Spacecraft ground microgravity simulation platform similarity analysis method

Abstract

The application discloses a kind of spacecraft ground microgravity simulation platform similarity analysis method, belong to space technology technical field.The following steps are included: the space dynamics model of spacecraft ground microgravity semi-physical simulation platform is established and the space dynamics model is rewritten to Lagrange dynamics, and the rewritten simulation platform is obtained;Similarity analysis is carried out on spacecraft ground microgravity semi-physical simulation platform and the rewritten simulation platform based on π theorem, and the space satellite platform parameters involved are obtained to determine the design parameters of the rewritten simulation platform;Space attitude scanning trajectory and attitude scanning PID control law are designed for the space satellite platform involved, and the space attitude scanning PID control law is obtained;Similarity analysis is carried out on space attitude scanning PID control law based on π theorem, and the ground microgravity simulation platform attitude scanning PID control law parameter is designed, to obtain ground space attitude scanning PID control law.The dynamics and control effect of the platform can be consistent with the effect of space actual satellite.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of aerospace technology, and relates to a similarity analysis method for a spacecraft ground microgravity simulation platform. BACKGROUND

[0002] With the deepening and expansion of human space activities, space vehicles for space application emerge as the times require, including spacecraft, space shuttles, space stations, and new concept space vehicles developed in recent years, which have various purposes and functions. Looking at the development of each space vehicle, it has gone through the processes of concept research, overall design, key technology verification, and ground test. Among them, the key technology experiment on the ground is an indispensable link. Considering the particularity of the space environment, the spacecraft must consider the space environment during ground testing, so it is necessary to simulate the on-orbit environment for performance testing and operation inspection.

[0003] Similarity theory is a basic theory for studying the relationship between systems and systems, and the relationship between prototype and model motion parameters. It can give the similarity criteria between systems, establish the similarity relationship between parameters, and thus deduce the characteristics of one system from the characteristics of another system, and deduce the characteristics of the prototype from the characteristics of the model. Based on the similarity theory, the similarity criteria and similarity relationship between the spacecraft ground experiment system and the space prototype system can be established, so as to give the corresponding relationship between the physical quantities describing the space operation motion in space and on the ground and the mutual constraints therebetween. Based on the relationships and constraints given by the similarity theory, we can deduce the space actual motion characteristics from the ground experiment results. Similarity analysis needs to associate two systems. There are various experimental methods for simulating spacecraft space motion in the ground environment, such as the wire suspension system, the air floating table system, and the neutral buoyancy pool system, but none of them can achieve the microgravity level required for gravitational wave detection. SUMMARY

[0004] The purpose of the present application is to solve the technical problem that the experimental methods for simulating spacecraft space motion in the ground environment in the prior art cannot achieve the microgravity level required for gravitational wave detection, and to provide a spacecraft ground microgravity simulation platform similarity analysis method. The spacecraft ground microgravity simulation platform analyzed in the present application can simulate extremely high microgravity levels in the ground environment through structural design, which effectively supports the ground experiments of gravitational wave detection satellites. Through the similarity analysis method in the present application, the dynamics and control effect of the platform can be consistent with the actual effect of the space satellite.

[0005] In order to achieve the above purpose, the technical scheme of the present application is as follows:

[0006] In the first aspect, the present application provides a spacecraft ground microgravity simulation platform similarity analysis method, comprising the following steps:

[0007] A space dynamics model of a spacecraft ground microgravity semi-physical simulation platform is established, and the space dynamics model is rewritten by Lagrange dynamics to obtain a rewritten simulation platform;

[0008] Similarity analysis is performed on the spacecraft ground microgravity semi-physical simulation platform and the rewritten simulation platform based on the pi theorem, and parameters of the space satellite platform involved are obtained to determine the design parameters of the rewritten simulation platform;

[0009] An attitude scanning trajectory and an attitude scanning PID control law are designed for the space satellite platform involved to obtain a space attitude scanning PID control law;

[0010] The space attitude scanning PID control law is subjected to similarity analysis based on the pi theorem, and the parameters of the ground microgravity simulation platform attitude scanning PID control law are designed to obtain a ground attitude scanning PID control law.

[0011] Further improvement of the present application is that:

[0012] The rewritten simulation platform is obtained by the following steps:

[0013] A dynamics analysis coordinate system is established for the spacecraft ground microgravity semi-physical simulation platform, and required variables are defined;

[0014] The dynamics model of the spacecraft ground microgravity semi-physical simulation platform is derived according to Lagrange dynamics in the dynamics analysis coordinate system;

[0015] Reasonable assumptions are made, and the dynamics model is rewritten by Lagrange dynamics to obtain the rewritten simulation platform.

[0016] The specific steps of establishing the dynamics analysis coordinate system are:

[0017] An inertial coordinate system is established: the origin is located at the center of the lower surface of the platform; the direction of the bisector of the telescope angle is the x-axis direction, and the direction opposite to the local gravity direction is the z-axis direction, and the relationship between the y-axis and the x-axis and the z-axis is determined by the right-hand coordinate system;

[0018] A platform coordinate system is established for the platform upper plate: the origin is located at the three-axis rotation center of the rotating part; the three coordinate axes are consistent with the three coordinate axes of the inertial coordinate system;

[0019] An outer frame coordinate system is established for the outer frame: the origin is located at the three-axis rotation center of the rotating part; in the nominal state, it coincides with the platform system; the pivot connecting the outer frame and the platform upper plate is arranged along the y-axis direction of the outer frame coordinate system;

