CN114756041A - Maneuvering path design method for magnetic suspension universal maneuvering satellite platform - Google Patents

Maneuvering path design method for magnetic suspension universal maneuvering satellite platform Download PDF

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CN114756041A
CN114756041A CN202210415476.6A CN202210415476A CN114756041A CN 114756041 A CN114756041 A CN 114756041A CN 202210415476 A CN202210415476 A CN 202210415476A CN 114756041 A CN114756041 A CN 114756041A
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任元
李磊
王卫杰
张激扬
廖鹤
孙津济
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Peoples Liberation Army Strategic Support Force Aerospace Engineering University
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Abstract

本发明涉及一种用于磁悬浮万向机动卫星平台的机动路径设计方法，磁悬浮万向机动卫星的平台舱和载荷舱通过洛伦兹力磁轴承连接，受卫星平台机动影响，载荷舱会发生振动。本发明基于洛伦兹力磁轴承刚度阻尼特性，建立在轨平台舱‑载荷舱洛伦兹力磁轴承偏转动力学模型。在此基础上，基于频率特性分析原理设计出一种用于磁悬浮万向机动卫星平台的机动路径设计方法，根据磁轴承刚度阻尼和控制器参数合理确定机动路径，从而尽可能降低平台舱机动引起的载荷舱振动。本发明属于新型卫星平台姿态控制技术领域，可应用于磁悬浮万向机动卫星平台的姿态机动控制系统。

Figure 202210415476

The invention relates to a maneuvering path design method for a maglev universal mobile satellite platform. The platform cabin and the load compartment of the maglev universal mobile satellite are connected by a Lorentz force-magnetic bearing, and the load compartment will vibrate under the influence of the satellite platform's maneuvering. . Based on the stiffness and damping characteristics of the Lorentz force and magnetic bearing, the invention establishes a deflection dynamics model of the Lorentz force and magnetic bearing in the on-orbit platform cabin-load cabin. On this basis, based on the principle of frequency characteristic analysis, a maneuvering path design method for the maglev gimbal maneuvering satellite platform is designed. The maneuvering path is reasonably determined according to the stiffness damping of the magnetic bearing and the controller parameters, so as to reduce the maneuvering caused by the platform cabin as much as possible. load compartment vibration. The invention belongs to the technical field of attitude control of a novel satellite platform, and can be applied to an attitude maneuver control system of a maglev universal maneuvering satellite platform.

Figure 202210415476

Description

一种用于磁悬浮万向机动卫星平台的机动路径设计方法A maneuvering path design method for maglev universal maneuvering satellite platform

技术领域technical field

本发明涉及一种用于磁悬浮万向机动卫星平台的机动路径设计方法，适用于磁悬浮万向机动卫星平台的姿态控制系统。The invention relates to a maneuvering path design method for a maglev universal mobile satellite platform, which is suitable for an attitude control system of the maglev universal mobile satellite platform.

技术背景technical background

磁悬浮万向机动卫星平台是一种新型卫星平台，由于卫星平台舱和载荷舱通过磁悬浮技术实现了隔离，两者之间不会产生接触，卫星平台受到的振动以及自身产生的振动不会传递到载荷上，为载荷提供了一个甚稳超静的工作环境。通过磁悬浮技术实现载荷的机动控制，避免了整星的姿态机动，载荷舱通过洛伦兹力磁轴承直接驱动控制，可以实现高精度高动态指向控制。The magnetic levitation universal mobile satellite platform is a new type of satellite platform. Since the satellite platform compartment and the payload compartment are isolated by magnetic levitation technology, there will be no contact between the two, and the vibration of the satellite platform and the vibration generated by itself will not be transmitted to the satellite platform. On the load, it provides a very stable and ultra-quiet working environment for the load. The maneuvering control of the load is realized through the magnetic levitation technology, which avoids the attitude maneuver of the whole satellite. The load compartment is directly driven and controlled by the Lorentz force magnetic bearing, which can realize high-precision and high-dynamic pointing control.

磁悬浮万向机动卫星平台进行大角度机动时，由于平台舱和载荷舱之间采用磁轴承连接，其刚度有限，会造成载荷舱振动的问题，不利于卫星平台姿态的稳定性和载荷舱的精确指向。When the maglev universal maneuvering satellite platform performs large-angle maneuvers, due to the magnetic bearing connection between the platform cabin and the load cabin, its rigidity is limited, which will cause the problem of vibration of the load cabin, which is not conducive to the stability of the satellite platform attitude and the accuracy of the load cabin. direction.

