CN109823572B - Actuator configuration and control method for rapid reciprocating swing of agile satellite attitude - Google Patents
Actuator configuration and control method for rapid reciprocating swing of agile satellite attitude Download PDFInfo
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Abstract
Description
技术领域technical field
本发明涉及航天控制技术领域,尤其涉及敏捷卫星姿态往复快速摆动的执行机构配置及控制方法。The invention relates to the technical field of aerospace control, in particular to the configuration and control method of an actuator for reciprocating and fast swinging of an agile satellite attitude.
背景技术Background technique
遥感卫星目前在民事和军事应用领域均具有不可替代的重要作用,为提高遥感卫星快速响应能力和成像能力,缩短对地目标重访周期,兼顾高分辨率与宽幅成像,具备高速姿态大角度机动能力的敏捷遥感卫星受到了越来越多的关注。由于敏捷卫星需在指定时间内完成姿态快速大角度机动,系统呈现出强非线性,并同时需保证高精度的姿态稳定,这对卫星姿态控制系统的设计提出了极大的挑战。Remote sensing satellites currently play an irreplaceable and important role in both civil and military applications. In order to improve the rapid response and imaging capabilities of remote sensing satellites, shorten the revisit cycle of ground targets, take into account high-resolution and wide-format imaging, and have high-speed attitude and large angles. Maneuverable agile remote sensing satellites have received increasing attention. Since the agile satellite needs to complete the attitude fast and large-angle maneuver within the specified time, the system exhibits strong nonlinearity, and at the same time, it needs to ensure high-precision attitude stability, which poses a great challenge to the design of the satellite attitude control system.
典型卫星姿态控制执行机构主要分为有源控制执行机构,包括喷管和磁力矩器,及角动量交换执行机构,包括反作用飞轮和控制力矩陀螺。由于输出控制力矩比相同功耗下的高,控制精度比喷管高,且不会对光学器件造成污染,因此是敏捷卫星较为理想的执行机构。当前为满足大角度快速机动的需求,国内外敏捷卫星主要采用作为其执行机构,卫星的姿态机动能力最大达到了4.5°/s。康奈尔大学Violet卫星以8个控制力矩陀螺作为执行机构,实验证实该卫星机动角速度可达10°/s。依靠大角度快速机动能力,敏捷卫星可以实现推扫拼幅成像、立体拼幅成像、多点目标快速成像、动态扫描成像等多类工作模式,大大提升了卫星的观测能力。Typical satellite attitude control actuators are mainly divided into active control actuators, including nozzles and magnetic torquers, and angular momentum exchange actuators, including reaction flywheels and control torque gyroscopes. Because the output control torque is higher than that under the same power consumption, the control accuracy is higher than that of the nozzle, and it will not cause pollution to the optical devices, so it is an ideal actuator for agile satellites. At present, in order to meet the needs of large-angle and fast maneuvering, domestic and foreign agile satellites are mainly used as their actuators, and the satellite's attitude maneuverability can reach a maximum of 4.5°/s. The Violet satellite of Cornell University uses eight control moment gyroscopes as the actuators, and experiments have confirmed that the satellite's maneuvering angular velocity can reach 10°/s. Relying on the ability of large-angle and fast maneuvering, Agile Satellite can realize various working modes such as push-broom mosaic imaging, three-dimensional mosaic imaging, multi-point target fast imaging, dynamic scanning imaging, etc., which greatly improves the observation capability of the satellite.
然而,随着当前战场侦察、灾区监测等任务对超大幅宽及高时效性成像数据的要求越来越高,现有的几类成像工作模式无法完成日益增长的任务需求。为在有限时间内实现对地目标的超大幅宽无缝连续成像,可控制敏捷卫星的姿态沿穿轨方向进行大角度往复快速摆动。如图1所示,通过敏捷卫星的姿态往复快速摆动,可完成多个成像条带(成像条带1、成像条带2、成像条带3…),利用多条带无缝拼接即可完成一次超大幅宽过顶拍摄。当敏捷卫星处于此类工作模式时,为保证其穿轨方向较大的扫描成像幅宽,同时保证其完成一个侧摆周期时间小于其星下点沿轨方向运动一个幅宽的时间,要求敏捷卫星在偏离星下点±45°范围进行侧摆机动,且机动角速度长时间保持在20°/s。以上对敏捷卫星的机动能力要求,已大幅超过现有敏捷卫星姿态控制系统的能力。如何在载荷有限及执行机构输出控制力矩有限的情况下,实现长时间大角度快速机动,这对敏捷卫星姿态控制系统的设计提出了新的挑战。However, as the current tasks such as battlefield reconnaissance and disaster area monitoring have higher and higher requirements for ultra-wide and time-sensitive imaging data, the existing several types of imaging work modes cannot meet the increasing task requirements. In order to realize the seamless continuous imaging of the ground target with super wide width in a limited time, the attitude of the agile satellite can be controlled to reciprocate rapidly at a large angle along the orbital direction. As shown in Figure 1, multiple imaging strips (imaging strip 1,
发明内容SUMMARY OF THE INVENTION
本发明所要解决的技术问题是:提供一种配置简单、机动能力强、快速性好且能有效实现卫星姿态大角度往复快速摆动的执行机构配置及控制方法。The technical problem to be solved by the present invention is to provide an actuator configuration and control method which is simple in configuration, strong in maneuverability, good in rapidity and can effectively realize the reciprocating and fast swinging of the satellite attitude at a large angle.