[0020] A middle frame coordinate system is established for the middle frame: the origin is located at the three-axis rotation center of the rotating part; in the nominal state, the middle frame coordinate system coincides with the platform coordinate system and rotates around the x-axis; the pivot connecting the middle frame and the outer frame is arranged along the x-axis direction of the middle frame coordinate system;

[0021] An inner frame coordinate system is established for the inner frame: the origin is located at the three-axis rotation center of the rotating part; in the nominal state, the inner frame coordinate system coincides with the platform coordinate system and rotates around the z-axis; the pivot connecting the inner frame and the middle frame is arranged along the z-axis direction of the inner frame coordinate system;

[0022] The inertia coordinate system is represented by I; the platform coordinate system is represented by P; the outer frame coordinate system is represented by O; the middle frame coordinate system is represented by M; and the inner frame coordinate system is represented by N;

[0023] The center coordinates of the inertia system are defined as (0, 0, 0) I ; the center coordinates of the four pivots of the upper plate of the platform are (0, 0, l) I , or (0, 0, -h1) P , where h1 is the distance from the center of the four pivots of the upper plate of the platform to the three-axis rotation center of the rotating part; the center of gravity of the upper plate of the platform is (x4, y4, z4) P ; the center of gravity of the outer frame is (x1, y1, z1) O ; the center of gravity of the middle frame is (x2, y2, z2) M ; the center of gravity of the inner frame is (x3, y3, z3) N ; the masses of the upper plate of the platform, the outer frame, the middle frame, and the inner frame are m P , m O , m M , and m N , respectively;

[0024] wherein the superscript I represents the coordinates in the I coordinate system; the superscript P represents the coordinates in the P coordinate system; the superscript O represents the coordinates in the O coordinate system; the superscript M represents the coordinates in the M coordinate system; the superscript N represents the coordinates in the N coordinate system; l is the length of the connecting rod; and h1 is the distance from the center of the four pivots of the upper plate of the platform to the three-axis rotation center of the rotating part;

[0025] For the outer frame, it is assumed that the rotation of the outer frame around the y-axis is θ4, and the principal axis of inertia of the frame coincides with the outer frame system, and the inertia matrix at the center of gravity is I O = diag(I 11,O , I 22,O , I 33,O ); and the rotation angular velocity relative to the inertia system is:

[0026]

[0027] For the middle frame, it is assumed that the rotation of the middle frame around the x-axis is θ3, and the principal axis of inertia of the frame coincides with the middle frame system, and the inertia matrix is I M= diag(I 11,M ,I 22,M ,I 33,M ); its angular velocity compared to the inertial system is:

[0028]

[0029] For the inner frame, assuming that the rotation of the outer frame around the z axis is θ5, its inertia matrix is:

[0030]

[0031] Its angular velocity compared to the inertial system is:

[0032]

[0033] The transfer matrix is:

[0034]

[0035] Subsequently, the above-mentioned various parameters are unified to the inertial coordinate system, and the coordinate of each parameter is obtained as follows: the center of the four pivots of the upper plate of the platform (lsinθ1cosθ2, lsinθ2, lcosθ1cosθ2), the center of the three-axis rotation of the platform (lsinθ1cosθ2, lsinθ2, lcosθ1cosθ2+h1), the center of gravity of the upper plate of the platform (lsinθ1cosθ2+z4, lsinθ4+z4, lcosθ1cosθ2+h1+z4), the center of gravity of the outer frame the center of gravity of the middle frame the center of gravity of the inner frame

[0036] The steps of deriving the Lagrange dynamics equation of the spacecraft ground microgravity semi-physical simulation platform are as follows:

[0037] The kinetic energy is divided into rotational kinetic energy around the center of mass and translational kinetic energy around the center of mass:

[0038]

[0039] Where, V O is the velocity of the outer frame, V M is the velocity of the middle frame, V N is the velocity of the inner frame, and VP is the velocity of the upper plate of the platform; T is the kinetic energy.

[0040] Solve the potential energy:

[0041]

[0042] Where, z O is the z-direction component of the center of gravity of the outer frame in the inertial coordinate system, and z Mis the z-direction component of the center of gravity of the middle frame in the inertial coordinate system, z N is the z-direction component of the center of gravity of the inner frame in the inertial coordinate system, z P is the z-direction component of the center of gravity of the platform upper plate in the inertial coordinate system; U is the potential energy;

[0043] The Lagrange quantity is calculated as L = T - U;

[0044] The formula for calculating the left end term of the Lagrange dynamics equation is:

[0045]

[0046] For the calculation of the right end term of the Lagrange equation, the position vector of the force in the inner frame system is (x F ,y F ,z F ) N , and the position vector in the inertial system is The force in the inner frame system is F N =(F x ;F y ;F z ) N , and in the inertial system, it is

[0047] The formula for calculating the right end term of the Lagrange dynamics equation is:

[0048]

[0049] The reasonable assumptions are made, the dynamics model is rewritten by Lagrange dynamics, and the rewritten simulation platform includes the following steps:

[0050] Small angle assumption: the rotation angles of each pivot of the spacecraft ground microgravity semi-physical simulation platform in the movement process are extremely small, satisfying the small angle assumption, i.e.

