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

Abstract

The application discloses a large-aperture space telescope flexible load vibration suppression method and device based on preset performance control, comprising: establishing a three-inertia system dynamics model for describing a large-aperture space telescope; converting the three-inertia system dynamics 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 using a full drive system theory; improving the amplitude margin and the phase angle margin of the three-inertia generalized full drive system model by using a pole placement method; fitting the response output of the three-inertia generalized full drive system model with improved amplitude margin and phase angle margin by using a BP neural network, and designing a preset performance function of the three-inertia system; using the preset performance function as a tracking error boundary of the three-inertia system, and using a proportional differential as a nonlinear controller of the preset performance control, to realize closed-loop control of the three-inertia system, and then indirectly realize flexible load vibration suppression of the large-aperture space telescope.

Description

TECHNICAL FIELD

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

[0002] With the rapid development of space technology 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. At present, 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 space debris monitoring, lunar asteroid exploration and other fields because they can effectively overcome atmospheric, weather and geographical limitations. In order to obtain more specific characteristics of the observation target, astronomical observation equipment needs to have the ability of "wide field of view, high imaging resolution, high precision and stable tracking", which promotes the development of large space telescopes. 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 to realize effective detection, which is of great significance to ensure the continuous detection of space observation equipment on the target.

[0003] In the deployment of space telescopes, they are usually placed on a two-dimensional space tracking mechanism with an azimuth axis and an elevation axis, and the azimuth motor and the elevation motor are driven to realize full-sky, full-azimuth target capture detection, stable tracking and other tasks. Lightweight design of large-aperture space telescopes is crucial for accurate orbiting of satellites, so various lightweight technologies have been widely used in recent years. However, lightweight design, such as lightweight main mirror, lightweight turntable structure and use of large-volume flexible sunshade, makes the space telescope develop towards large-aperture, lightweight and flexible, and its natural frequency is constantly decreasing, which poses a serious threat to the performance of the control system. Flexible accessories and lightweight design can easily cause electromechanical resonance and vibration of the control system. At the same time, due to structural limitations, it is not possible to deploy a large number of sensors on the flexible load sunshade of the large-aperture telescope, which poses a great challenge to the handling of vibrations in the system, presenting the characteristics of a partially state-undriven system. In addition, nonlinear friction, model uncertainty and environmental disturbances in actual system operation make the system exhibit strong nonlinear characteristics.

[0004] In the prior art, the dynamics model of a servo motor driving a flexible load is mostly described by a double-inertia system. This method makes the system have a fixed resonance point, and most studies are based on the double-inertia system to solve the resonance problem. Common control algorithms include pole placement PI control, sliding mode control, notch filter, and design observer. However, for a system such as a large-aperture space telescope, the load driven by the motor has a flexible structure at the end, and the double-inertia system cannot accurately describe the dynamics behavior of the system. For such a system, the prior art mostly uses the method of increasing nodes and reducing order to convert the system into a generalized first-order system, then analyzes the state controllability and observability, and further designs a controller. However, this method is difficult to improve the amplitude margin and phase angle margin of the system, and ignores the generalized full-drive characteristics of the system itself. In the aspect of preset performance control, the prior art mostly realizes the constraint of system error based on the existing first-order inertia system response constraint. However, this method does not consider the characteristics of the system itself, so the constraint of the system error may not be optimal. That is, the double-inertia system cannot accurately describe the dynamics behavior of the large-aperture space telescope, because the load end of the large-aperture space telescope is a flexible structure. The increasing node and reducing order method is difficult to improve the amplitude margin and phase angle margin of the system, and ignores the full-drive characteristics of the system itself, which may lead to poor control effect. The preset performance function does not consider the characteristics of the system itself, so the constraint of the system error is not optimal. SUMMARY

[0005] In view of the problems in the prior art, the present application provides a large-aperture space telescope flexible load vibration suppression method and device based on preset performance control, which solves the problems of end vibration and electromechanical resonance of a large-aperture space telescope.

[0006] To solve the above technical problems, the present application is implemented by the following technical solutions:

[0007] According to a first aspect of the present application, a large-aperture space telescope flexible load vibration suppression method based on preset performance control is provided, comprising:

[0008] establishing a three-inertia system dynamics model for describing a large-aperture space telescope;

[0009] converting the three-inertia system dynamics model into a three-inertia system state space equation;

[0010] using full-drive system theory to convert the three-inertia system state space equation into a three-inertia generalized full-drive system model;

[0011] using a pole placement method to improve the amplitude margin and phase angle margin of the three-inertia generalized full-drive system model;

[0012] The response output of the three-inertia generalized full-drive system model with increased amplitude margin and phase angle margin is fitted by using a BP neural network, and a preset performance function of the three-inertia system is designed;

[0013] The preset performance function is used as a tracking error boundary of the three-inertia system, and a proportional differential is used as a nonlinear controller of the preset performance control, so as to realize closed-loop control of the three-inertia system and indirectly realize vibration suppression of the flexible load of the large-aperture space telescope.