为了解决上述技术问题,本发明是通过以下技术方案实现的:In order to solve the above-mentioned technical problems, the present invention is achieved through the following technical solutions:
一种敏捷卫星姿态往复快速摆动的执行机构配置方法,所述执行机构设置为搭载安装在敏捷卫星平台上的复合姿态控制执行机构,包括控制力矩陀螺以及反作用飞轮,所述控制力矩陀螺以及反作用飞轮的数量均设置为两个,其配置方法为:A method for configuring an actuator for agile satellite attitude reciprocating rapid swing, the actuator is configured to carry a composite attitude control actuator installed on an agile satellite platform, including a control torque gyro and a reaction flywheel, the control torque gyro and the reaction flywheel The number of are set to two, and the configuration method is:
以敏捷卫星平台为中心构建直角三维坐标系Oxyz,其中,两个所述反作用飞轮分别安装在y,z轴上且其转子转动正方向分别朝向y,z轴负方向,两个所述控制力矩陀螺的框架轴安装方向与y轴平行,且构成双控制力矩陀螺结构,其输出的控制力矩作用在x轴方向,其中x轴为敏捷卫星的滚转轴,敏捷卫星在x轴方向具备快速机动能力,通过控制力矩陀螺控制敏捷卫星绕滚转轴往复快速机动,反作用飞轮控制敏捷卫星在y,z两轴方向上的姿态稳定。A rectangular three-dimensional coordinate system Oxyz is constructed with the agile satellite platform as the center, wherein the two reaction flywheels are respectively installed on the y and z axes, and the positive directions of their rotor rotations are respectively directed towards the negative directions of the y and z axes, and the two control torques The installation direction of the frame axis of the gyro is parallel to the y-axis, and constitutes a dual-control torque gyro structure. The output control torque acts in the x-axis direction, where the x-axis is the roll axis of the agile satellite, and the agile satellite has the ability to quickly maneuver in the x-axis direction. , by controlling the moment gyro to control the agile satellite to reciprocate quickly around the roll axis, and the reaction flywheel to control the attitude stability of the agile satellite in the y and z directions.
作为优选,两个所述的控制力矩陀螺结构参数相同。Preferably, the structural parameters of the two control torque gyroscopes are the same.
作为优选,两个所述的控制力矩陀螺结构的框架轴互相平行,转速相等但相反,一个框架轴沿y轴正方向转动,另一个沿y轴负方向转动。Preferably, the frame axes of the two control torque gyro structures are parallel to each other, and the rotational speeds are equal but opposite.
作为优选,两个所述的控制力矩陀螺结构的框架角及框架角速度等值反向。Preferably, the frame angles and frame angular velocities of the two control torque gyro structures are equivalently reversed.
所述的敏捷卫星姿态往复快速摆动的控制方法,包括The control method for the reciprocating rapid swing of the agile satellite attitude, comprising:
构建基于所述复合姿态控制执行机构的卫星姿态动力学模型,具体步骤是利用矢量力学的建模方法,首先建立包括控制力矩陀螺以及反作用飞轮在内的整星关于其系统质心的角动量方程,然后利用角动量定理得到系统角动量变化与力矩之间的关系,最后再将上述方程向卫星本体系进行投影,继而建立卫星姿态动力学模型;Constructing a satellite attitude dynamics model based on the compound attitude control actuator, the specific steps are to use the modeling method of vector mechanics to first establish the angular momentum equation of the whole satellite including the control moment gyroscope and the reaction flywheel about its system center of mass, Then, the relationship between the system angular momentum change and the moment is obtained by using the angular momentum theorem, and finally the above equation is projected to the satellite system, and then the satellite attitude dynamics model is established;
构建基于所述复合姿态控制执行机构的卫星姿态运动学模型,具体步骤是利用四元数姿态参数表示方法,首先建立卫星在本体系下的姿态运动学方程,然后根据期望姿态四元数及当前姿态四元数的关系,建立卫星姿态运动学误差方程;Constructing the satellite attitude kinematics model based on the compound attitude control actuator, the specific steps are to use the quaternion attitude parameter representation method, first establish the attitude kinematic equation of the satellite under this system, and then according to the expected attitude quaternion and current The relationship between attitude quaternions, establish satellite attitude kinematic error equation;
利用所构建的敏捷卫星姿态动力学及运动学模型,设计基于复合姿态控制执行机构且能控制敏捷卫星按照期望姿态进行机动的姿态控制器。具体步骤是首先针对姿态误差系统构造系统的Lyapunov函数并对其求导,然后利用Lyapunov定理和LaSalle不变集原理,设计姿态控制器,通过姿态控制器输出指令信号,将指令信号输入所述复合姿态控制执行机构,继而使得复合姿态控制执行机构控制卫星按照期望姿态进行机动。Using the constructed agile satellite attitude dynamics and kinematics model, an attitude controller based on a compound attitude control actuator that can control the agile satellite to maneuver according to the desired attitude is designed. The specific steps are to first construct the Lyapunov function of the system for the attitude error system and derive it, and then use the Lyapunov theorem and the LaSalle invariant set principle to design the attitude controller, output the command signal through the attitude controller, and input the command signal into the composite The attitude control actuator, and then the composite attitude control actuator controls the satellite to maneuver according to the desired attitude.