[0051] cosθ1=1,sinθ1=θ1,cosθ2=1,sinθ2=θ2,cosθ3=1,sinθ3=θ3,cosθ4=1,sinθ4=θ4,cosθ5=1,sinθ5=θ5

[0052] Inner frame rotation inertia leveling assumption: the inner frame of the spacecraft ground microgravity semi-physical simulation platform is leveled during design and assembly, so the rotation inertia satisfies a certain relationship:

[0053] I 12,N =0, I 13,N =0, I 21,N =0, I 23,N =0, I 31,N =0, I 32,N =0

[0054] Since the translational freedom in z direction is not considered in the spacecraft ground microgravity semi-physical simulation platform, only 5 degrees of freedom of the space satellite platform are considered; the translational equation in z direction is abandoned, and the dynamics equation of the space satellite platform is:

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] Therefore, the following assumptions are introduced again:

[0061] The first order term of the degrees of freedom θ1 and θ2 of the dynamics equation of the spacecraft ground microgravity semi-physical simulation platform is retained, and the second order term of other degrees of freedom is retained; the obtained dynamics equation is:

[0062]

[0063]

[0064]

[0065]

[0066]

[0067] The above equation is arranged as:

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075] Wherein:

[0076] I′ y-z =I 11,N -I22,N +I 33,N

[0077] I′ z-x =I 11,N -I 22,N -I 33,N

[0078] I′ x-y =-I 11,N +I 22,N -I 33,N

[0079]

[0080]

[0081] I z =I 33,N

[0082] Rewrite the cross term of the moment of inertia of the ground dynamics relative to the space dynamics, get:

[0083]

[0084]

[0085] I y-x =I 22,O +I 22,M +I 22,N -I 11,M -I 11,N

[0086] Arrangement:

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094] Arrangement:

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102] Finally, we get:

[0103]

[0104]

[0105]

[0106]

[0107]

[0108] The similarity analysis of the spacecraft ground microgravity semi-physical simulation platform and the modified simulation platform based on the π theorem includes the following steps:

[0109] The similarity analysis is performed according to the π theorem to determine the π group;

[0110] The dynamics of the space satellite platform is described by the following 25 parameters:

[0111] Variables x, y, dimension [L]; variables dimension [L][T] -1 ; variables dimension [L][T] -2 ; variables θ x , θ y , θ z ; variables dimension [T] -1 ; variables dimension [T] -2 ; variables m S , dimension [M]; variables J x , J y , J z , dimension [M][L] 2 ; variables F x , F y , dimension [M][L][T] -2 ; variables M x , M y , Mz dimension [M] [L] 2 [T] -2 dimension [T] ; variable t, dimension [T] ;

[0112] According to the π theorem, the π group contains 22 variables; taking the complete dynamics subset {m S ,J z ,t}, the dynamics π group of the simulation platform is derived

[0113]

[0114]

[0115]

[0116]

[0117] The dynamics of the rewritten simulation platform describes the system by the following 25 parameters:

[0118] variable x, y, dimension [L] ; variable dimension [L] [T] -1 ; variable dimension [L] [T] -2 ; variable θ3, θ4, θ5; variable dimension [T] -1 ; variable dimension [T] -2 ; variable m G , dimension [M] ; variable I x , I y , I z , dimension [M] [L] 2 ; variable dimension [M] [L] [T] -2 ; variable t, dimension [T] ;

[0119] According to the π theorem, the π group contains 22 variables; taking the complete dynamics subset {m G ,I z ,t}, the dynamics π group of the rewritten simulation platform is derived

[0120]

[0121]

[0122]

[0123] ​​

[0124] The space satellite platform parameters involved in the acquisition are used to determine the design parameters of the rewritten simulation platform, and specifically include the following steps:

[0125] For the dynamics of the space satellite platform and the dynamics of the rewritten simulation platform, the design parameters are {m S x y z} and {m G x y z}, and the obtained subset of dynamics is obtained by the π theorem:

[0126]

[0127] Therefore, when determining the design parameters of the ground microgravity simulation platform, {m G z} need to be determined first, and the remaining two parameters are determined by the π theorem relationship:

[0128]

[0129] The space satellite platform design attitude scanning trajectory involved specifically includes the following steps:

[0130] For the attitude scanning of the satellite and the ground test bench without drag, the scanning axis is determined as the x-axis, and the Archimedes curve is used as the scanning curve; the distance between the two spacecraft platforms is L, and the radius of the scanning area is D max , the interval between adjacent helical lines is d = 2rα, where r is the radius of the telescope field of view cone, and α is the correction coefficient:

[0131] The parameter equation of the Archimedes curve in the y-z plane is

[0132]

[0133] Where T is the total scanning time set;

[0134] For the satellite rotating θ and ψ around the y-axis and z-axis respectively, the spacecraft angle change relationship is

[0135]

[0136] The angle in the x-axis direction remains 0.

[0137] The space attitude scanning PID control law is specifically obtained by the following steps:

[0138] ​​​​​​​For three rotation channels of the space satellite platform, the attitude scanning PID control law is set as:

[0139]

[0140] wherein, is the difference between the designed angle and the actual angle.

