CN115509245A - Continuous moment spacecraft attitude tracking control method based on ratio transformation - Google Patents

Continuous moment spacecraft attitude tracking control method based on ratio transformation Download PDF

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CN115509245A
CN115509245A CN202211159466.7A CN202211159466A CN115509245A CN 115509245 A CN115509245 A CN 115509245A CN 202211159466 A CN202211159466 A CN 202211159466A CN 115509245 A CN115509245 A CN 115509245A
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spacecraft
quaternion
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CN115509245B (en
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肖岩
杨玉龙
叶东
张刚
姜锐
张豪
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Harbin Institute of Technology Shenzhen
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Abstract

The invention discloses a continuous moment spacecraft attitude tracking control method based on scale transformation, and relates to a continuous moment spacecraft attitude tracking control method based on scale transformation. The invention aims to solve the problem that the attitude of a spacecraft cannot be controlled to reach the accuracy range expected by a task before the time expected by the task due to discontinuous control moment given by an attitude tracking control algorithm aiming at the preset time and preset accuracy. A continuous moment spacecraft attitude tracking control method based on proportional transformation comprises the following steps: the method comprises the following steps: constructing a posture motion model of the spacecraft; the attitude motion model of the spacecraft is composed of an attitude kinematics equation and an attitude dynamics equation of the spacecraft; representing the attitude motion model of the spacecraft as an attitude error quaternion; step two: selecting a control variable; step three: and obtaining the control torque output by the controller based on the first step and the second step. The invention belongs to the technical field of spacecraft attitude control.

Description

一种基于比例变换的连续力矩航天器姿态跟踪控制方法A Continuous Moment Spacecraft Attitude Tracking Control Method Based on Scale Transformation

技术领域technical field

本发明涉及基于比例变换的连续力矩航天器姿态跟踪控制方法，属于航天器姿态控制技术领域。The invention relates to a continuous moment spacecraft attitude tracking control method based on proportional transformation, and belongs to the technical field of spacecraft attitude control.

背景技术Background technique

所谓航天器姿态跟踪控制问题，即设法控制航天器的姿态，使其在各种干扰的影响下，尽可能按照任务期望的姿态变化进行变化的问题。其中，任务期望的姿态变化由具体的任务需求给定，属于任务需求，不由姿态跟踪的控制方法进行设计。航天器所受到的各种干扰的具体值是未知的，但干扰的大小范围是已知的。控制方式为由控制方法计算出控制力矩交由执行机构进行实现，执行机构的实现过程不由控制方法管理。The so-called spacecraft attitude tracking control problem is the problem of trying to control the attitude of the spacecraft so that it can change as much as possible according to the attitude change expected by the mission under the influence of various disturbances. Among them, the attitude change expected by the task is given by the specific task requirements, which belongs to the task requirements, and is not designed by the control method of attitude tracking. The specific values of the various disturbances suffered by the spacecraft are unknown, but the magnitude range of the disturbances is known. The control method is that the control torque calculated by the control method is delivered to the actuator for realization, and the realization process of the actuator is not managed by the control method.

该问题的需求可以较为科学的概括为：控制航天器的姿态，使其在任务期望的时间之前达到任务期望的精度范围。任务期望的时间与精度范围均为任务需求，不由姿态跟踪控制方法进行设计。The requirements of this problem can be more scientifically summarized as: control the attitude of the spacecraft so that it can reach the expected accuracy range of the mission before the expected time of the mission. The expected time and accuracy range of the task are the requirements of the task, and are not designed by the attitude tracking control method.

对于这类任务，相对新颖的方法是通过预设时间控制理论来处理这一问题。所谓预设时间控制即确保被控对象在预设的时间点稳定到0。如果将这个时间点取为姿态跟踪任务期望的时间，所给出的控制输出将十分契合时间方面的需求。但该理论所得出的控制输出在预设时间点前的一小段时间会突然增大，理论上在预设时间点会趋于无穷。Song Y,Wang Y,Holloway J,et al.Time-varying feedback for regulation of normal-formnonlinear systems in prescribed finite time[J].Automatica,2017,83:243-251.对这一问题进行了阐述，并给出了一种基于比例变换的预设时间控制，该方法能够使得预设时间理论中控制力矩的突增点后移，但无法提供预设时间之后的控制力矩，仅在预设时间之前有较好的实用价值。For this type of task, a relatively novel approach is to deal with this problem through the theory of preset temporal control. The so-called preset time control is to ensure that the controlled object is stable to 0 at the preset time point. If this time point is taken as the expected time of the attitude tracking task, the given control output will be very consistent with the time requirements. However, the control output derived from the theory will increase suddenly in a short period of time before the preset time point, and theoretically will tend to infinity at the preset time point. Song Y, Wang Y, Holloway J, et al. Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time [J]. Automatica, 2017, 83:243-251. Elaborated on this issue, and A preset time control based on proportional transformation is given. This method can make the sudden increase point of the control torque in the preset time theory move backward, but it cannot provide the control torque after the preset time. Good practical value.

若需要将预设时间控制理论应用在姿态跟踪控制上，仍然存在三个问题需要解决：一是预设时间控制理论往往无法提供预设时间点之后的控制力矩(典型代表为K.-K.Zhang,B.Zhou,and G.-R.Duan,“Prescribed-time input-to-state stabilization ofnormal nonlinear systems by bounded time-varying feedback,”IEEE Transactionson Circuits and Systems I:Regular Papers,pp.1–11,2022)；二是预设时间理论所给出的控制输力矩可能会随时间趋向预设时间点而趋于无穷，无法被任何的执行机构实现。三是姿态误差收敛到0是不必要的，只要能够满足期望的误差范围即可，过高的精度要求会给执行机构带来额外的负担。If it is necessary to apply the preset time control theory to attitude tracking control, there are still three problems to be solved: First, the preset time control theory often cannot provide the control torque after the preset time point (typical representatives are K.-K. Zhang, B. Zhou, and G.-R. Duan, “Prescribed-time input-to-state stabilization of normal nonlinear systems by bounded time-varying feedback,” IEEE Transactions on Circuits and Systems I: Regular Papers, pp. 1–11 , 2022); Second, the control output torque given by the preset time theory may tend to infinity as time approaches the preset time point, which cannot be realized by any actuator. Third, it is not necessary for the attitude error to converge to 0, as long as the expected error range can be met. Excessively high precision requirements will bring additional burden to the actuator.