与现有技术相比,本发明的有益之处是:所述敏捷卫星姿态往复快速摆动的执行机构配置及控制方法,其执行机构的配置简单,控制方法简洁明了,具有以下优点:Compared with the prior art, the advantages of the present invention are: the configuration and control method of the actuator for the agile satellite attitude reciprocating fast swing, the configuration of the actuator is simple, the control method is concise and clear, and has the following advantages:
一、敏捷卫星的姿态机动性强、快速性好,通过控制敏捷卫星的姿态在规定时间内,沿穿轨方向进行大角度往复快速摆动,在短时间内大幅提高了目标信息获取量,可满足当前战场态势侦察、灾区目标监测等超大幅宽及高时效性成像任务需求;1. The attitude of the agile satellite is highly maneuverable and fast. By controlling the attitude of the agile satellite, it swings back and forth at a large angle along the orbiting direction within a specified time, which greatly improves the acquisition of target information in a short period of time. Current requirements for ultra-wide and time-sensitive imaging tasks such as battlefield situational reconnaissance and target monitoring in disaster-stricken areas;
二、其复合姿态控制执行机构的配置简单,可实现重量轻、体积小的敏捷性微小型搜索卫星,提高了使用的灵活性。2. The configuration of its composite attitude control actuator is simple, which can realize the agility of light weight and small volume, and improve the flexibility of use.
附图说明Description of drawings
下面结合附图对本发明进一步说明:Below in conjunction with accompanying drawing, the present invention is further described:
图1是现有的敏捷卫星姿态大角度往复快速摆动实现超大幅宽无缝连续成像原理示意图;Figure 1 is a schematic diagram of the existing agile satellite attitude reciprocating and fast swinging at a large angle to achieve ultra-large-width seamless continuous imaging;
图2是本发明中敏捷卫星的复合姿态控制执行机构配置示意图;Fig. 2 is the composite attitude control executive mechanism configuration schematic diagram of the agile satellite in the present invention;
图3是本发明中双控制力矩陀螺结构构型配置示意图;3 is a schematic diagram of the configuration and configuration of the dual control moment gyro in the present invention;
图4是本发明的仿真实验过程中生成的敏捷卫星姿态角时间响应曲线;Fig. 4 is the agile satellite attitude angle time response curve generated in the simulation experiment process of the present invention;
图5是本发明的仿真实验过程中生成的敏捷卫星姿态角速度时间响应曲线;Fig. 5 is the agile satellite attitude angular velocity time response curve generated in the simulation experiment process of the present invention;
图6是本发明的仿真实验过程中生成的控制力矩陀螺框架角时间响应曲线。FIG. 6 is a control torque gyro frame angle time response curve generated during the simulation experiment of the present invention.