[0141] The ground attitude scanning PID control law is obtained through the following steps:

[0142] The dynamics of the space satellite platform and the dynamics of the rewritten simulation platform are applied to the attitude scanning PID control law:

[0143] The control parameters of the space satellite platform are:

[0144]

[0145] The rewritten simulation platform is:

[0146]

[0147] The ground control parameters are obtained by corresponding to the same group:

[0148]

[0149] Compared with the prior art, the present application has the following beneficial effects:

[0150] The present application discloses a spacecraft ground microgravity simulation platform similarity analysis method, through similarity analysis, the designed parameters of the rewritten simulation platform and the ground attitude scanning PID control law are obtained, simulation proves that the method involved in the present application can make the spacecraft ground microgravity simulation platform and the space real system achieve similar dynamics effect, provides a ground experiment scheme for the design and test of the space satellite platform, through dynamics similarity analysis and control similarity analysis, the method provided by the present application can make the spacecraft ground microgravity simulation platform involved in the present application achieve similar dynamics and control effect with the space platform under the ground environment. The method can be further applied to the further design of the ground microgravity facility, realizes the similarity between the ground experiment and the space actual situation in more complex tasks, and provides corresponding guidance for the ground experiment of the gravitational wave detection satellite. BRIEF DESCRIPTION OF DRAWINGS

[0151] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments. It should be understood that the following drawings only show some of the embodiments of the present application, and therefore should not be regarded as limiting the scope. For those skilled in the art, other related drawings can also be obtained without creative labor.

[0152] Figure 1 The flow chart of the similarity analysis method of the spacecraft ground microgravity simulation platform in the present application;

[0153] Figure 2 The structural schematic diagram of the novel spacecraft ground microgravity semi-physical simulation platform involved in the present application;

[0154] Figure 3 The coordinate system schematic diagram of the novel spacecraft ground microgravity semi-physical simulation platform involved in the present application;

[0155] Figure 4 The attitude scanning schematic diagram involved in the present application;

[0156] Figure 5 The x-direction angular velocity change over time diagram in the specific embodiment of the present application;

[0157] Figure 6 The y-direction angular velocity change over time diagram in the specific embodiment of the present application;

[0158] Figure 7 The z-direction angular velocity change over time diagram in the specific embodiment of the present application. DETAILED DESCRIPTION

[0159] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the following will combine the drawings in the embodiments of the present application to make a clear and complete description of the technical solutions in the embodiments of the present application. Obviously, the described embodiments are some of the embodiments of the present application, but not all the embodiments. The components of the embodiments of the present application described and shown in the drawings can be arranged and designed in various different configurations.

[0160] Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of the present application.

[0161] It should be noted that: similar numbers and letters represent similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined and explained in the subsequent drawings.

[0162] The application will be further described in detail below with reference to the accompanying drawings:

[0163] Referring to Figure 1 The embodiment of the application discloses a space vehicle ground microgravity simulation platform similarity analysis method, comprising the following steps:

[0164] S1, a space dynamics model of a space vehicle ground microgravity semi-physical simulation platform is established, and the space dynamics model is rewritten by Lagrange dynamics to obtain a rewritten simulation platform;

[0165] S2, similarity analysis is performed on the space vehicle ground microgravity semi-physical simulation platform and the rewritten simulation platform based on the π theorem, and space satellite platform parameters involved are acquired to determine design parameters of the rewritten simulation platform;

[0166] S3, an attitude scanning trajectory and an attitude scanning PID control law are designed for the space satellite platform involved to obtain a space attitude scanning PID control law;

[0167] S4, similarity analysis is performed on the space attitude scanning PID control law based on the π theorem, and a ground microgravity simulation platform attitude scanning PID control law parameter is designed to obtain a ground attitude scanning PID control law.

[0168] The method provided by the application can make the space vehicle ground microgravity simulation platform involved achieve similar dynamics and control effects in a ground environment as a space platform. The method can be further applied to further design of the ground microgravity facility, and realize similarity between ground experiments and space actual situations in more complex tasks, thereby providing corresponding guidance for ground experiments of gravitational wave detection satellites.

[0169] The content of the application will be described in detail below in combination with specific embodiments:

[0170] Referring to Figure 2 The space vehicle ground microgravity simulation platform involved in the application is composed of a base, a platform upper plate, four equal-length connecting rods, two kinds of pivots, an outer frame, a middle frame and an inner frame. When performing dynamics modeling, coordinate systems are designed for the platform upper plate, the outer frame, the middle frame and the inner frame.

[0171] The proposed microgravity semi-physics simulation platform for spacecraft consists of a base fixed to a ground foundation. The platform's upper plate is connected to the base via four links and pivots. An outer frame is pivoted to the platform's upper plate, a middle frame is pivoted to the outer frame, and an inner frame is pivoted to the middle frame. The platform's base is fixed to a vibration-isolated foundation. The translational mechanism (or platform upper plate) is connected to the base by four support rods and 16 identical pivots. The rotational mechanism consists of an outer frame, a middle frame, and an inner frame. The inner frame is also fixed to the simulated satellite platform, while the outer frame is connected to the translational mechanism. The satellite simulation platform carries three sets of micro-thrust clusters, a telescope simulation mechanism, and optical motion measurement equipment. The translational mechanism and the outer frame, as well as the three parts within the rotational mechanism, are all connected via two pivots. When the platform is subjected to forces and torques, the four-bar linkage formed by the platform upper plate, the base, and the support rods and pivots reflects the system's translational motion. The rotational mechanism reflects the system's rotational motion. It should be noted that the stiffness of the pivot used to characterize translational motion is different from that used to characterize rotational motion. The translational and rotational motions of the system are accurately measured using optical measuring equipment to evaluate the performance of the control system and correct errors.

[0172] Step 1, see Figure 3 A dynamic analysis coordinate system is established for the spacecraft's ground-based microgravity semi-physical simulation platform, and the required variables are specified:

[0173] Inertial coordinate system (I): The origin is located at the center of the bottom surface of the platform. The direction of the angle bisector of the telescope is the x-axis, and the direction opposite to the local gravity is the z-axis. The relationship between the y-axis and the x and z axes is determined by the right-hand coordinate system.