[0014] In a possible implementation manner of the first aspect, the three-inertia system dynamics model used for describing the large-aperture space telescope, in particular,

[0015]

[0016] J1 is an equivalent inertia of a large-aperture space telescope drive motor; θ1 is a rotation angle of the large-aperture space telescope drive motor; T1 is an output torque of the large-aperture space telescope drive motor; T1 is a torsional torque of an equivalent elastic system between the large-aperture space telescope drive motor and a load; K1 is a stiffness coefficient of the equivalent elastic system between the large-aperture space telescope drive motor and the load; θ1 is a rotation angle of the load end of the large-aperture space telescope; C1 is a damping coefficient of the equivalent elastic system between the large-aperture space telescope drive motor and the load; J2 is an equivalent inertia of the large-aperture space telescope load; T2 is a torque acting on the load end of the large-aperture space telescope; T2 is a torsional torque of an equivalent elastic system between the large-aperture space telescope load and a baffle; K2 is a stiffness coefficient of the equivalent elastic system between the large-aperture space telescope load and the baffle; θ2 is a rotation angle of the baffle of the large-aperture space telescope; C2 is a damping coefficient of the equivalent elastic system between the large-aperture space telescope load and the baffle; J3 is an equivalent inertia of the baffle of the large-aperture space telescope; ω1 is a rotation angular velocity of the large-aperture space telescope drive motor; ω1 is a rotation angular velocity of the load end of the large-aperture space telescope; ω2 is a rotation angular velocity of the baffle of the large-aperture space telescope. m m e S1 L1 L1 L S2 L2 L2 m L1 L2

[0017] In a possible implementation manner of the first aspect, the three-inertia system dynamics model is converted into a three-inertia system state space equation, including:

[0018] ​​​​​​​​​​​​​The three-inertia system dynamics model is converted into a three-inertia system state space equation by using a modern control theory method, and the three-inertia system state space equation is specifically as follows:

[0019] The three-inertia system state x = [θ m ω m θ L1 ω L1 θ L2 ω L2 ] is selected, and the three-inertia system state space equation is established as follows:

[0020]

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

[0022] In a possible implementation manner of the first aspect, the three-inertia system state space equation is converted into a three-inertia generalized full drive system model by using a full drive system theory, and the three-inertia generalized full drive system model is specifically as follows:

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

[0024] det (sI-A) = s 6 + α5s 5 + … α1s + α0

[0025] In the formula, det (sI-A) is a determinant of sI-A; s is a Laplace operator; I is a 6x6 unit matrix; A is a characteristic matrix of the three-inertia system; and α0, α1, …, α5 are constants.

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

[0027]

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

[0029] The three-inertia system state space equation is linearly and non-singularly transformed so that the three-inertia system state space equation is converted into a Luenberger second controllability standard form:

[0030]

[0031] In the formula: A c = P -1 AP,B c = P -1 B,C c = CP, D c=D;A c B is a feature matrix of the generalized full drive system; B c C is an input matrix of the generalized full drive system; C c D is an output matrix of the generalized full drive system; D c G is a transfer matrix of the generalized full drive system;

[0032] Further, the three-inertia system state space equation is converted into a three-inertia generalized full drive system model:

[0033] z (6) = -α0z - α1z (1) - α2z (2) - α3z (3) - α4z (4) - α5z (5) + u

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

[0035] In a possible implementation manner of the first aspect, the pole configuration method is used to improve the amplitude margin and the phase margin of the three-inertia generalized full drive system model, specifically:

[0036] By constructing the control input u = -[φ5z (5) + φ4z (4) + φ3z (3) + φ2z (2) + φ1z (1) + φ0z (0) - α0z - α1z (1) - α2z (2) - α3z (3) - α4z (4) - α5z (5) - v] of the three-inertia system, the characteristic polynomial of the closed-loop system can be obtained:

[0037]

[0038] For the control problem of the three-inertia generalized full drive system model, it is essentially equivalent to find a set of coefficients such that the characteristic polynomial of the closed-loop system has the desired characteristic structure;

[0039] In order to find the 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:

[0040]

[0041] For the state space equation of the closed-loop system, the coefficients is equivalent to the pole placement problem of the following open-loop system: by constructing the control law u1 = -Kx + u, select Improve the amplitude margin and phase margin of the three-inertia generalized full-drive system model:

[0042]

[0043] Where v is the reference input.

[0044] In a possible implementation manner of the first aspect, a structure of the BP neural network comprises: 1 input layer, 7 hidden layers, and 1 output layer, the output layer adopts linear activation, and a sigmoid function is used as an activation function; during training, the number of training times is 10000, and the learning rate is 0.01.

