技术领域technical field
本发明涉及基于干扰观测器的挠性卫星轨迹线性化姿态控制方法。The invention relates to a method for controlling the linearized attitude of a flexible satellite trajectory based on an interference observer.
背景技术Background technique
随着时代的发展和社会的进步，人类对外太空的探索已经上升到一个新的高度。中国已经跨入了空间大国的行列。航天技术对于国民经济、国防建设、文化教育和科学研究起到至关重要的作用，是国家综合实力的集中体现。With the development of the times and the progress of society, human exploration of outer space has risen to a new height. China has entered the ranks of space powers. Aerospace technology plays a vital role in the national economy, national defense construction, cultural education and scientific research, and is a concentrated expression of the country's comprehensive strength.
航天技术是将航天学的理论应用于航天器和运载器的研究、设计、制造、试验、发射、飞行、返回、控制、管理等工航天工程实践而形成的一门综合性工程技术。卫星系统包括七部分：位置与姿态控制系统、天线系统、转发器系统、遥测指令系统、电源系统、温控系统以及入轨和推进系统。其中姿态控制系统决定了卫星的跟踪性能，是卫星顺利完成太空任务的重要保障。Aerospace technology is a comprehensive engineering technology formed by applying the theory of astronautics to the research, design, manufacture, test, launch, flight, return, control, management and other engineering practices of spacecraft and vehicles. The satellite system includes seven parts: position and attitude control system, antenna system, transponder system, telemetry command system, power supply system, temperature control system, orbit entry and propulsion system. Among them, the attitude control system determines the tracking performance of the satellite and is an important guarantee for the satellite to successfully complete the space mission.
由于太空探索的领域不断拓宽，探索任务难度不断加大，航天器的结构也呈现复杂化的趋势，不可避免地受到各种干扰力矩以及参数不确定性的影响。外部及自身的干扰很大程度上影响了航天器的工作性能，加大了姿态控制的难度。并且干扰的数学模型不易清晰描述。因此挠性航天器的干扰抑制问题是航天领域的研究热点，直接决定了卫星的控制精度。Due to the continuous expansion of the field of space exploration and the increasing difficulty of exploration tasks, the structure of spacecraft is also showing a trend of complexity, which is inevitably affected by various disturbance torques and parameter uncertainties. External and self-interference greatly affect the performance of the spacecraft and increase the difficulty of attitude control. And the mathematical model of interference is not easy to describe clearly. Therefore, the interference suppression of flexible spacecraft is a research hotspot in the field of aerospace, which directly determines the control accuracy of satellites.
针对航天器的干扰抑制问题，国内外学者进行了深入研究，提出了很多控制算法，现将部分控制算法介绍如下：Aiming at the problem of spacecraft interference suppression, domestic and foreign scholars have conducted in-depth research and proposed many control algorithms. Some of the control algorithms are introduced as follows:
HuaLiu等人[1](LiuH,GuoL,ZhangY.Ananti-disturbancePDcontrolschemeforattitudecontrolandstabilizationofflexiblespacecrafts[J].NonlinearDynamics,2012,67(3):2081-2088)针对挠性航天器的干扰问题设计了干扰观测器和PD控制器，抑制了两种不同的干扰，提高了航天器的控制精度和姿态稳定性。虽然基于PID的控制算法对于线性系统的控制性能良好，但是对于复杂非线性系统和复杂信号追踪具有很大的局限性，在对干扰的抑制方面鲁棒性不强，必须结合其他算法才能达到控制要求。HuaLiu et al. [1] (LiuH, GuoL, ZhangY.Ananti-disturbancePDcontrolschemeforattitudecontrolandstabilizationoffflexiblespacecrafts[J].NonlinearDynamics,2012,67(3):2081-2088) designed a disturbance observer and PD controller for the disturbance problem of flexible spacecraft , which suppresses two different disturbances and improves the control accuracy and attitude stability of the spacecraft. Although the PID-based control algorithm has good control performance for linear systems, it has great limitations for complex nonlinear systems and complex signal tracking, and is not robust to interference suppression. It must be combined with other algorithms to achieve control. Require.
钱勇等人[2](钱勇,满顺强.基于变结构控制减小扫描镜运动对卫星姿态的影响分析[J].上海航天,2013,29(6):7-10)利用解耦变结构控制器对静止轨道卫星进行控制，考虑了星上载荷的扫描镜和卫星本体间的耦合，对四元数四个分量分别设计滑动模态，避免了奇异问题态的影响。由仿真结果可看出，采用变结构控制可以提高姿态角的跟踪精度和稳定性，很大程度减小了扫描镜运动对卫星产生的干扰。但是由于变结构控制相当于起到开关作用，控制不连续，很容易导致抖振，而抖振易激发系统的未建模特性，从而影响了系统的控制性能。Qian Yong et al. [2] (Qian Yong, Man Shunqiang. Analysis of the influence of scanning mirror motion on satellite attitude based on variable structure control[J]. Shanghai Aerospace, 2013, 29(6): 7-10) using the solution The coupling variable structure controller controls the geostationary orbit satellite, considering the coupling between the scanning mirror loaded on the satellite and the satellite body, and designing sliding modes for the four components of the quaternion to avoid the influence of singular problem states. It can be seen from the simulation results that the use of variable structure control can improve the tracking accuracy and stability of the attitude angle, and greatly reduce the interference of the scanning mirror movement on the satellite. However, since the variable structure control is equivalent to a switch, the control is discontinuous, which easily leads to chattering, and chattering is easy to excite the unmodeled characteristics of the system, thus affecting the control performance of the system.
朱亮等人[3](ShaoX,WangH.ANovelMethodofRobustTrajectoryLinearizationControlBasedonDisturbanceRejection[J].MathematicalProblemsinEngineering,2014,2014)利用轨迹线性化控制(TLC)方法和神经网络技术设计了直接自适应TLC控制方案，通过仿真可以看出，通过神经网络的作用提高了系统的性能，弥补了之前TLC的不足。但是很多基于轨迹线性化的控制算法未考虑外界干扰及自身参数不确定性影响，导致系统的鲁棒性较差。Zhu Liang et al. [3] (ShaoX, WangH. ANovelMethod of RobustTrajectoryLinearizationControlBasedonDisturbanceRejection[J]. MathematicalProblemsinEngineering, 2014, 2014) designed a direct adaptive TLC control scheme using the Trajectory Linearization Control (TLC) method and neural network technology. It can be seen from the simulation that , the performance of the system is improved through the function of the neural network, and the deficiency of the previous TLC is made up. However, many control algorithms based on trajectory linearization do not consider the external disturbance and the influence of their own parameter uncertainty, resulting in poor robustness of the system.
ZhengZhu等人[4](周军.航天器控制原理.西北工业大学出版社,2001)设计了扩张状态观测器来实现对刚体航天器干扰的观测。由于星体存在燃料消耗，质量时变，星体的转动惯量无法确定，同时，外部干扰不可忽略。ZhengZhu等人设计滑模控制器保证了参考姿态状态的收敛性。从仿真结果可以看出，此控制方法具有良好的控制性能，姿态跟踪精度较高。但是，该文献是针对刚体卫星进行设计，未考虑挠性部件的影响。ZhengZhu et al. [4] (Zhou Jun. Spacecraft Control Principles. Northwestern Polytechnical University Press, 2001) designed an extended state observer to realize the observation of the interference of rigid-body spacecraft. Due to the fuel consumption of the star and the time-varying mass, the moment of inertia of the star cannot be determined, and at the same time, the external disturbance cannot be ignored. ZhengZhu et al. designed a sliding mode controller to ensure the convergence of the reference attitude state. It can be seen from the simulation results that this control method has good control performance and high attitude tracking accuracy. However, this document is designed for rigid satellites, without considering the influence of flexible components.