解决上述问题的思路之一是将控制器按照某一时间或条件分两段进行设计。前段按照预设时间控制器进行控制，直到姿态误差能够满足预设精度；后段则采取其他的控制方法，保证姿态误差一直在精度范围内即可。这样设计出的控制器即预设时间预设精度控制器。这一方法的具体实现手段较为多样，如KAIRUZ R I V,ORLOV Y,AGUILAR LT.Prescribed-time stabilization of controllable planar systems using switchedstate feedback[J].IEEE Control Systems Letters,2020,5(6):2048-2053.直接将控制力矩分为两段进行设计，虽然很好的实现了预设时间预设精度的要求，但得到的控制力矩会在预设时间附近发生突变，且其设计的第二段控制力矩不连续。D.Ye,A.-M.Zou,andZ.Sun,“Predefined-time predefined-bounded attitude tracking control for rigidspacecraft,”IEEE Transactions on Aerospace and Electronic Systems,vol.58,no.1,pp.464–472,2022.在设计过程中将预设时间稳定引理的不等式包含的奇异项进行了分段设计，也可实现预设时间预设精度的需求，但得到的控制力矩依旧会在航天器姿态误差进入预设精度范围的瞬间发生突变。对于以飞轮为姿态控制执行机构的航天器而言，突变的控制力矩需要突变的飞轮转速来实现，这意味着飞轮的角加速度在瞬间达到了无穷大，该点的能量需求也是无穷大，而实际的飞轮并不可能提供无穷大的能量。One of the ideas to solve the above problems is to design the controller in two stages according to a certain time or condition. The front section is controlled according to the preset time controller until the attitude error can meet the preset accuracy; the latter section adopts other control methods to ensure that the attitude error is always within the accuracy range. The controller designed in this way is the preset time preset precision controller. There are various specific implementation methods for this method, such as KAIRUZ R I V, ORLOV Y, AGUILAR LT. Prescribed-time stabilization of controllable planar systems using switched state feedback[J].IEEE Control Systems Letters,2020,5(6):2048-2053 .Directly divide the control torque into two sections for design. Although the preset accuracy requirements of the preset time are well realized, the obtained control torque will change suddenly around the preset time, and the second stage of the design of the control torque Discontinuous. D. Ye, A.-M. Zou, and Z. Sun, “Predefined-time predefined-bounded attitude tracking control for rigid spacecraft,” IEEE Transactions on Aerospace and Electronic Systems, vol.58, no.1, pp.464–472 ,2022. In the design process, the singular items contained in the inequality of the preset time stability lemma were designed in sections, which can also meet the preset time preset accuracy requirements, but the obtained control torque will still be in the spacecraft attitude error A sudden change occurs at the moment of entering the preset accuracy range. For the spacecraft with the flywheel as the attitude control actuator, the sudden change in the control torque requires a sudden change in the flywheel speed, which means that the angular acceleration of the flywheel reaches infinity in an instant, and the energy demand at this point is also infinite, while the actual It is impossible for a flywheel to provide infinite energy.

总之，目前虽然对于预设时间预设精度的姿态跟踪控制算法已经具备了一定的研究，但现有的控制算法还不完善，大多数算法给出的控制力矩并不连续，且其不连续的主要原因即姿态误差到达预设精度后的控制力矩设计不够完善。In short, although some research has been done on the attitude tracking control algorithm with preset time and preset precision, the existing control algorithms are not perfect. The control torque given by most algorithms is not continuous, and its discontinuous The main reason is that the design of the control torque after the attitude error reaches the preset accuracy is not perfect.

发明内容Contents of the invention

本发明的目的是为了解决现有针对预设时间预设精度的姿态跟踪控制算法给出的控制力矩并不连续，导致无法控制航天器姿态在任务期望的时间之前达到任务期望的精度范围的问题，而提出一种基于比例变换的连续力矩航天器姿态跟踪控制方法。The purpose of the present invention is to solve the problem that the control moment given by the existing attitude tracking control algorithm for the preset time and preset precision is discontinuous, resulting in the inability to control the attitude of the spacecraft to reach the expected accuracy range of the task before the expected time of the task , and a continuous moment spacecraft attitude tracking control method based on scale transformation is proposed.

一种基于比例变换的连续力矩航天器姿态跟踪控制方法具体过程为：The specific process of a continuous moment spacecraft attitude tracking control method based on proportional transformation is as follows:

步骤一：构建航天器的姿态运动模型；Step 1: Construct the attitude motion model of the spacecraft;

航天器的姿态运动模型由航天器的姿态运动学方程和姿态动力学方程构成；The attitude motion model of the spacecraft is composed of the attitude kinematics equation and the attitude dynamic equation of the spacecraft;

将航天器的姿态运动模型表示为姿态误差四元数；Express the attitude motion model of the spacecraft as an attitude error quaternion;

步骤二：选取控制变量；Step 2: Select control variables;

步骤三：基于步骤一和步骤二获得控制器输出的控制力矩。Step 3: Obtain the control torque output by the controller based on Step 1 and Step 2.

本发明的有益效果为：The beneficial effects of the present invention are:

本发明方法针对预设时间预设精度的姿态跟踪控制问题进行了研究，采用比例变换的方法对控制器进行了设计，实现了连续控制力矩下的预设时间预设精度姿态跟踪控制。The method of the invention studies the attitude tracking control problem of preset time and preset precision, adopts the method of proportional transformation to design the controller, and realizes the gesture tracking control of preset time and preset precision under continuous control torque.

本发明实现了航天器的预设时间预设精度的姿态跟踪控制，控制目的更加贴合姿态跟踪的实际需求。The invention realizes the attitude tracking control of the spacecraft with preset time and preset accuracy, and the control purpose is more in line with the actual demand of attitude tracking.

本发明方法确保了控制力矩连续性，确保利用飞轮可实现控制目的。The method of the invention ensures the continuity of the control moment and ensures that the control purpose can be realized by using the flywheel.

本发明方法将比例变换方法中的比例函数进行了改善，提升其应用价值。The method of the invention improves the proportional function in the proportional transformation method, and enhances its application value.

附图说明Description of drawings

图1为本发明的控制流程图；Fig. 1 is a control flowchart of the present invention;

图2为航天器姿态误差图，[qe1；qe2；qe3]表示航天器姿态误差四元数的矢量部分，qe1、qe2、qe3分别为姿态误差四元数矢量部分的第一、第二、第三个分量；Figure 2 is the spacecraft attitude error diagram, [q e1 ; q e2 ; q e3 ] represents the vector part of the spacecraft attitude error quaternion, q e1 , q e2 , q e3 are the first vector part of the attitude error quaternion 1st, 2nd, 3rd component;

图3为航天器角速度误差图，ωe＝[ωex；ωey；ωez]表示航天器本体相对期望姿态的角速度误差，ωex表示航天器本体相对期望姿态的角速度误差在本体系的x轴方向分量，ωey为表示航天器本体相对期望姿态的角速度误差在本体系的y轴方向分量，ωez为表示航天器本体相对期望姿态的角速度误差在本体系的z轴方向分量；Figure 3 is the angular velocity error diagram of the spacecraft, ω e = [ω ex ; ω ey ; ω ez ] represents the angular velocity error of the spacecraft body relative to the expected attitude, ω ex represents the angular velocity error of the spacecraft body relative to the expected attitude at x of the system axis direction component, ω ey represents the angular velocity error of the spacecraft body relative to the expected attitude in the y-axis direction component of the system, and ω ez represents the angular velocity error of the spacecraft body relative to the expected attitude in the z-axis direction component of the system;

图4为航天器控制力矩曲线图，τ＝[τx；τy；τz]表示飞轮作用在航天器上的控制力矩τx表示飞轮作用在航天器上的控制力矩在本体系的x轴方向分量，τy表示飞轮作用在航天器上的控制力矩在本体系的y轴方向分量，τz表示飞轮作用在航天器上的控制力矩在本体系的z轴方向分量。Figure 4 is a graph of the control torque of the spacecraft, τ=[τ x ; τ y ; τ z ] represents the control torque of the flywheel acting on the spacecraft τ x represents the control torque of the flywheel acting on the spacecraft on the x-axis of the system The direction component, τ y represents the y-axis direction component of the control moment of the flywheel acting on the spacecraft, and τ z represents the z-axis direction component of the control moment of the flywheel acting on the spacecraft.

