阅读说明：本技术 一种磁悬浮控制敏感陀螺角动量包络计算方法 (Magnetic suspension control sensitive gyroscope angular momentum envelope calculation method ) 是由 王卫杰 杨洋 任元 樊亚洪 汪洲 张天良 苏楠 吴俊儒 于 2020-12-10 设计创作，主要内容包括：一种磁悬浮控制敏感陀螺角动量包络计算方法。分析磁悬浮控制敏感陀螺三自由度动量交换原理,定义定子坐标系和转子坐标系。利用坐标变换原理建立磁悬浮控制敏感陀螺角动量包络模型。将转子径向两自由度耦合偏转角映射为解耦遍历经、纬度,进而重构出可遍历求解的磁悬浮控制敏感陀螺角动量包络模型。在此基础上,通过转速和经、纬度的三层嵌套循环遍历得到磁悬浮控制敏感陀螺角动量包络分布。本发明将转子径向偏转角映射为遍历经纬度,实现了万向耦合偏转角的解耦,重构了磁悬浮控制敏感陀螺角动量包络模型,为磁悬浮控制敏感陀螺的角动量包络计算提供了高效准确的方法,有利于磁悬浮控制敏感陀螺的空间应用。(A magnetic suspension control sensitive gyro angular momentum envelope calculation method. And (3) analyzing the three-degree-of-freedom momentum exchange principle of the magnetic suspension control sensitive gyroscope, and defining a stator coordinate system and a rotor coordinate system. And establishing a magnetic suspension control sensitive gyroscope angular momentum envelope model by utilizing a coordinate transformation principle. And mapping the radial two-degree-of-freedom coupling deflection angle of the rotor into a decoupling traversal longitude and latitude, and further reconstructing a magnetic suspension control sensitive gyroscope angular momentum envelope model capable of being solved in a traversal mode. On the basis, the angular momentum envelope distribution of the magnetic suspension control sensitive gyroscope is obtained through three-layer nested loop traversal of the rotating speed, the longitude and the latitude. The method maps the radial deflection angle of the rotor into the traversal longitude and latitude, realizes the decoupling of the universal coupling deflection angle, reconstructs the angular momentum envelope model of the magnetic suspension control sensitive gyroscope, provides an efficient and accurate method for the angular momentum envelope calculation of the magnetic suspension control sensitive gyroscope, and is favorable for the space application of the magnetic suspension control sensitive gyroscope.)

1. A magnetic suspension control sensitive gyro angular momentum envelope calculation method is characterized by comprising the following steps: the method comprises the steps of establishing a magnetic suspension control sensitive gyroscope angular momentum envelope model according to a coordinate transformation principle, solving traversal longitude and latitude based on rotor radial deflection angle mapping, further reconstructing the magnetic suspension control sensitive gyroscope angular momentum envelope model, and traversing the rotation speed and the traversal longitude and latitude of a magnetic suspension rotor through three layers of nested circulation to obtain the magnetic suspension control sensitive gyroscope angular momentum envelope. The method comprises the following steps:

(1) definition of stator and rotor coordinate systems

The magnetic suspension control sensitive gyroscope can realize three-degree-of-freedom momentum exchange with an external carrier by utilizing the universal deflection characteristic of a high-speed rotor. The magnetic suspension rotor changes the angular momentum through the change of the rotating speed and outputs axial flywheel torque; the magnetic suspension rotor changes the direction of angular momentum through radial universal deflection and outputs two-degree-of-freedom radial deflection torque. The three-degree-of-freedom momentum exchange envelope model of the magnetically levitated control sensitive gyroscope is generally described in a stator coordinate system and a rotor coordinate system.