方案一：Option One:
文献[6](ZhuZ,XiaY,FuM,etal.Attitudetrackingofrigidspacecraftbasedonextendedstateobserver[C].SystemsandControlinAeronauticsandAstronautics(ISSCAA),20103rdInternationalSymposiumon.IEEE,2010:621-626)提出了一种基于扩张状态观测器的卫星姿态控制方法。首先用四元数建立卫星动力学方程，基于该模型设计滑模控制算法。针对转动惯量不确定性和外部干扰设计状态观测器，将干扰的估计值带入之前设计的控制律中，实现了对卫星的跟踪控制。方案具体内容如下：Literature [6] (ZhuZ, XiaY, FuM, et al. Attitude tracking of rigid spacecraft based on extended state observer [C]. Systems and Control in Aeronautics and Astronautics (ISSCAA), 2010 3rd International Symposium on. IEEE, 2010: 621-626) proposed a satellite attitude control method based on an extended state observer. Firstly, the satellite dynamic equation is established with quaternion, and the sliding mode control algorithm is designed based on the model. A state observer is designed for the uncertainty of the moment of inertia and external disturbance, and the estimated value of the disturbance is brought into the previously designed control law to realize the tracking control of the satellite. The details of the program are as follows:
(1)卫星动力学模型：(1) Satellite dynamic model:
用四元数表示卫星动力学模型，减少了奇异点的影响。引入误差四元数，将控制目标转换为在有限时间内误差四元数收敛到0。定义The satellite dynamics model is represented by quaternions, which reduces the influence of singular points. The error quaternion is introduced, and the control target is converted to the error quaternion converging to 0 within a finite time. definition
x＝ω+Kev(71)x=ω+Kev (71)
其中ev代表误差四元数向量部分。通过式(71)，将控制目标变为在有限时间内使变量x收敛到0。考虑到卫星转动惯量的不确定性，将转动惯量J表示为J＝J0+△J，其中J0表示常量部分，△J表示不确定部分。采用等效误差的思想，将外部误差和转动惯量不确定部分合并，用表示。则卫星动力学模型可以简化为where ev represents the error quaternion vector part. Through formula (71), the control target is changed to make the variable x converge to 0 within a limited time. Considering the uncertainty of the satellite's moment of inertia, the moment of inertia J is expressed as J=J0 +△J, where J0 represents the constant part and △J represents the uncertain part. Using the idea of equivalent error, the external error and the uncertain part of the moment of inertia are combined, and the express. Then the satellite dynamic model can be simplified as
(2)设计滑模控制律(2) Design sliding mode control law
选择滑模面S＝C2x，其中，S＝[S1,S2,S3]T∈R3,C2∈R3×3。选择趋近律Choose a sliding surface S=C2 x , where S=[S1 , S2 , S3 ]T ∈ R3 , C2 ∈ R3×3 . selection reaching law
保证了滑模到达条件。由于The sliding mode arrival condition is guaranteed. because
求得控制律control law
(3)设计观测器(3) Design observer
由于等效干扰是未知的，所以需要观测器对其进行估计。引入新的变量x2代表系统总的干扰则式(37)可以写成如下形式：due to equivalent interference is unknown, so the observer needs to estimate it. Introduce a new variable x2 to represent the total disturbance of the system Equation (37) can be written as follows:
其中g(t)代表总干扰的微分，仍然是未知的。二阶扩张状态观测器设计如下：where g(t) represents the total interference The differential of , is still unknown. The second-order extended state observer is designed as follows:
式中E1代表观测器的估计误差，Z1和Z2是观测器的输出向量，β01和β02是观测器的增益，函数fal(·)定义如下where E1 represents the estimation error of the observer, Z1 and Z2 are the output vectors of the observer, β01 and β02 are the gains of the observer, and the function fal( ) is defined as follows
其中in
式中0<α1<1,δ>0。In the formula, 0<α1 <1, δ>0.
选取合适的参数，可以保证状态观测器的输出Z1等于状态x，输出Z2等于Selecting appropriate parameters can ensure that the output Z1 of the state observer is equal to the state x, and the output Z2 is equal to
因此，将控制律式(75)进一步完善得到Therefore, the control law formula (75) is further improved to get
uESO(t)＝(C2B0)-1(-τS-σsgn(S)-C2F-C2Z2)(80)uESO (t)＝(C2 B0 )-1 (-τS-σsgn(S)-C2 FC2 Z2 )(80)
系统在此控制律作用下有较强的抗干扰能力和鲁棒性，可以很好的实现姿态跟踪。Under the action of this control law, the system has strong anti-interference ability and robustness, and can realize attitude tracking very well.
方案的缺点描述如下：The disadvantages of the scheme are described as follows:
根据系统的动力学模型可知，系统未考虑卫星帆板的挠性振动的影响，没有模态方程，把卫星作为刚体进行控制律设计。但是实际卫星挠性部件对系统影响很大，破坏系统的动态性能，甚至导致系统不稳定。According to the dynamic model of the system, it can be known that the system does not consider the influence of the flexible vibration of the satellite sailboard, and there is no modal equation, and the satellite is regarded as a rigid body for control law design. However, the flexible components of the actual satellite have a great influence on the system, destroying the dynamic performance of the system, and even causing the system to be unstable.
方案二：Option II:
文献[7](ZhiW,Bao-huaL.Compoundcontrolsystemdesignbasedonbacksteppingtechniquesandneuralnetworkslidingmodeforflexiblesatellite[C].ComputerDesignandApplications(ICCDA),2010InternationalConferenceon.IEEE,2010,2:V2-418-V2-422)针对有挠性部件的航天器设计变结构控制律，利用三级滑模控制，有效抑制了外部干扰，使航天器跟踪误差为0。同时，利用神经网络对不确定性因素进行估计，很好地减弱了由于不连续控制产生的抖动。方案具体内容如下：Literature [7] (ZhiW, Bao-huaL. Compound control system design based on backstepping techniques and neural network sliding mode for flexible satellite [C]. Computer Design and Applications (ICCDA), 2010 International Conference on. IEEE, 2010, 2: V2-418-V2-422) Design variable structure control law for spacecraft with flexible components , using three-stage sliding mode control, the external disturbance is effectively suppressed, and the tracking error of the spacecraft is zero. At the same time, the uncertain factors are estimated by using the neural network, and the jitter caused by the discontinuous control is well weakened. The details of the program are as follows:
(1)卫星运动学和动力学建模(1) Satellite kinematics and dynamics modeling
考虑卫星天线、太阳帆板等挠性附件，采用三正交飞轮作为执行元件，分别对卫星整体、天线、太阳帆板动力学建模，同时考虑太阳帆板和天线的振动模态。为便于控制器设计，将挠性附件的振动视为作用在卫星上的外部干扰，简化卫星动力学模型。Considering flexible accessories such as satellite antennas and solar panels, three orthogonal flywheels are used as actuators to model the dynamics of the satellite as a whole, antennas, and solar panels, and the vibration modes of the solar panels and antennas are also considered. For the convenience of controller design, the vibration of the flexible attachment is regarded as the external disturbance acting on the satellite, and the dynamic model of the satellite is simplified.
(2)滑模控制律设计(2) Design of sliding mode control law
基于反步控制技术，采用三层滑模控制，反推出控制输入变量。Based on the backstepping control technology, three-layer sliding mode control is adopted, and the control input variables are deduced backwards.
首先设计第一层滑模面，目标是快速准确地跟踪目标四元数，定义角速度虚拟控制并给出其具体形式，构造第一层的V函数；然后设计第二层滑模面，目标是快速准确跟踪定义力矩虚拟控制选择合适的指数趋近律，推导出的具体形式，构造第二层的V函数；最后设计第三层滑模面，利用伺服系统的动力学模型来获得更高的控制精度。其跟踪指令为控制输入为飞轮角速度ωc，选择合适的指数趋近律，确定出ωc的具体表达式。First design the first layer of sliding surface, the goal is to quickly and accurately track the target quaternion, define the virtual control of angular velocity And give its specific form, construct the V function of the first layer; then design the second layer of sliding surface, the goal is to quickly and accurately track Define moment virtual control Choosing an appropriate exponential reaching law, deriving Construct the V function of the second layer; finally design the third layer of sliding surface, and use the dynamic model of the servo system to obtain higher control accuracy. Its trace command is The control input is flywheel angular velocity ωc , and the specific expression of ωc is determined by selecting an appropriate exponential reaching law.
通过分析可得，控制输入ωc可以保证系统跟踪误差为0。It can be obtained through analysis that the control input ωc can ensure that the tracking error of the system is 0.
(3)控制律的完善(3) Perfection of the control law
为了防止“微分爆炸”现象的发生，采用低通滤波器分别对和进行滤波。同时，为了抑制由于参数不确定性引起的系统振动，采用RBF神经网络对不确定参数进行估计。In order to prevent the phenomenon of "differential explosion", a low-pass filter is used to separate the and to filter. At the same time, in order to suppress the system vibration caused by parameter uncertainty, RBF neural network is used to estimate the uncertain parameters.
通过仿真结果可以看出，系统在较短时间内实现姿态的跟踪，在外界干扰和参数扰动条件下跟踪精度依然很高。但是系统的控制器过于复杂，控制算法的实现只能在计算速度足够快的计算机上完成，很难在工程上应用。除此之外，此方案未考虑航天器转动惯量的不确定性，忽略了其对于控制精度的影响。It can be seen from the simulation results that the system realizes attitude tracking in a relatively short period of time, and the tracking accuracy is still high under the conditions of external disturbance and parameter disturbance. However, the controller of the system is too complex, and the realization of the control algorithm can only be completed on a computer with a fast enough calculation speed, which is difficult to apply in engineering. In addition, this scheme does not consider the uncertainty of the spacecraft's moment of inertia, ignoring its influence on the control accuracy.