[0045] In a possible implementation manner of the first aspect, the preset performance function is used as a tracking error boundary of the three-inertia system, and a proportional differential is used as a preset performance control nonlinear controller to realize closed-loop control of the three-inertia system, specifically as follows:

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

[0047] Step 1: The preset performance function is used to constrain the error of the three-inertia system:

[0048]

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

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

[0051]

[0052] Where e0 is an initial error of the three-inertia system; δ∈(0,1] is a constraint on the overshoot of the three-inertia system; and ρ(t) is a preset performance function.

[0053] Step 2: The three-inertia system is mapped in space by using a homeomorphism

[0054] The normalized tracking error of the three-inertia system is defined according to the constraint of the three-inertia system error to a preset performance function:

[0055]

[0056] The constraint of the three-inertia system error is converted into:

[0057] {e * ∈R,-δ<e * <1}if e0≥0

[0058] {e * ∈R,-1<e * <δ}else e0≤0

[0059] In the formula, e * is the normalized tracking error of the three-inertia system; R is a real number set;

[0060] The following function is used to realize the conversion bijection of the normalized tracking error of the three-inertia system:

[0061]

[0062] In the formula, alpha is the normalized tracking error of the three-inertia system after the conversion bijection;

[0063] Step 3: Design of the nonlinear controller

[0064] The PD controller is used as the nonlinear controller to realize the discussion of the preset performance control:

[0065]

[0066] In the formula, K p is a proportional constant; K d is a differential constant.

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

[0068] The establishment module is used to establish a three-inertia system dynamics model for describing a large-aperture space telescope;

[0069] The first conversion module is used to convert the three-inertia system dynamics model into a three-inertia system state space equation;

[0070] The second conversion module is used to convert the three-inertia system state space equation into a three-inertia generalized full-drive system model by using the full-drive system theory;

[0071] The configuration module is configured to improve the amplitude margin and the phase margin of the three-inertia generalized full-drive system model by using a pole configuration method;

[0072] The fitting module is configured to fit the response output of the three-inertia generalized full-drive 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;

[0073] The control module is configured to use the preset performance function as a tracking error boundary of the three-inertia system, and use a proportional differential as a nonlinear controller of the preset performance control, so as to realize closed-loop control of the three-inertia system, and indirectly realize vibration suppression of the flexible load of the large-aperture space telescope.

[0074] According to a third aspect of the present application, a computer device is provided, which comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the method for vibration suppression of the flexible load of the large-aperture space telescope based on the preset performance control when executing the computer program.

[0075] According to a fourth aspect of the present application, a computer readable storage medium is provided, which stores a computer program, and the computer program is executed by a processor to implement the method for vibration suppression of the flexible load of the large-aperture space telescope based on the preset performance control.

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

[0077] The application provides a large-aperture space telescope flexible load vibration suppression method based on preset performance control, which can more accurately reflect the actual dynamic behavior of the space large-aperture telescope by establishing a three-inertia system dynamic model for describing the large-aperture space telescope. Compared with a traditional double-inertia system model, the three-inertia system model can better describe the flexible load characteristics of the telescope. The three-inertia system state space equation is transformed by using a full-drive system theory to obtain a three-inertia generalized full-drive system model, and the amplitude margin and the phase angle margin of the three-inertia generalized full-drive system model can be directly improved by using a pole placement method, so that the stability of the system is significantly enhanced. Compared with a meta-reduction method, the application avoids the problem of poor control effect caused by ignoring the full-drive characteristics of the system. The response output of the three-inertia generalized full-drive system model after the amplitude margin and the phase angle margin are improved is fitted by using a BP neural network as a preset performance function of the three-inertia system, and this design enables the preset performance function to more closely combine the dynamic characteristics of the system and realize more optimal constraints on the system error. Compared with a traditional first-order inertia system response constraint, the preset performance function of the application can significantly reduce the probability of system vibration. The preset performance control strategy can ensure the dynamic and steady-state performance of the three-inertia system during tracking. By using the preset performance function as the boundary of the system tracking error and combining a proportional-derivative nonlinear controller, the closed-loop control of the system is realized, which not only realizes the vibration suppression of the flexible load of the large-aperture space telescope, but also ensures the stability of the system during tracking.

[0078] In order to make the above objectives, characteristics and advantages of the present application more apparent, the following will describe a preferred embodiment in detail, and the accompanying drawings will be described as follows. BRIEF DESCRIPTION OF DRAWINGS

[0079] In order to more clearly illustrate the technical solutions in the specific embodiments of the present application, the following will briefly introduce the drawings needed to be used in the specific embodiment description. Obviously, the drawings described below are some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without any creative labor on the basis of these drawings.