具体实施方式detailed description

具体实施方式一：本实施方式一种基于比例变换的连续力矩航天器姿态跟踪控制方法具体过程为：Specific implementation mode one: the specific process of a continuous moment spacecraft attitude tracking control method based on proportional transformation in this implementation mode is as follows:

下面结合附图及实施例对本发明进行详细说明，一种基于比例变换的连续力矩航天器姿态跟踪控制方法，具体包括了图1中的模型转换和控制器两个部分。在航天器的姿态信息被敏感元件获取后，安装本发明中的方式计算出控制力矩作用在航天器上即可实现预设时间预设精度姿态跟踪控制。包括以下步骤：The present invention will be described in detail below in conjunction with the accompanying drawings and embodiments. A continuous moment spacecraft attitude tracking control method based on scale transformation specifically includes two parts, the model conversion and the controller in FIG. 1 . After the attitude information of the spacecraft is acquired by the sensitive element, the method of the present invention is installed to calculate the control torque and act on the spacecraft to realize the attitude tracking control with preset time and preset precision. Include the following steps:

针对航天器姿态跟踪控制问题，在考虑外界干扰与参数不确定性的综合影响下，建立航天器姿态运动模型，并选取合适的控制变量。具体过程为：Aiming at the problem of spacecraft attitude tracking control, considering the comprehensive influence of external disturbance and parameter uncertainty, a spacecraft attitude motion model is established, and appropriate control variables are selected. The specific process is:

步骤一：构建航天器的姿态运动模型；Step 1: Construct the attitude motion model of the spacecraft;

航天器的姿态运动模型由航天器的姿态运动学方程和姿态动力学方程构成；The attitude motion model of the spacecraft is composed of the attitude kinematics equation and the attitude dynamic equation of the spacecraft;

将航天器的姿态运动模型表示为姿态误差四元数；Express the attitude motion model of the spacecraft as an attitude error quaternion;

步骤二：选取控制变量；Step 2: Select control variables;

步骤三：基于步骤一和步骤二获得控制器输出的控制力矩。Step 3: Obtain the control torque output by the controller based on Step 1 and Step 2.

具体实施方式二：本实施方式与具体实施方式一不同的是，所述步骤一中构建航天器的姿态运动模型；Embodiment 2: The difference between this embodiment and Embodiment 1 is that the attitude motion model of the spacecraft is constructed in the step 1;

航天器的姿态运动模型由航天器的姿态运动学方程和姿态动力学方程构成；The attitude motion model of the spacecraft is composed of the attitude kinematics equation and the attitude dynamic equation of the spacecraft;

将航天器的姿态运动模型表示为姿态误差四元数；Express the attitude motion model of the spacecraft as an attitude error quaternion;

具体过程为：The specific process is:

以单位四元数作为姿态参数，姿态运动学方程为：Taking the unit quaternion as the attitude parameter, the attitude kinematics equation is:

Figure BDA0003858958470000041
Figure BDA0003858958470000041

Figure BDA0003858958470000042
Figure BDA0003858958470000042

其中，

Figure BDA0003858958470000043
为航天器的姿态四元数，ω为航天器的角速度矢量，
Figure BDA0003858958470000044
为3×3单位矩阵；qv为四元数的矢量部分，q4为四元数的标量部分，
Figure BDA0003858958470000045
表示实数集合，
Figure BDA0003858958470000046
表示由4个实数构成的列向量集合，
Figure BDA0003858958470000047
表示3行3列的实数矩阵集合，
Figure BDA0003858958470000048
为qv的一阶导数，
Figure BDA0003858958470000049
为qv的坐标方阵，
Figure BDA00038589584700000410
qv1、qv2、qv3分别表示四元数的矢量部分qv的第1，2，3个分量；
Figure BDA00038589584700000411
表示了q是一个由实数构成的四维矢量；in,
Figure BDA0003858958470000043
is the attitude quaternion of the spacecraft, ω is the angular velocity vector of the spacecraft,
Figure BDA0003858958470000044
is a 3×3 identity matrix; q v is the vector part of the quaternion, and q 4 is the scalar part of the quaternion,
Figure BDA0003858958470000045
represents the set of real numbers,
Figure BDA0003858958470000046
Represents a set of column vectors consisting of 4 real numbers,
Figure BDA0003858958470000047
Represents a set of real matrixes with 3 rows and 3 columns,
Figure BDA0003858958470000048
is the first derivative of q v ,
Figure BDA0003858958470000049
is the coordinate matrix of q v ,
Figure BDA00038589584700000410
q v1 , q v2 , and q v3 represent the 1st, 2nd, and 3rd components of the vector part qv of the quaternion, respectively;
Figure BDA00038589584700000411
Indicates that q is a four-dimensional vector composed of real numbers;

对任意三维列矢量

Figure BDA00038589584700000412
y×表示三维列矢量y的坐标方阵，y×＝[0,-y3,y2；y3,0,-y1；-y2,y3,0]；For any 3D column vector
Figure BDA00038589584700000412
y × represents the coordinate matrix of the three-dimensional column vector y, y × =[0,-y 3 ,y 2 ; y 3 ,0,-y 1 ;-y 2 ,y 3 ,0];

其中，y1、y2、y3分别表示三维列矢量y的第1，2，3个分量，

Figure BDA00038589584700000414
表示由3个实数构成的列向量集合；Among them, y 1 , y 2 , and y 3 represent the first, second, and third components of the three-dimensional column vector y, respectively,
Figure BDA00038589584700000414
Represents a set of column vectors composed of 3 real numbers;

Figure BDA00038589584700000415
表示该矢量的一阶导数，
Figure BDA00038589584700000416
表示该矢量的二阶导数，yT为该矢量的转置；
Figure BDA00038589584700000415
represents the first derivative of this vector,
Figure BDA00038589584700000416
Indicates the second order derivative of the vector, y T is the transpose of the vector;

姿态动力学方程为The attitude dynamic equation is

Figure BDA00038589584700000413
Figure BDA00038589584700000413

其中，J为航天器的惯性矩阵，τ为控制力矩，d为外界干扰力矩，ω×为ω的坐标方阵，ω×＝[0,-ω3,ω2；ω3,0,-ω1；-ω2,ω3,0]，ω1、ω2、ω3分别表示ω的第1，2，3个分量，

Figure BDA00038589584700000510
为ω的一阶导数；Among them, J is the inertia matrix of the spacecraft, τ is the control torque, d is the external disturbance torque, ω × is the coordinate matrix of ω, ω × = [0,-ω 3 ,ω 2 ; ω 3 ,0,-ω 1 ; -ω 2 ,ω 3 ,0], ω 1 , ω 2 , ω 3 represent the 1st, 2nd, 3rd components of ω respectively,
Figure BDA00038589584700000510
is the first derivative of ω;

考虑到航天器的参数不确定性，J＝ΔJ+J0，其中ΔJ为惯性矩阵的不确定部分，J0为惯性矩阵的标称部分；Considering the parameter uncertainty of the spacecraft, J=ΔJ+J 0 , where ΔJ is the uncertain part of the inertia matrix, and J 0 is the nominal part of the inertia matrix;

考虑到需处理姿态跟踪问题，故将航天器的姿态运动采用姿态误差四元数描述更为适合。Considering the need to deal with the attitude tracking problem, it is more appropriate to describe the attitude motion of the spacecraft using the attitude error quaternion.