发明内容Contents of the invention
本发明是为了解决目前挠性航天器的干扰抑制问题的研究中，单一的轨迹线性化控制方法对干扰的抑制能力不强、鲁棒性较差，未考虑到外部干扰以及挠性附件影响的问题，而提出的基于干扰观测器的挠性卫星轨迹线性化姿态控制方法。The present invention is to solve the current research on interference suppression of flexible spacecraft. The single trajectory linearization control method has weak interference suppression ability and poor robustness, and does not take into account the influence of external interference and flexible accessories. problem, and a disturbance observer-based attitude control method for flexible satellite trajectory linearization is proposed.
一种基于干扰观测器的挠性卫星轨迹线性化姿态控制方法按以下步骤实现：A method for attitude control of flexible satellite trajectory linearization based on disturbance observer is realized in the following steps:
步骤一：挠性航天器动力学建模，得到模型为Step 1: Dynamic modeling of flexible spacecraft, the obtained model is
其中ω＝[ωxωyωz]T∈R3为航天器本体角速度，ωx、ωy、ωz分别为航天器本体系相对于惯性系角速度在本体坐标系滚动轴、俯仰轴和偏航轴方向投影；ω×为
步骤二：利用步骤一得到的模型，进行航天器名义控制设计；Step 2: Use the model obtained in Step 1 to carry out nominal control design of the spacecraft;
当被控对象的逆不可求时，通过求状态变量的伪逆，得到跟踪系统的名义控制；When the inverse of the controlled object cannot be obtained, the nominal control of the tracking system is obtained by obtaining the pseudo-inverse of the state variable;
对将等效干扰忽略，求得系统运动学和动力学模型相对于名义状态变量和的逆，得到equivalent interference Neglecting, the kinematic and dynamic models of the system are obtained with respect to the nominal state variables and the inverse of
其中所述为航天器本体坐标系相对于轨道坐标系的旋转角速度名义值，为滚动轴方向、俯仰轴方向和偏航轴方向名义控制力矩，Jxx、Jyy、Jzz为航天器沿滚动轴、俯仰轴和偏航轴的转动惯量；which stated is the nominal value of the rotational angular velocity of the spacecraft body coordinate system relative to the orbital coordinate system, Jxx , Jyy , Jzz are the moment of inertia of the spacecraft along the roll axis, pitch axis and yaw axis;
公式(15)和式(16)可以精确表示出控制变量的逆；Formula (15) and formula (16) can accurately express the inverse of the control variable;
步骤三：利用步骤二求得系统运动学和动力学模型相对于名义状态变量和的逆，设计跟踪误差的线性时变调节器，求得状态反馈控制律u1和u2；Step 3: Use Step 2 to obtain the system kinematics and dynamics model relative to the nominal state variable and Inverse of , design a linear time-varying regulator of tracking error, and obtain state feedback control laws u1 and u2 ;
步骤四：根据步骤三得到的状态反馈控制律u2，设计非线性干扰观测器，将观测器的输出作为系统控制律的一部分；得到整个系统的控制律Step 4: According to the state feedback control law u2 obtained in Step 3, design a nonlinear disturbance observer, and the output of the observer As part of the control law of the system; get the control law of the whole system
发明效果：Invention effect:
本发明设计了针对挠性航天器的干扰抑制和姿态跟踪的控制算法。用欧拉角描述航天器姿态，采用等效干扰的思想，建立挠性航天器动力学和运动学方程；忽略等效干扰的情况下求被控对象的伪逆，设计特定形式的准微分器，得到期望轨迹的名义控制；用比例—积分控制设计线性时变调节器。考虑等效干扰的影响，设计干扰观测器，保证挠性航天器的跟踪误差渐近收敛。The invention designs a control algorithm for interference suppression and attitude tracking of a flexible spacecraft. Use Euler angles to describe the attitude of the spacecraft, adopt the idea of equivalent disturbance, establish the dynamics and kinematics equations of flexible spacecraft; ignore the equivalent disturbance, find the pseudo inverse of the controlled object, and design a specific form of quasi-differentiator , get the nominal control of the desired trajectory; design a linear time-varying regulator with proportional-integral control. Considering the effect of equivalent disturbance, the disturbance observer is designed to ensure the asymptotic convergence of the tracking error of the flexible spacecraft.
与现有技术方案相比，本发明专利具有以下优点：Compared with the prior art solutions, the patent of the present invention has the following advantages:
1、控制算法易于实现，有较强的工程实用性；1. The control algorithm is easy to implement and has strong engineering practicability;
2、考虑了转动惯量的不确定性和挠性附件带来的影响，利用非线性干扰观测器抑制了系统干扰；2. Taking into account the uncertainty of the moment of inertia and the influence of flexible accessories, the system disturbance is suppressed by using a nonlinear disturbance observer;
3、利用轨迹线性化方法，其特有的伪逆不影响闭环系统的稳定性，适用于非最小相位系统；3. Using the trajectory linearization method, its unique pseudo-inverse does not affect the stability of the closed-loop system, and is suitable for non-minimum phase systems;
4、利用PD谱特征原理设计的线性时变调节器提高了系统的抗干扰能力，增强了系统的鲁棒性；4. The linear time-varying regulator designed using the principle of PD spectrum characteristics improves the anti-interference ability of the system and enhances the robustness of the system;
5、采用非线性干扰观测器与轨迹线性化相结合的方法，缩短了系统到达期望姿态的时间，同时也提高了跟踪精度；5. Using the method of combining nonlinear disturbance observer and trajectory linearization, the time for the system to reach the desired attitude is shortened, and the tracking accuracy is also improved;
6、控制力矩的稳态幅值和挠性帆板模态振动幅值相对较小。6. The steady-state amplitude of the control moment and the modal vibration amplitude of the flexible sailboard are relatively small.
附图说明Description of drawings
图1为轨迹线性化控制示意图，图中和y分别代表系统输出的期望值和实际值，η代表线性时变反馈控制律，和u代表系统名义控制和总的控制律。Figure 1 is a schematic diagram of trajectory linearization control, in which and y represent the expected value and actual value of the system output respectively, η represents the linear time-varying feedback control law, and u represent the system nominal control and the overall control law.
图2为基于非线性干扰观测器的TLC控制框图，图中r代表系统期望输出，y代表系统实际输出；e代表系统期望输出和实际输出的误差；u代表线性时变反馈控制律；代表系统名义控制；代表观测器对干扰的估计值；d代表系统总干扰。Figure 2 is a TLC control block diagram based on a nonlinear disturbance observer. In the figure, r represents the expected output of the system, and y represents the actual output of the system; e represents the error between the expected output and the actual output of the system; u represents the linear time-varying feedback control law; Represents system nominal control; Represents the estimated value of the interference by the observer; d represents the total interference of the system.
图3为航天器在0～400s内期望和实际欧拉角曲线图；其中上图、中图和下图分别代表航天器滚转角、俯仰角和偏航角在0～400s内期望值和实际值变化曲线图；图中代表航天器本体坐标系相对于轨道坐标系的欧拉角；代表航天器滚转角、俯仰角和偏航角的期望值。Figure 3 is the expected and actual Euler angle curves of the spacecraft within 0-400s; the upper, middle and lower figures respectively represent the expected and actual values of the spacecraft roll angle, pitch angle and yaw angle within 0-400s change curve; chart Represents the Euler angle of the spacecraft body coordinate system relative to the orbital coordinate system; Represents the expected values of the spacecraft's roll, pitch, and yaw angles.
图4为航天器在0～10s内期望和实际欧拉角曲线图；其中上图、中图和下图分别代表航天器滚转角、俯仰角和偏航角在0～10s内期望值和实际值变化曲线；图中代表航天器本体坐标系相对于轨道坐标系的欧拉角；代表航天器滚转角、俯仰角和偏航角的期望值。Figure 4 is the expected and actual Euler angle curves of the spacecraft within 0-10s; the upper, middle and lower figures respectively represent the expected and actual values of the spacecraft roll angle, pitch angle and yaw angle within 0-10s change curve; Represents the Euler angle of the spacecraft body coordinate system relative to the orbital coordinate system; Represents the expected values of the spacecraft's roll, pitch, and yaw angles.
图5为航天器0～400s内期望和实际角速度曲线图；其中上图、中图和下图分别代表航天器滚转角速度、俯仰角速度和偏航角速度在0～400s内期望值和实际值变化曲线；图中ω1,ω2,ω3代表航天器滚转角速度、俯仰角速度和偏航角速度的实际值；ωd1,ωd2,ωd3代表航天器滚转角速度、俯仰角速度和偏航角速度的期望值。Figure 5 is the expected and actual angular velocity curves of the spacecraft within 0-400s; the upper, middle and lower figures respectively represent the expected and actual value change curves of the spacecraft's roll angular velocity, pitch angular velocity and yaw angular velocity within 0-400s ; in the figure, ω1 , ω2 , ω3 represent the actual values of the spacecraft’s roll angular velocity, pitch angular velocity and yaw angular velocity; ωd1 , ωd2 , ωd3 represent the spacecraft’s roll angular velocity, pitch angular velocity and yaw angular velocity expectations.