具体实施方式Detailed ways
下面将对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例仅是本发明的一部分实施例,而不是全部的实施例。基于本发明中的实施例,本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其它实施例,都属于本发明保护的范围:The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative work all belong to the protection scope of the present invention:
如图2至图3所示的一种敏捷卫星姿态往复快速摆动的执行机构配置方法,所述执行机构设置为搭载安装在敏捷卫星平台上的复合姿态控制执行机构,包括控制力矩陀螺以及反作用飞轮,所述控制力矩陀螺以及反作用飞轮的数量均设置为两个,其配置方法为:以敏捷卫星平台为中心构建直角三维坐标系Oxyz,其中,两个所述反作用飞轮分别安装在y,z轴上且其转子转动正方向分别朝向y,z轴负方向,其中,v1,v2分别为两个转子的转动方向单位矢量,两个所述控制力矩陀螺的框架轴安装方向与y轴平行,且构成双控制力矩陀螺结构,其输出的控制力矩作用在x轴方向,其中x轴为敏捷卫星的滚转轴,敏捷卫星在x轴方向具备快速机动能力,通过控制力矩陀螺控制敏捷卫星绕滚转轴往复快速机动,通过反作用飞轮提供的精确连续但幅值较小的力矩来控制敏捷卫星在y,z两轴方向上的姿态稳定,在实际应用中,为满足敏捷卫星对地目标的超大幅宽无缝连续成像需求,敏捷卫星需在穿轨方向进行大角度往复快速摆动,因此,敏捷卫星仅需在滚转轴具备快速机动能力,其他两轴保持姿态稳定即可,而选用上述控制力矩陀螺以及反作用飞轮的执行结构,有效减小了整星的转动惯量,而依靠控制力矩陀螺输出控制力矩较大的特性能保证绕滚转轴的快速机动能力,依靠反作用飞轮提供的精确连续但幅值较小的力矩来保证其他两轴的姿态稳定,进一步地,由于作用在滚转轴方向的控制力矩陀螺会对偏航轴方向也产生耦合效应,考虑到反作用飞轮和控制力矩陀螺力矩输出能力相差很大,所以作用在偏航轴方向的反作用飞轮无法对此种干扰力矩进行有效补偿,因此,采用上述的用双控制力矩陀螺结构能有效消除反作用飞轮对偏航轴方向的影响。As shown in FIG. 2 to FIG. 3 , a method for configuring an actuator for agile satellite attitude reciprocating and rapid swing, the actuator is configured to carry a compound attitude control actuator installed on the agile satellite platform, including a control moment gyroscope and a reaction flywheel , the number of the control moment gyroscope and the reaction flywheel is set to two, and the configuration method is: constructing a rectangular three-dimensional coordinate system Oxyz with the agile satellite platform as the center, wherein the two reaction flywheels are respectively installed on the y and z axes. and the positive directions of its rotor rotation are respectively toward the negative directions of the y and z axes, where v 1 and v 2 are the unit vectors of the rotation directions of the two rotors, respectively, and the frame axes of the two control torque gyroscopes are installed in the direction parallel to the y axis. , and constitutes a dual control torque gyroscope structure, the output control torque acts in the x-axis direction, where the x-axis is the roll axis of the agile satellite, the agile satellite has the ability to quickly maneuver in the x-axis direction, and the agile satellite is controlled by the control torque gyroscope. The rotating shaft reciprocates rapidly, and the precise and continuous torque provided by the reaction flywheel is used to control the attitude stability of the agile satellite in the y and z directions. To meet the requirements of wide and seamless continuous imaging, the agile satellite needs to swing back and forth at a large angle in the orbital direction. Therefore, the agile satellite only needs to have fast maneuvering ability in the roll axis, and the other two axes can keep the attitude stable, and the above control torque gyroscope is used. And the execution structure of the reaction flywheel can effectively reduce the rotational inertia of the whole star, and rely on the large output control torque of the control torque gyro to ensure the rapid maneuverability around the roll axis, relying on the reaction flywheel. A small torque is used to ensure the attitude stability of the other two axes. Furthermore, since the control torque gyroscope acting in the direction of the roll axis will also have a coupling effect on the yaw axis direction, considering that the torque output capability of the reaction flywheel and the control torque gyroscope is very different , so the reaction flywheel acting in the direction of the yaw axis cannot effectively compensate for this interference torque. Therefore, the above-mentioned dual-control torque gyro structure can effectively eliminate the influence of the reaction flywheel on the direction of the yaw axis.
进一步地,为提高控制精度和整体稳定性,满足快速性控制需求,两个所述的控制力矩陀螺结构参数相同,且两个所述的控制力矩陀螺结构的框架轴互相平行,转速相等但相反,一个框架轴转动角速度矢量方向沿y轴正方向,另一个框架轴转动角速度矢量方向沿y轴负方向,两个所述的控制力矩陀螺结构的框架角及框架角速度等值反向,另外,进一步地,当控制力矩陀螺临近奇异,或反作用飞轮的角动量达到饱和时,利用磁力矩器的有源特性,对控制力矩陀螺及反作用飞轮的角动量进行卸载。Further, in order to improve the control accuracy and overall stability and meet the rapid control requirements, the two control torque gyroscopes have the same structural parameters, and the frame axes of the two control torque gyroscope structures are parallel to each other, and the rotational speeds are equal but opposite. , the direction of the rotational angular velocity vector of one frame axis is along the positive direction of the y-axis, and the direction of the rotational angular velocity vector of the other frame axis is along the negative direction of the y-axis. Further, when the control torque gyroscope is approaching the singularity, or the angular momentum of the reaction flywheel reaches saturation, the angular momentum of the control torque gyroscope and the reaction flywheel is unloaded by using the active characteristics of the magnetic torquer.