[0080] Figure 1 The flow chart of the large-aperture space telescope flexible load vibration suppression method based on preset performance control;

[0081] Figure 2 The structure diagram of the large-aperture space telescope;

[0082] Figure 3 The three-inertia system dynamic model;

[0083] Figure 4 The structure diagram of the BP neural network;

[0084] Figure 5 A block diagram of the pre-set performance control structure for three inertia;

[0085] Figure 6 The Bode plot is for a three-inertia system, where (a) represents the magnitude and (b) represents the phase angle.

[0086] Figure 7 Bode plot of the three-inertia system with poles configured, where (a) is the magnitude and (b) is the phase angle;

[0087] Figure 8 Designed for preset performance functions;

[0088] Figure 9 For the step response comparison, (a) is the motor angle output and (b) is the load-side angle output.

[0089] In the diagram: 1-sunshade; 2-optical load; 3-azimuth axis + encoder; 4-U-shaped frame; 5-pitch axis + encoder. Detailed Implementation

[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 only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0091] Combination Figure 1 and Figure 5 As shown, this invention provides a method for suppressing vibrations of a flexible load on a large-aperture space telescope based on preset performance control, specifically including the following steps:

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

[0093] Specifically, combined Figure 2 and Figure 3 As shown, the large-aperture space telescope is abstracted as a dynamic model of a three-inertia system. The equivalent inertia J of the large-aperture space telescope's drive motor is... m Equivalent inertia J of a large-aperture space telescope payload L1 The equivalent inertia J of the large-aperture space telescope load is connected to an elastic system with stiffness coefficient K1 and damping coefficient C1, which is an equivalent elastic system of a large-aperture space telescope drive motor and a load. L1 The equivalent inertia J of the large-aperture space telescope's sunshadeL2 The elastic system is connected with the stiffness coefficient K2 of the equivalent elastic system of the large-aperture space telescope load and the light shield, and the damping coefficient C2 of the equivalent elastic system of the large-aperture space telescope load and the light shield, under the action of the output torque T e of the large-aperture space telescope driving motor, the rotation angle of the large-aperture space telescope driving motor, the rotation angle of the large-aperture space telescope load end, and the rotation angle of the large-aperture space telescope light shield are θ m , θ L1 and θ L2 respectively.

[0094] According to Figure 3 , the differential equation set of the three-inertia system can be established, that is, the three-inertia system dynamics model for describing the large-aperture space telescope, specifically:

[0095]

[0096] In the formula, J m is the equivalent inertia of the large-aperture space telescope driving motor; θ m is the rotation angle of the large-aperture space telescope driving motor; T e is the output torque of the large-aperture space telescope driving motor; T S1 is the torsional torque of the equivalent elastic system between the large-aperture space telescope driving motor and the load; K1 is the stiffness coefficient of the equivalent elastic system of the large-aperture space telescope driving motor and the load; θ L1 is the rotation angle of the large-aperture space telescope load end; C1 is the damping coefficient of the equivalent elastic system of the large-aperture space telescope driving motor and the load; J L1 is the equivalent inertia of the large-aperture space telescope load; T L is the torque acting on the large-aperture space telescope load end; T S2 is the torsional torque 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 of the large-aperture space telescope load and the light shield; θ L2 is the rotation angle of the large-aperture space telescope light shield; C2 is the damping coefficient of the equivalent elastic system of the large-aperture space telescope load and the light shield; J L2 is the equivalent inertia of the large-aperture space telescope light shield; ω m is the rotation angular velocity of the large-aperture space telescope driving motor; ω L1 is the rotation angular velocity of the large-aperture space telescope load end; ω L2 is the rotation angular velocity of the large-aperture space telescope light shield.

[0097] S2, convert the three-inertia system dynamics model into a three-inertia system state space equation, specifically:

[0098] Select three-inertia system state x = [θ m ω m θ L1 ω L1 θ L2 ω L2 ], the three-inertia system state space equation 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, the three-inertia system state space equation is converted into a three-inertia generalized full drive system model by using full drive system theory, as follows:

[0102] From the three-inertia system state space equation, it is not difficult to obtain that the three-inertia system belongs to a typical underactuated system. In order to make the three-inertia system have the desired closed-loop characteristics, the three-inertia system state space equation is converted by using full drive system theory.