图6为航天器0～10s内期望和实际角速度曲线图；其中上图、中图和下图分别代表航天器滚转角速度、俯仰角速度和偏航角速度在0～10s内期望值和实际值变化曲线；图中ω1,ω2,ω3代表航天器滚转角速度、俯仰角速度和偏航角速度的实际值；ωd1,ωd2,ωd3代表航天器滚转角速度、俯仰角速度和偏航角速度的期望值。Figure 6 is the expected and actual angular velocity curves of the spacecraft within 0-10s; the upper, middle and lower figures respectively represent the expected and actual value change curves of the spacecraft's roll angular velocity, pitch angular velocity and yaw angular velocity within 0-10s ; in the figure, ω1 , ω2 , ω3 represent the actual values of the spacecraft’s roll angular velocity, pitch angular velocity and yaw angular velocity; ωd1 , ωd2 , ωd3 represent the spacecraft’s roll angular velocity, pitch angular velocity and yaw angular velocity expectations.
图7为航天器欧拉角误差曲线图；图中分别代表航天器滚转角、俯仰角和偏航角的误差。Fig. 7 is the Euler angle error curve diagram of the spacecraft; Represent the errors of the spacecraft roll angle, pitch angle and yaw angle, respectively.
图8为航天器角速度误差曲线图；图中ωe1,ωe2,ωe3分别代表航天器滚转角速度、俯仰角速度和偏航角速度的误差。Fig. 8 is a graph of spacecraft angular velocity error; in the figure, ωe1 , ωe2 , and ωe3 respectively represent the errors of spacecraft roll angular velocity, pitch angular velocity and yaw angular velocity.
图9为控制力矩曲线图；图中Tc1,Tc2,Tc3分别代表航天器滚动轴、俯仰轴和偏航轴的控制力矩。Fig. 9 is a control torque curve; in the figure Tc1 , Tc2 , Tc3 respectively represent the control torque of the spacecraft roll axis, pitch axis and yaw axis.
图10为航天器帆板模态振动曲线图；图中η1,η2,η3,η4代表四个模态坐标。Fig. 10 is the modal vibration curve of the spacecraft sail; in the figure η1 , η2 , η3 , η4 represent four modal coordinates.
图11为系统实际和估计干扰曲线图；其中上图、中图和下图分别代表滚动轴、俯仰轴和偏航轴上的实际干扰和估计干扰；图中d1,d2,d3分别代表航天器滚动轴、俯仰轴和偏航轴上的实际干扰；d1',d2',d3'分别代表航天器滚动轴、俯仰轴和偏航轴上的估计干扰。Figure 11 is the actual and estimated interference curves of the system; the upper, middle and lower figures represent the actual and estimated interference on the roll axis, pitch axis and yaw axis respectively; d1 , d2 , and d3 in the figure are respectively Represents the actual disturbance on the roll axis, pitch axis and yaw axis of the spacecraft; d1 ', d2 ', d3 ' represent the estimated disturbance on the roll axis, pitch axis and yaw axis of the spacecraft, respectively.
图12为航天器干扰估计误差曲线图；图中de1,de2,de3分别代表航天器滚动轴、俯仰轴和偏航轴上的干扰估计误差。Fig. 12 is a curve diagram of spacecraft interference estimation error; de1 , de2 , de3 in the figure represent the interference estimation error on the roll axis, pitch axis and yaw axis of the spacecraft respectively.
具体实施方式detailed description
具体实施方式一：一种基于干扰观测器的挠性卫星轨迹线性化姿态控制方法包括以下步骤：Specific embodiment one: a kind of attitude control method of flexible satellite trajectory linearization based on disturbance observer comprises the following steps:
本发明的关键步骤：Key steps of the present invention:
1、卫星姿态控制1. Satellite attitude control
卫星的姿态控制包括姿态确定、姿态稳定控制和姿态机动控制。姿态确定是研究空间飞行器相对于某参考基准的方位或方向，进而获取姿态角参数，其精度取决于姿态敏感器和姿态算法的精度。姿态稳定控制是使飞行器的姿态保持在预期制定方向和指定值上。姿态机动控制是使飞行器从一个姿态过渡到另一个姿态的再定向过程。本发明专利主要对挠性卫星受干扰情况下姿态跟踪控制进行深入研究。The attitude control of the satellite includes attitude determination, attitude stabilization control and attitude maneuvering control. Attitude determination is to study the orientation or direction of the spacecraft relative to a reference datum, and then obtain the attitude angle parameters, and its accuracy depends on the accuracy of the attitude sensor and attitude algorithm. Attitude stabilization control is to keep the attitude of the aircraft in the expected direction and specified value. Attitude maneuvering is the process of reorienting an aircraft from one attitude to another. The patent of the present invention mainly conducts in-depth research on the attitude tracking control of the flexible satellite when it is disturbed.
姿态控制系统保证卫星以预定的姿态精度在轨道上运行。按姿态稳定方式分为两种基本类型：被动稳定系统和主动稳定系统。这两种系统的结合又派生出半被动、半主动和混合稳定系统三种类型。从控制观念上看，被动稳定系统属于开环控制系统，主动稳定系统属于闭环负反馈控制系统。被动稳定系统是利用自然环境力矩或物理力矩源，如自旋、重力梯度、地磁场、太阳辐射压力矩和气动力矩，来控制卫星的姿态。主动控制从控制原理上看就是三自由度的姿态闭环控制系统，不依赖于地面指挥中心的干预，完全由飞行器所载设备实现姿态控制的过程。按稳定方式主要分为自旋稳定和三轴稳定。本发明主要对三轴稳定的情况进行研究。The attitude control system ensures that the satellite moves in orbit with a predetermined attitude accuracy. There are two basic types of attitude stabilization systems: passive stabilization systems and active stabilization systems. The combination of these two systems has derived three types of semi-passive, semi-active and hybrid stabilization systems. From the perspective of control concept, the passive stabilization system belongs to the open-loop control system, and the active stabilization system belongs to the closed-loop negative feedback control system. The passive stabilization system uses the natural environment moment or physical moment source, such as spin, gravity gradient, geomagnetic field, solar radiation pressure moment and aerodynamic moment, to control the attitude of the satellite. From the perspective of control principle, active control is a three-degree-of-freedom attitude closed-loop control system, which does not depend on the intervention of the ground command center, and is completely controlled by the equipment onboard the aircraft. According to the stabilization method, it is mainly divided into spin stabilization and triaxial stabilization. The present invention mainly studies the situation of triaxial stability.
2、轨迹线性化2. Trajectory linearization
轨迹线性化控制适用于解决非线性跟踪问题，其本质为解耦控制，将开环的非线性动态逆和线性时变的反馈线性化控制相结合，保证了系统输出在名义轨迹上的指数稳定性。轨迹线性化的设计思想是：首先利用非线性动态逆方法将轨迹跟踪问题转化为一个跟踪误差调节问题，然后利用线性时变系统PD谱理论设计状态反馈控制律，使得系统跟踪误差收敛到零。控制器结构图如图1所示。Trajectory linearization control is suitable for solving nonlinear tracking problems. Its essence is decoupling control. It combines open-loop nonlinear dynamic inverse and linear time-varying feedback linearization control to ensure the exponential stability of the system output on the nominal trajectory. sex. The design idea of trajectory linearization is: firstly, the nonlinear dynamic inverse method is used to transform the trajectory tracking problem into a tracking error adjustment problem, and then the state feedback control law is designed using the linear time-varying system PD spectrum theory, so that the system tracking error converges to zero. The structure diagram of the controller is shown in Figure 1.
考虑如下形式的多输入多输出非线性系统：Consider a multiple-input multiple-output nonlinear system of the form:
x∈Rn，u∈Rm，y∈Rm,分别为系统的状态，输入和输出；f(x)，g(x)和h(x)为适当位数的光滑有界函数。令分别表示系统标称的状态，输出和控制输入，则相应有：x∈Rn , u∈Rm , y∈Rm , are the state, input and output of the system respectively; f(x), g(x) and h(x) are smooth bounded functions with appropriate digits. make Respectively represent the nominal state of the system, output and control input, then correspondingly have:
定义如下的状态跟踪误差：The state tracking error is defined as follows:
并构造控制律为And construct the control law as
其中，η即为所需设计的线性时变反馈控制率，在后面给出。则对应的非线性跟踪误差动态系统为Among them, η is the linear time-varying feedback control rate to be designed, which will be given later. Then the corresponding nonlinear tracking error dynamic system is
此时，原非线性系统跟踪问题就转化为一个非线性调节问题，控制器包括两部分：At this point, the original nonlinear system tracking problem is transformed into a nonlinear regulation problem, and the controller consists of two parts:
一个开环的被控对象的伪动态逆控制器，根据期望的系统输出值产生一个标称的控制输入An open-loop pseudodynamic inverse controller of the plant, according to the desired system output value produces a nominal control input
一个闭环的线性时变反馈调节器η＝η(e)用以镇定系统，并使系统具有一定的响应特性。A closed-loop linear time-varying feedback regulator η=η(e) is used to stabilize the system and make the system have certain response characteristics.