假设期望姿态的四元数表示为

Figure BDA0003858958470000051
期望角速度为ωd；Suppose the quaternion representation of the desired pose is
Figure BDA0003858958470000051
The desired angular velocity is ω d ;

其中qdv为期望姿态四元数的矢量部分，qd4为期望姿态四元数的标量部分，期望角速度为ωd；Wherein q dv is the vector part of the desired attitude quaternion, q d4 is the scalar part of the desired attitude quaternion, and the desired angular velocity is ω d ;

姿态误差为当前姿态与期望姿态之间的差值；The attitude error is the difference between the current attitude and the expected attitude;

则姿态的误差四元数可表示为：Then the attitude error quaternion can be expressed as:

Figure BDA0003858958470000052
Figure BDA0003858958470000052

ωe＝ω-Cωd (5)ω e ＝ω-Cω d (5)

其中，

Figure BDA0003858958470000053
和ωe分别为姿态的误差四元数和角速度误差，qev为误差姿态四元数的矢量部分，qe4为误差姿态四元数的标称部分，
Figure BDA0003858958470000054
为qdv的坐标方阵，
Figure BDA0003858958470000055
qdv1、qdv2、qdv3分别表示期望姿态四元数的矢量部分qdv的第1，2，3个分量；C为从期望状态到本体状态的方向余弦矩阵；in,
Figure BDA0003858958470000053
and ω e are the error quaternion and angular velocity error of the attitude respectively, q ev is the vector part of the error attitude quaternion, q e4 is the nominal part of the error attitude quaternion,
Figure BDA0003858958470000054
is the coordinate matrix of q dv ,
Figure BDA0003858958470000055
q dv1 , q dv2 , and q dv3 respectively represent the first, second, and third components of the vector part q dv of the desired attitude quaternion; C is the direction cosine matrix from the desired state to the body state;

将(4)带入航天器的姿态运动学方程公式(1)、(2)中，可以得到：Putting (4) into the attitude kinematics equations (1) and (2) of the spacecraft, we can get:

Figure BDA0003858958470000056
Figure BDA0003858958470000056

其中，

Figure BDA0003858958470000057
为qev的一阶导数，Q为运动学矩阵；in,
Figure BDA0003858958470000057
is the first derivative of q ev , Q is the kinematics matrix;

将(4)和(5)带入航天器的姿态动力学方程公式(3)中，可以得到：Putting (4) and (5) into the attitude dynamics equation (3) of the spacecraft, we can get:

Figure BDA0003858958470000058
Figure BDA0003858958470000058

其中，f表示航天器的动力学项，Td表示航天器所受到的总干扰，

Figure BDA0003858958470000059
为ωe的一阶导数；Among them, f represents the dynamics term of the spacecraft, T d represents the total disturbance received by the spacecraft,
Figure BDA0003858958470000059
is the first derivative of ω e ;

经过上述处理后，航天器的姿态运动模型已完全由姿态误差四元数表示，整理如下：After the above processing, the attitude motion model of the spacecraft has been completely expressed by the attitude error quaternion, which is organized as follows:

Figure BDA0003858958470000061
Figure BDA0003858958470000061

其中，

Figure BDA0003858958470000062
为qev的一阶导数。in,
Figure BDA0003858958470000062
is the first derivative of q ev .

其它步骤及参数与具体实施方式一相同。Other steps and parameters are the same as those in Embodiment 1.

具体实施方式三：本实施方式与具体实施方式一或二不同的是，所述从期望状态到本体状态的方向余弦矩阵C计算方式如下：Specific embodiment three: the difference between this embodiment and specific embodiment one or two is that the calculation method of the direction cosine matrix C from the desired state to the body state is as follows:

Figure BDA0003858958470000063
Figure BDA0003858958470000063

其中，

Figure BDA0003858958470000064
为qev的转置，
Figure BDA0003858958470000065
为qev的坐标方阵，
Figure BDA0003858958470000066
qev1、qev2、qev3分别表示误差姿态四元数的矢量部分qev的第1，2，3个分量。in,
Figure BDA0003858958470000064
is the transpose of q ev ,
Figure BDA0003858958470000065
is the coordinate matrix of q ev ,
Figure BDA0003858958470000066
q ev1 , q ev2 , and q ev3 represent the 1st, 2nd, and 3rd components of the vector part q ev of the error attitude quaternion, respectively.

其它步骤及参数与具体实施方式一或二相同。Other steps and parameters are the same as those in Embodiment 1 or Embodiment 2.

具体实施方式四：本实施方式与具体实施方式一至三之一不同的是，所述运动学矩阵

Figure BDA0003858958470000067
Embodiment 4: The difference between this embodiment and one of Embodiments 1 to 3 is that the kinematics matrix
Figure BDA0003858958470000067

其它步骤及参数与具体实施方式一至三之一相同。Other steps and parameters are the same as those in Embodiments 1 to 3.

具体实施方式五：本实施方式与具体实施方式一至四之一不同的是，所述航天器的动力学项

Figure BDA0003858958470000068
Embodiment 5: The difference between this embodiment and one of Embodiments 1 to 4 is that the dynamic term of the spacecraft
Figure BDA0003858958470000068

其它步骤及参数与具体实施方式一至四之一相同。Other steps and parameters are the same as in one of the specific embodiments 1 to 4.

具体实施方式六：本实施方式与具体实施方式一至五之一不同的是，所述航天器所受到的总干扰Td包括了外界干扰力矩d和内部由于惯性矩阵的不确定部分ΔJ所带来的内干扰，满足关系式

Figure BDA0003858958470000069
Specific embodiment 6: The difference between this embodiment and one of specific embodiments 1 to 5 is that the total disturbance T d suffered by the spacecraft includes the external disturbance torque d and the internal disturbance due to the uncertain part ΔJ of the inertia matrix. The internal interference of satisfies the relation
Figure BDA0003858958470000069

其中，

Figure BDA00038589584700000610
为ωe的坐标方阵，
Figure BDA00038589584700000611
ωe1、ωe2、ωe3分别表示角速度误差ωe的第1，2，3个分量；
Figure BDA00038589584700000612
为ωd的一阶导数。in,
Figure BDA00038589584700000610
is the coordinate matrix of ω e ,
Figure BDA00038589584700000611
ω e1 , ω e2 , and ω e3 represent the first, second, and third components of the angular velocity error ω e , respectively;
Figure BDA00038589584700000612
is the first derivative of ω d .

