An active-passive hybrid vibration control method based on modal frequency separation domain optimization

Abstract

The present invention discloses an active-passive hybrid vibration control method based on modal frequency separation domain optimization, which belongs to the field of large spacecraft dynamics and control. The present invention is a method suitable for solving the optimal vibration controller layout by applying an optimization algorithm in the "intermediate frequency vibration region" obtained by modal frequency separation, which overcomes the defect of the prior art that the modal frequency separation method is implemented in the "intermediate frequency vibration region" that does not have obvious high-frequency or low-frequency vibration characteristics during the on-orbit assembly process of large spacecraft with relatively complex structures, and can obtain the active-passive hybrid vibration controller layout that is still optimal in the case of relatively complex large space structures at a faster solution speed, thereby achieving efficient and high-performance vibration suppression effects for large spacecraft.

Description

Technical Field

[0001] The invention belongs to the field of large spacecraft dynamics and control, and specifically relates to an active-passive hybrid control method based on modal frequency separation domain optimization. Background Art

[0002] Large space structures are important strategic aerospace equipment for my country's future. They can reach a size of kilometers and usually need to be assembled on-orbit. As the on-orbit assembly proceeds, the spacecraft will experience high-frequency and low-frequency vibrations, which is not conducive to the normal on-orbit operation of the spacecraft, and the spacecraft needs to be subjected to vibration suppression. The integration of active and passive vibration control methods can effectively take into account the suppression effects of low-frequency and high-frequency vibrations. A distributed vibration control method based on modal frequency game separation is disclosed in the Chinese invention patent specification CN202311138233.3. This method aims at the structural dynamic characteristics of large spacecraft, realizes the optimal separation of modal frequencies based on the game idea, combines the advantages of active and passive vibration control, considers control energy consumption, timeliness, accuracy and other factors, and then optimizes the layout of distributed vibration controllers, so that better vibration suppression effects can be achieved with lower control energy consumption.

[0003] In this modal frequency game separation method, the cooperative game method is used to solve the optimal modal frequency separation point, and then the modules with modal frequencies higher than the separation point in the on-orbit assembly process of large spacecraft adopt passive vibration control methods, and the modules with modal frequencies lower than the separation point adopt active vibration control methods to obtain the optimal vibration controller layout and establish a distributed dynamic model of active and passive hybrid vibration control. However, in the case of complex structures of large spacecraft, the modal frequencies and characteristic changes in the on-orbit assembly process are complex, and there may be "intermediate frequency vibrations" that do not fully meet the "passive vibration control has a good suppression effect on high-frequency vibrations, and active vibration control has a good suppression effect on low-frequency vibrations". The modules corresponding to the "intermediate frequency vibrations" are suitable for active control or passive control methods. It is necessary to compare and judge, that is, the modules in the area formed by this type of "intermediate vibration frequency" no longer depend on the relative height of the modal frequency itself, and can be either active controllers or passive controllers. It is necessary to solve the optimal active and passive vibration controller layout. At this time, the modal frequency game separation method does not take into account the acquisition of the active and passive controller layout of the modules at the "intermediate frequency", so the obtained vibration controller layout is not globally optimal. If we consider directly generalizing the modal frequency game separation method to solve the vibration controller layout for the corresponding modules in the "intermediate frequency vibration area", it will bring a large amount of calculation. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the active-passive hybrid vibration control method based on modal frequency separation domain optimization provided by the present invention solves the problem of the prior art in implementing the modal frequency separation method for the "intermediate frequency vibration region" that does not have obvious high-frequency or low-frequency vibration characteristics during the on-orbit assembly process of large spacecraft with complex structures. It can obtain the active-passive hybrid vibration controller layout that is still optimal in the case of complex large space structures at a faster solution speed, thereby achieving efficient and high-performance vibration suppression effects for large spacecraft.