考虑到式(4)中的可视为系统的时变参数，因此式(4)可简记为Considering the formula (4) in can be regarded as a time-varying parameter of the system, so formula (4) can be abbreviated as
考虑如下的线性时变系统:Consider the following linear time-varying system:
考虑如下的线性时变系统:Consider the following linear time-varying system:
式中，
假设1：e＝0为式(5)的一个孤立平衡点，并且连续可微，Jacobian矩阵关于t一致有界，在D上满足Lipschitz条件。Assumption 1: e=0 is an isolated equilibrium point of equation (5), and Continuously Differentiable, Jacobian Matrix It is uniformly bounded on t and satisfies the Lipschitz condition on D.
假设2：式(6)中的A(t)，B(t)完全可控。Assumption 2: A(t) and B(t) in formula (6) are completely controllable.
由假设2可设计线性时变反馈控制器：By assumption 2, a linear time-varying feedback controller can be designed:
η＝K(t)e(7)η=K(t)e(7)
使得线性时变系统(6)平衡点e＝0为指数稳定，并记Make the equilibrium point e=0 of the linear time-varying system (6) exponentially stable, and record
AC＝A(t)+B(t)K(t)(8)AC =A(t)+B(t)K(t)(8)
由文献[3](ShaoX,WangH.ANovelMethodofRobustTrajectoryLinearizationControlBasedonDisturbanceRejection[J].MathematicalProblemsinEngineering,2014,2014)可知，线性时变反馈控制律(7)可保证系统(4)在平衡点e＝0指数稳定。According to literature [3] (ShaoX, WangH. ANovelMethod of RobustTrajectoryLinearizationControlBasedonDisturbanceRejection[J]. MathematicalProblemsinEngineering, 2014, 2014), the linear time-varying feedback control law (7) can ensure that the system (4) is exponentially stable at the equilibrium point e=0.
3、非线性干扰观测器3. Nonlinear Disturbance Observer
非线性干扰观测器是针对非线性系统模型中外部干扰，对其进行观测，并通过前馈来抑制干扰的影响。The nonlinear disturbance observer aims at the external disturbance in the nonlinear system model, observes it, and suppresses the influence of the disturbance through feedforward.
典型非线性系统描述如下：A typical nonlinear system is described as follows:
其中，x∈Rn,u∈R,d∈R分别代表状态向量，系统输入和外界干扰。Among them, x∈Rn , u∈R, d∈R represent the state vector, system input and external disturbance respectively.
为了估计和抑制外界干扰，需要设计干扰观测器。假设系统干扰来源于线性外源系统In order to estimate and suppress external interference, it is necessary to design an interference observer. It is assumed that the system disturbance comes from a linear exogenous system
为了估计未知干扰d，设计观测器如下：In order to estimate the unknown disturbance d, the observer is designed as follows:
其中，z是观测器内部状态变量，p(x)是待设计的非线性向量函数，观测器增益
根据文献[8](ChenWH.Disturbanceobserverbasedcontrolfornonlinearsystems[J].Mechatronics,IEEE/ASMETransactionson,2004,9(4):706-710.)可知，观测器的估计误差渐近收敛到0。According to literature [8] (ChenWH. Disturbance observer based control for nonlinear systems [J]. Mechatronics, IEEE/ASME Transactionson, 2004, 9 (4): 706-710.), it can be seen that the estimation error of the observer asymptotically converges to 0.
4、挠性航天器姿态模型4. Attitude model of flexible spacecraft
帆板作为航天器主要的挠性部件，其运动和航天器本体姿态运动相互耦合。挠性附件的运动要用无限自由度的分布参数描述。As the main flexible part of the spacecraft, the windsurfing is coupled with the attitude motion of the spacecraft body. The motion of the flexible attachment is described by distributed parameters with infinite degrees of freedom.
采用混合坐标法来描述带挠性附件航天器的运动，即中心刚体使用通常描述刚体姿态的坐标(如欧拉角)，挠性附件使用离散的模态坐标描述。从而建立既能足够准确描述航天器的运动，又便于航天器控制系统分析和设计的动力学模型。不考虑帆板相对于航天器本体的转动，挠性航天器的动力学方程如下：The hybrid coordinate method is used to describe the motion of the spacecraft with flexible appendages, that is, the central rigid body uses the coordinates (such as Euler angles) that usually describe the attitude of the rigid body, and the flexible appendages are described using discrete modal coordinates. In this way, a dynamic model that can accurately describe the motion of the spacecraft and facilitate the analysis and design of the spacecraft control system is established. Regardless of the rotation of the sail relative to the spacecraft body, the dynamic equation of the flexible spacecraft is as follows:
其中，ω＝[ωxωyωz]T∈R3为航天器本体角速度，T＝[TxTyTz]T∈R3为航天器滚动轴、俯仰轴和偏航轴的控制力矩，d＝[dxdydz]T∈R3为作用在航天器上的干扰力矩，J∈R3×3为航天器的转动惯量，其形式为，Among them, ω＝[ωx ωy ωz ]T ∈ R3 is the angular velocity of the spacecraft body, T＝[Tx Ty Tz ]T ∈ R3 is the control of the spacecraft roll axis, pitch axis and yaw axis Moment, d=[dx dy dz ]T ∈ R3 is the disturbance moment acting on the spacecraft, J ∈ R3×3 is the moment of inertia of the spacecraft, and its form is,
η∈Rn代表挠性模态坐标，n代表模态阶数，δ∈R3×n代表挠性附件和航天器本体的耦合系数矩阵，C＝diag{2ξiΩi,i＝1,2,…n},分别代表挠性附件振动阻尼系数和频率系数矩阵，ξi,Ωi分别表示挠性附件的第i阶模态阻尼比和模态频率。η∈Rn represents the coordinates of the flexible mode, n represents the mode order, δ∈R3×n represents the coupling coefficient matrix of the flexible attachment and the spacecraft body, C=diag{2ξi Ωi ,i=1, 2,...n}, Represent the vibration damping coefficient and frequency coefficient matrix of the flexible attachment, respectively, and ξi , Ωi represent the ith-order modal damping ratio and modal frequency of the flexible attachment, respectively.
为便于分析，采用等效干扰的思想，将刚柔耦合项和干扰d合并为视为系统的总干扰，简化了系统模型，此时挠性航天器动力学模型为For the convenience of analysis, the idea of equivalent interference is adopted, and the rigid-flexible coupling term and interference d combined into As the total disturbance of the system, the system model is simplified, and the dynamic model of the flexible spacecraft is
忽略转动惯量矩阵J∈R3×3中的耦合项，也不必考虑帆板振动方程，系统运动学模型和动力学模型如下所示：Neglecting the coupling items in the moment of inertia matrix J∈R3×3 , and not having to consider the sailboard vibration equation, the kinematics model and dynamics model of the system are as follows:
5、跟踪误差线性时变调节器的设计5. Design of tracking error linear time-varying regulator
调节器设计原则Regulator Design Principles
跟踪误差线性时变调节器采用状态反馈PI控制方法，控制器增益设计方法如下：The tracking error linear time-varying regulator adopts the state feedback PI control method, and the controller gain design method is as follows:
(1)对外环欧拉角进行控制，定义新的状态变量和输入变量如下：(1) To control the Euler angles of the outer ring, define new state variables and input variables as follows:
其中，θint＝∫θdt,ψint＝∫ψdt，得到新的非线性状态空间模型in, θint ＝∫θdt, ψint ＝∫ψdt, get a new nonlinear state space model
其中in
得到线性化跟踪系统get linearized tracking system
其中in
(2)对于内环角速度控制利用同样的方法，定义新的状态变量和输入变量如下：(2) Using the same method for inner-loop angular velocity control, define new state variables and input variables as follows:
其中，ωxint＝∫ωxdt,ωyint＝∫ωydt,ωzint＝∫ωzdt，得到新的非线性状态空间模型
得到线性化跟踪系统get linearized tracking system
其中in
其中in
(3)设计状态反馈控制律，使欧拉角跟踪误差渐近稳定，控制输入u1＝-K1γaug，(3) Design the state feedback control law to make the Euler angle tracking error asymptotically stable, control input u1 =-K1 γaug ,
根据设计要求确定闭环系统的期望阻尼和期望带宽ξ1j,ωn1j,j＝1,2,3，则闭环系统的特征方程为Determine the expected damping and expected bandwidth of the closed-loop system according to the design requirements ξ1j , ωn1j , j=1, 2, 3, then the characteristic equation of the closed-loop system is
λ2+α1j2λ+α1j1＝0,j＝1,2,3(57)λ2 +α1j2 λ+α1j1 =0,j=1,2,3(57)
其中α1j2＝2·ξ1j·ωn1j,
闭环系统矩阵Closed Loop System Matrix
欧拉角跟踪控制系统增益矩阵K1满足The Euler angle tracking control system gain matrix K1 satisfies
Acl1＝A1-B1K1(59)Acl1 ＝A1 -B1 K1 (59)
K1可由式(48)，(49)，(50)，(58)，(59)求得。K1 can be obtained by formulas (48), (49), (50), (58), and (59).