其它步骤及参数与具体实施方式一至五之一相同。Other steps and parameters are the same as one of the specific embodiments 1 to 5.

具体实施方式七：本实施方式与具体实施方式一至六之一不同的是，所述步骤二中选取控制变量；具体过程为：Specific embodiment seven: this embodiment is different from one of the specific embodiments one to six in that the control variable is selected in the step two; the specific process is:

本控制器将采用反步法进行设计，同时为得到连续的控制变量，将采用改善比例函数对系统进行变换。The controller will be designed by using the backstepping method, and at the same time, in order to obtain continuous control variables, the system will be transformed by improving the proportional function.

按照反步法需要，定义控制变量z1、z2为：According to the needs of the backstepping method, the control variables z 1 and z 2 are defined as:

z1＝qev (10)z 1 =q ev (10)

z2＝ωe-z1ref (11)z 2 =ω e -z 1ref (11)

其中，z1ref为设计过程中出现的中间变量，在控制器设计过程中将作为ωe的跟踪目标存在；Among them, z 1ref is an intermediate variable that appears in the design process, and will exist as the tracking target of ω e in the controller design process;

Figure BDA0003858958470000071
Figure BDA0003858958470000071

设计的比例函数为The designed proportional function is

Figure BDA0003858958470000072
Figure BDA0003858958470000072

其中in

Figure BDA0003858958470000073
Figure BDA0003858958470000073

其中，m为一正数，TP为任务要求的预设时间，t为任务开始到当前时刻所经历时间长度，tf为姿态误差恰好进入预设精度范围的时间，ted为待人为设计的一时间点；μf为μ函数在自变量为tf时对应的取值，μed(待人为设计)为μ函数在自变量为ted时对应的取值；

Figure BDA0003858958470000074
为μ(tf)的一阶导数，
Figure BDA0003858958470000076
为μ(tf)的二阶导数，μ(tf)为μ函数在自变量为tf时对应的取值，Cqp为平滑过渡系数；Among them, m is a positive number, T P is the preset time required by the task, t is the length of time elapsed from the beginning of the task to the current moment, t f is the time when the attitude error just enters the preset accuracy range, and t ed is the time to be artificially designed A time point of ; μ f is the corresponding value of the μ function when the independent variable is t f , and μ ed (to be artificially designed) is the corresponding value of the μ function when the independent variable is t ed ;
Figure BDA0003858958470000074
is the first derivative of μ(t f ),
Figure BDA0003858958470000076
is the second derivative of μ(t f ), μ(t f ) is the corresponding value of μ function when the independent variable is t f , and C qp is the smooth transition coefficient;

该函数的设计思路为：将满足

Figure BDA0003858958470000075
的函数μ(t)在航天器的姿态误差达到预设精度的时刻阶段并与一条ted时刻后的水平直线通过一条五次曲线平滑相连，拼接形成的新曲线满足二阶导数连续。因此，该水平直线的起点坐标(ted,μed)需要人为设计，设计时需要确保ted≥tf,μed＞0且使得拼接后的曲线恒增且尽量平滑。因此建议直接在tf和μf的基础上乘以大于1的正数或加一正数得到ted和μed。The design idea of this function is: will satisfy
Figure BDA0003858958470000075
The function μ(t) of the spacecraft is smoothly connected with a horizontal straight line after the time t ed through a quintic curve at the moment when the attitude error of the spacecraft reaches the preset accuracy, and the new curve formed by splicing satisfies the continuity of the second derivative. Therefore, the starting point coordinates (t ed , μ ed ) of the horizontal straight line need to be designed artificially. During the design, it is necessary to ensure that t ed ≥t f , μ ed >0 and make the spliced curve constant increase and as smooth as possible. Therefore, it is recommended to directly multiply t f and μ f by a positive number greater than 1 or add a positive number to obtain t ed and μ ed .

综上所述，出于比例变换与反步法结合需要，定义新的控制变量w1、w2为：To sum up, in order to combine proportional transformation and backstepping method, the new control variables w 1 and w 2 are defined as:

w1＝μz1 (15)w 1 = μ z 1 (15)

w2＝μz2 (16)。w 2 =μ z 2 (16).

其它步骤及参数与具体实施方式一至六之一相同。Other steps and parameters are the same as one of the specific embodiments 1 to 6.

具体实施方式八：本实施方式与具体实施方式一至七之一不同的是，所述步骤三中基于步骤一和步骤二获得控制器输出的控制力矩；具体过程为：Embodiment 8: The difference between this embodiment and one of Embodiments 1 to 7 is that in Step 3, the control torque output by the controller is obtained based on Step 1 and Step 2; the specific process is:

控制器输出的控制力矩通过以下公式获取：The control torque output by the controller is obtained by the following formula:

Figure BDA0003858958470000081
Figure BDA0003858958470000081

其中in

Figure BDA0003858958470000082
Figure BDA0003858958470000082

Figure BDA0003858958470000083
Figure BDA0003858958470000083

其中，

Figure BDA0003858958470000084
为z1ref的一阶导数，
Figure BDA0003858958470000085
为μ的一阶导数，k为一正的常数，ψ1为鲁棒项，κ1为鲁棒项幅值，z2i为控制变量z2的第i个分量，ε2i为ε2的第i个分量；ε2是一认为设定的小量，κ1是一正数，二者取值视航天器所受到的总干扰情况与执行机构的性能而定。该控制力矩能够使得航天器实现预设时间预设精度的姿态跟踪控制，且控制力矩连续非奇异，下面将给出证明过程：in,
Figure BDA0003858958470000084
is the first derivative of z 1ref ,
Figure BDA0003858958470000085
is the first derivative of μ, k is a positive constant, ψ 1 is the robust term, κ 1 is the magnitude of the robust term, z 2i is the i-th component of the control variable z 2 , ε 2i is the i-th component of ε 2 i components; ε 2 is a presumed small amount, κ 1 is a positive number, and the values of the two depend on the total disturbance received by the spacecraft and the performance of the actuator. The control torque can enable the spacecraft to achieve attitude tracking control with preset time and preset precision, and the control torque is continuous and non-singular. The proof process will be given below:

其它步骤及参数与具体实施方式一至七之一相同。Other steps and parameters are the same as one of the specific embodiments 1 to 7.