[0174] Platform coordinate system (P): The origin is located at the center of rotation of the rotating part along its three axes. The three coordinate axes point in the same direction as the three coordinate axes of the inertial coordinate system.

[0175] Outer frame coordinate system (O): The origin is located at the three-axis rotation center of the rotating part. Under nominal conditions, it coincides with the platform system; the pivot connecting the outer frame and the platform plate is arranged along the y-axis of the outer frame coordinate system.

[0176] The middle frame coordinate system (M) has its origin located at the center of rotation of the rotating part along the three axes. In its nominal state, it coincides with the platform system (rotating about the x-axis); the pivot connecting the middle frame and the outer frame is arranged along the x-axis of the middle frame coordinate system.

[0177] Inner frame coordinate system (N): The origin is located at the three-axis rotation center of the rotating part. In the nominal state, it coincides with the platform system (rotating about the z-axis); the pivot connecting the inner frame and the middle frame is arranged along the z-axis direction of the inner frame coordinate system.

[0178] For the coordinate system defined above, the coordinates of the center of the inertial frame are specified as (0,0,0). Iwhere the superscript I represents the coordinate expressed in the I frame, and the same below). The center of the four-pivot of the upper platform is (0, 0, 1) I , where 1 is the length of the connecting rod, or can be expressed as (0, 0, -h1) P , h1 is the distance from the center of the four-pivot of the upper platform to the center of the three-axis rotation of the rotating part. The center of gravity of the upper platform is (x4, y4, z4) P . The center of gravity of the outer frame is (x1, y1, z1) O . The center of gravity of the middle frame is (x2, y2, z2) M . The center of gravity of the inner frame is (x3, y3, z3) N . The masses of the upper platform, the outer frame, the middle frame, and the inner frame are m P , m O , m M , and m N , respectively.

[0179] where the superscript I represents the coordinate expressed in the I frame; the superscript P represents the coordinate expressed in the P frame; the superscript O represents the coordinate expressed in the O frame; the superscript M represents the coordinate expressed in the M frame; the superscript N represents the coordinate expressed in the N frame; 1 is the length of the connecting rod; h1 is the distance from the center of the four-pivot of the upper platform to the center of the three-axis rotation of the rotating part;

[0180] For the outer frame, it is assumed that the rotation of the outer frame around the y-axis is θ4, and the principal axis of inertia of the frame coincides with the outer frame system, and the inertia matrix at the center of mass is I O = diag(I 11,O , I 22,O , I 33,O ). The rotational angular velocity relative to the inertial system is

[0181]

[0182] For the middle frame, it is assumed that the rotation of the middle frame around the x-axis is θ3, and the principal axis of inertia of the frame coincides with the middle frame system, and the inertia matrix is I M = diag(I 11,M , I 22,M , I 33,M ). The rotational angular velocity relative to the inertial system is

[0183]

[0184] For the inner frame, it is assumed that the rotation of the outer frame around the z-axis is θ5, and the inertia matrix is

[0185]

[0186] The rotational angular velocity relative to the inertial system is

[0187]

[0188] The transfer matrix is

[0189]

[0190] Subsequently, the above-mentioned each parameter is unified to the inertial coordinate system, and each parameter coordinate is obtained as follows. The four-pivot center of the upper plate of the platform (lsinθ1cosθ2, lsinθ2, lcosθ1cosθ2), the three-axis rotation center of the platform (lsinθ1cosθ2, lsinθ2, lcosθ1cosθ2+h1), the gravity center of the upper plate of the platform (lsinθ1cosθ2+z4, lsinθ4+z4, lcosθ1cosθ2+h1+z4), the gravity center of the outer frame The gravity center of the middle frame The gravity center of the inner frame

[0191] As shown in Figs. Figure 5 , Figure 6 and Figure 7 are respectively the variation diagrams of the angular velocity of the x direction, the y direction and the z direction of the present application with time.

[0192] Step two, the dynamics model of the spacecraft ground microgravity semi-physical simulation platform is derived according to the Lagrange dynamics in the dynamics analysis coordinate system:

[0193] The kinetic energy is divided into the kinetic energy of rotation around the center of mass and the kinetic energy of translation around the center of mass.

[0194]

[0195] In the formula, V O is the speed of the outer frame, V M is the speed of the middle frame, V N is the speed of the inner frame, and V P is the speed of the upper plate of the platform.

[0196] Subsequently, the potential energy is solved as

[0197]

[0198] In the formula, z O is the component of the gravity center of the outer frame in the z direction of the inertial coordinate system, z M is the component of the gravity center of the middle frame in the z direction of the inertial coordinate system, z N is the component of the gravity center of the inner frame in the z direction of the inertial coordinate system, and z P is the component of the gravity center of the upper plate of the platform in the z direction of the inertial coordinate system.

[0199] The Lagrange quantity is calculated as L=T-U.

[0200] The formula for calculating the left end term of Lagrange equation is

[0201]

[0202] For the calculation of the right end term of Lagrange equation, the position vector of the inner frame under the inner frame system is (x F ,y F ,z F ) N , and the position vector of the inertial system is The force under the inner frame system is F N =(F x ;F y ;F z ) N , and under the inertial system, it is

[0203] The formula for calculating the right end term of Lagrange equation is

[0204]

[0205] Step three, make reasonable assumptions, and rewrite the dynamics model by Lagrange dynamics to get the rewritten simulation platform:

[0206] 1. Small angle assumption. The rotation angle of each pivot in the motion process of this simulation table is very small, which satisfies the small angle assumption, i.e.