(4)同理，为实现对航天器姿态角速度控制，设计状态反馈控制律，u2＝-K2ωaug，根据设计要求确定闭环系统的期望阻尼和期望带宽ξ1j,ωn1j,j＝1,2,3，则闭环系统的特征方程为(4) Similarly, in order to realize the attitude control of the spacecraft, the state feedback control law is designed, u2 =-K2 ωaug , and the expected damping and expected bandwidth of the closed-loop system are determined according to the design requirements ξ1j , ωn1j , j = 1, 2, 3, then the characteristic equation of the closed-loop system is
λ2+α2j2λ+α2j1＝0,j＝1,2,3(60)λ2 +α2j2 λ+α2j1 =0,j=1,2,3(60)
其中，α2j2＝2·ξ2j·ωn2j，
闭环系统矩阵Closed Loop System Matrix
姿态角速度控制增益矩阵K2满足Attitude angular velocity control gain matrix K2 satisfies
Acl2＝A2-B2K2(62)Acl2 = A2 -B2 K2 (62)
由式(54)，(55)，(56)，(61)，(62)可求得控制增益矩阵K2。The control gain matrix K2 can be obtained from formulas (54), (55), (56), (61), and (62).
误差收敛性证明Error Convergence Proof
定义跟踪误差系统
假设1：e＝0是的孤立平衡点，F:[0,∞)×De→Rn连续可微，De＝{e∈Rn|||e||<Re}，Jacobian矩阵有界且在De上满足Lipschitz条件。Assumption 1: e=0 is The isolated equilibrium point of , F:[0,∞)×De →Rn is continuously differentiable, De ＝{e∈Rn |||e||<Re }, Jacobian matrix is bounded and satisfies the Lipschitz condition on De .
假设2：系统矩阵对(Ai(t),Bi(t))一致完全可控。Assumption 2: The system matrix pair (Ai (t), Bi (t)) is consistent and fully controllable.
由以上假设条件，当系统等效误差时，设计线性时变的状态反馈控制律ui＝Ki(t)ei,(ei＝γaug,ωaug)，根据文献[3]可知，系统的解在原点指数稳定。Based on the above assumptions, when the system equivalent error When , design a linear time-varying state feedback control law ui =Ki (t)ei ,(ei =γaug ,ωaug ). According to literature [3], the solution of the system is exponentially stable at the origin.
为了简化设计，令Acli＝Ai+BiKi，Acli是Hurwitz矩阵，其参数可由PD特征谱原理选取。In order to simplify the design, let Acli =Ai +Bi Ki , Acli is a Hurwitz matrix, and its parameters can be selected by the principle of PD characteristic spectrum.
6、非线性干扰观测器设计6. Design of nonlinear disturbance observer
观测器设计原理Observer Design Principles
考虑等效干扰对系统的影响，挠性航天器的动力学方程形式如下：Consider equivalent interference The influence on the system, the dynamic equation of the flexible spacecraft is as follows:
其中，f2(ω)＝J-1·(-ω×Jω),g2＝J-1。针对未知干扰设计如下的非线性干扰观测器：Wherein, f2 (ω)=J−1 ·(−ω× Jω), g2 =J−1 . The following nonlinear disturbance observer is designed for unknown disturbances:
其中，代表对未知等效干扰的估计，z是非线性观测器的内部状态变量，p(ω)是待设计的非线性向量函数，观测器的增益定义为in, Represents the estimate of the unknown equivalent disturbance, z is the internal state variable of the nonlinear observer, p(ω) is the nonlinear vector function to be designed, and the gain of the observer is defined as
估计误差收敛性证明Estimate error convergence proof
为简单起见，假设等效干扰是慢时变的，即For simplicity, it is assumed that the equivalent disturbance is slowly time-varying, namely
令估计误差Let estimate error
则but
将式(64)代入中，得到Substitute (64) into in, get
由于because
将式(63)，(69)代入式(68)中，得到Substituting equations (63), (69) into equation (68), we get
设计p(ω)，使得式(70)全局稳定。则估计误差趋近于0。Design p(ω) so that formula (70) is globally stable. then the estimated error tends to 0.
为了抑制航天器跟踪过程中干扰问题，本发明专利采用非线性干扰观测器和轨迹线性化控制相结合的方法，利用轨迹线性化适合解决非线性跟踪问题的优点，结合非线性干扰观测器进行干扰抑制，提高了系统的鲁棒性。主要思想是在给定挠性航天器转动惯量、挠性帆板模态阻尼矩阵、挠性帆板耦合系数、初始姿态和目标姿态的前提下，忽略转动惯量中的耦合项，采用等效干扰思想，先将等效误差忽略，求得航天器名义控制，然后根据PD特征谱原理确定线性时变调节器参数，解耦非线性系统，使得系统跟踪误差渐近收敛。最后考虑等效干扰，设计非线性干扰观测器对干扰进行补偿。系统控制结构图如图2所示，控制律由三部分组成：In order to suppress the interference problem in the tracking process of the spacecraft, the patent of the present invention adopts the method of combining the nonlinear interference observer and the trajectory linearization control, and utilizes the advantage that the trajectory linearization is suitable for solving the nonlinear tracking problem, and combines the nonlinear interference observer for interference suppression, which improves the robustness of the system. The main idea is to ignore the coupling term in the moment of inertia and use the equivalent disturbance The idea is to first ignore the equivalent error, obtain the nominal control of the spacecraft, and then determine the parameters of the linear time-varying regulator according to the PD characteristic spectrum principle, decouple the nonlinear system, and make the system tracking error asymptotically converge. Finally, considering the equivalent disturbance, a nonlinear disturbance observer is designed to compensate the disturbance. The system control structure diagram is shown in Figure 2. The control law consists of three parts:
其中分别表示名义控制，时变反馈控制和干扰补偿控制。in Respectively represent nominal control, time-varying feedback control and disturbance compensation control.