[0005] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is: an active-passive hybrid vibration control method based on modal frequency separation domain optimization, comprising the following steps:

[0006] S1. Establish a vibration dynamics model suitable for vibration control during the on-orbit assembly process of large spacecraft;

[0007] S2. Based on the constructed vibration dynamics model, passive vibration controllers and active vibration controllers are designed for modular large-scale spatial structures, and then a distributed active-passive hybrid vibration control system model under the active-passive hybrid collaborative vibration control strategy is constructed;

[0008] S3. Based on the active-passive hybrid vibration control system model, the optimization index is considered to start from the assembly module corresponding to the highest modal frequency and the assembly module corresponding to the lowest modal frequency respectively, and the modal frequency separation method is used to obtain the preliminary layout of the active and passive vibration controllers, and the modal frequency separation domain is determined;

[0009] S4. Under the same optimization index, solve the optimal active and passive vibration controller layout in the modal frequency separation domain, and combine the preliminary layout to obtain the global optimal vibration controller layout to suppress the vibration of the spacecraft.

[0010] Further, in step S1, the vibration dynamics model is expressed as:

[0011]

[0012] In the formula, represents the mass matrix, represents the damping matrix, represents the stiffness matrix, Indicates The mass matrix of the assembled modules, Indicates The stiffness matrix of the assembly module, x i1 , x i2 Respectively represent The first-order modal damping ratio and the second-order modal damping ratio of the assembled modules are represents the displacement vector of the system node under the finite element model, and denote the corresponding velocity vector and acceleration vector respectively, represents the control input, represents the allocation matrix of the actuators, Indicates external interference. Represents the allocation matrix of external disturbances.

[0013] Furthermore, in step S3, the passive vibration controller is provided with a viscoelastic damper;

[0014] The active vibration controller adopts a distributed PD collaborative controller, and its expression is:

[0015]

[0016] In the formula, u i Indicates i The control vector of the assembled active module, Indicates i The proportional gain matrix of the assembled active modules is K iP and the differential gain matrix K iD The proportional-derivative controller gain matrix is, Indicates i The coordinated parameters of the assembled active modules, Indicates i The displacement and velocity vectors measured by the assembled active modules are Indicates i The first assembled active module adjacent to the j The displacement and velocity vectors measured by the active modules are represents all measurement vectors, represents the displacement measurement vector, represents the velocity measurement vector, and the superscript T indicates the transpose;

[0017] The constructed distributed active-passive hybrid vibration control system model is expressed as:

[0018]

[0019]

[0020] In the formula, represents the first-order derivative of all state vectors, represents the sensor measurement position matrix, Represents the identity matrix.

[0021] Furthermore, the step S3 includes the following sub-steps:

[0022] S31. Based on the first-order mode reflecting the basic vibration form of the structure, the change of the first-order modal natural frequency of the entire structure during the on-orbit assembly of the large-scale space structure as the assembly proceeds is obtained, and its modal frequency is rearranged in descending order;

[0023] S32, determining optimization indicators based on control energy consumption, time efficiency and accuracy;

[0024] S33, based on the determined optimization index, starting from the assembly module corresponding to the highest modal frequency and the assembly module corresponding to the lowest modal frequency, respectively, a modal frequency separation method is used to obtain a preliminary layout of the active and passive vibration controllers, until assembly modules with intermediate frequency vibrations that do not have obvious high-frequency or low-frequency vibration characteristics appear in both directions;

[0025] S34. The modal frequencies corresponding to the two assembly modules are used as the upper and lower bounds of the region, respectively, to obtain a modal frequency separation domain.

[0026] Furthermore, in step S32, the preliminary layout of the active and passive vibration controller is:

[0027] The assembly modules with modal frequencies higher than the modal frequency separation domain are controlled by a passive vibration controller, and the assembly modules with modal frequencies lower than the modal frequency separation domain are controlled by an active vibration controller.

[0028] Furthermore, in step S4, the method for solving the optimal active and passive vibration controller layout in the modal frequency separation domain is specifically:

[0029] In the modal frequency separation domain, for the number [ m 0, …, m i , …, m f ] assembly module, define ( m f - m 0+1)-dimensional vector x =[ x 1, …, x i , …, x mf-m0+1 ] T Each element is used as an optimization parameter, and the lower and upper bounds of the optimization parameters are defined as 0 and 1 respectively;

[0030] The optimization index is used as the fitness function, and the optimization algorithm is used to solve the optimal active and passive vibration controller layout in the modal frequency separation domain based on the defined optimization parameters and their upper and lower bounds. x opt=[ x 1,…, x i ,…, x mf-m0+1 ] T ; Among them, for the optimization parameters x i It is expressed as:

[0031] .