Defining a stator coordinate system o_fx_fy_fz_f: is fixedly connected with the gyro room, and the origin of coordinates is coincided with the mass center of the gyro room o_fx_fPointing in the direction of rotation of the frame o_fz_fFor the direction of rotation of the rotor when the frame is at zero position, o_fy_fAccording with the right-hand screw rule. Defining a rotor coordinate system o_rx_ry_rz_r: is fixedly connected with the magnetic suspension rotor but does not wind around with the rotor_rz_rRotating at high speed. When the rotor is initially static floating and is not deflected, the rotor coordinate system is superposed with the stator coordinate system. Let alpha denote the magnetic levitation rotor winding x_fAngle of rotation of the shaft, beta representing the magnetic levitation rotor around y_fThe angle of rotation of the shaft.

(2) Magnetic suspension control sensitive gyro angular momentum envelope modeling based on rotor deflection angle

Initial angular momentum of the rotor is

H₀＝[0 0 J_zΩ₀]^T (1)

Wherein omega₀The initial rotation speed of the magnetic suspension rotor. When the rotating speed is constant, the angular momentum of the magnetic suspension rotor can be expressed as

Wherein the content of the first and second substances,is a transformation matrix from a stator coordinate system to a rotor coordinate system, which can be expressed as

When the rotating speed of the rotor is not changed, the angular momentum of the magnetic suspension rotor can be expressed as

Finding H_{Fixed rotation speed}The modulus of the direction vector can be obtained

It is stated that a change in the radial deflection angle of the rotor can only change the direction of the angular momentum. Whereas a change in rotational speed can only change the magnitude of the angular momentum. Therefore, when considering the change of the rotation speed of the magnetic suspension rotor, the angular momentum of the magnetic suspension rotor can be expressed as:

it is easy to know that the rotor can only have one deflection angle at the moment of universal deflection, and the radial deflection angles alpha and beta of the rotor in the formula (6) are the deflection angles of the rotor along the x axis and the y axis respectively, and cannot directly represent the space direction of the instantaneous space of the rotor, so that a solution thought of traversing longitude and latitude based on the deflection angle of the rotor is provided.

(3) Traversal longitude and latitude mapping and solving method based on rotor deflection angle

And defining a traversal angle delta as an included angle between the angular momentum direction and the initial angular momentum, wherein the traversal angle theta represents an included angle between the projection of the angular momentum on the plane xoy and the x axis. The expression of the angular momentum pointing deflection angle delta of the rotor is

The formula (7) can be obtained by bringing the formula (1) and the formula (6)

δ＝arccos(cosαcosβ) (8)

The cosine values of the two sides of the equation (8) are obtained

cosδ＝cosαcosβ (9)

On the basis of this, define

(4) Magnetic suspension control sensitive gyroscope angular momentum envelope model reconstruction based on traversal longitude and latitude

The formula (6) is replaced by the formula (9) and the formula (10), and the expression of the angular momentum of the magnetic suspension rotor can be obtained

The above formula is a magnetic suspension control sensitive gyroscope angular momentum envelope decoupling model reconstructed based on the deflection longitude and latitude, and obviously, the variables omega, theta and delta on the right side of the formula (11) are not coupled any more.

(5) Traversal solution for angular momentum envelope of magnetically suspended control sensitive gyroscope

Based on the formula (11), nested loop traversal solving is carried out on the momentum space distribution of the magnetic suspension control sensitive gyroscope by taking the rotating speed omega as an outer variable, the traversal angle delta as a middle variable and the traversal angle theta as an inner variable. The value range of the given traverse angle delta is [0, a ] (a belongs to (0,3 ℃), the value range of the traverse angle theta is [ -pi, pi ], and the minimum rotating speed of the rotating speed omega is k (k belongs to [0.5,1)) times of the maximum rotating speed.

