3. The method for suppressing vibration of flexible load of large aperture space telescope based on preset performance control according to claim 2, characterized in that: The converting the three-inertia system dynamics model into a three-inertia system state space equation comprises: The three-inertia system dynamics model is converted into the three-inertia system state space equation using modern control theory methods, specifically: Select the three-inertia system state x=[θ m ω m θ L1 ω L1 θ L2 ω L2 ], the state space equation of the three-inertia system can be established as follows: Where u is the control input of the three-inertia system; y is the control output of the three-inertia system.

4. The method for suppressing vibration of flexible load of large-aperture space telescope based on preset performance control according to claim 3 is characterized in that: The full drive system theory is used to transform the three-inertia system state space equation into a three-inertia generalized full drive system model, specifically: Based on the state space equation of the three-inertia system, the characteristic polynomial of the three-inertia system is obtained as follows: det(sI-A)=s 6 +α5s 5 +…α1s+α0 Where det(sI-A) is the determinant of sI-A; s is the Laplace operator; I is the 6x6 identity matrix; A is the characteristic matrix of the three-inertia system; α0, α1, …, α5 are constants; The non-singular transformation of the state space equation of the three-inertia system is realized by constructing a non-singular transformation matrix P: In the formula, Q c is the controllability matrix of the three-inertia system; Linear non-singular transformation of the state space equations of a three-inertia system The state space equation of the three-inertia system is transformed into the Luenberger second controllable standard form: Where: A c =P -1 AP,B c =P -1 B,C c =CP,D c =D; A c is the characteristic matrix of the generalized full-drive system; B c is the input matrix of the generalized full-drive system; C c is the output matrix of the generalized full-drive system; D c is the transfer matrix of the generalized full drive system; Then the state space equation of the three-inertia system is converted into a three-inertia generalized full-drive system model: z (6) =-α0z-α1z (1) -a2z (2) -a3z (3) -α4z (4) -α5z (5) +u In the formula, z (i) is the i-th order derivative of the state of the three-inertia system after non-singular transformation, i = 0, 1, …, 6.

5. The method for suppressing vibration of flexible load of large aperture space telescope based on preset performance control according to claim 4, characterized in that: The pole configuration method is used to improve the amplitude margin and phase margin of the three-inertia generalized full-drive system model, specifically: By constructing the control input u of the three-inertia system = -[φ5z (5) +φ4z (4) +φ3z (3) +φ2z (2) +φ1z (1) +φ0z (0) +-α0z-α1z (1) -α2z (2) -α3z (3) -α4z (4) -α5z (5) -v], then the characteristic polynomial of the closed-loop system can be obtained: The control problem of the three-inertia generalized full-drive system model is essentially equivalent to finding a set of coefficients Make the characteristic polynomial of the closed-loop system have a desired characteristic structure; In order to obtain this set of coefficients The characteristic polynomial of the closed-loop system is rewritten as the state space equation of the closed-loop system as follows: For the state space equation of the closed-loop system, find the coefficients It is equivalent to the pole configuration problem for the following open-loop system: By constructing the control law u1=-Kx+u, select Improving the amplitude margin and phase margin of the three-inertia generalized full-drive system model: Where v is the reference input.

6. The method for suppressing vibration of flexible load of large aperture space telescope based on preset performance control according to claim 1, characterized in that: The structure of the BP neural network includes: 1 input layer, 7 hidden layers, and 1 output layer. The output layer uses linear activation, and the activation function uses a sigmoid function. During training, the number of training times is 10,000 and the learning rate is 0.

01.

7. The method for suppressing vibration of flexible load of large-aperture space telescope based on preset performance control according to claim 5, characterized in that: The preset performance function is used as the tracking error boundary of the three-inertia system, and the proportional differential is used as the nonlinear controller of the preset performance control to realize the closed-loop control of the three-inertia system, specifically: In order to ensure that the dynamic characteristics of the system controller are expected, a preset performance function is used to constrain the tracking error e(t) of the three-inertia system to ensure that the dynamic performance of the three-inertia system is improved. The design steps usually include the following three steps: Step 1: Use the preset performance function to constrain the three-inertia system error: Where: e is the tracking error variable of the three-inertia system; H (t) is the upper boundary of the tracking error; is the lower boundary of the tracking error; t is the time; The upper and lower boundaries depend on the design of the preset performance function, so the boundary function is designed according to the preset performance function: Where: e0 is the initial error of the three-inertia system; δ∈(0,1] is the constraint on the overshoot of the three-inertia system; ρ(t) is the preset performance function; Step 2: Use homeomorphic mapping to perform spatial equivalence mapping on the three-inertia system The normalized tracking error of the three-inertia system is defined according to the constraints of the three-inertia system error imposed by the preset performance function: The constraints of the three-inertia system error are transformed into: {e * ∈R,-δ<e * <1}if e0≥0 {e * ∈R,-1<e * <δ}else e0≤0 In the formula, e * is the normalized tracking error of the three-inertia system; R is a real number set; The following function is used to realize the transformation bijection of the normalized tracking error of the three-inertia system: Where α is the normalized tracking error of the three-inertia system after the transformation bijection; Step 3: Design of nonlinear controller Discussion on using PD controller as nonlinear controller to achieve preset performance control: In the formula, K p is the proportional constant; K d is the differential constant.

8. A flexible load vibration suppression device for a large-aperture space telescope based on preset performance control, characterized in that: include: Establish a module for establishing a three-inertia system dynamics model for describing a large-aperture space telescope; A first conversion module, used for converting the three-inertia system dynamics model into a three-inertia system state space equation; A second conversion module is used to convert the three-inertia system state space equation into a three-inertia generalized full-drive system model by adopting the full-drive system theory; A configuration module, used for improving the amplitude margin and phase angle margin of the three-inertia generalized full-drive system model by using a pole configuration method; A fitting module is used to fit the response output of the three-inertia generalized full-drive system model after the amplitude margin and the phase margin are improved by using a BP neural network, and to design a preset performance function of the three-inertia system; The control module is used to use the preset performance function as the tracking error boundary of the three-inertia system and use the proportional differential as a nonlinear controller of the preset performance control to achieve closed-loop control of the three-inertia system, thereby indirectly achieving vibration suppression of the flexible load of the large-aperture space telescope.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the method for suppressing vibration of flexible load of a large aperture space telescope based on preset performance control as described in any one of claims 1 to 7 is implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, a method for suppressing vibration of flexible loads of a large-aperture space telescope based on preset performance control is implemented as described in any one of claims 1 to 7.

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