[0032] The beneficial effects of the present invention are:

[0033] (1) Aiming at the on-orbit assembly process of large spacecraft with complex structures, a method for obtaining the modal frequency separation domain is given. It ensures that the assembly modules with modal frequencies higher than this region are subject to passive vibration control, while the assembly modules with modal frequencies lower than this region are subject to active vibration control. This ensures that the layout of active and passive controllers outside the region has the optimal vibration suppression effect.

[0034] (2) Considering factors such as control energy consumption, time efficiency, and accuracy as optimization indicators, an optimization algorithm is used to solve the optimal active and passive controller layout in the modal frequency separation domain. Together with the optimal controller layout obtained outside the region, a globally optimal active and passive controller layout is constructed to achieve low-energy consumption, high-performance, and high-precision vibration suppression effects during the in-orbit assembly process of large spacecraft when the types and parameters of the active and passive controllers are determined. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 A flow chart of the active-passive hybrid vibration control method based on modal frequency separation domain optimization provided by the present invention. DETAILED DESCRIPTION

[0036] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0037] The embodiment of the present invention provides an active-passive hybrid vibration control method based on modal frequency separation domain optimization, such as Figure 1 As shown, the following steps are included:

[0038] S1. Establish a vibration dynamics model suitable for vibration control during the on-orbit assembly process of large spacecraft;

[0039] S2. Based on the constructed vibration dynamics model, passive vibration controllers and active vibration controllers are designed for modular large-scale spatial structures, and then a distributed active-passive hybrid vibration control system model under the active-passive hybrid collaborative vibration control strategy is constructed;

[0040] S3. Based on the active-passive hybrid vibration control system model, the optimization index is considered to start from the assembly module corresponding to the highest modal frequency and the assembly module corresponding to the lowest modal frequency respectively, and the modal frequency separation method is used to obtain the preliminary layout of the active and passive vibration controllers, and the modal frequency separation domain is determined;

[0041] S4. Under the same optimization index, solve the optimal active and passive vibration controller layout in the modal frequency separation domain, and combine the preliminary layout to obtain the global optimal vibration controller layout to suppress the vibration of the spacecraft.

[0042] In step S1 of the embodiment of the present invention, based on the discrete and gradual dynamic characteristics of the on-orbit assembly process of the large space structure, a finite element model dynamically updated with the on-orbit assembly process is obtained, and then a vibration dynamics model suitable for vibration control of the on-orbit assembly process of the large spacecraft is established, which is expressed as:

[0043]

[0044] In the formula, represents the mass matrix, represents the damping matrix, represents the stiffness matrix, Indicates The mass matrix of the assembled modules, Indicates The stiffness matrix of the assembly module, x i1 , x i2 Respectively represent The first-order modal damping ratio and the second-order modal damping ratio of the assembled modules are represents the displacement vector of the system node under the finite element model, and denote the corresponding velocity vector and acceleration vector respectively, represents the control input, represents the allocation matrix of the actuators, Indicates external interference. Represents the allocation matrix of external disturbances.

[0045] In step S3 of the embodiment of the present invention, the passive vibration controller adopts the installation of viscoelastic dampers, so that the damping ratio corresponding to the first-order mode and the second-order mode of the structure is significantly improved.

[0046] The active vibration controller adopts a distributed PD cooperative controller, and its expression is:

[0047]

[0048] In the formula, u i Indicates i The control vector of the assembled active module, Indicates i The proportional gain matrix of the assembled active modules is K iP and the differential gain matrix K iD The proportional-derivative controller gain matrix is, Indicates i The coordinated parameters of the assembled active modules, Indicates i The displacement and velocity vectors measured by the assembled active modules are Indicates i The first assembled active module adjacent to the j The displacement and velocity vectors measured by the active modules are represents all measurement vectors, represents the displacement measurement vector, represents the velocity measurement vector, and the superscript T represents the transpose; as the on-orbit assembly proceeds, the matrices and vectors will be partially expanded and updated, and K P and K D The specific form is as follows:

[0049]

[0050] In the formula, N Represents the total number of assembled modules; the main diagonal elements number adjoin ( i ) indicates that at this time i The number of adjacent modules of the assembled module, for the first i row; in the i The block matrix position of the adjacent module of the assembly module is the coordination parameter - right , and the remaining positions are zero matrices of the corresponding dimensions.