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

[0104] det(sI-A) = s 6 +α5s 5 +…α1s+α0

[0105] In the formula, det(sI-A) is the determinant of sI-A; s is the Laplace operator; I is a 6x6 unit matrix; A is the characteristic matrix of the three-inertia system; α0, α1, …, α5 are constants;

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

[0107]

[0108] Where the nonsingular transformation matrix P ∈ R 6×6 is a reversible matrix, so that under this transformation, the three-inertia system state space equation is equivalent to the standard high-order full drive system:

[0109] z (6) +α5z (5) +…+α1z (1) +α0z=u

[0110] From the theorem, it can be seen that the transformation of the full drive system can be realized by constructing a nonsingular transformation matrix P, so that the nonsingular transformation of the three-inertia system state space equation is realized by constructing a nonsingular transformation matrix P:

[0111]

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

[0113] linearly non-singularly transforming the state space equation of the three-inertia system so that the state space equation of the three-inertia system is converted into the Luenberger second controllable canonical form:

[0114]

[0115] wherein: 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-driven system; B c is the input matrix of the generalized fully-driven system; C c is the output matrix of the generalized fully-driven system; D c is the transfer matrix of the generalized fully-driven system;

[0116] and further converting the state space equation of the three-inertia system into a three-inertia generalized fully-driven system model:

[0117] z (6) = -α0z - α1z (1) - α2z (2) - α3z (3) - α4z (4) - α5z (5) + u

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

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

[0120] by constructing the control input u = -[φ5z (5) + φ4z (4) + φ3z (3) + φ2z (2) + φ1z (1) + φ0z (0) - α0z - α1z (1) - α2z (2) - α3z (3) - α4z (4)-a5z (5) -v], the characteristic polynomial of the closed loop system can be obtained as:

[0121]

[0122] The control problem of the three-inertia generalized full drive 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;

[0123] In order to find 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:

[0124]

[0125] For the state space equation of the closed loop system, finding the coefficients is equivalent to the pole placement problem of the open loop system as follows: by constructing the control law u1=-Kx+u, selecting improve the amplitude margin and phase margin of the three-inertia generalized full drive system model:

[0126]

[0127] where v is the reference input.

[0128] S5, the response output of the three-inertia generalized full drive system model after the amplitude margin and phase margin are improved is fitted by using the BP neural network, and the preset performance function of the three-inertia system is designed.

[0129] In an implementation manner, in order to realize the design of the stable output curve formed after the pole placement as the preset performance function, the BP neural network is used to fit it, and the structure is as shown in Figure 4 The training set of the BP neural network is the response output of the three-inertia generalized full drive system model after the amplitude margin and phase margin are improved, the training times are 10000, and the learning rate is 0.01. The structure of the BP neural network is that the input layer is 1 layer, the hidden layer is 7 layers, and the output layer is 1 layer, the activation function adopts the sigmoid function, and the output layer adopts the linear activation.

[0130] More specifically, the training parameters are discussed, and the loss function is defined:

[0131]

[0132] The data forward propagation of the neural network can be obtained as:

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

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

[0135] q8 = Vx + g

[0136] Y = q8

[0137] The above formula shows the forward propagation process of data, and the training of neural network parameters is realized by back propagation. That is, by taking the derivative of the loss function, the change of each connection parameter can be obtained, thereby realizing the process of training the parameters

[0138]

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

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

[0141] Step 1: using the preset performance function to constrain the error of the three-inertia system:

[0142]

[0143] In the formula: 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 time;

[0144] 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:

[0145]

[0146] In the formula: 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;

[0147] Step 2: using homeomorphism to map the three-inertia system in space

[0148] It can be seen from the three-inertia system error constraint that the preset performance function is introduced to make the three-inertia system a constrained system, which is not convenient for the control law design of the three-inertia system. Therefore, in order to simplify the design of the control law, the inequality constraint (three-inertia system error constraint) of the system is converted into an equality constraint through homeomorphism mapping. The normalized tracking error of the three-inertia system is defined according to the constraint of the three-inertia system error of the preset performance function:

[0149]

[0150] The constraint of the three-inertia system error is converted into:

[0151] {e * ∈R,-δ<e * <1}if e0≥0

[0152] {e * ∈R,-1<e * <δ}else e0≤0

[0153] In the formula, e * is the normalized tracking error of the three-inertia system; R is a real number set;

[0154] The following function is used to realize the conversion bijection of the normalized tracking error of the three-inertia system:

[0155]

[0156] In the formula, α is the normalized tracking error of the three-inertia system after the conversion bijection;

[0157] Step 3: Design of the nonlinear controller

[0158] The method of the nonlinear controller of the preset performance control is arbitrary, and in this embodiment, the widely used PD controller is mainly used as the nonlinear controller to realize the discussion of the preset performance control:

[0159]

[0160] In the formula, K p is a proportional constant; K d is a differential constant.

[0161] This embodiment is implemented on the premise of the technical scheme of the application, and detailed implementation modes and specific operation processes are given, but the protection scope of the application 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: a three-inertia system dynamics model is established, and model parameters are selected as: C1=0.052 N·m·s / rad, C2=0.002 N·m·s / rad, K1=572958 N·m / rad, K2=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 frequency characteristics of the three-inertia system are analyzed to obtain a Bode diagram as shown in Figure 6 It can be seen that amplitude margin and phase margin of the three-inertia system are-194 dB and-4.17x10 -11 deg respectively.