步骤一：挠性航天器动力学建模，得到模型为Step 1: Dynamic modeling of flexible spacecraft, the obtained model is
其中ω＝[ωxωyωz]T∈R3为航天器本体角速度，ωx、ωy、ωz分别为航天器本体系相对于惯性系角速度在本体坐标系滚动轴、俯仰轴和偏航轴方向投影；ω×为
步骤二：利用步骤一得到的模型，进行航天器名义控制设计；Step 2: Use the model obtained in Step 1 to carry out nominal control design of the spacecraft;
当被控对象的逆不可求时，通过求状态变量的伪逆，得到跟踪系统的名义控制；When the inverse of the controlled object cannot be obtained, the nominal control of the tracking system is obtained by obtaining the pseudo-inverse of the state variable;
对将等效干扰忽略，求得系统运动学和动力学模型相对于名义状态变量和的逆，得到equivalent interference Neglecting, the kinematic and dynamic models of the system are obtained with respect to the nominal state variables and the inverse of
其中所述为航天器本体坐标系相对于轨道坐标系的旋转角速度名义值，为滚动轴方向、俯仰轴方向和偏航轴方向名义控制力矩，Jxx、Jyy、Jzz为航天器沿滚动轴、俯仰轴和偏航轴的转动惯量；which stated is the nominal value of the rotational angular velocity of the spacecraft body coordinate system relative to the orbital coordinate system, Jxx , Jyy , Jzz are the moment of inertia of the spacecraft along the roll axis, pitch axis and yaw axis;
公式(15)和式(16)可以精确表示出控制变量的逆；Formula (15) and formula (16) can accurately represent the inverse of the control variable;
步骤三：利用步骤二求得系统运动学和动力学模型相对于名义状态变量和的逆，设计跟踪误差的线性时变调节器，求得状态反馈控制律u1和u2；Step 3: Use Step 2 to obtain the system kinematics and dynamics model relative to the nominal state variable and Inverse of , design a linear time-varying regulator of tracking error, and obtain state feedback control laws u1 and u2 ;
步骤四：根据步骤三得到的状态反馈控制律u2，设计非线性干扰观测器，将观测器的输出作为系统控制律的一部分；得到整个系统的控制律Step 4: According to the state feedback control law u2 obtained in Step 3, design a nonlinear disturbance observer, and the output of the observer As part of the control law of the system; get the control law of the whole system
ωx，ωy，ωz——航天器本体系相对于惯性系角速度在本体坐标系滚动轴、俯仰轴和偏航轴方向投影；ωx , ωy , ωz ——the projection of the angular velocity of the spacecraft body system relative to the inertial system in the direction of the roll axis, pitch axis and yaw axis of the body coordinate system;
ω×——定义为
——航天器本体系相对于惯性系角加速度在本体坐标系滚动轴、俯仰轴和偏航轴方向投影； ——The projection of the angular acceleration of the spacecraft body system relative to the inertial system in the direction of the roll axis, pitch axis and yaw axis of the body coordinate system;
——航天器本体系相对于惯性系角速度在本体坐标系滚动轴、俯仰轴和偏航轴方向投影的名义状态变量； ——The nominal state variables projected in the direction of the roll axis, pitch axis and yaw axis of the body coordinate system with respect to the angular velocity of the spacecraft body system relative to the inertial system;
——航天器本体系相对于惯性系角加速度在本体坐标系滚动轴、俯仰轴和偏航轴方向投影的名义状态变量； ——The nominal state variable projected in the direction of the roll axis, pitch axis and yaw axis of the body coordinate system relative to the angular acceleration of the spacecraft body system relative to the inertial system;
——航天器本体坐标系相对于轨道坐标系的欧拉角； ——the Euler angle of the spacecraft body coordinate system relative to the orbital coordinate system;
——航天器本体坐标系相对于轨道坐标系的旋转角速度名义值； ——The nominal value of the rotational angular velocity of the spacecraft body coordinate system relative to the orbital coordinate system;
Tx，Ty，Tz——滚动轴方向、俯仰轴方向和偏航轴方向控制力矩；Tx , Ty , Tz ——control torque in the direction of roll axis, pitch axis and yaw axis;
——滚动轴方向、俯仰轴方向和偏航轴方向名义控制力矩； ——Nominal control moment in the direction of roll axis, pitch axis and yaw axis;
dx，dy，dz——滚动轴方向、俯仰轴方向和偏航轴方向干扰力矩；dx , dy , dz —disturbance moment in the direction of roll axis, pitch axis and yaw axis;
η∈Rn——挠性模态坐标，n为模态阶数；η∈Rn —coordinates of flexible mode, n is mode order;
Jx(Jxx)，Jy(Jyy)，Jz(Jzz)——航天器沿滚动轴、俯仰轴和偏航轴的转动惯量；Jx (Jxx ), Jy (Jyy ), Jz (Jzz )——Moments of inertia of the spacecraft along the roll axis, pitch axis and yaw axis;
δ∈R3×n——挠性附件和航天器本体的耦合系数矩阵；δ∈R3×n —coupling coefficient matrix of flexible attachment and spacecraft body;
ξi——挠性附件的第i阶模态阻尼比；ξi ——the i-th order modal damping ratio of the flexible attachment;
Ωi——模态频率；Ωi ——modal frequency;
ωn,diff——衰减高频增益的低通滤波器的带宽；ωn,diff — the bandwidth of the low-pass filter that attenuates the high-frequency gain;
——欧拉角积分变量； —— Euler angle integral variable;
ξ1j——外环闭环系统的期望阻尼；ξ1j ——the expected damping of the outer loop closed-loop system;
ωn1j——外环闭环系统的带宽系数；ωn1j ——Bandwidth coefficient of the outer loop closed-loop system;
ei——跟踪误差；ei ——tracking error;
——未知等效干扰的估计； - estimation of unknown equivalent interference;
z——非线性观测器的内部状态变量；z—the internal state variable of the nonlinear observer;
p(ω)——待设计的非线性向量函数；p(ω)——Nonlinear vector function to be designed;
l(ω)——观测器的增益。l(ω)—the gain of the observer.
d＝[dxdydz]T∈R3为作用在航天器上的干扰力矩；d=[dx dy dz ]T ∈ R3 is the disturbance moment acting on the spacecraft;
——名义控制输入，反馈控制输入和观测器干扰补偿。 - Nominal control input, feedback control input and observer disturbance compensation.
具体实施方式二：本实施方式与具体实施方式一不同的是：所述步骤一中挠性航天器动力学建模的具体过程为：Embodiment 2: The difference between this embodiment and Embodiment 1 is that the specific process of dynamic modeling of the flexible spacecraft in the step 1 is:
采用混合坐标法来描述带挠性附件航天器的运动，即中心刚体使用通常描述刚体姿态的坐标(如欧拉角)，挠性附件使用离散的模态坐标描述。从而建立既能足够准确描述航天器的运动，又便于航天器控制系统分析和设计的动力学模型。A hybrid coordinate method is used to describe the motion of a spacecraft with flexible appendages, that is, the central rigid body uses coordinates (such as Euler angles) that usually describe the attitude of the rigid body, and the flexible appendages are described using discrete modal coordinates. In this way, a dynamic model that can accurately describe the motion of the spacecraft and facilitate the analysis and design of the spacecraft control system is established.
不考虑帆板相对于航天器本体的转动，挠性航天器的动力学方程如下：Regardless of the rotation of the sail relative to the spacecraft body, the dynamic equation of the flexible spacecraft is as follows:
为便于分析，采用等效干扰的思想，将刚柔耦合项和干扰d合并为视为系统的总干扰，简化了系统模型，此时挠性航天器动力学模型为For the convenience of analysis, the idea of equivalent interference is adopted, and the rigid-flexible coupling term and interference d combined into As the total disturbance of the system, the system model is simplified, and the dynamic model of the flexible spacecraft is
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：所述步骤二中名义控制中出现控制变量的微分形式，需要准微分器以得到名义状态的导数，本发明采用一阶准微分器，形式为：Specific embodiment three: the difference between this embodiment and specific embodiment one or two is: the differential form of the control variable appears in the nominal control in the step two, and a quasi-differentiator is needed to obtain the derivative of the nominal state. The present invention uses a first-order A quasi-differentiator of the form:
其中s为拉普拉斯算子，ωn,diff为低通滤波器的带宽，决定了微分器抑制高频分量的能力。Among them, s is the Laplacian operator, ωn,diff is the bandwidth of the low-pass filter, which determines the ability of the differentiator to suppress high-frequency components.
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：所述步骤三中设计跟踪误差的线性时变调节器，求得状态反馈控制律u1和u2的具体过程为：Embodiment 4: The difference between this embodiment and Embodiment 1 to 3 is: in the step 3, the linear time-varying regulator of the tracking error is designed, and the specific process of obtaining the state feedback control law u1 and u2 is as follows: :
步骤一：新的非线性状态空间模型和线性化跟踪系统的获得；Step 1: New nonlinear state-space model and linearized tracking system the acquisition;
对外环欧拉角进行控制，定义新的状态变量和输入变量如下：To control the Euler angle of the outer ring, define new state variables and input variables as follows:
其中θint＝∫θdt,ψint＝∫ψdt，得到新的非线性状态空间模型in θint ＝∫θdt, ψint ＝∫ψdt, get a new nonlinear state space model
其中in
得到线性化跟踪系统为：The linearized tracking system is obtained as:
其中in
步骤二：新的非线性状态空间模型和线性化跟踪系统的获得：Step 2: New nonlinear state-space model and linearized tracking system The acquisition of:
对于内环角速度控制利用同样的方法，定义新的状态变量和输入变量如下：Using the same method for inner loop angular velocity control, define new state variables and input variables as follows:
其中，ωxint＝∫ωxdt,ωyint＝∫ωydt,ωzint＝∫ωzdt，得到新的非线性状态空间模型
得到线性化跟踪系统为：The linearized tracking system is obtained as:
其中in
其中in
步骤三：状态反馈控制律u1的获得；Step 3: Obtaining the state feedback control law u1 ;
设计状态反馈控制律，控制输入u1＝-K1γaug，Design state feedback control law, control input u1 ＝-K1 γaug ,
根据设计要求确定闭环系统的期望阻尼和期望带宽ξ1j,ωn1j,j＝1,2,3，则闭环系统的特征方程为：Determine the expected damping and expected bandwidth of the closed-loop system according to the design requirements ξ1j , ωn1j , j=1, 2, 3, then the characteristic equation of the closed-loop system is:
λ2+α1j2λ+α1j1＝0,j＝1,2,3(30)λ2 +α1j2 λ+α1j1 =0,j=1,2,3(30)
其中α1j2＝2·ξ1j·ωn1j,
闭环系统矩阵Closed Loop System Matrix
欧拉角跟踪控制系统增益矩阵K1满足The Euler angle tracking control system gain matrix K1 satisfies
Acl1＝A1-B1K1(32)Acl1 ＝A1 -B1 K1 (32)
K1可由式(21)，(22)，(23)，(31)，(32)求得；K can be obtained by formula (21 ), (22), (23), (31), (32);
由于u1＝-K1γaug，由K1和γaug可求得u1；Since u1 =-K1 γaug , u1 can be obtained from K1 and γaug ;
步骤四：状态反馈控制律u2的获得；Step 4: obtain the state feedback control law u2 ;
设计状态反馈控制律，控制输入u2＝-K2ωaug，根据设计要求确定闭环系统的期望阻尼和期望带宽ξ1j,ωn1j,j＝1,2,3，则闭环系统的特征方程为：Design the state feedback control law, control input u2 =-K2 ωaug , determine the expected damping and expected bandwidth ξ1j ,ωn1j ,j=1,2,3 of the closed-loop system according to the design requirements, then the characteristic equation of the closed-loop system is :
λ2+α2j2λ+α2j1＝0,j＝1,2,3(33)λ2 +α2j2 λ+α2j1 =0,j=1,2,3(33)
其中，α2j2＝2·ξ2j·ωn2j,
闭环系统矩阵为：The closed-loop system matrix is:
姿态角速度控制增益矩阵K2满足Attitude angular velocity control gain matrix K2 satisfies
Acl2＝A2-B2K2(35)Acl2 = A2 -B2 K2 (35)
由式(26)，(27)，(28)，(34)，(35)可求得控制增益矩阵K2；By formula (26), (27), (28), (34), (35) can obtain control gain matrix K2 ;
由于u2＝-K2ωaug，由K2和ωaug可求得u2。Since u2 =-K2 ωaug , u2 can be obtained from K2 and ωaug .