本发明基于动力学仿真并结合洛伦兹力磁轴承机理特性，建立在轨平台舱-载荷舱洛伦兹力磁轴承偏转动力学模型；在此基础上，基于频率特性分析原理设计出一种用于磁悬浮万向机动卫星平台的机动路径设计方法，根据磁轴承刚度阻尼和控制器参数合理确定机动路径，从而达到尽可能降低平台舱机动引起的载荷舱振动的目的。Based on the dynamic simulation and combined with the mechanism characteristics of the Lorentz force and magnetic bearing, the invention establishes the deflection dynamics model of the on-orbit platform cabin-load cabin Lorentz force and magnetic bearing; The maneuvering path design method used for the maglev gimbal maneuvering satellite platform reasonably determines the maneuvering path according to the stiffness damping of the magnetic bearing and the controller parameters, so as to achieve the purpose of reducing the vibration of the load cabin caused by the maneuvering of the platform cabin as much as possible.

发明内容SUMMARY OF THE INVENTION

本发明解决的技术问题是：为磁悬浮万向机动卫星平台大角度机动造成载荷舱振动的问题，提出了一种用于磁悬浮万向机动卫星平台的机动路径设计方法。该方法通过分析磁轴承刚度阻尼特性和控制器参数，合理确定机动路径，从而达到尽可能降低平台舱机动引起的载荷舱振动的目的。The technical problem solved by the present invention is: to solve the problem of the vibration of the load compartment caused by the large-angle maneuvering of the maglev universal mobile satellite platform, a maneuvering path design method for the maglev universal mobile satellite platform is proposed. The method determines the maneuvering path reasonably by analyzing the stiffness and damping characteristics of the magnetic bearing and the controller parameters, so as to reduce the vibration of the load cabin caused by the maneuvering of the platform cabin as much as possible.

具体包括以下步骤：Specifically include the following steps:

(1)建立在轨平台舱-载荷舱洛伦兹力磁轴承偏转动力学模型(1) Establish a dynamic model of the Lorentz force-magnetic bearing deflection of the on-orbit platform cabin-load cabin

磁悬浮万向机动卫星平台由平台舱和载荷舱组成，载荷舱主要由磁悬浮吊舱和有效载荷(光学跟踪或定向能武器)组成；其中径向磁轴承控制磁悬浮吊舱的径向两自由度悬浮，轴向磁轴承控制磁悬浮吊舱的轴向悬浮，偏转磁轴承控制磁悬浮吊舱的两自由度偏转，由于航天器平台进行姿态机动时，主要涉及两个旋转自由度，故以洛伦兹力磁轴承为研究对象；设航天器本体系为oxyz，惯性系为OXYZ，初始时刻对应坐标轴平行。The maglev universal mobile satellite platform is composed of a platform cabin and a load cabin. The load cabin is mainly composed of a maglev pod and a payload (optical tracking or directed energy weapon); the radial magnetic bearing controls the radial two-degree-of-freedom suspension of the maglev pod. , the axial magnetic bearing controls the axial suspension of the magnetic levitation pod, and the deflection magnetic bearing controls the two-degree-of-freedom deflection of the magnetic-levitation pod. Since the spacecraft platform mainly involves two rotational degrees of freedom during attitude maneuvering, the Lorentz force is used. The magnetic bearing is the research object; the main system of the spacecraft is oxyz, the inertial system is OXYZ, and the corresponding coordinate axes at the initial moment are parallel.

当磁悬浮载荷舱绕x轴和y轴偏转时，机动过程产生的控制力矩可以表示为：When the maglev load cabin is deflected around the x-axis and y-axis, the control torque generated by the maneuvering process can be expressed as:

Figure BDA0003601910380000021
Figure BDA0003601910380000021

其中Tα为x轴控制力矩，Tβ为y轴控制力矩，α为载荷舱绕x轴的偏转角，β为载荷舱绕y轴的偏转角，Jx为载荷舱径向转动惯量；where T α is the x-axis control moment, T β is the y-axis control moment, α is the deflection angle of the load cabin around the x-axis, β is the deflection angle of the load cabin around the y-axis, and J x is the radial moment of inertia of the load cabin;

由于载荷舱的机动通过偏转洛伦兹力磁轴承控制，偏转洛伦兹力磁轴承产生的控制力矩可以表示为：Since the maneuvering of the load compartment is controlled by deflecting the Lorentz force-magnetic bearing, the control torque produced by deflecting the Lorentz force-magnetic bearing can be expressed as:

Figure BDA0003601910380000022
Figure BDA0003601910380000022

其中N表示线圈匝数，B表示磁场强度大小，φ为洛伦兹力磁轴承的每组线圈对应的圆心角，Lr为洛伦兹力磁轴承定子骨架半径，Ix为x轴方向控制电流，Iy为y轴方向控制电流，联立等式(1)和等式(2)可以得到：Among them, N is the number of turns of the coil, B is the strength of the magnetic field, φ is the central angle corresponding to each group of coils of the Lorentz force and magnetic bearing, L r is the radius of the stator skeleton of the Lorentz force and magnetic bearing, and I x is the control of the x-axis direction. current, I y is the control current in the y-axis direction, and equation (1) and equation (2) can be obtained simultaneously:

Figure BDA0003601910380000023
Figure BDA0003601910380000023

通过(3)式可知，洛伦兹力磁轴承控制磁悬浮载荷舱的二个自由度是相互解耦的；According to formula (3), it can be seen that the two degrees of freedom of the Lorentz force magnetic bearing to control the magnetic suspension load compartment are decoupled from each other;

(2)确定载荷舱洛伦兹力磁轴承偏转系统刚度阻尼特性(2) Determine the stiffness and damping characteristics of the load compartment Lorentz force magnetic bearing deflection system

当只有载荷舱偏转时，针对载荷舱绕x轴偏转自由度，载荷舱采用状态反馈控制，反馈控制信号采用：When only the load cabin is deflected, for the deflection degree of freedom of the load cabin around the x-axis, the load cabin adopts state feedback control, and the feedback control signal adopts:

Figure BDA0003601910380000031
Figure BDA0003601910380000031

其中k1和k2为状态反馈参数，则载荷舱绕x轴偏转自由度动力学方程可以表示为：Where k 1 and k 2 are the state feedback parameters, the dynamic equation of the deflection degree of freedom of the load cabin around the x-axis can be expressed as:

Figure BDA0003601910380000032
Figure BDA0003601910380000032

可以得到绕x轴偏转自由度的系统刚度为：The stiffness of the system for the deflection degrees of freedom around the x-axis can be obtained as:

Figure BDA0003601910380000033
Figure BDA0003601910380000033

载荷舱绕x轴偏转自由度的系统阻尼为：The system damping for the deflection degree of freedom of the load cell about the x-axis is:

Figure BDA0003601910380000034
Figure BDA0003601910380000034

可以得到载荷舱绕x轴偏转自由度的系统阻尼比为：The system damping ratio of the deflection degree of freedom of the load cabin around the x-axis can be obtained as:

Figure BDA0003601910380000035
Figure BDA0003601910380000035

载荷舱绕x轴偏转自由度的系统无阻尼固有频率为：The undamped natural frequency of the system with the deflection degree of freedom of the load cell about the x-axis is:

Figure BDA0003601910380000036
Figure BDA0003601910380000036

可以得到载荷舱绕x轴偏转自由度的系统有阻尼固有频率为：The damped natural frequency of the system where the deflection degree of freedom of the load cell about the x-axis can be obtained is:

Figure BDA0003601910380000037
Figure BDA0003601910380000037

由于参数对称特性，载荷舱绕y轴偏转自由度的相关参数与绕x轴偏转自由度相同；Due to the parametric symmetry, the relevant parameters of the deflection degree of freedom about the y-axis of the load compartment are the same as those of the deflection degree of freedom about the x-axis;

(3)确定激振幅值最小的机动路径(3) Determine the maneuvering path with the smallest excitation amplitude value

当平台舱带动载荷舱进行机动时，为保持载荷舱随动的同时可以进行偏转控制，线圈电流应包含两部分，偏转电流Is和机动电流Im，于是惯性系下载荷舱绕X轴偏转自由度系统可以表示为：When the platform cabin drives the load cabin to maneuver, in order to keep the load cabin follow-up and to perform deflection control, the coil current should include two parts, the deflection current Is and the maneuvering current Im , so the load cabin is deflected around the X-axis under the inertial system The system of degrees of freedom can be expressed as:

Figure BDA0003601910380000038
Figure BDA0003601910380000038

其中θ为惯性系下载荷舱绕X轴偏转角，

Figure BDA0003601910380000039
则式(14)可以表示为：where θ is the deflection angle of the load cabin around the X-axis in the inertial frame,
Figure BDA0003601910380000039
Then formula (14) can be expressed as:

Figure BDA0003601910380000041
Figure BDA0003601910380000041

可得：Available:

Figure BDA0003601910380000042
Figure BDA0003601910380000042

设计航天器平台舱的机动角加速度指令为正弦型：The maneuvering angular acceleration command of the spacecraft platform cabin is designed to be sinusoidal:

Figure BDA0003601910380000043
Figure BDA0003601910380000043

其中

Figure BDA0003601910380000044
表示惯性系下平台舱机动角加速度，由频率特性可知，当指令频率等于载荷舱共振频率时，系统发生共振，即：in
Figure BDA0003601910380000044
Represents the maneuvering angular acceleration of the platform cabin under the inertial system. It can be seen from the frequency characteristics that when the command frequency is equal to the resonance frequency of the load cabin, the system will resonate, namely:

Figure BDA0003601910380000045
Figure BDA0003601910380000045

设机动总姿态角为Ω，由(17)有：Let the total maneuvering attitude angle be Ω, from (17):