应用上述执行机构的敏捷卫星姿态往复快速摆动的控制方法,包括The control method of the agile satellite attitude reciprocating fast swing using the above-mentioned actuator, including
首先,构建基于所述复合姿态控制执行机构的卫星姿态动力学模型;First, construct a satellite attitude dynamics model based on the composite attitude control actuator;
在下文中,对于任意矩阵Aa,矩阵或表示矩阵Aa的转置;对于任意矢量aa,矢量表示矢量aa的导数,矢量表示矢量aa的转置;若任意矢量aa可表示为aa=[aa1,aa2,aa3]T,则[aa ×]表示由矢量aa生成的反对称阵,表示为In the following, for any matrix A a , the matrix or represents the transpose of matrix A a ; for any vector a a , the vector represents the derivative of the vector a a , the vector Represents the transpose of the vector a a ; if any vector a a can be represented as a a =[a a1 ,a a2 ,a a3 ] T , then [a a × ] represents the antisymmetric matrix generated by the vector a a , which is expressed as
[aa]diag表示由矢量aa生成的对角阵,表示为[a a ] diag represents the diagonal matrix generated by the vector a a , denoted as
具体地,首先,设整星的质心为O,整星除去控制力矩陀螺及反作用飞轮外卫星平台质量和质心为mB、C,卫星本体坐标系b,控制力矩陀螺的质量和质心为下文中关于下标i皆有相同的定义,反作用飞轮的质量和质心为Qi,控制力矩陀螺框架转轴方向单位矢量gi、自转轴方向单位矢量si、输出力矩反方向单位矢量ti,控制力矩陀螺框架固连坐标系ci,反作用飞轮转轴方向单位矢量vi、另两轴方向单位矢量为pi、li,卫星平台、控制力矩陀螺及反作用飞轮的质心相对于系统质心的位置矢量分别为rB、卫星平台绝对角速度在本体系中投影为ω,控制力矩陀螺和反作用飞轮转子的转速矢量分别为控制力矩陀螺框架角及框架角速度矢量为δi、卫星平台、控制力矩陀螺、反作用飞轮的转动惯量为 控制力矩陀螺框架和飞轮部分的转动惯量分别为 Specifically, first, let the center of mass of the whole star be O, the mass and center of mass of the satellite platform outside the control moment gyro and the reaction flywheel are m B , C, the satellite body coordinate system b, the mass and center of mass of the control moment gyro are The following subscript i has the same definition, the mass and center of mass of the reaction flywheel are Q i , the unit vector g i in the direction of the rotation axis of the control moment gyro frame, the unit vector s i in the direction of the rotation axis, the unit vector t i in the reverse direction of the output torque, the fixed coordinate system c i of the control moment gyro frame, the unit vector v i in the direction of the rotation axis of the reaction flywheel , the other two axis direction unit vectors are p i , li , the position vectors of the center of mass of the satellite platform, the control moment gyro and the reaction flywheel relative to the center of mass of the system are r B , The absolute angular velocity of the satellite platform is projected as ω in this system, and the rotational speed vectors of the control moment gyro and the reaction flywheel rotor are respectively The frame angle and frame angular velocity vector of the control moment gyro are δ i , The moment of inertia of the satellite platform, control moment gyroscope, and reaction flywheel is The moment of inertia of the control moment gyro frame and the flywheel part are respectively
首先根据整星关于系统质心的角动量计算公式:First, according to the calculation formula of the angular momentum of the whole star about the center of mass of the system:
式(1)中,为平台关于系统质心的角动量,计算公式为:其中,为卫星平台的转动惯量,ω为卫星平台绝对角速度在本体系中投影,mB为整星除去控制力矩陀螺及反作用飞轮外卫星平台质量,rB为卫星平台相对于系统质心的位置矢量;In formula (1), is the angular momentum of the platform about the center of mass of the system, the calculation formula is: in, is the moment of inertia of the satellite platform, ω is the projection of the absolute angular velocity of the satellite platform in this system, m B is the mass of the satellite platform outside the whole satellite except the control moment gyro and the reaction flywheel, r B is the position vector of the satellite platform relative to the center of mass of the system;