[0207] cosθ1=1,sinθ1=θ1,cosθ2=1,sinθ2=θ2,cosθ3=1,sinθ3=θ3,cosθ4=1,sinθ4=θ4,cosθ5=1,sinθ5=θ5

[0208] 2. Inner frame rotation inertia leveling assumption. The inner frame of this simulation table is leveled during design and assembly, so the rotation inertia satisfies certain relationship

[0209] I 12,N =0,I 13,N =0,I 21,N =0,I 23,N =0,I 31,N =0,I 32,N =0

[0210] Since the translational freedom in the z direction of the microgravity simulation platform involved is not considered, only the five degrees of freedom of the space satellite platform are considered. The z direction translational equation is discarded, and the dynamics equation of the space satellite platform is:

[0211]

[0212]

[0213]

[0214]

[0215]

[0216] So the hypothesis is introduced again:

[0217] The degrees of freedom θ1 and θ2 of the dynamics equation of the simulation platform retain the first order term, and the other degrees of freedom retain the second order term.

[0218] The obtained dynamics equation is:

[0219]

[0220]

[0221]

[0222]

[0223]

[0224] Arranged as:

[0225]

[0226]

[0227]

[0228]

[0229]

[0230]

[0231]

[0232] Wherein:

[0233] I y ′ -z =I 11,N -I 22,N +I 33,N

[0234] I z ′ -x =I 11,N -I 22,N -I 33,N

[0235] I x ′-y = -I 11,N + I 22,N - I 33,N

[0236]

[0237]

[0238] I z = I 33,N

[0239] Rewrite the cross term of the moment of inertia for ground dynamics with respect to spatial dynamics, hoping to get

[0240]

[0241]

[0242] I y-x = I 22,O + I 22,M + I 22,N - I 11,M - I 11,N

[0243] The arrangement has

[0244]

[0245]

[0246]

[0247]

[0248]

[0249]

[0250]

[0251] After sorting out

[0252]

[0253]

[0254]

[0255]

[0256]

[0257]

[0258]

[0259] Finally, we get

[0260]

[0261]

[0262]

[0263]

[0264]

[0265] Step four, similarity analysis of spacecraft ground microgravity semi-physical simulation platform and rewritten simulation platform based on π theorem.

[0266] Space satellite platform dynamics is described by 25 parameters shown in Table 1.

[0267] Table 1 Space satellite platform dynamics system parameters

[0268]

[0269] According to π theorem, π group contains 22 variables. Take the complete dynamics subset {m S ,J z ,t}, derive Get the dynamics π group of space satellite platform:

[0270]

[0271]

[0272]

[0273]

[0274] Ground simulation platform dynamics is described by 25 parameters shown in Table 2.

[0275] Table 2 Ground simulation platform dynamics system parameters

[0276]

[0277] According to π theorem, π group contains 22 variables. Take the complete dynamics subset {m G ,I z ,t}, derive Get the dynamics π group of rewritten simulation platform:

[0278]

[0279]

[0280]

[0281]

[0282] Step five, get the involved space satellite platform parameters for determining the design parameters of the rewritten simulation platform.

[0283] For the space satellite platform dynamics and the ground microgravity simulation platform dynamics, the design parameters are {m S ,J x ,J y ,J z} and {m G ,I x ,I y ,I z}. And according to the obtained dynamics subset and the π theorem, it is expected to obtain:

[0284]

[0285] Therefore, the ground microgravity simulation platform design parameters need to be determined first when determining the design parameters of the ground microgravity simulation platform. G ,I z}. The remaining two parameters are determined by the π theorem relationship:

[0286]

[0287] Step six, design the attitude scanning trajectory and the attitude scanning PID control law for the involved space satellite platform, and obtain the space attitude scanning PID control law.

[0288] Referring to Figure 4 , the attitude scanning is a necessary procedure before the space gravitational wave detection formation enters the scientific mode. The space gravitational wave detection formation perceives the size of the gravitational wave through the distance fluctuation of the laser light path between the three satellites, so establishing the laser link between each satellite is the key to completing the corresponding task. The alignment of the laser link is roughly divided into two parts of coarse alignment and fine alignment. The spacecraft platform in the fine alignment stage has reached the expected attitude, so the spacecraft platform in this state needs to detect the possible strongest laser coming direction according to a certain attitude guide law, so this process is also called attitude scanning.

[0289] The Archimedes curve belongs to the equal velocity ratio spiral, and it can also be called the equal distance spiral because it expands outward by equal distance in each rotation period. Without loss of generality, it is assumed that the space platform scans the sky with the axis, and the scanning curve is shown in Fig. 1. Figure 3 The distance between two space platforms is L, and the radius of the scanning area is D max , and the interval between adjacent spiral lines is d = 2rα, where r is the radius of the telescope field of view cone, and α is the correction coefficient.

[0290] The parameter equation of the Archimedes curve in the y-z plane is

[0291]

[0292] where T is the total scanning time set, and in addition, the coordinates of the point on the Archimedes curve in the initial coordinate system are For the satellite to rotate θ and ψ around the y-axis and z-axis respectively, it is assumed that the unit vector in the x-direction in the initial coordinate system is x0, and

[0293]

[0294] Then make the corresponding components proportional, that is, the vectors are collinear, and

[0295]

[0296] According to the small angle assumption, we have

[0297]

[0298] The relationship between the angles of the space platform is

[0299]

[0300] In addition, it should be pointed out that the direction angle of the x-axis is expected to remain 0.