[0164] Design step 2: the three-inertia underactuated system is converted into a generalized full-actuated system by constructing a nonsingular transformation matrix P.

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

[0166] Design step 3: a BP neural network is used to fit the response of the three-inertia system after pole configuration, network parameters are selected as input layer number 1, hidden layer number 7, output layer number 1, iteration number 3000, learning rate 0.01, and the fitted three-inertia system output is designed as a preset performance function as shown in Figure 8 .

[0167] Design step 4: nonlinear controller parameters are selected as K p =3.3, K d =7.5. Simulation experiment results are as shown in Figure 9 .

[0168] It can be seen from Figure 9 that the PID fails to effectively suppress the vibration problem of the motor end and the load end, resulting in vibration of the motor end and the load end. While the preset performance control-based large-aperture space telescope flexible load vibration suppression method of the application achieves obvious effect, and the classic PID controller will have obvious overshoot, while the preset performance control-based large-aperture space telescope flexible load vibration suppression method of the application can realize dynamic performance guarantee of the controller.

[0169] This invention provides a vibration suppression device for a flexible load on a large-aperture space telescope based on preset performance control, used to implement the aforementioned vibration suppression method for a flexible load on a large-aperture space telescope based on preset performance control, specifically including the following modules:

[0170] A module is established to create a dynamic model of a three-inertia system for describing a large-aperture space telescope.

[0171] The first conversion module is used to convert the dynamic model of the three-inertia system into the state-space equation of the three-inertia system.

[0172] The second conversion module is used to convert the state-space equation of the three-inertia system into a three-inertia generalized full-drive system model using the full-drive system theory.

[0173] The configuration module is used to improve the gain margin and phase margin of the three-inertia generalized full-drive system model by employing the pole configuration method.

[0174] The fitting module is used to fit the response output of the three-inertia generalized full-drive system model after the magnitude margin and phase margin are improved using a BP neural network, and to design the preset performance function of the three-inertia system.

[0175] The control module is used to utilize the preset performance function as the tracking error boundary of the three-inertial system and to use the proportional-derivative nonlinear controller as the preset performance control to realize closed-loop control of the three-inertial system, thereby indirectly realizing the vibration suppression of the flexible load of the large-aperture space telescope.

[0176] All relevant content regarding the steps involved in the aforementioned embodiment of a method for suppressing vibrations under a flexible load on a large-aperture space telescope based on preset performance control can be referenced to the functional description of the corresponding functional module of the device for suppressing vibrations under a flexible load on a large-aperture space telescope based on preset performance control in this invention embodiment, and will not be repeated here. The module division in this invention embodiment is illustrative and only represents a logical functional division. In actual implementation, there may be other division methods. Furthermore, the functional modules in the various embodiments of this invention can be integrated into a processor, exist as separate physical entities, or have two or more modules integrated into one module. The integrated modules described above can be implemented in hardware or as software functional modules.

[0177] In another embodiment of the present application, a computer device is provided, which comprises a processor and a memory for storing a computer program, the computer program comprising program instructions, and the processor is configured to execute the program instructions stored in the computer storage medium. The processor can be a central processing unit (CPU), and can also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc., which are the computing core and control core of the terminal, and are suitable for implementing one or more instructions, and are particularly suitable for loading and executing one or more instructions in the computer storage medium to implement a corresponding method process or a corresponding function; the processor in the embodiments of the present application can be used for the operation of the large-aperture space telescope flexible load vibration suppression method based on preset performance control.

[0178] In another embodiment of the present application, the present application further provides a storage medium, specifically a computer readable storage medium (Memory), which is a memory device in the computer device, and is used for storing programs and data. It can be understood that the computer readable storage medium herein can include the built-in storage medium in the computer device, and of course can also include the expansion storage medium supported by the computer device. The computer readable storage medium provides a storage space, which stores the operating system of the terminal. Moreover, one or more instructions suitable for being loaded and executed by the processor are also stored in the 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 herein 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 large-aperture space telescope flexible load vibration suppression method based on preset performance control in the above embodiments.

[0179] Those skilled in the art will appreciate that embodiments of the present application can be readily used as a method, a system or a computer program product. Accordingly, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) embodying computer readable program code.

[0180] The present application is described in reference to the flowchart illustrations and / or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded processor or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart illustrations and / or block diagrams block or blocks. Figure 1 Figure 1

[0181] These computer program instructions can also be stored in a computer- readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart illustrations and / or block diagrams block or blocks. Figure 1 Figure 1

[0182] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart illustrations and / or block diagrams block or blocks. Figure 1 Figure 1

[0183] ​​​​​​This invention also provides a computer program product, which is used to execute any of the above-described methods for suppressing vibrations under a flexible load on a large-aperture space telescope based on preset performance control. Since the computer program product provided by this invention and the above-described method for suppressing vibrations under a flexible load on a large-aperture space telescope based on preset performance control belong to the same inventive concept, the computer program product provided by this invention possesses all the advantages of the above-described method for suppressing vibrations under a flexible load on a large-aperture space telescope based on preset performance control. Therefore, the beneficial effects of the computer program product provided by this invention will not be elaborated upon here.