式(1)中,为控制力矩陀螺关于质心的角动量,计算公式为:其中,为控制力矩陀螺的转动惯量,具体地其中,分别为控制力矩陀螺在gi、si、ti方向的转动惯量,ω为卫星平台绝对角速度在本体系中投影,为控制力矩陀螺框架角速度矢量,为控制力矩陀螺飞轮部分的转动惯量,具体地,其中,分别为控制力矩陀螺飞轮部分在gi、si、ti方向的转动惯量,为控制力矩陀螺的转速矢量,为控制力矩陀螺的质量,为控制力矩陀螺的质心相对于系统质心的位置矢量;In formula (1), In order to control the angular momentum of the moment gyro about the center of mass, the calculation formula is: in, In order to control the moment of inertia of the moment gyro, specifically in, are the moment of inertia of the control moment gyro in the directions of g i , s i and t i respectively, ω is the projection of the absolute angular velocity of the satellite platform in this system, To control the angular velocity vector of the moment gyro frame, In order to control the moment of inertia of the flywheel part of the moment gyro, specifically, in, are the moment of inertia of the flywheel part of the control moment gyro in the directions of g i , s i , and t i , respectively, To control the rotational speed vector of the moment gyro, To control the mass of the moment gyro, is the position vector of the center of mass of the control moment gyro relative to the center of mass of the system;
式(1)中,为反作用飞轮关于质心的角动量,其计算公式为:其中,为反作用飞轮的转动惯量,具体地,其中,分别为反作用飞轮在pi、vi、li方向的转动惯量,ω为卫星平台绝对角速度在本体系中投影,为反作用飞轮转子的转速矢量,为反作用飞轮的质心,为反作用飞轮的质心相对于系统质心的位置矢量;In formula (1), is the angular momentum of the reaction flywheel about the center of mass, and its calculation formula is: in, is the moment of inertia of the reaction flywheel, specifically, in, are the moment of inertia of the reaction flywheel in the directions of p i , vi , and li respectively , ω is the projection of the absolute angular velocity of the satellite platform in this system, is the rotational speed vector of the reaction flywheel rotor, is the center of mass of the reaction flywheel, is the position vector of the center of mass of the reaction flywheel relative to the center of mass of the system;
将整星转动惯量中的不变部分表示为下式:The invariant part of the moment of inertia of the whole star is expressed as the following formula:
其中,E为单位矩阵,分别为rB、的转置。 where E is the identity matrix, are r B , transposition of .
由于在框架固连坐标系ci中也为常量,则根据动量矩定理,合外力矩because is also constant in the frame-fixed coordinate system c i , then according to the moment of momentum theorem, the combined external moment
上式中的分别为卫星平台绝对角速度、控制力矩陀螺框架角速度及飞轮转子角速度的导数。in the above formula are the absolute angular velocity of the satellite platform, the angular velocity of the control moment gyro frame and the derivative of the angular velocity of the flywheel rotor.
将上式在本体系b中进行投影,由于从控制力矩陀螺框架固连系ci到本体系b的坐标转换阵可表示为:The above formula is projected in the system b, because the coordinate transformation matrix from the control moment gyro frame fixed connection c i to the system b can be expressed as:
上式中,gi为控制力矩陀螺框架转轴方向单位矢量、si为自转轴方向单位矢量、ti为输出力矩反方向单位矢量,δi为控制力矩陀螺框架角,g0i、s0i、t0i分别为gi、si、ti的初始值。In the above formula, gi is the unit vector of the direction of the rotation axis of the control torque gyro frame, s i is the unit vector of the direction of the rotation axis, t i is the unit vector of the reverse direction of the output torque, δ i is the frame angle of the control torque gyro, g 0i , s 0i , t 0i are the initial values of g i , s i , and t i respectively.
根据转动惯量在不同坐标系下投影的关系式,在本体系b中投影可表示为:According to the relational expression of the moment of inertia projected in different coordinate systems, Projection in this system b can be expressed as:
上式中,矩阵Ap、Av、Al分别为Ap=[p1,p2]、Av=[v1,v2]、Al=[l1,l2],矩阵Ip、Iv、Il分别为 在本体系b中投影可表示为:In the above formula, the matrices A p , A v , and A l are respectively A p =[p 1 ,p 2 ], A v =[v 1 ,v 2 ], A l =[l 1 ,l 2 ], the matrix I p , I v , I l are respectively Projection in this system b can be expressed as:
上式中,矩阵Ag、As、At分别为Ag=[g1,g2]、As=[s1,s2]、At=[t1,t2],矩阵Ig、Is、It分别为 In the above formula, the matrices A g , A s and At are respectively A g =[g 1 ,g 2 ], A s =[s 1 ,s 2 ],A t =[ t 1 ,t 2 ], the matrix I g , Is , and It are respectively
再令, order again,
由于(分别为在相应方向的投影),because ( respectively projection in the corresponding direction),
则合力外矩:Then the resultant external moment is:
令 make
上式可化为下式,The above formula can be transformed into the following formula,
其中,in,
Cδ1=Cδ+R(ω)+ω×AgIg,C δ1 =C δ +R(ω)+ω×A g I g ,
DΩ=AvIv,D Ω =A v I v ,
上述方程(2)即为构建的敏捷卫星姿态动力学模型。The above equation (2) is the constructed agile satellite attitude dynamics model.