[0301] Step seven, design the PID control law of the attitude scan. For the three rotation channels of the space platform,

[0302] After the control parameters are given, the control law is set as:

[0303]

[0304] where is the difference between the designed angle and the actual angle.

[0305] Step eight, based on the π theorem, the similarity of the space attitude scanning PID control law is analyzed, the parameters of the ground microgravity simulation platform attitude scanning PID control law are designed, and the ground attitude scanning PID control law is obtained:

[0306] The control parameters of the space satellite platform are:

[0307]

[0308] The rewritten simulation platform is:

[0309]

[0310] The ground control parameters are obtained by corresponding π groups being equal:

[0311]

[0312] The above are only preferred embodiments of the present application and are not used to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A spacecraft ground microgravity simulation platform similarity analysis method, characterized in that, The method comprises the following steps: A space dynamics model of the spacecraft ground microgravity semi-physical simulation platform is established, and Lagrange dynamics rewriting is performed on the space dynamics model to obtain a rewritten simulation platform; Based on Theorem Similarity analysis is performed on the spacecraft ground microgravity semi-physical simulation platform and the modified simulation platform, and the involved space satellite platform parameters are obtained to determine the design parameters of the modified simulation platform. The method comprises the following steps of: The theorem includes the following steps of similarity analysis on the spacecraft ground microgravity semi-physical simulation platform and the modified simulation platform. According to Theorem similarity analysis to determine group; The dynamics of the space satellite platform is described by the following 25 parameters: variable , , dimension [L]; variable , , dimension [L][T] -1 ; variable , , dimension [L][T] -2 ; variable , , ; variable , , , dimension [T] -1 ; variable , , , dimension [T] -2 ; variable m S , dimension [M]; variable , , , dimension [M][L] 2 ; variable , , dimension [M][L][T] -2 ; variable , , , dimension [M][L] 2 [T] -2 ; variable t , dimension [T] According to theorem, group contains 22 variables; take the complete dynamic subset , derived ; get the space satellite platform dynamics group: The dynamics of the rewritten simulation platform is described by the following 25 parameters: variable , , dimension [L]; variable , , dimension [L][T] -1 ; variable , , dimension [L][T] -2 ; variable , , ; variable , , , dimension [T] -1 ; variable , , , dimension [T] -2 ; variable m G , dimension [M]; variable , , , dimension [M][L] 2 ; variable , , , , , dimension [M][L][T] -2 ; variable t , dimension [T] According to theorem, group contains 22 variables; take the full dynamics subset , derive : get the dynamics of the rewritten simulation platform group: The space satellite platform parameters involved in the acquisition are used to determine the design parameters of the rewritten simulation platform, and the method comprises the following steps: For the dynamics of the spatial satellite platform and the modified dynamics of the simulation platform, the design parameters are and and the obtained dynamics subset is Theorem: Therefore, the design parameters of the ground microgravity simulation platform need to be determined first , and the remaining two parameters are determined by the theorem relationship: An attitude scanning trajectory and an attitude scanning PID control law are designed for the space satellite platform to obtain a space attitude scanning PID control law; The method for designing the attitude scanning trajectory for the space satellite platform comprises the following steps: For the attitude scanning of the no-drag satellite and the ground test-bed, the scanning axis is determined as x the axis, using the Archimedes curve as the scanning curve; the distance between the two spacecraft platforms is , the radius of the scanning area is , and the interval between adjacent helical lines is , wherein is the radius of the telescope field-of-view cone, and is a correction coefficient: There are y-z The parametric equation of Archimedean curve in plane is wherein, T is the total duration of the scan set; For the satellite rotates first around y axis and then around z axis With , the angular change relationship of the spacecraft is x The axial angle remains at 0. The space attitude scanning PID control law is obtained by the following steps: For the three rotation channels of the space satellite platform, the attitude scanning PID control law is set as follows after the control parameters are given: wherein is the difference between the design angle and the actual angle; Based on Theorem Similarity analysis is made on the space attitude scanning PID control law, and the attitude scanning PID control law parameters of the ground microgravity simulation platform are designed to obtain the ground attitude scanning PID control law. The ground attitude scanning PID control law is obtained by the following steps: Dynamics of a space satellite platform Dynamics of a reconfigured simulation platform The group application is on the attitude scanning PID control law: Control parameters for a space satellite platform The group is: Rewritten emulation platform Group is: corresponding group phase also gets ground control parameters:

2. The spacecraft ground microgravity simulation platform similarity analysis method of claim 1, wherein, The rewritten simulation platform is obtained by the following steps: A dynamics analysis coordinate system is established for the spacecraft ground microgravity semi-physical simulation platform, and required variables are defined; A dynamics model of the spacecraft ground microgravity semi-physical simulation platform is derived in the dynamics analysis coordinate system according to Lagrange dynamics; Reasonable assumptions are made, and Lagrange dynamics rewriting is performed on the dynamics model to obtain a rewritten simulation platform.