证明过程：proving process:

在证明过程中需要用到SONG Y,WANG Y,HOLLOWAY J,et al.Time-varyingfeedback for regulation of normal-form nonlinear systems in prescribed finitetime[J].Automatica,2017,83:243-251提出的引理：The lemma proposed by SONG Y, WANG Y, HOLLOWAY J, et al. Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finitetime [J]. Automatica, 2017, 83: 243-251 is needed in the proof process :

引理1：若系统

Figure BDA0003858958470000091
满足f(0,t)＝0，存在李雅普诺夫函数
Figure BDA0003858958470000092
满足Lemma 1: If the system
Figure BDA0003858958470000091
Satisfying f(0,t)=0, there is a Lyapunov function
Figure BDA0003858958470000092
satisfy

Figure BDA0003858958470000093
Figure BDA0003858958470000093

其中，x为系统状态，f(x0,t)为系统方程，f为系统函数，x0为系统初始状态，t为时间，V为系统

Figure BDA0003858958470000094
的Lyapunov函数，
Figure BDA00038589584700000921
为由n个实数构成的列向量集合，
Figure BDA0003858958470000095
为V的一阶导数，
Figure BDA0003858958470000096
为正实数，μ(t)为t时对应的函数，k＞0，函数μ(t)满足
Figure BDA0003858958470000097
则系统
Figure BDA0003858958470000098
在状态为0的点预设时间稳定，预设时间为TP；
Figure BDA0003858958470000099
表示预设时间在极限运算
Figure BDA00038589584700000910
中由变量t从小于预设时间TP的一侧趋近；Among them, x is the system state, f(x 0 ,t) is the system equation, f is the system function, x 0 is the initial state of the system, t is the time, V is the system
Figure BDA0003858958470000094
The Lyapunov function,
Figure BDA00038589584700000921
is a column vector set composed of n real numbers,
Figure BDA0003858958470000095
is the first derivative of V,
Figure BDA0003858958470000096
is a positive real number, μ(t) is the corresponding function when t, k>0, the function μ(t) satisfies
Figure BDA0003858958470000097
system
Figure BDA0003858958470000098
At the point where the state is 0, the preset time is stable, and the preset time is T P ;
Figure BDA0003858958470000099
Indicates that the preset time is operating at the limit
Figure BDA00038589584700000910
In the middle, the variable t approaches from the side smaller than the preset time T P ;

设

Figure BDA00038589584700000911
分别求导可得Assume
Figure BDA00038589584700000911
can be derived separately

Figure BDA00038589584700000912
Figure BDA00038589584700000912

Figure BDA00038589584700000913
Figure BDA00038589584700000913

其中，V1、V2分别为姿态跟踪系统的运动学Lyapunov函数与动力学Lyapunov函数，

Figure BDA00038589584700000914
为w1的转置，
Figure BDA00038589584700000915
为w2的转置，
Figure BDA00038589584700000916
为w1的一阶导数，
Figure BDA00038589584700000917
为w2的一阶导数；Among them, V 1 and V 2 are the kinematics Lyapunov function and dynamics Lyapunov function of the attitude tracking system respectively,
Figure BDA00038589584700000914
is the transpose of w 1 ,
Figure BDA00038589584700000915
is the transpose of w 2 ,
Figure BDA00038589584700000916
is the first derivative of w 1 ,
Figure BDA00038589584700000917
is the first derivative of w 2 ;

控制力矩中设计对z1ref求导，对z1ref求导可得：In the control moment, the design takes the derivative of z 1ref , and the derivative of z 1ref can be obtained as follows:

Figure BDA00038589584700000918
Figure BDA00038589584700000918

其中，

Figure BDA00038589584700000919
为Q的一阶导数，
Figure BDA00038589584700000920
为μ的二阶导数；in,
Figure BDA00038589584700000919
is the first derivative of Q,
Figure BDA00038589584700000920
is the second derivative of μ;

航天器姿态跟踪控制系统的Lyapunov函数选取为

Figure BDA0003858958470000101
求导可得：The Lyapunov function of the spacecraft attitude tracking control system is selected as
Figure BDA0003858958470000101
Derivation can be obtained:

Figure BDA0003858958470000102
Figure BDA0003858958470000102

当ψ1项中的κ1满足κ1≥‖Td‖即可确保V在t≤tf时满足引理1，进而得出w1满足预设时间稳定，预设时间为TP。即当t＝TP时w1＝0，因此必有一时间点，满足变量w1恰好使得姿态误差进入预设误差范围，这证明了tf存在的必然性。When κ 1 in ψ 1 satisfies κ 1 ≥‖T d ‖, it can ensure that V satisfies Lemma 1 when t≤t f , and then w 1 is stable at the preset time, and the preset time is T P . That is, when t= TP , w 1 =0, so there must be a point in time, satisfying the variable w 1 just makes the attitude error enter the preset error range, which proves the inevitability of the existence of t f .

在t≥tf可以确保函数μ有正的下界，因此当ψ1项中的κ1满足κ1≥‖Td‖即可确保V在t≥tf时候w1指数收敛，即确保了在预设时间之后姿态误差也能保持在预设精度范围内。At t≥t f , it can be ensured that the function μ has a positive lower bound, so when κ 1 in the ψ 1 item satisfies κ 1 ≥‖T d ‖, it can ensure that V 1 is exponentially convergent when t≥t f , that is, it ensures that in After the preset time, the attitude error can also be kept within the preset accuracy range.

控制力矩中的各项均连续且有界，故控制力矩连续有界。All items in the control torque are continuous and bounded, so the control torque is continuous and bounded.

实施例Example

此处提供案例验证所提出算法的案例，所选择的航天器质量特性为：A case is provided here to validate the proposed algorithm, and the selected mass characteristics of the spacecraft are:

Figure BDA0003858958470000104
Figure BDA0003858958470000104

ΔJ＝10％J0 ΔJ = 10% J 0

航天器的初始姿态与角速度为q0＝[0.3；-0.3；-0.25；0.8703]，ω0＝03×1rad/sThe initial attitude and angular velocity of the spacecraft are q 0 =[0.3; -0.3; -0.25; 0.8703], ω 0 =0 3×1 rad/s

所受到的外界干扰为：The external interference received is:

Figure BDA0003858958470000103
Figure BDA0003858958470000103

ωt＝0.01 ωt = 0.01

ωt为常数； ωt is a constant;

任务需求为：The task requirements are:

1)初始期望姿态为qd0＝[0；0；0；1]，期望角速度为

Figure BDA0003858958470000111
1) The initial desired attitude is q d0 = [0; 0; 0; 1], and the desired angular velocity is
Figure BDA0003858958470000111

2)预设时间为TP＝200s，预设精度为εi＝1×10-3(i＝1,2,3)2) The preset time is T P =200s, and the preset precision is ε i =1×10 -3 (i=1,2,3)

控制器参数选取为：m＝3，k＝20，κ1＝0.04，ε2i＝1×10-4，ted＝tf+10，μed＝20μf。The controller parameters are selected as: m=3, k=20, κ 1 =0.04, ε 2i =1×10 -4 , t ed =t f +10, μ ed =20μ f .

控制效果如附图2-4中所示。The control effect is shown in Figure 2-4.

本发明还可有其它多种实施例，在不背离本发明精神及其实质的情况下，本领域技术人员当可根据本发明作出各种相应的改变和变形，但这些相应的改变和变形都应属于本发明所附的权利要求的保护范围。The present invention also can have other multiple embodiments, without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and deformations according to the present invention, but these corresponding changes and deformations Should belong to the scope of protection of the appended claims of the present invention.