然后,构建基于所述复合姿态控制执行机构的姿态运动学方程;Then, construct the attitude kinematics equation based on the compound attitude control actuator;
具体地,设敏捷卫星姿态四元素为用姿态四元数表示的敏捷卫星姿态运动学方程为Specifically, let the four elements of agile satellite attitude be The attitude kinematics equation of agile satellite expressed by attitude quaternion is:
设敏捷卫星期望姿态四元素和期望姿态角速度为误差四元素和误差角速度为则有Let the four elements of the desired attitude of the agile satellite and the angular velocity of the desired attitude be The error four elements and the error angular velocity are then there are
其中,由卫星期望姿态固连系到体坐标系的坐标转换矩阵为其中,E3为3×3单位矩阵。同时,误差四元素和误差角速度也满足下式:Among them, the coordinate transformation matrix that is fixedly connected to the body coordinate system by the desired attitude of the satellite for where E 3 is a 3×3 identity matrix. At the same time, the error four elements and the error angular velocity also satisfy the following formula:
最后根据上述所构建的敏捷卫星姿态动力学及运动学方程,设计基于符合姿态控制执行机构且能使得卫星按照期望姿态进行机动的算法模型,也即所述姿态控制器。Finally, according to the above constructed agile satellite attitude dynamics and kinematic equations, an algorithm model based on compliance with the attitude control actuator and enabling the satellite to maneuver according to the desired attitude, that is, the attitude controller is designed.
具体地,根据所构建的敏捷卫星姿态动力学及运动学方程,利用Lyapunov定理和LaSalle不变集原理,可设计姿态控制器使得姿态误差系统渐近稳定,即使得卫星按照期望姿态进行机动。Specifically, according to the constructed agile satellite attitude dynamics and kinematic equations, using Lyapunov theorem and LaSalle invariant set principle, the attitude controller can be designed to make the attitude error system asymptotically stable, that is, the satellite can maneuver according to the desired attitude.
根据矢量相对于不同坐标系对时间的导数关系定理,有According to the theorem of the derivatives of vectors with respect to different coordinate systems with respect to time, we have
再根据方程(2)和(6),有Then according to equations (2) and (6), we have
设k1,k2>0,其中k1,k2分别为角度误差增益以及角速度误差增益,则由Lyapunov函数可得:Assuming k 1 , k 2 >0, where k 1 , k 2 are the angular error gain and the angular velocity error gain, respectively, then the Lyapunov function can be obtained:
对上式求导得,Deriving from the above formula,
令make
则且等号仅在ωe=0时才取到。要求则需ωe≡0。将Tc表达式代入系统动力学方程(2)中可得but And the equal sign is only taken when ω e =0. Require Then ω e ≡ 0 is required. Substituting the expression of T c into the system dynamics equation (2), we can get
当ωe≡0时,有且qe=0。根据LaSalle不变集原理,系统任何轨线都趋向于qe=0,ωe=0。从而,误差系统渐近稳定。When ω e ≡ 0, we have and q e =0. According to the LaSalle invariant set principle, any trajectory of the system tends to q e =0,ω e =0. Thus, the error system is asymptotically stable.
再根据方程(3),可得控制力矩陀螺和反作用飞轮的操纵方程:Then according to equation (3), the steering equations for controlling the moment gyro and the reaction flywheel can be obtained:
其中in
由于远小于产生的力矩,ω远小于Ωc,因此可将操纵方程简化为because much smaller than The resulting moment, ω is much smaller than Ω c , so the steering equation can be simplified to
根据双控制力矩陀螺结构配置,两只控制力矩陀螺的框架角及框架角速度等值反向,由此可令再依据执行机构的配置方案,可得敏捷卫星的执行机构的的输入如下式:According to the configuration of the dual control torque gyroscope, the frame angles and frame angular velocities of the two control torque gyroscopes are equivalently reversed, so that the Then according to the configuration scheme of the actuator, the input of the actuator of the agile satellite can be obtained as follows:
uc即为姿态控制器的输出指令信号,通过将指令信号输入至复合姿态执行机构,继而使得敏捷卫星按期望姿态机动。u c is the output command signal of the attitude controller. By inputting the command signal to the compound attitude actuator, the agile satellite can maneuver according to the desired attitude.
下面结合Matlab的Simulink仿真,对本发明的具体实施方式做出更为详细的说明,Below in conjunction with the Simulink simulation of Matlab, the specific embodiments of the present invention are described in more detail,
设敏捷卫星要求探测的幅宽D为1000km,卫星对地的相对运动速度Vd=6.8km/s,星下点幅宽L×W=117×21km,对应视场θL×θW=13.41×2.41,L=117km为沿轨方向。因此,整星成像幅宽为D时所需完成的穿轨方向摆动角度θD=DθW/W=90°。若要实现无缝连续成像,则卫星回摆至初始位置,完成一个钟摆的最长时限tmax=L/Vd=17.2s。Let the width D required to be detected by the agile satellite be 1000km, the relative motion speed of the satellite to the ground V d = 6.8km/s, the width of the sub-satellite point L × W = 117 × 21km, the corresponding field of view θ L × θ W = 13.41 ×2.41, L=117km is the direction along the track. Therefore, the swing angle θ D = Dθ W /W = 90° in the orbiting direction needs to be completed when the entire star imaging width is D. To achieve seamless continuous imaging, the satellite is swung back to the initial position, and the longest time limit of one pendulum is t max =L/V d =17.2s.