Figure BDA0003601910380000046
Figure BDA0003601910380000046

则系统幅频特性为：Then the amplitude-frequency characteristics of the system are:

Figure BDA0003601910380000047
Figure BDA0003601910380000047

令航天器平台的最大机动角速度为

Figure BDA0003601910380000048
为避免共振，机动角加速度应尽量远离共振频率，由式(20)可知，卫星以最大机动角速度恰好引起共振时，有：Let the maximum maneuvering angular velocity of the spacecraft platform be
Figure BDA0003601910380000048
In order to avoid resonance, the maneuvering angular acceleration should be as far away from the resonance frequency as possible. From equation (20), it can be known that when the satellite just causes resonance at the maximum maneuvering angular velocity, there are:

Figure BDA0003601910380000049
Figure BDA0003601910380000049

经仿真验证，为了尽可能避免共振，机动策略可由下式给出：It has been verified by simulation that in order to avoid resonance as much as possible, the maneuvering strategy can be given by the following formula:

Figure BDA00036019103800000410
Figure BDA00036019103800000410

其中

Figure BDA00036019103800000411
in
Figure BDA00036019103800000411

2.为保证机动速度，系统应为欠阻尼或临界阻尼，即：2. To ensure maneuvering speed, the system should be under-damped or critically damped, namely:

Figure BDA00036019103800000412
Figure BDA00036019103800000412

可得：Available:

Figure BDA0003601910380000051
Figure BDA0003601910380000051

为兼顾机动速度和精度，λ应尽可能远离1，

Figure BDA0003601910380000052
应尽可能接近1，经仿真可知，λ、
Figure BDA0003601910380000053
满足如下条件时，机动速度和精度能够同时得到满足：In order to take into account the maneuvering speed and accuracy, λ should be as far as possible from 1,
Figure BDA0003601910380000052
It should be as close to 1 as possible. It can be seen from simulation that λ,
Figure BDA0003601910380000053
When the following conditions are met, the maneuvering speed and accuracy can be satisfied at the same time:

Figure BDA0003601910380000054
Figure BDA0003601910380000054

则k1和k2可通过如下方法确定：Then k 1 and k 2 can be determined by the following methods:

Figure BDA0003601910380000055
Figure BDA0003601910380000055

载荷绕Y轴偏转自由度的相关参数与绕X轴偏转自由度相同。The relevant parameters of the load deflection degree of freedom about the Y-axis are the same as the deflection degree of freedom about the X-axis.

本发明的方案与现有方案相比，主要优点在于：现有的磁悬浮万向卫星平台在机动时未考虑磁轴承的刚度和阻尼特性，在机动过程中容易引起载荷舱的振动，不利于有效载荷的应用。本发明通过设计一种用于磁悬浮万向机动卫星平台的机动路径，在控制器参数确定的情况下，可以根据航天器平台舱的最大机动能力合理确定机动角速度路径，保证了载荷舱机动的快速性和稳定性。Compared with the existing solution, the main advantage of the solution of the present invention is that the existing magnetic levitation universal satellite platform does not consider the stiffness and damping characteristics of the magnetic bearing during maneuvering, which is easy to cause vibration of the load compartment during the maneuvering process, which is not conducive to effective load application. By designing a maneuvering path for the magnetic levitation universal maneuvering satellite platform, the invention can reasonably determine the maneuvering angular velocity path according to the maximum maneuvering capability of the spacecraft platform cabin under the condition that the controller parameters are determined, so as to ensure the fast maneuvering of the load cabin. stability and stability.

附图说明Description of drawings

图1为本发明的流程图；Fig. 1 is the flow chart of the present invention;

图2为磁悬浮万向卫星平台结构及坐标系图；Figure 2 is a diagram of the structure and coordinate system of the maglev universal satellite platform;

图3为传统机动方法本体系下载荷舱x轴角位移仿真图；Figure 3 is a simulation diagram of the x-axis angular displacement of the load cabin under the system of the traditional maneuvering method;

图4为本发明实施例本体系下载荷舱x轴角位移仿真图；4 is a simulation diagram of the x-axis angular displacement of the load cabin under the system according to the embodiment of the present invention;

具体实施方案specific implementation

本发明的实施对象为磁悬浮万向机动卫星平台，具体实施方案如图1所示，具体实施步骤如下：The implementation object of the present invention is a magnetic levitation universal mobile satellite platform, and the specific implementation is shown in Figure 1, and the specific implementation steps are as follows:

当磁悬浮载荷舱绕x轴和y轴偏转时，机动过程产生的控制力矩可以表示为：When the maglev load cabin is deflected around the x-axis and y-axis, the control torque generated by the maneuvering process can be expressed as:

Figure BDA0003601910380000061
Figure BDA0003601910380000061

其中Tα为x轴控制力矩，Tβ为y轴控制力矩，α为载荷舱绕x轴的偏转角，β为载荷舱绕y轴的偏转角，Jx为载荷舱径向转动惯量；where T α is the x-axis control moment, T β is the y-axis control moment, α is the deflection angle of the load cabin around the x-axis, β is the deflection angle of the load cabin around the y-axis, and J x is the radial moment of inertia of the load cabin;

由于载荷舱的机动通过偏转洛伦兹力磁轴承控制，偏转洛伦兹力磁轴承产生的控制力矩可以表示为：Since the maneuvering of the load compartment is controlled by deflecting the Lorentz force-magnetic bearing, the control torque produced by deflecting the Lorentz force-magnetic bearing can be expressed as:

Figure BDA0003601910380000062
Figure BDA0003601910380000062

其中N表示线圈匝数，B表示磁场强度大小，φ为洛伦兹力磁轴承的每组线圈对应的圆心角，Lr为洛伦兹力磁轴承定子骨架半径，Ix为x轴方向控制电流，Iy为y轴方向控制电流，联立等式(1)和等式(2)可以得到：Among them, N represents the number of turns of the coil, B represents the strength of the magnetic field, φ is the central angle corresponding to each coil of the Lorentz force and magnetic bearing, L r is the radius of the stator skeleton of the Lorentz force and magnetic bearing, and I x is the control of the x-axis direction. current, I y is the control current in the y-axis direction. Simultaneous equation (1) and equation (2) can be obtained:

Figure BDA0003601910380000063
Figure BDA0003601910380000063

通过(3)式可知，洛伦兹力磁轴承控制磁悬浮载荷舱的二个自由度是相互解耦的；According to formula (3), it can be seen that the two degrees of freedom of the Lorentz force magnetic bearing to control the magnetic suspension load compartment are decoupled from each other;

(2)确定载荷舱洛伦兹力磁轴承偏转系统刚度阻尼特性(2) Determine the stiffness and damping characteristics of the load compartment Lorentz force magnetic bearing deflection system

当只有载荷舱偏转时，针对载荷舱绕x轴偏转自由度，载荷舱采用状态反馈控制，反馈控制信号采用：When only the load cabin is deflected, for the deflection degree of freedom of the load cabin around the x-axis, the load cabin adopts state feedback control, and the feedback control signal adopts:

Figure BDA0003601910380000064
Figure BDA0003601910380000064

其中k1和k2为状态反馈参数，则载荷舱绕x轴偏转自由度动力学方程可以表示为：Where k 1 and k 2 are the state feedback parameters, the dynamic equation of the deflection degree of freedom of the load cabin around the x-axis can be expressed as:

Figure BDA0003601910380000065
Figure BDA0003601910380000065

可以得到绕x轴偏转自由度的系统刚度为：The stiffness of the system for the deflection degrees of freedom around the x-axis can be obtained as:

Figure BDA0003601910380000066
Figure BDA0003601910380000066

载荷舱绕x轴偏转自由度的系统阻尼为：The system damping for the deflection degree of freedom of the load cell about the x-axis is:

Figure BDA0003601910380000067
Figure BDA0003601910380000067

可以得到载荷舱绕x轴偏转自由度的系统阻尼比为：The system damping ratio of the deflection degree of freedom of the load cabin around the x-axis can be obtained as:

Figure BDA0003601910380000071
Figure BDA0003601910380000071

载荷舱绕x轴偏转自由度的系统无阻尼固有频率为：The undamped natural frequency of the system with the deflection degree of freedom of the load cell about the x-axis is:

Figure BDA0003601910380000072
Figure BDA0003601910380000072

可以得到载荷舱绕x轴偏转自由度的系统有阻尼固有频率为：The damped natural frequency of the system where the deflection degree of freedom of the load cell about the x-axis can be obtained is:

Figure BDA0003601910380000073
Figure BDA0003601910380000073

由于参数对称特性，载荷舱绕y轴偏转自由度的相关参数与绕x轴偏转自由度相同；Due to the parametric symmetry, the relevant parameters of the deflection degree of freedom about the y-axis of the load compartment are the same as those of the deflection degree of freedom about the x-axis;

(3)确定激振幅值最小的机动路径(3) Determine the maneuvering path with the smallest excitation amplitude value

当平台舱带动载荷舱进行机动时，为保持载荷舱随动的同时可以进行偏转控制，线圈电流应包含两部分，偏转电流Is和机动电流Im，于是惯性系下载荷舱绕X轴偏转自由度系统可以表示为：When the platform cabin drives the load cabin to maneuver, in order to keep the load cabin follow-up and to perform deflection control, the coil current should include two parts, the deflection current Is and the maneuvering current Im , so the load cabin is deflected around the X-axis under the inertial system The system of degrees of freedom can be expressed as:

Figure BDA0003601910380000074
Figure BDA0003601910380000074

其中θ为惯性系下载荷舱绕X轴偏转角，

Figure BDA0003601910380000075
则式(14)可以表示为：where θ is the deflection angle of the load cabin around the X-axis in the inertial frame,
Figure BDA0003601910380000075
Then formula (14) can be expressed as:

Figure BDA0003601910380000076
Figure BDA0003601910380000076

可得：Available:

Figure BDA0003601910380000077
Figure BDA0003601910380000077

设计航天器平台舱的机动角加速度指令为正弦型：The maneuvering angular acceleration command of the spacecraft platform cabin is designed to be sinusoidal:

Figure BDA0003601910380000078
Figure BDA0003601910380000078

其中

Figure BDA0003601910380000079
表示惯性系下平台舱机动角加速度，由频率特性可知，当指令频率等于载荷舱共振频率时，系统发生共振，即：in
Figure BDA0003601910380000079
Represents the maneuvering angular acceleration of the platform cabin under the inertial system. It can be seen from the frequency characteristics that when the command frequency is equal to the resonance frequency of the load cabin, the system will resonate, namely:

Figure BDA00036019103800000710
Figure BDA00036019103800000710

设机动总姿态角为Ω，由(17)有：Let the total maneuvering attitude angle be Ω, from (17):

Figure BDA00036019103800000711
Figure BDA00036019103800000711

则系统幅频特性为：Then the amplitude-frequency characteristics of the system are:

Figure BDA0003601910380000081
Figure BDA0003601910380000081

令航天器平台的最大机动角速度为

Figure BDA0003601910380000082
为避免共振，机动角加速度应尽量远离共振频率，由式(20)可知，卫星以最大机动角速度恰好引起共振时，有：Let the maximum maneuvering angular velocity of the spacecraft platform be
Figure BDA0003601910380000082
In order to avoid resonance, the maneuvering angular acceleration should be as far away from the resonance frequency as possible. From equation (20), it can be known that when the satellite just causes resonance at the maximum maneuvering angular velocity, there are:

Figure BDA0003601910380000083
Figure BDA0003601910380000083

经仿真验证，为了尽可能避免共振，机动策略可由下式给出：It has been verified by simulation that in order to avoid resonance as much as possible, the maneuvering strategy can be given by the following formula:

Figure BDA0003601910380000084
Figure BDA0003601910380000084

其中

Figure BDA0003601910380000085
in
Figure BDA0003601910380000085

2.为保证机动速度，系统应为欠阻尼或临界阻尼，即：2. To ensure maneuvering speed, the system should be under-damped or critically damped, namely:

Figure BDA0003601910380000086
Figure BDA0003601910380000086

可得：Available:

Figure BDA0003601910380000087
Figure BDA0003601910380000087

为兼顾机动速度和精度，λ应尽可能远离1，

Figure BDA0003601910380000088
应尽可能接近1，经仿真可知，λ、
Figure BDA0003601910380000089
满足如下条件时，机动速度和精度能够同时得到满足：In order to take into account the maneuvering speed and accuracy, λ should be as far as possible from 1,
Figure BDA0003601910380000088
It should be as close to 1 as possible. It can be seen from simulation that λ,
Figure BDA0003601910380000089
When the following conditions are met, the maneuvering speed and accuracy can be satisfied at the same time:

Figure BDA00036019103800000810
Figure BDA00036019103800000810

则k1和k2可通过如下方法确定：Then k 1 and k 2 can be determined by the following methods:

Figure BDA00036019103800000811
Figure BDA00036019103800000811

载荷绕Y轴偏转自由度的相关参数与绕X轴偏转自由度相同。The relevant parameters of the load deflection degree of freedom about the Y-axis are the same as the deflection degree of freedom about the X-axis.

在本体系下，未使用本发明所述机动路径设计方法的载荷舱x轴角位移仿真图如图3所示，采用本发明所述机动方法的载荷舱x轴角位移仿真图如图4所示，可以看出本发明所述的机动路径设计方法有着更好的姿态稳定度和机动速度。Under this system, the simulation diagram of the x-axis angular displacement of the load cabin without using the maneuvering path design method of the present invention is shown in Figure 3, and the simulation diagram of the x-axis angular displacement of the load cabin using the maneuvering method of the present invention is shown in Figure 4 It can be seen that the maneuvering path design method of the present invention has better attitude stability and maneuvering speed.

本发明书中未作详细描述的内容属于本领域专业技术人员公知的现有技术。Contents not described in detail in the present invention belong to the prior art known to those skilled in the art.