After the fixed rotation speed and the angular momentum deflection angle, the traversal angle theta is between [ -pi, pi [ -pi [ ]]The change causing the direction of angular momentum to wind around o_fz_fRotate a circle and are parallel to the plane x_fo_fy_fThe locus is a circle. The traversal angle δ is used as a second layer loop to traverse the magnitude of the angular momentum deflection angle. The radius of the circle formed by the change of the traversal angle theta is larger as the deflection angle of the angular momentum becomes larger, and the distance from the plane x is larger_fo_fy_fMore recently. And traversing the angular momentum direction by the traversing angles delta and theta to form a spherical crown. The change of the outmost layer of the cyclic rotation speed omega can only change the size of the angular momentum, and the rotation speed changesSo that the radius of the ball on which the spherical cap is located varies. And after traversing, carrying out normalization processing on the image to obtain the angular momentum envelope of the magnetic suspension control sensitive gyroscope.

Technical Field

The invention relates to a magnetic suspension control sensitive gyroscope angular momentum envelope calculation method which is suitable for the angular momentum envelope calculation of a magnetic suspension control sensitive gyroscope.

Background

With the development of microelectronics and manufacturing, the development of satellites is moving toward miniaturization. Although the modern small satellite has the characteristics of low weight, small volume, and functions comparable to those of a common large satellite, the limit of the weight and the size of the modern small satellite puts higher requirements on the volume, the weight and the power consumption of an attitude control system, and the task of a reconnaissance and remote sensing satellite puts higher requirements on the attitude control precision and the attitude stability of a spacecraft. The aerospace engineering university invents a magnetic suspension control sensitive gyroscope. The magnetic suspension control sensitive gyroscope integrates attitude sensitivity, high-precision control and vibration detection and inhibition, and can well realize the high-precision control of the attitude of the small satellite and the vibration inhibition. Therefore, the calculation of the angular momentum envelope of the magnetic suspension control sensitive gyroscope has great significance for promoting the space application of the magnetic suspension control sensitive gyroscope.

The mechanical structure of the magnetic suspension control sensitive gyroscope is greatly different from that of the traditional control moment gyroscope, so that the coupling phenomenon exists between two radial deflection angles of a rotor. The traditional angular momentum envelope calculation method cannot solve the coupling phenomenon of two radial deflection angles. Therefore, the traditional angular momentum envelope calculation method cannot be applied to the angular momentum envelope calculation of the magnetic suspension control sensitive gyroscope.

Disclosure of Invention

The purpose of the invention is: the method for calculating the angular momentum envelope of the magnetic suspension control sensitive gyroscope solves the coupling problem of the radial deflection angle of the rotor, analyzes the output capacity of the magnetic suspension control sensitive gyroscope and lays a foundation for the space application of the magnetic suspension control sensitive gyroscope.

The technical solution of the invention is as follows: the method comprises the steps of establishing a magnetic suspension control sensitive gyroscope angular momentum envelope model according to a coordinate transformation principle, solving traversal longitude and latitude based on rotor radial deflection angle mapping, further reconstructing the magnetic suspension control sensitive gyroscope angular momentum envelope model, and traversing the rotation speed and the traversal longitude and latitude of a magnetic suspension rotor through three layers of nested circulation to obtain the magnetic suspension control sensitive gyroscope angular momentum envelope. The steps of the method include the following;

(1) definition of stator and rotor coordinate systems

The magnetic suspension control sensitive gyroscope can realize three-degree-of-freedom momentum exchange with an external carrier by utilizing the universal deflection characteristic of a high-speed rotor. The magnetic suspension rotor changes the angular momentum through the change of the rotating speed and outputs axial flywheel torque; the magnetic suspension rotor changes the direction of angular momentum through radial universal deflection and outputs two-degree-of-freedom radial deflection torque. The three-degree-of-freedom momentum exchange envelope model of the magnetically levitated control sensitive gyroscope is generally described in a stator coordinate system and a rotor coordinate system.