[0051] Considering the co-location of the displacement velocity sensor and the force actuator, the constructed distributed active-passive hybrid vibration control system model can be obtained, which is expressed as:

[0052]

[0053]

[0054] In the formula, represents the first-order derivative of all state vectors, represents the sensor measurement position matrix, Represents the identity matrix.

[0055] Step S3 of the embodiment of the present invention includes the following sub-steps:

[0056] S31. Based on the first-order mode reflecting the basic vibration form of the structure, the change of the first-order modal natural frequency of the entire structure during the on-orbit assembly of the large-scale space structure as the assembly proceeds is obtained, and its modal frequency is rearranged in descending order;

[0057] Specifically, each assembly module corresponds to the first-order modal natural frequency of the entire structure after the module is assembled, which is recorded as [ oh 11 , …, oh 1i ,…, oh 1N ],in i is the module number for a given on-orbit assembly sequence, N is the total number of assembled modules; further, the first-order modal natural frequency sequence is rearranged in descending order as [ oh 1t1 , …, oh 1 ti ,…, oh 1 tN ],in t 1, …, t i ,…, t N is 1, …, i ,…, N A frequency-decreasing arrangement of oh 1t1 >…> oh 1 ti >…> oh 1 tN ;

[0058] S32, determining optimization indicators based on control energy consumption, time efficiency and accuracy;

[0059] S33, based on the determined optimization index, starting from the assembly module corresponding to the highest modal frequency and the assembly module corresponding to the lowest modal frequency, respectively, a modal frequency separation method is used to obtain a preliminary layout of the active and passive vibration controllers, until assembly modules with intermediate frequency vibrations that do not have obvious high-frequency or low-frequency vibration characteristics appear in both directions;

[0060] S34. The modal frequencies corresponding to the two assembly modules are used as the upper and lower bounds of the region, respectively, to obtain a modal frequency separation domain.

[0061] In step S32 of this embodiment, the preliminary layout of the active and passive vibration controllers is:

[0062] The assembly modules with modal frequencies higher than the modal frequency separation domain are controlled by a passive vibration controller, and the assembly modules with modal frequencies lower than the modal frequency separation domain are controlled by an active vibration controller.

[0063] Specifically, the modal frequency sequence after descending rearrangement can be equivalently written as [ oh 1t1 ,…, oh 1m0-1 , oh 1m0 ,…, oh 1mi ,…, oh 1mf , oh 1mf+1 ,…, oh 1 tN ], and for the number [ t 1,…, m 0 - 1] adopts passive vibration control; the module numbered [ m f +1,…, t N ]'s module uses active vibration control.

[0064] Defining vibration control effects without considering modal frequency separation domain optimization f = f ( oh 1s ), so that f The smaller it is, the better the vibration control effect is. oh 1s is the modal frequency separation point, s is the module number, and the meanings are as follows:

[0065]

[0066] in i ≠s, then the module m 0. m f They have local optimality and satisfy the relationship:

[0067]

[0068] In step S4 of the embodiment of the present invention, the method for solving the optimal active and passive vibration controller layout in the modal frequency separation domain is specifically:

[0069] In the modal frequency separation domain, for the number [ m 0, …, m i , …, m f ] assembly module, define ( m f - m 0+1)-dimensional vector x =[ x 1, …, x i , …, x mf-m0+1 ] T Each element is used as an optimization parameter, and the lower and upper bounds of the optimization parameters are defined as 0 and 1 respectively;

[0070] The optimization index is used as the fitness function, and the optimization algorithm is used to solve the optimal active and passive vibration controller layout in the modal frequency separation domain based on the defined optimization parameters and their upper and lower bounds. x opt =[ x 1,…, x i ,…, x mf-m0+1 ] T ; Among them, for the optimization parameters x i It is expressed as:

[0071] .

[0072] In step S4 of this embodiment, x opt Together with the vibration controller layout preliminarily obtained outside the modal frequency separation domain, it constitutes the global optimal vibration controller layout to achieve vibration suppression of large spacecraft.