3. The spacecraft ground microgravity simulation platform similarity analysis method of claim 2, wherein, The specific steps of establishing the dynamics analysis coordinate system are as follows: An inertial coordinate system is established: the origin is located at the center of the bottom surface of the platform; the bisector of the angle between the two telescopes is the X-axis x The Y-axis is the axis direction, and the direction opposite to the local gravity direction is the Z-axis z The Y-axis is the axis direction, y The Y-axis is the axis direction, x The Y-axis is the axis direction, z The relationship between the Y-axis and the Z-axis is determined by the right-handed coordinate system; A platform coordinate system is established for the upper plate of the platform: the origin is located at the three-axis rotation center of the rotating part; the three coordinate axes are consistent with the three coordinate axes of the inertial coordinate system; An outer frame coordinate system is established for the outer frame: the origin is located at the three-axis rotation center of the rotating part; in the nominal state, the outer frame coordinate system is consistent with the platform coordinate system; The pivot connecting the outer frame and the upper plate of the platform is arranged along the y-axis direction of the outer frame coordinate system; A middle frame coordinate system is established for the middle frame: the origin is located at the three-axis rotation center of the rotating part; In the nominal state, the middle frame coordinate system is consistent with the platform coordinate system and rotates around the x-axis; The pivot connecting the middle frame and the outer frame is arranged along the x-axis direction of the middle frame coordinate system; An inner frame coordinate system is established for the inner frame: the origin is located at the three-axis rotation center of the rotating part; in the nominal state, the inner frame coordinate system is consistent with the platform coordinate system and rotates around the z-axis; the pivot connecting the inner frame and the middle frame is arranged along the z-axis direction of the inner frame coordinate system; The inertial coordinate system is represented by I; the platform coordinate system is represented by P; the outer frame coordinate system is represented by O; the middle frame coordinate system is represented by M; and the inner frame coordinate system is represented by N; The center coordinates of the inertial system are defined as ; the center coordinates of the four-pivot of the upper plate of the platform are , or expressed as , is the distance from the center of the four-pivot of the upper plate of the platform to the center of the three-axis rotation of the rotating part; the center coordinates of the gravity center of the upper plate of the platform are ; the center coordinates of the gravity center of the outer frame are ; the center coordinates of the gravity center of the middle frame are ; the center coordinates of the gravity center of the inner frame are ; the masses of the upper plate of the platform, the outer frame, the middle frame and the inner frame are , , and ; wherein the superscript I represents coordinates expressed in the I coordinate system; the superscript P represents coordinates expressed in the P coordinate system; the superscript O represents coordinates expressed in the O coordinate system; the superscript M represents coordinates expressed in the M coordinate system; and the superscript N represents coordinates expressed in the N coordinate system; is the length of the connecting rod; is the distance from the center of the four pivots of the upper platform plate to the center of the three-axis rotation of the rotating part. For the outer frame, assume that the rotation of the outer frame about the y-axis is , and that the principal axis of inertia of the frame coincides with the outer frame, and that the inertia matrix at the center of mass of the frame is ; the angular velocity of the frame relative to the inertial frame is For the middle frame, assume that the rotation of the middle frame around the x-axis is , and the principal axis of inertia of the frame coincides with the middle frame, and its inertia matrix is ; The rotation angular velocity of the platform coordinate system relative to the inertial coordinate system is as follows: For the inner frame, assume that the rotation of the outer frame about the z axis is and its inertia matrix is The rotation angular velocity of the outer frame coordinate system relative to the inertial coordinate system is as follows: The transfer matrix is as follows: ， ， Subsequently, the above each variable is unified to the inertial coordinate system, and each variable coordinate is obtained as follows: platform upper plate four-pivot center , platform three-axis rotation center , platform upper plate gravity center , outer frame gravity center , middle frame gravity center , inner frame gravity center .

4. The spacecraft ground microgravity simulation platform similarity analysis method of claim 3, wherein, The steps of deriving the Lagrange dynamics equation of the spacecraft ground microgravity semi-physical simulation platform are as follows: The kinetic energy is divided into rotational kinetic energy around the center of mass and translational kinetic energy around the center of mass: wherein, is the rate of the outer frame, is the rate of the middle frame, is the rate of the inner frame, is the rate of the platform top plate; T is the kinetic energy; The potential energy is solved: wherein, is the z-component of the center of gravity of the outer frame in the inertial coordinate system, is the z-component of the center of gravity of the middle frame in the inertial coordinate system, is the z-component of the center of gravity of the inner frame in the inertial coordinate system, is the z-component of the center of gravity of the platform upper plate in the inertial coordinate system; U is the potential energy; The Lagrangian quantity is calculated as ; The calculation formula of the left end term of the Lagrange dynamics equation is as follows: For the calculation of the right-hand side of the Lagrange equation, the displacement of the force in the inner frame system is and for the inertial system displacement ; the force in the inner frame system is and in the inertial system ; The calculation formula of the right end term of the Lagrange dynamics equation is as follows: 。 5. The spacecraft ground microgravity simulation platform similarity analysis method of claim 4, wherein, The method for making reasonable assumptions, performing Lagrange dynamics rewriting on the dynamics model, and obtaining a rewritten simulation platform comprises the following steps: Small angle assumption: the rotation angle of each pivot of the spacecraft ground microgravity semi-physical simulation platform is very small during the movement process, which meets the small angle assumption, that is Inner frame rotation inertia leveling assumption: The inner frame of the spacecraft ground microgravity semi-physical simulation platform is leveled during the design and assembly process, so the rotation inertia satisfies a certain relationship: Since the translational freedom in the z direction of the spacecraft ground microgravity semi-physical simulation platform is not considered, only the 5 degrees of freedom of the space satellite platform are considered; the z direction translational equation is discarded, and the space satellite platform dynamics equation is: Therefore, the assumption is introduced again: Degrees of freedom of the dynamics equation of a spacecraft ground microgravity semi-physical simulation platform and The first order term is reserved, and the second order term is reserved for other degrees of freedom; the obtained dynamics equation is: Arranged as: Where: Relative to space dynamics, the cross term of the rotational inertia of the ground dynamics is rewritten as: The arrangement is obtained: Arranged as: Finally, we get

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