[0184] In this invention, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0185] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for flexible load vibration suppression of a large-aperture space telescope based on preset performance control, characterized in that, The application relates to a method for vibration suppression of a large-aperture space telescope, and belongs to the field of control theory. The application comprises the following steps: In the formula, is the equivalent inertia of the large-aperture space telescope drive motor; is the rotation angle of the large-aperture space telescope drive motor; is the output torque of the large-aperture space telescope drive motor; is the torsional torque of the equivalent elastic system between the large-aperture space telescope drive motor and the load; is the stiffness coefficient of the equivalent elastic system of the large-aperture space telescope drive motor and the load; is the rotation angle of the large-aperture space telescope load end; is the damping coefficient of the equivalent elastic system of the large-aperture space telescope drive motor and the load; is the equivalent inertia of the large-aperture space telescope load; is the torque acting on the large-aperture space telescope load end; is the torsional torque of the equivalent elastic system between the large-aperture space telescope load and the baffle; is the stiffness coefficient of the equivalent elastic system of the large-aperture space telescope load and the baffle; is the rotation angle of the large-aperture space telescope baffle; is the damping coefficient of the equivalent elastic system of the large-aperture space telescope load and the baffle; is the equivalent inertia of the large-aperture space telescope baffle; is the rotation angular velocity of the large-aperture space telescope drive motor; is the rotation angular velocity of the large-aperture space telescope load end; is the rotation angular velocity of the large-aperture space telescope baffle; A three-inertia system dynamics model for describing a large-aperture space telescope is established, specifically as follows: The three-inertia system dynamics model is converted 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 adopting a full drive system theory; The amplitude margin and the phase angle margin of the three-inertia generalized full drive system model are improved by adopting a pole placement method; The response output of the three-inertia generalized full drive system model with improved amplitude margin and phase angle margin is fitted by adopting a BP neural network, and a preset performance function of the three-inertia system is designed; 2. The method of claim 1, wherein the method is a method of flexible load vibration suppression of a large-aperture space telescope based on preset performance control. The preset performance function is used as a tracking error boundary of the three-inertia system, and a proportional differential is used as a nonlinear controller of the preset performance control, so that closed-loop control of the three-inertia system is realized, and vibration suppression of a flexible load of the large-aperture space telescope is indirectly realized. The three-inertia system dynamics model is converted into a three-inertia system state space equation, and the conversion comprises the following steps: Selecting the three-inertia system state x [ The three-inertia system dynamics model is converted into a three-inertia system state space equation by adopting a modern control theory method, specifically as follows: m theta m omega L1 theta L1 omega L2 theta L2 ], the three-inertia system state space equation can be established as follows: wherein is a control input for the three-inertia system; is a control output for the three-inertia system.

3. The method of claim 2, wherein the method is a method of flexible load vibration suppression of a large-aperture space telescope based on preset performance control. omega The three-inertia system state space equation is converted into a three-inertia generalized full drive system model by adopting a full drive system theory, and the conversion comprises the following steps: wherein is the determinant of is the Laplacian operator; is the 6x6 identity matrix; is the characteristic matrix of the three-inertia system; , , is a constant;​ Based on the three-inertia system state space equation, a characteristic polynomial of the three-inertia system is obtained as follows: wherein is the controllability matrix of the three-inertia system; Performing a linear nonsingular transformation on the three-inertia system state-space equation such that the three-inertia system state-space equation is transformed into the Luenberger second controllable canonical form: wherein: ; is the characteristic matrix of the generalized full drive system; is the input matrix of the generalized full drive system; is the output matrix of the generalized full drive system; is the transfer matrix of the generalized full drive system; The non-singular transformation of the three-inertia system state space equation is realized by constructing a non-singular transformation matrix P: wherein is the three-inertia system state after a non-singular transformation i derivative, i = 0, 1,..., 6.

4. The method of claim 3, wherein the method is a method of flexible load vibration suppression of a large-aperture space telescope based on preset performance control. The three-inertia system state space equation is converted into a three-inertia generalized full drive system model: Controlling input for a three-inertia system The characteristic polynomial of the closed loop system can then be obtained as The control problem for the three-inertia generalized full drive system model is essentially equivalent to finding a set of coefficients φ 0~5 such that the characteristic polynomial of the closed loop system has the desired characteristic structure; To find this set of coefficients φ 0~5 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, the coefficient φ 0~5 is equivalent to the pole placement problem for the following open loop system: by constructing the control law u1=-K x +u, selecting K=[φ0 φ1 φ2 φ3 φ4 φ5], the amplitude margin and phase margin of the three-inertia generalized full-drive system model are improved: In the formulae, is a reference input.