Defining a stator coordinate system o_fx_fy_fz_f: is fixedly connected with the gyro room, and the origin of coordinates is coincided with the mass center of the gyro room o_fx_fPointing in the direction of rotation of the frame o_fz_fFor the direction of rotation of the rotor when the frame is at zero position, o_fy_fAccording with the right-hand screw rule. Defining a rotor coordinate system o_rx_ry_rz_r: is fixedly connected with the magnetic suspension rotor but does not wind around with the rotor_rz_rRotating at high speed. When the rotor is initially static floating and is not deflected, the rotor coordinate system is superposed with the stator coordinate system. Let alpha denote the magnetic levitation rotor winding x_fAngle of rotation of the shaft, beta representing the magnetic levitation rotor around y_fThe angle of rotation of the shaft.

(2) Magnetic suspension control sensitive gyro angular momentum envelope modeling based on rotor deflection angle

Initial angular momentum of the rotor is

H₀＝[0 0 J_zΩ₀]^T (1)

Wherein omega₀The initial rotation speed of the magnetic suspension rotor. When the rotating speed is constant, the angular momentum of the magnetic suspension rotor can be expressed as

Wherein the content of the first and second substances,is a transformation matrix from a stator coordinate system to a rotor coordinate system, which can be expressed as

When the rotating speed of the rotor is not changed, the angular momentum of the magnetic suspension rotor can be expressed as

Finding H_{Fixed rotation speed}The modulus of the direction vector can be obtained

It is stated that a change in the radial deflection angle of the rotor can only change the direction of the angular momentum. Whereas a change in rotational speed can only change the magnitude of the angular momentum. Therefore, when considering the change of the rotation speed of the magnetic suspension rotor, the angular momentum of the magnetic suspension rotor can be expressed as:

it is easy to know that the rotor can only have one deflection angle at the moment of universal deflection, and the radial deflection angles alpha and beta of the rotor in the formula (6) are the deflection angles of the rotor along the x axis and the y axis respectively, and cannot directly represent the space direction of the instantaneous space of the rotor, so that a solution thought of traversing longitude and latitude based on the deflection angle of the rotor is provided.

(3) Traversal longitude and latitude mapping and solving method based on rotor deflection angle

And defining a traversal angle delta as an included angle between the angular momentum direction and the initial angular momentum, wherein the traversal angle theta represents an included angle between the projection of the angular momentum on the plane xoy and the x axis. The expression of the angular momentum pointing deflection angle delta of the rotor is

The formula (7) can be obtained by bringing the formula (1) and the formula (6)

δ＝arccos(cosαcosβ) (8)

The cosine values of the two sides of the equation (8) are obtained

cosδ＝cosαcosβ (9)

On the basis of this, define

(4) Magnetic suspension control sensitive gyroscope angular momentum envelope model reconstruction based on traversal longitude and latitude

The formula (6) is replaced by the formula (9) and the formula (10), and the expression of the angular momentum of the magnetic suspension rotor can be obtained

The above formula is a magnetic suspension control sensitive gyroscope angular momentum envelope decoupling model reconstructed based on the deflection longitude and latitude, and obviously, the variables omega, theta and delta on the right side of the formula (11) are not coupled any more.

(5) Traversal solution for angular momentum envelope of magnetically suspended control sensitive gyroscope

Based on the formula (11), nested loop traversal solving is carried out on the momentum space distribution of the magnetic suspension control sensitive gyroscope by taking the rotating speed omega as an outer variable, the traversal angle delta as a middle variable and the traversal angle theta as an inner variable. The value range of the given traverse angle delta is [0, a ] (a belongs to (0,3 degrees) ], the value range of the traverse angle theta is [ -pi, pi ], and the minimum rotating speed of the rotating speed omega is k (k belongs to [0.5,1)) times of the maximum rotating speed.