Claims (2)

1.一种用于磁悬浮万向机动卫星平台的机动路径设计方法，其特征在于：基于动力学仿真并结合洛伦兹力磁轴承机理特性，建立在轨平台舱-载荷舱洛伦兹力磁轴承偏转动力学模型；在此基础上，基于频率特性分析原理设计出一种用于磁悬浮万向机动卫星平台的机动路径设计方法，根据磁轴承刚度阻尼和控制器参数合理确定机动路径，从而尽可能降低平台舱机动引起的载荷舱振动，具体包括以下步骤：1. a maneuvering path design method for a magnetic levitation universal motorized satellite platform, it is characterized in that: based on dynamic simulation and in conjunction with the Lorentz force and magnetic bearing mechanism characteristics, establish on-orbit platform cabin-load cabin Lorentz force and magnetic Bearing deflection dynamics model; on this basis, based on the principle of frequency characteristic analysis, a maneuvering path design method for maglev gimbal maneuvering satellite platform is designed. It is possible to reduce the vibration of the load compartment caused by the maneuvering of the platform compartment, which includes the following steps: (1)建立在轨平台舱-载荷舱洛伦兹力磁轴承偏转动力学模型(1) Establish a dynamic model of the Lorentz force-magnetic bearing deflection of the on-orbit platform cabin-load cabin 当磁悬浮载荷舱绕x轴和y轴偏转时，机动过程产生的控制力矩可以表示为：When the maglev load cabin is deflected around the x-axis and y-axis, the control torque generated by the maneuvering process can be expressed as:
Figure FDA0003601910370000011
Figure FDA0003601910370000011
 其中Tα为x轴控制力矩，Tβ为y轴控制力矩，α为载荷舱绕x轴的偏转角，β为载荷舱绕y轴的偏转角，Jx为载荷舱径向转动惯量；where T α is the x-axis control moment, T β is the y-axis control moment, α is the deflection angle of the load cabin around the x-axis, β is the deflection angle of the load cabin around the y-axis, and J x is the radial moment of inertia of the load cabin; 由于载荷舱的机动通过偏转洛伦兹力磁轴承控制，偏转洛伦兹力磁轴承产生的控制力矩可以表示为：Since the maneuvering of the load compartment is controlled by deflecting the Lorentz force-magnetic bearing, the control torque produced by deflecting the Lorentz force-magnetic bearing can be expressed as:
Figure FDA0003601910370000012
Figure FDA0003601910370000012
 其中N表示线圈匝数，B表示磁场强度大小，φ为洛伦兹力磁轴承的每组线圈对应的圆心角，Lr为洛伦兹力磁轴承定子骨架半径，Ix为x轴方向控制电流，Iy为y轴方向控制电流，联立等式(1)和等式(2)可以得到：Among them, N represents the number of turns of the coil, B represents the strength of the magnetic field, φ is the central angle corresponding to each coil of the Lorentz force and magnetic bearing, L r is the radius of the stator skeleton of the Lorentz force and magnetic bearing, and I x is the control of the x-axis direction. current, I y is the control current in the y-axis direction. Simultaneous equation (1) and equation (2) can be obtained:
Figure FDA0003601910370000013
Figure FDA0003601910370000013
 通过(3)式可知，洛伦兹力磁轴承控制磁悬浮载荷舱的二个自由度是相互解耦的；According to formula (3), it can be seen that the two degrees of freedom of the Lorentz force magnetic bearing to control the magnetic suspension load compartment are decoupled from each other; (2)确定载荷舱洛伦兹力磁轴承偏转系统刚度阻尼特性(2) Determine the stiffness and damping characteristics of the load compartment Lorentz force magnetic bearing deflection system 当只有载荷舱偏转时，针对载荷舱绕x轴偏转自由度，载荷舱采用状态反馈控制，反馈控制信号采用：When only the load cabin is deflected, for the deflection degree of freedom of the load cabin around the x-axis, the load cabin adopts state feedback control, and the feedback control signal adopts:
Figure FDA0003601910370000021
Figure FDA0003601910370000021
 其中k1和k2为状态反馈参数，则载荷舱绕x轴偏转自由度动力学方程可以表示为：Where k 1 and k 2 are the state feedback parameters, the dynamic equation of the deflection degree of freedom of the load cabin around the x-axis can be expressed as:
Figure FDA0003601910370000022
Figure FDA0003601910370000022
 可以得到绕x轴偏转自由度的系统刚度为：The stiffness of the system for the deflection degrees of freedom around the x-axis can be obtained as:
Figure FDA0003601910370000023
Figure FDA0003601910370000023
 载荷舱绕x轴偏转自由度的系统阻尼为：The system damping for the deflection degree of freedom of the load cell about the x-axis is:
Figure FDA0003601910370000024
Figure FDA0003601910370000024
 可以得到载荷舱绕x轴偏转自由度的系统阻尼比为：The system damping ratio of the deflection degree of freedom of the load cabin around the x-axis can be obtained as:
Figure FDA0003601910370000025
Figure FDA0003601910370000025
 载荷舱绕x轴偏转自由度的系统无阻尼固有频率为：The undamped natural frequency of the system with the deflection degree of freedom of the load cell about the x-axis is:
Figure FDA0003601910370000026
Figure FDA0003601910370000026
 可以得到载荷舱绕x轴偏转自由度的系统有阻尼固有频率为：The damped natural frequency of the system where the deflection degree of freedom of the load cell about the x-axis can be obtained is:
Figure FDA0003601910370000027
Figure FDA0003601910370000027
 由于参数对称特性，载荷舱绕y轴偏转自由度的相关参数与绕x轴偏转自由度相同；Due to the parametric symmetry, the relevant parameters of the deflection degree of freedom about the y-axis of the load compartment are the same as those of the deflection degree of freedom about the x-axis; (3)确定激振幅值最小的机动路径(3) Determine the maneuvering path with the smallest excitation amplitude value 当平台舱带动载荷舱进行机动时，为保持载荷舱随动的同时可以进行偏转控制，线圈电流应包含两部分，偏转电流Is和机动电流Im，于是惯性系下载荷舱绕X轴偏转自由度系统可以表示为：When the platform cabin drives the load cabin to maneuver, in order to keep the load cabin follow-up and to perform deflection control, the coil current should include two parts, the deflection current Is and the maneuvering current Im , so the load cabin is deflected around the X-axis under the inertial system The system of degrees of freedom can be expressed as:
Figure FDA0003601910370000028
Figure FDA0003601910370000028
 其中θ为惯性系下载荷舱绕X轴偏转角，
Figure FDA0003601910370000029
则式(11)可以表示为：where θ is the deflection angle of the load cabin around the X-axis in the inertial frame,
Figure FDA0003601910370000029
Then formula (11) can be expressed as:
Figure FDA0003601910370000031
Figure FDA0003601910370000031
 可得：Available:
Figure FDA0003601910370000032
Figure FDA0003601910370000032
 设计航天器平台舱的机动角加速度路径为正弦型：The maneuvering angular acceleration path of the spacecraft platform cabin is designed to be sinusoidal:
Figure FDA0003601910370000033
Figure FDA0003601910370000033
 其中
Figure FDA0003601910370000034
表示平台舱惯性系下机动角加速度，由频率特性可知，当指令频率等于载荷舱共振频率时，系统发生共振，即：in
Figure FDA0003601910370000034
Represents the maneuvering angular acceleration under the inertial system of the platform cabin. It can be seen from the frequency characteristics that when the command frequency is equal to the resonance frequency of the load cabin, the system will resonate, namely:
Figure FDA0003601910370000035
Figure FDA0003601910370000035
 设机动总姿态角为Ω，由(14)有：Let the total maneuvering attitude angle be Ω, from (14):
Figure FDA0003601910370000036
Figure FDA0003601910370000036
 则系统幅频特性为：Then the amplitude-frequency characteristics of the system are:
Figure FDA0003601910370000037
Figure FDA0003601910370000037
 令航天器平台的最大机动角速度为
Figure FDA0003601910370000038
为避免共振，机动角加速度应尽量远离共振频率，则机动策略可由下式给出：Let the maximum maneuvering angular velocity of the spacecraft platform be
Figure FDA0003601910370000038
In order to avoid resonance, the maneuvering angular acceleration should be as far away from the resonance frequency as possible, and the maneuvering strategy can be given by the following formula:
Figure FDA0003601910370000039
Figure FDA0003601910370000039
 其中
Figure FDA00036019103700000310
载荷绕Y轴偏转自由度的相关参数与绕X轴偏转自由度相同。in
Figure FDA00036019103700000310
The relevant parameters of the load deflection degree of freedom about the Y-axis are the same as the deflection degree of freedom about the X-axis. 2.对于权利要求1中的反馈参数k1和k2，可通过如下方法确定：2. The feedback parameters k 1 and k 2 in claim 1 can be determined by the following methods: 为保证机动速度，系+统应为欠阻尼或临界阻尼，即：In order to ensure the maneuvering speed, the system + system should be under-damped or critically damped, namely:
Figure FDA00036019103700000311
Figure FDA00036019103700000311
 可得：Available:
Figure FDA00036019103700000312
Figure FDA00036019103700000312
 为兼顾机动速度和精度，λ应尽可能远离1，
Figure FDA0003601910370000043
应尽可能接近1，则k1和k2可通过如下方法确定：In order to take into account the maneuvering speed and accuracy, λ should be as far as possible from 1,
Figure FDA0003601910370000043
should be as close to 1 as possible, then k 1 and k 2 can be determined as follows:
Figure FDA0003601910370000041
Figure FDA0003601910370000041
 即：which is:
Figure FDA0003601910370000042
Figure FDA0003601910370000042
 载荷绕Y轴偏转自由度的相关参数与绕X轴偏转自由度相同。The relevant parameters of the load deflection degree of freedom about the Y-axis are the same as the deflection degree of freedom about the X-axis.
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