5. The method of claim 1, wherein the method is a large aperture space telescope flexible payload vibration suppression method based on preset performance control. The amplitude margin and the phase angle margin of the three-inertia generalized full drive system model are improved by adopting a pole placement method, and the improvement comprises the following steps:

6. The method of claim 4, wherein the method is a large aperture space telescope flexible payload vibration suppression method based on preset performance control. The structure of the BP neural network comprises the following steps: 1 input layer, 7 hidden layers, 1 output layer, the output layer adopts linear activation, and the activation function adopts a sigmoid function; during training, the training frequency is 10000, and the learning rate is 0.

01. The preset performance function is used as a tracking error boundary of the three-inertia system, and a proportional differential is used as a nonlinear controller of the preset performance control, so that closed-loop control of the three-inertia system is realized, and the realization comprises the following steps: In order to ensure that the dynamic characteristics of the system controller have expectations, the preset performance function is used to constrain the tracking error e(t) of the three-inertia system, so that the dynamic performance of the three-inertia system is improved, and the design steps usually comprise the following three steps: where: e is the tracking error variable of the three-inertial system; is the upper bound of the tracking error; is the lower bound of the tracking error; t is time; Step 1: the preset performance function is used to constrain the error of the three-inertia system: wherein: is the initial error for the three-inertial system; is a constraint on the overshoot of the three-inertial system; is a pre-set performance function; The upper boundary and the lower boundary depend on the design of the preset performance function, so the boundary function is designed according to the preset performance function: Step 2: the space of the three-inertia system is mapped by adopting a homeomorphism According to the constraint of the preset performance function on the error of the three-inertia system, the normalized tracking error of the three-inertia system is defined as: wherein is the normalized tracking error for a three-inertial system; is the real set; The constraint of the error of the three-inertia system is converted into: wherein is the normalized tracking error for the transformed bijective three-inertial system; The following function is used to realize the conversion bijection of the normalized tracking error of the three-inertia system: Step 3: design of the nonlinear controller wherein is a proportional constant; is a differential constant.

7. A flexible load vibration suppression device for a large aperture space telescope based on preset performance control, characterized in that, The PD controller is used as the nonlinear controller, and the preset performance control is discussed: The application relates to a method for vibration suppression of a large-aperture space telescope, and belongs to the field of control theory. The establishment module is configured to establish a three-inertia system dynamics model for describing a large-aperture space telescope, specifically: In the formula, is the equivalent inertia of the large-aperture space telescope drive motor; is the rotation angle of the large-aperture space telescope drive motor; is the output torque of the large-aperture space telescope drive motor; is the torsional moment of the equivalent elastic system between the large-aperture space telescope drive motor and the load; is the stiffness coefficient of the equivalent elastic system of the large-aperture space telescope drive motor and the load; is the rotation angle of the large-aperture space telescope load end; is the damping coefficient of the equivalent elastic system of the large-aperture space telescope drive motor and the load; is the equivalent inertia of the large-aperture space telescope load; is the torque acting on the large-aperture space telescope load end; is the torsional moment of the equivalent elastic system between the large-aperture space telescope load and the baffle; is the stiffness coefficient of the equivalent elastic system of the large-aperture space telescope load and the baffle; is the rotation angle of the large-aperture space telescope baffle; is the damping coefficient of the equivalent elastic system of the large-aperture space telescope load and the baffle; is the equivalent inertia of the large-aperture space telescope baffle; is the rotation angular velocity of the large-aperture space telescope drive motor; is the rotation angular velocity of the large-aperture space telescope load end; is the rotation angular velocity of the large-aperture space telescope baffle; The first conversion module is configured to convert the three-inertia system dynamics model into a three-inertia system state space equation; The second conversion module is configured to convert the three-inertia system state space equation into a three-inertia generalized full drive system model by using a full drive system theory; The configuration module is configured to improve the amplitude margin and phase margin of the three-inertia generalized full drive system model by using a pole placement method; The fitting module is configured to fit the response output of the three-inertia generalized full drive 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; The control module is configured to use the preset performance function as a tracking error boundary of the three-inertia system, and use a proportional differential as a nonlinear controller of the preset performance control, to realize closed-loop control of the three-inertia system, and thereby indirectly realize vibration suppression of a flexible load of a large-aperture space telescope.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, The processor executes the computer program to realize the large-aperture space telescope flexible load vibration suppression method based on preset performance control according to any one of claims 1 to 6.

9. A computer-readable storage medium storing a computer program, the computer program comprising instructions that, when executed by a computer, cause the computer to perform the method of any one of claims 1 to 8. The computer program is executed by the processor to realize the large-aperture space telescope flexible load vibration suppression method based on preset performance control according to any one of claims 1 to 6.

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