After the fixed rotation speed and the angular momentum deflection angle, the traversal angle theta is between [ -pi, pi [ -pi [ ]]The change causing the direction of angular momentum to wind around o_fz_fRotate a circle and are parallel to the plane x_fo_fy_fThe locus is a circle. The traversal angle δ is used as a second layer loop to traverse the magnitude of the angular momentum deflection angle. The radius of the circle formed by the change of the traversal angle theta is larger as the deflection angle of the angular momentum becomes larger, and the distance from the plane x is larger_fo_fy_fMore recently. And traversing the angular momentum direction by the traversing angles delta and theta to form a spherical crown. The change of the outmost layer of the cyclic rotation speed omega only can change the size of the angular momentum, and the change of the rotation speed enables the radius of the ball where the spherical crown is located to change. And after traversing, carrying out normalization processing on the image to obtain the angular momentum envelope of the magnetic suspension control sensitive gyroscope.

The invention solves the coupling problem of the radial deflection angle of the rotor. The invention realizes the calculation of the angular momentum envelope of the magnetic suspension control sensitive gyroscope.

The technical scheme of the invention has the following beneficial technical effects: the method is used for calculating the angular momentum envelope of the magnetic suspension control sensitive gyroscope, the simulation result is shown in figure 5, the simulation result shows that the angular momentum envelope of the magnetic suspension control sensitive gyroscope is obtained by overlapping spherical crowns which are different in size and identical in shape, and the variation range of the axial angular momentum is two orders of magnitude larger than the variation range of two radial degrees of freedom.

Drawings

FIG. 1 is a flow diagram of an embodiment of the present invention;

FIG. 2 is a schematic diagram of the relative motion relationship of three-degree-of-freedom angular momentum exchange coordinates of a magnetic suspension control sensitive gyro rotor;

FIG. 3 is a schematic diagram of traversing longitude and latitude based on magnetic suspension control sensitive gyro rotor deflection angle mapping;

FIG. 4 is a diagram of the envelope simulation of the rotating speed angular momentum of the magnetically suspended control sensitive gyroscope when the change of the rotating speed is not considered;

FIG. 5 is a diagram showing the envelope simulation of the rotating speed and angular momentum of a magnetically suspended control sensitive gyroscope;

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings in conjunction with the following detailed description. It should be understood that the description is intended to be exemplary only, and is not intended to limit the scope of the present invention. Moreover, in the following description, descriptions of well-known structures and techniques are omitted so as to not unnecessarily obscure the concepts of the present invention.

The specific implementation scheme of the invention is shown in figure 1, and the specific implementation steps are as follows:

(1) definition of stator and rotor coordinate systems

The magnetic suspension control sensitive gyroscope can realize three-degree-of-freedom momentum exchange with an external carrier by utilizing the universal deflection characteristic of a high-speed rotor. The magnetic suspension rotor changes the angular momentum through the change of the rotating speed and outputs axial flywheel torque; the magnetic suspension rotor changes the direction of angular momentum through radial universal deflection and outputs two-degree-of-freedom radial deflection torque. The three-degree-of-freedom momentum exchange envelope model of the magnetically levitated control sensitive gyroscope is generally described in a stator coordinate system and a rotor coordinate system.

As shown in fig. 2, a stator coordinate system o is defined_fx_fy_fz_f: is fixedly connected with the gyro room, and the origin of coordinates is coincided with the mass center of the gyro room o_fx_fPointing in the direction of rotation of the frame o_fz_fFor the direction of rotation of the rotor when the frame is at zero position, o_fy_fAccording with the right-hand screw rule. Defining a rotor coordinate system o_rx_ry_rz_r: is fixedly connected with the magnetic suspension rotor but does not wind around with the rotor_rz_rRotating at high speed. When the rotor is initially static floating and is not deflected, the rotor coordinate system is superposed with the stator coordinate system. Let alpha denote the magnetic levitation rotor winding x_fAngle of rotation of the shaft, beta representing the magnetic levitation rotor around y_fThe angle of rotation of the shaft.