Claims (8)

1.一种基于比例变换的连续力矩航天器姿态跟踪控制方法，其特征在于：所述方法具体过程为：1. a continuous moment spacecraft attitude tracking control method based on proportional transformation, is characterized in that: the specific process of the method is: 步骤一：构建航天器的姿态运动模型；Step 1: Construct the attitude motion model of the spacecraft; 航天器的姿态运动模型由航天器的姿态运动学方程和姿态动力学方程构成；The attitude motion model of the spacecraft is composed of the attitude kinematics equation and the attitude dynamic equation of the spacecraft; 将航天器的姿态运动模型表示为姿态误差四元数；Express the attitude motion model of the spacecraft as an attitude error quaternion; 步骤二：选取控制变量；Step 2: Select control variables; 步骤三：基于步骤一和步骤二获得控制器输出的控制力矩。Step 3: Obtain the control torque output by the controller based on Step 1 and Step 2. 2.根据权利要求1所述的一种基于比例变换的连续力矩航天器姿态跟踪控制方法，其特征在于：所述步骤一中构建航天器的姿态运动模型；2. a kind of continuous moment spacecraft attitude tracking control method based on scale transformation according to claim 1, is characterized in that: in the described step 1, construct the attitude motion model of spacecraft; 航天器的姿态运动模型由航天器的姿态运动学方程和姿态动力学方程构成；The attitude motion model of the spacecraft is composed of the attitude kinematics equation and the attitude dynamic equation of the spacecraft; 将航天器的姿态运动模型表示为姿态误差四元数；Express the attitude motion model of the spacecraft as an attitude error quaternion; 具体过程为：The specific process is: 以单位四元数作为姿态参数，姿态运动学方程为：Taking the unit quaternion as the attitude parameter, the attitude kinematics equation is:
Figure FDA0003858958460000011
Figure FDA0003858958460000011
Figure FDA0003858958460000012
Figure FDA0003858958460000012
 其中，
Figure FDA0003858958460000013
为航天器的姿态四元数，ω为航天器的角速度矢量，
Figure FDA0003858958460000014
为3×3单位矩阵；qv为四元数的矢量部分，q4为四元数的标量部分，
Figure FDA0003858958460000015
表示实数集合，
Figure FDA0003858958460000016
表示由4个实数构成的列向量集合，
Figure FDA0003858958460000017
表示3行3列的实数矩阵集合，
Figure FDA0003858958460000018
为qv的一阶导数，
Figure FDA0003858958460000019
为qv的坐标方阵，
Figure FDA00038589584600000113
qv1、qv2、qv3分别表示四元数的矢量部分qv的第1，2，3个分量；
Figure FDA00038589584600000110
表示了q是一个由实数构成的四维矢量；in,
Figure FDA0003858958460000013
is the attitude quaternion of the spacecraft, ω is the angular velocity vector of the spacecraft,
Figure FDA0003858958460000014
is a 3×3 identity matrix; q v is the vector part of the quaternion, and q 4 is the scalar part of the quaternion,
Figure FDA0003858958460000015
represents the set of real numbers,
Figure FDA0003858958460000016
Represents a set of column vectors consisting of 4 real numbers,
Figure FDA0003858958460000017
Represents a set of real matrixes with 3 rows and 3 columns,
Figure FDA0003858958460000018
is the first derivative of q v ,
Figure FDA0003858958460000019
is the coordinate matrix of q v ,
Figure FDA00038589584600000113
q v1 , q v2 , and q v3 represent the 1st, 2nd, and 3rd components of the vector part qv of the quaternion, respectively;
Figure FDA00038589584600000110
Indicates that q is a four-dimensional vector composed of real numbers; 姿态动力学方程为The attitude dynamic equation is
Figure FDA00038589584600000111
Figure FDA00038589584600000111
 其中，J为航天器的惯性矩阵，τ为控制力矩，d为外界干扰力矩，ω×为ω的坐标方阵，ω×＝[0,-ω3,ω2；ω3,0,-ω1；-ω2,ω3,0]，ω1、ω2、ω3分别表示ω的第1，2，3个分量，
Figure FDA00038589584600000112
为ω的一阶导数；Among them, J is the inertia matrix of the spacecraft, τ is the control torque, d is the external disturbance torque, ω × is the coordinate matrix of ω, ω × = [0,-ω 3 ,ω 2 ; ω 3 ,0,-ω 1 ; -ω 2 ,ω 3 ,0], ω 1 , ω 2 , ω 3 represent the 1st, 2nd, 3rd components of ω respectively,
Figure FDA00038589584600000112
is the first derivative of ω; 考虑到航天器的参数不确定性，J＝ΔJ+J0，其中ΔJ为惯性矩阵的不确定部分，J0为惯性矩阵的标称部分；Considering the parameter uncertainty of the spacecraft, J=ΔJ+J 0 , where ΔJ is the uncertain part of the inertia matrix, and J 0 is the nominal part of the inertia matrix; 假设期望姿态的四元数表示为
Figure FDA0003858958460000021
期望角速度为ωd；Suppose the quaternion representation of the desired pose is
Figure FDA0003858958460000021
The desired angular velocity is ω d ; 其中qdv为期望姿态四元数的矢量部分，qd4为期望姿态四元数的标量部分，期望角速度为ωd；Wherein q dv is the vector part of the desired attitude quaternion, q d4 is the scalar part of the desired attitude quaternion, and the desired angular velocity is ω d ; 姿态误差为当前姿态与期望姿态之间的差值；The attitude error is the difference between the current attitude and the expected attitude; 则姿态的误差四元数可表示为：Then the attitude error quaternion can be expressed as:
Figure FDA0003858958460000022
Figure FDA0003858958460000022
 ωe＝ω-Cωd (5)ω e ＝ω-Cω d (5) 其中，
Figure FDA0003858958460000023
和ωe分别为姿态的误差四元数和角速度误差，qev为误差姿态四元数的矢量部分，qe4为误差姿态四元数的标称部分，
Figure FDA0003858958460000024
为qdv的坐标方阵，
Figure FDA0003858958460000025
qdv1、qdv2、qdv3分别表示期望姿态四元数的矢量部分qdv的第1，2，3个分量；C为从期望状态到本体状态的方向余弦矩阵；in,
Figure FDA0003858958460000023
and ω e are the error quaternion and angular velocity error of the attitude respectively, q ev is the vector part of the error attitude quaternion, q e4 is the nominal part of the error attitude quaternion,
Figure FDA0003858958460000024
is the coordinate matrix of q dv ,
Figure FDA0003858958460000025
q dv1 , q dv2 , and q dv3 respectively represent the first, second, and third components of the vector part q dv of the desired attitude quaternion; C is the direction cosine matrix from the desired state to the body state; 将(4)带入航天器的姿态运动学方程公式(1)、(2)中，可以得到：Putting (4) into the attitude kinematics equations (1) and (2) of the spacecraft, we can get:
Figure FDA0003858958460000026
Figure FDA0003858958460000026
 其中，
Figure FDA0003858958460000027
为qev的一阶导数，Q为运动学矩阵；in,
Figure FDA0003858958460000027
is the first derivative of q ev , Q is the kinematics matrix; 将(4)和(5)带入航天器的姿态动力学方程公式(3)中，可以得到：Putting (4) and (5) into the attitude dynamics equation (3) of the spacecraft, we can get:
Figure FDA0003858958460000028
Figure FDA0003858958460000028
 其中，f表示航天器的动力学项，Td表示航天器所受到的总干扰，
Figure FDA0003858958460000029
为ωe的一阶导数；Among them, f represents the dynamics term of the spacecraft, T d represents the total disturbance received by the spacecraft,