为了验证本发明在敏捷卫星频繁进行大角度往复机动任务时的有效性,姿态机动指令为:从0s开始-45°→45°执行的滚转指令,当卫星滚转角达到45°后,再执行45°→-45°的滚转指令,并重复这个过程。基于此,各项仿真参数可设置为:In order to verify the effectiveness of the present invention when the agile satellite frequently performs large-angle reciprocating maneuvering tasks, the attitude maneuvering command is: a roll command executed from -45°→45° from 0s, and then executed when the satellite roll angle reaches 45° 45°→-45° roll command, and repeat the process. Based on this, various simulation parameters can be set as:
1、卫星参数1. Satellite parameters
转动惯量矩阵:J=[7,0,0;0,12,0;0,0,12]kgm2,Moment of inertia matrix: J=[7,0,0;0,12,0;0,0,12]kgm 2 ,
初始欧拉角: Initial Euler angles:
初始角速度:ω0=[0,0,0]T,Initial angular velocity: ω 0 =[0,0,0] T ,
期望欧拉角: Expected Euler angles:
钟摆周期:T=16s,Pendulum period: T=16s,
2、控制力矩陀螺参数2. Control torque gyro parameters
转子转轴方向转动惯量: The moment of inertia in the direction of the rotor axis:
转子转速: Rotor speed:
初始框架角: Initial frame corners:
框架角速度最大值: Maximum frame angular velocity:
3、反作用飞轮参数3. Reaction flywheel parameters
反作用飞轮轴向转动惯量: Reaction flywheel axial moment of inertia:
反作用飞轮初始转速: Reaction flywheel initial speed:
反作用飞轮最大转速: Reaction flywheel maximum speed:
反作用飞轮最大角加速度: Maximum angular acceleration of the reaction flywheel:
4、控制器参数4. Controller parameters
角度误差增益:k1=100,Angle error gain: k 1 =100,
角速度误差增益:k2=100。Angular velocity error gain: k 2 =100.
根据上述仿真参数,进行Simulink仿真过程,其仿真时间设定为160s,即十个钟摆周期。According to the above simulation parameters, the Simulink simulation process is performed, and the simulation time is set to 160s, that is, ten pendulum cycles.
其仿真结果如下:The simulation results are as follows:
如图4所示,卫星在16s内完成了由-45°→45°,再由45°→-45°的滚转机动,且卫星三轴的姿态角跟踪精度优于0.1°。As shown in Figure 4, the satellite completed the roll maneuver from -45°→45°, and then from 45°→-45° within 16s, and the satellite three-axis attitude angle tracking accuracy was better than 0.1°.
如图5所示,卫星在4s内完成了由0°/s→17.7°/s的加速过程,在8s内完成了由17.7°/s→0→-17.7°/s先减速再加速的过程。As shown in Figure 5, the satellite completed the acceleration process from 0°/s→17.7°/s within 4s, and completed the process of first decelerating and then accelerating from 17.7°/s→0→-17.7°/s within 8s .
如图6所示,初始框架角为90°,逐渐增加到121°,再减小到59°。当一个钟摆周期完成后,框架角回到了初始框架角附近,避免了框架角奇异情况的出现。As shown in Figure 6, the initial frame angle is 90°, which gradually increases to 121° and then decreases to 59°. When one pendulum cycle is completed, the frame angle returns to the vicinity of the initial frame angle, avoiding the occurrence of the singularity of the frame angle.
上述图4至图6的仿真结果,验证了本发明所提出的姿态控制方法,可实现滚转角大角度快速往复摆动,可满足对地目标的超大幅宽无缝连续机动成像需求,且具有机动能力强、快速性好、避免框架角奇异等特点。The above simulation results of Fig. 4 to Fig. 6 verify that the attitude control method proposed by the present invention can realize the rapid reciprocating swing of the roll angle and large angle, and can meet the requirements of ultra-large-width seamless continuous maneuvering imaging of ground targets, and has the ability to maneuver. It has the characteristics of strong ability, good speed, and avoiding the singularity of frame corners.
需要强调的是:以上仅是本发明的较佳实施例而已,并非对本发明作任何形式上的限制,凡是依据本发明的技术实质对以上实施例所作的任何简单修改、等同变化与修饰,均仍属于本发明技术方案的范围内。It should be emphasized that the above are only preferred embodiments of the present invention, and are not intended to limit the present invention in any form. Any simple modifications, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention are Still belong to the scope of the technical solution of the present invention.
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