[0073] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0074] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. An active-passive hybrid vibration control method based on modal frequency separation domain optimization, characterized in that: The following steps are involved: S1. Establish a vibration dynamics model suitable for vibration control during the on-orbit assembly process of large spacecraft; S2. Based on the constructed vibration dynamics model, passive vibration controllers and active vibration controllers are designed for modular large-scale spatial structures, and then a distributed active-passive hybrid vibration control system model under the active-passive hybrid collaborative vibration control strategy is constructed; S3. Based on the active-passive hybrid vibration control system model, the optimization index is considered to start from the assembly module corresponding to the highest modal frequency and the assembly module corresponding to the lowest modal frequency respectively, and the modal frequency separation method is used to obtain the preliminary layout of the active and passive vibration controllers, and the modal frequency separation domain is determined; Among them, based on the determination of the optimization index, the modal frequency separation method is used to obtain the preliminary layout of the active and passive vibration controllers starting from the assembly module corresponding to the highest state frequency and the assembly module corresponding to the lowest state frequency, until assembly modules with intermediate frequency vibrations that do not have obvious high-frequency or low-frequency vibration characteristics appear in two directions respectively; the modal frequencies corresponding to the two assembly modules are used as the upper and lower bounds of the region, respectively, to obtain the modal frequency separation domain; S4. Under the same optimization index, solve the optimal active and passive vibration controller layout in the modal frequency separation domain, and combine the preliminary layout to obtain the global optimal vibration controller layout to suppress the vibration of the spacecraft; The optimization index is used as the fitness function, and the optimization algorithm is used to solve the optimal active and passive vibration controller layout in the modal frequency separation domain based on the defined optimization parameters and their upper and lower bounds. x opt =[ x 1,…, x i ,…, x mf-m0+1 ] T ; The optimization parameters x i It is expressed as: ； In the modal frequency separation domain, for the number [ m 0, …, m i , …, m f ] assembly module, define ( m f - m 0+1)-dimensional vector x =[ x 1, …, x i , …, x mf-m0+1 ] T Each element is used as an optimization parameter, and the lower and upper bounds of the optimization parameters are defined as 0 and 1 respectively.

2. The active-passive hybrid vibration control method based on modal frequency separation domain optimization according to claim 1 is characterized in that: In step S1, the vibration dynamics model is expressed as: In the formula, represents the mass matrix, represents the damping matrix, represents the stiffness matrix, Indicates The mass matrix of the assembled modules, Indicates The stiffness matrix of the assembly module, ξ i1 , ξ i2 Respectively represent The first-order modal damping ratio and the second-order modal damping ratio of the assembled modules are represents the displacement vector of the system node under the finite element model, and denote the corresponding velocity vector and acceleration vector respectively, represents the control input, represents the allocation matrix of the actuators, Indicates external interference. Represents the allocation matrix of external disturbances.

3. The active-passive hybrid vibration control method based on modal frequency separation domain optimization according to claim 2 is characterized in that: In the step S3, the passive vibration controller is provided with a viscoelastic damper; The active vibration controller adopts a distributed PD collaborative controller, and its expression is: In the formula, u i Indicates i The control vector of the assembled active module, Indicates i The proportional gain matrix of the assembled active modules is K iP and the differential gain matrix K iD The proportional-derivative controller gain matrix is, Indicates i The coordinated parameters of the assembled active modules, Indicates i The displacement and velocity vectors measured by the assembled active modules are Indicates i The first assembled active module adjacent to the j The displacement and velocity vectors measured by the active modules are represents all measurement vectors, represents the displacement measurement vector, represents the velocity measurement vector, and the superscript T indicates the transpose; The constructed distributed active-passive hybrid vibration control system model is expressed as: In the formula, represents the first-order derivative of all state vectors, represents the sensor measurement position matrix, Represents the identity matrix.

4. The active-passive hybrid vibration control method based on modal frequency separation domain optimization according to claim 1 is characterized in that: The step S3 further comprises: S31. Based on the first-order mode reflecting the basic vibration form of the structure, the change of the first-order modal natural frequency of the entire structure during the on-orbit assembly of the large-scale space structure as the assembly proceeds is obtained, and its modal frequency is rearranged in descending order; S32. Determine optimization indicators based on control energy consumption, time efficiency and accuracy.

5. The active-passive hybrid vibration control method based on modal frequency separation domain optimization according to claim 4 is characterized in that: In step S32, the preliminary layout of the active and passive vibration controller is: The assembly modules with modal frequencies higher than the modal frequency separation domain are controlled by a passive vibration controller, and the assembly modules with modal frequencies lower than the modal frequency separation domain are controlled by an active vibration controller.

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