(2) Magnetic suspension control sensitive gyro angular momentum envelope modeling based on rotor deflection angle

Initial angular momentum of the rotor is

H₀＝[0 0 J_zΩ₀]^T (1)

Wherein omega₀The initial rotation speed of the magnetic suspension rotor. When the rotating speed is constant, the angular momentum of the magnetic suspension rotor can be expressed as

Wherein the content of the first and second substances,is a transformation matrix from a stator coordinate system to a rotor coordinate system, which can be expressed as

When the rotating speed of the rotor is not changed, the angular momentum of the magnetic suspension rotor can be expressed as

Finding H_{Fixed rotation speed}The modulus of the direction vector can be obtained

It is stated that a change in the radial deflection angle of the rotor can only change the direction of the angular momentum. Whereas a change in rotational speed can only change the magnitude of the angular momentum. Therefore, when considering the change of the rotation speed of the magnetic suspension rotor, the angular momentum of the magnetic suspension rotor can be expressed as:

it is easy to know that the rotor can only have one deflection angle at the moment of universal deflection. And the radial deflection angles alpha and beta of the rotor in the formula (6) are the deflection angles of the rotor along the x axis and the y axis respectively. The rotor radial deflection angles alpha and beta cannot directly represent the instantaneous spatial orientation of the rotor, and therefore a solution thought of traversing longitude and latitude based on the rotor deflection angles is provided.

(3) Traversal longitude and latitude mapping and solving method based on rotor deflection angle

As shown in fig. 3, the traversal angle δ is defined as the angle between the angular momentum direction and the initial angular momentum, and the traversal angle θ represents the angle between the projection of the angular momentum on the plane xoy and the x-axis. The expression of the angular momentum pointing deflection angle delta of the rotor is

The formula (7) can be obtained by bringing the formula (1) and the formula (6)

δ＝arccos(cosαcosβ) (8)

The cosine values of the two sides of the equation (8) are obtained

cosδ＝cosαcosβ (9)

On the basis of this, define

(4) Magnetic suspension control sensitive gyroscope angular momentum envelope model reconstruction based on traversal longitude and latitude

The formula (6) is replaced by the formula (9) and the formula (10), and the expression of the angular momentum of the magnetic suspension rotor can be obtained

The above formula is a magnetic suspension control sensitive gyroscope angular momentum envelope decoupling model reconstructed based on the deflection longitude and latitude, and obviously, the variables omega, theta and delta on the right side of the formula (11) are not coupled any more.

(5) Traversal solution for angular momentum envelope of magnetically suspended control sensitive gyroscope

Based on the formula (11), nested loop traversal solving is carried out on the momentum space distribution of the magnetic suspension control sensitive gyroscope by taking the rotating speed omega as an outer variable, the traversal angle delta as a middle variable and the traversal angle theta as an inner variable. The value range of the given traverse angle delta is [0, 2 degrees ], the value range of the traverse angle theta is [ -pi, pi ], and the minimum rotating speed of the rotating speed omega is 0.7 times of the maximum rotating speed.

After the fixed rotation speed and the angular momentum deflection angle, the traversal angle theta is between [ -pi, pi [ -pi [ ]]The change causing the direction of angular momentum to wind around o_fz_fRotate a circle and are parallel to the plane x_fo_fy_fThe locus is a circle. The traversal angle δ is used as a second layer loop to traverse the magnitude of the angular momentum deflection angle. The radius of the circle formed by the change of the traversal angle theta is larger as the deflection angle of the angular momentum becomes larger, and the distance from the plane x is larger_fo_fy_fMore recently. The traversal of the angular momentum directions is completed by the traversal angles δ and θ, and a spherical cap is formed, as shown in fig. 4. The change of the outmost layer of the cyclic rotation speed omega only can change the size of the angular momentum, and the change of the rotation speed enables the radius of the ball where the spherical crown is located to change. After traversing, the image is normalized to obtain the angular momentum envelope of the magnetically suspended control sensitive gyroscope, as shown in fig. 5.

Those skilled in the art will appreciate that the invention may be practiced without these specific details.