Figure FDA0003858958460000029
is the first derivative of ω e ; 经过上述处理后，航天器的姿态运动模型已完全由姿态误差四元数表示，整理如下：After the above processing, the attitude motion model of the spacecraft has been completely expressed by the attitude error quaternion, which is organized as follows:
Figure FDA00038589584600000210
Figure FDA00038589584600000210
 其中，
Figure FDA00038589584600000211
为qev的一阶导数。in,
Figure FDA00038589584600000211
is the first derivative of q ev . 3.根据权利要求2所述的一种基于比例变换的连续力矩航天器姿态跟踪控制方法，其特征在于：所述从期望状态到本体状态的方向余弦矩阵C计算方式如下：3. a kind of continuous moment spacecraft attitude tracking control method based on scale transformation according to claim 2, is characterized in that: described direction cosine matrix C calculation method from desired state to body state is as follows:
Figure FDA0003858958460000031
Figure FDA0003858958460000031
 其中，
Figure FDA0003858958460000032
为qev的转置，
Figure FDA0003858958460000033
为qev的坐标方阵，
Figure FDA0003858958460000034
qev1、qev2、qev3分别表示误差姿态四元数的矢量部分qev的第1，2，3个分量。in,
Figure FDA0003858958460000032
is the transpose of q ev ,
Figure FDA0003858958460000033
is the coordinate matrix of q ev ,
Figure FDA0003858958460000034
q ev1 , q ev2 , and q ev3 represent the 1st, 2nd, and 3rd components of the vector part q ev of the error attitude quaternion, respectively. 4.根据权利要求3所述的一种基于比例变换的连续力矩航天器姿态跟踪控制方法，其特征在于：所述运动学矩阵
Figure FDA0003858958460000035
4. A kind of continuous moment spacecraft attitude tracking control method based on scale transformation according to claim 3, characterized in that: said kinematics matrix
Figure FDA0003858958460000035
 5.根据权利要求4所述的一种基于比例变换的连续力矩航天器姿态跟踪控制方法，其特征在于：所述航天器的动力学项
Figure FDA0003858958460000036
5. a kind of continuous moment spacecraft attitude tracking control method based on scale transformation according to claim 4, is characterized in that: the dynamic term of described spacecraft
Figure FDA0003858958460000036
 6.根据权利要求5所述的一种基于比例变换的连续力矩航天器姿态跟踪控制方法，其特征在于：所述航天器所受到的总干扰Td包括了外界干扰力矩d和内部由于惯性矩阵的不确定部分ΔJ所带来的内干扰，满足关系式
Figure FDA0003858958460000037
6. A kind of continuous moment spacecraft attitude tracking control method based on proportional transformation according to claim 5, characterized in that: the total disturbance T d suffered by the spacecraft includes external disturbance torque d and internal due to inertia matrix The internal disturbance brought by the uncertain part ΔJ satisfies the relation
Figure FDA0003858958460000037
 其中，
Figure FDA0003858958460000038
为ωe的坐标方阵，
Figure FDA0003858958460000039
ωe1、ωe2、ωe3分别表示角速度误差ωe的第1，2，3个分量；
Figure FDA00038589584600000310
为ωd的一阶导数。in,
Figure FDA0003858958460000038
is the coordinate matrix of ω e ,
Figure FDA0003858958460000039
ω e1 , ω e2 , and ω e3 represent the first, second, and third components of the angular velocity error ω e , respectively;
Figure FDA00038589584600000310
is the first derivative of ω d . 7.根据权利要求6所述的一种基于比例变换的连续力矩航天器姿态跟踪控制方法，其特征在于：所述步骤二中选取控制变量；具体过程为：7. a kind of continuous moment spacecraft attitude tracking control method based on proportional transformation according to claim 6, is characterized in that: select control variable in described step 2; Concrete process is: 定义控制变量z1、z2为：Define the control variables z 1 and z 2 as: z1＝qev (10)z 1 =q ev (10) z2＝ωe-z1ref (11)z 2 =ω e -z 1ref (11) 其中，z1ref为中间变量；Among them, z 1ref is an intermediate variable;
Figure FDA00038589584600000311
Figure FDA00038589584600000311
 设计的比例函数为The designed proportional function is
Figure FDA0003858958460000041
Figure FDA0003858958460000041
 其中in
Figure FDA0003858958460000042
Figure FDA0003858958460000042
 其中，m为一正数，TP为任务要求的预设时间，t为任务开始到当前时刻所经历时间长度，tf为姿态误差恰好进入预设精度范围的时间，ted为时间点；μf为μ函数在自变量为tf时对应的取值，μed为μ函数在自变量为ted时对应的取值；
Figure FDA0003858958460000043
为μ(tf)的一阶导数，
Figure FDA0003858958460000044
为μ(tf)的二阶导数，μ(tf)为μ函数在自变量为tf时对应的取值，Cqp为平滑过渡系数；Among them, m is a positive number, T P is the preset time required by the task, t is the time elapsed from the beginning of the task to the current moment, t f is the time when the attitude error just enters the preset accuracy range, and t ed is the time point; μ f is the corresponding value of μ function when the independent variable is t f , μ ed is the corresponding value of μ function when the independent variable is t ed ;
Figure FDA0003858958460000043
is the first derivative of μ(t f ),
Figure FDA0003858958460000044
is the second derivative of μ(t f ), μ(t f ) is the corresponding value of μ function when the independent variable is t f , and C qp is the smooth transition coefficient; 定义新的控制变量w1、w2为：Define new control variables w 1 and w 2 as: w1＝μz1 (15)w 1 = μ z 1 (15) w2＝μz2 (16)。w 2 =μ z 2 (16). 8.根据权利要求7所述的一种基于比例变换的连续力矩航天器姿态跟踪控制方法，其特征在于：所述步骤三中基于步骤一和步骤二获得控制器输出的控制力矩；具体过程为：8. a kind of continuous moment spacecraft attitude tracking control method based on proportional transformation according to claim 7, is characterized in that: in described step 3, obtain the control moment of controller output based on step 1 and step 2; Concrete process is : 控制器输出的控制力矩通过以下公式获取：The control torque output by the controller is obtained by the following formula:
Figure FDA0003858958460000045
Figure FDA0003858958460000045
 其中in
Figure FDA0003858958460000046
Figure FDA0003858958460000046
Figure FDA0003858958460000051
Figure FDA0003858958460000051
 其中，
Figure FDA0003858958460000052
为z1ref的一阶导数，
Figure FDA0003858958460000053
为μ的一阶导数，k为一正的常数，ψ1为鲁棒项，κ1为鲁棒项幅值，z2i为控制变量z2的第i个分量，ε2i为ε2的第i个分量；ε2是设定的小量，κ1是一正数。in,
Figure FDA0003858958460000052
is the first derivative of z 1ref ,
Figure FDA0003858958460000053
is the first derivative of μ, k is a positive constant, ψ 1 is the robust term, κ 1 is the magnitude of the robust term, z 2i is the i-th component of the control variable z 2 , ε 2i is the i-th component of ε 2 i components; ε 2 is a set small amount, κ 1 is a positive number.
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