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：所述步骤四中设计非线性干扰观测器的具体过程为：Specific embodiment five: the difference between this embodiment and one of the specific embodiments one to four is: the specific process of designing the nonlinear disturbance observer in the step four is:
考虑等效干扰对系统的影响，挠性航天器的动力学方程形式如下：Consider equivalent interference The influence on the system, the dynamic equation of the flexible spacecraft is as follows:
其中，f2(ω)＝J-1·(-ω×Jω),g2＝J-1；Among them, f2 (ω) = J-1 ·(-ω× Jω), g2 = J-1 ;
针对未知干扰设计非线性干扰观测器为：The nonlinear disturbance observer designed for unknown disturbance is:
其中所述代表对未知等效干扰的估计，z是非线性观测器的内部状态变量，p(ω)是待设计的非线性向量函数，观测器的增益定义为：which stated Represents the estimation of the unknown equivalent disturbance, z is the internal state variable of the nonlinear observer, p(ω) is the nonlinear vector function to be designed, and the gain of the observer is defined as:
假设等效干扰是慢时变的，即Assuming that the equivalent disturbance is slowly time-varying, that is
定义估计误差当假设时，如果p(ω)的选取满足式(39)是全局稳定的，则ed(t)趋近于0；待设计的非线性向量函数p(ω)满足上述条件；Define estimation error when assuming , if the selection of p(ω) satisfies that formula (39) is globally stable, then ed (t ) tends to 0; the nonlinear vector function p(ω) to be designed satisfies the above conditions;
将观测器的输出作为系统控制律的一部分，用于补偿外界干扰。由文献[9](朱亮.基于非线性干扰观测器的空天飞行器轨迹线性化控制.[J].南京航空航天大学学报.2007,39(4):492-494)可知，用观测器的输出来补偿外界干扰可以避免干扰对系统的影响。The output of the observer As part of the system control law, it is used to compensate for external disturbances. According to literature [9] (Zhu Liang. Linearization control of aerospace vehicle trajectory based on nonlinear disturbance observer. [J]. Journal of Nanjing University of Aeronautics and Astronautics. 2007,39(4):492-494), it can be known that the observer The output to compensate for external interference can avoid the influence of interference on the system.
综上，整个系统的控制律根据文献[9]可知，复合闭环系统误差动态特性局部指数稳定。In summary, the control law of the whole system According to literature [9], it can be seen that the error dynamic characteristics of the composite closed-loop system are locally exponentially stable.
实施例一：Embodiment one:
1、仿真参数：1. Simulation parameters:
本发明专利采用如下仿真参数；The patent of the present invention adopts the following simulation parameters;
航天器转动惯量:
跟踪目标的角速度为：
外部干扰为：
挠性太阳帆板模态频率矩阵：Ω＝diag(0.7681；1.1038；1.8733；2.5490)×2π(rad/s)Modal frequency matrix of flexible solar panels: Ω＝diag(0.7681; 1.1038; 1.8733; 2.5490)×2π(rad/s)
挠性太阳帆板模态阻尼矩阵：ξ＝diag(0.056；0.0086；0.013；0.025)Modal damping matrix of flexible solar panels: ξ=diag(0.056; 0.0086; 0.013; 0.025)
挠性太阳帆板耦合系数：
航天器初始姿态为：θ＝0.1°,ψ＝0.1°，The initial attitude of the spacecraft is: θ=0.1°, ψ=0.1°,
2、控制器参数：2. Controller parameters:
设计名义控制时，用到了准微分器来估计名义状态的导数，内环和外环一阶准微分调节器参数，即低通滤波器的带宽分别为：ωn,diff_i＝15(rad/s),ωn,diff_o＝5(rad/s)，有效衰减了高频增益。When designing the nominal control, a quasi-differentiator is used to estimate the derivative of the nominal state. The parameters of the first-order quasi-differential regulator of the inner loop and the outer loop, that is, the bandwidth of the low-pass filter are: ωn,diff_i = 15(rad/s ), ωn,diff_o =5(rad/s), which effectively attenuates the high-frequency gain.
系统的阻尼频率决定了系统的调节时间和超调量，进而决定了系统平稳性。本专利中内环和外环期望阻尼设计为：ξ1j＝0.707,ξ2j＝0.707,j＝1,2,3The damping frequency of the system determines the adjustment time and overshoot of the system, and then determines the stability of the system. In this patent, the desired damping design of the inner and outer rings is: ξ1j = 0.707, ξ2j = 0.707, j = 1,2,3
系统的带宽同样影响了闭环系统的动态性能，本专利中内环和外环期望带宽设计为：The bandwidth of the system also affects the dynamic performance of the closed-loop system. In this patent, the expected bandwidth of the inner loop and the outer loop is designed as:
ωn11＝0.01(rad/s),ωn12＝0.01(rad/s),ωn13＝0.01(rad/s)ωn11 = 0.01(rad/s), ωn12 = 0.01(rad/s), ωn13 = 0.01(rad/s)
ωn21＝1(rad/s),ωn22＝1(rad/s),ωn23＝0.5(rad/s)ωn21 ＝1(rad/s), ωn22 ＝1(rad/s), ωn23 ＝0.5(rad/s)
观测器的增益矩阵可以配置系统的闭环极点，调节稳态性能，本专利中非线性干扰观测器增益为：l＝[101010]T。The gain matrix of the observer can configure the closed-loop poles of the system to adjust the steady-state performance. In this patent, the gain of the nonlinear disturbance observer is: l=[101010]T .
3、仿真分析3. Simulation analysis
本发明专利控制目标是使挠性航天器无误差跟踪期望姿态。考虑到实际情况，执行机构的执行能力有限，所以仿真中对控制力矩进行幅值限制，使其不超过2(N.m)。仿真结果如图3～10所示：The control goal of the patent of the present invention is to make the flexible spacecraft track the desired attitude without error. Considering the actual situation, the execution ability of the actuator is limited, so the amplitude of the control torque is limited in the simulation so that it does not exceed 2 (N.m). The simulation results are shown in Figure 3-10:
从仿真结果可以看出，航天器达到预期姿态的时间为4s，欧拉角稳态误差幅值为5×10-5rad，角速度稳态误差为2×10-4rad/s，控制力矩稳态幅值为0.1Nm，挠性模态振动最大幅值为0.018。From the simulation results, it can be seen that the time for the spacecraft to reach the expected attitude is 4s, the steady-state error amplitude of Euler angle is 5×10-5 rad, the steady-state error of angular velocity is 2×10-4 rad/s, and the control torque is stable. The state amplitude is 0.1Nm, and the maximum amplitude of the flexural mode vibration is 0.018.
综上，只要合理选择误差调节器参数和观测器的增益，基于非线性干扰观测器的轨迹线性化控制就可以实现航天器姿态跟踪，精度较高，挠性帆板模态振动幅值较小。此外，利用非线性干扰观测器对不确定性干扰进行了估计和抑制，取得了较理想的效果。In summary, as long as the parameters of the error regulator and the gain of the observer are selected reasonably, the trajectory linearization control based on the nonlinear disturbance observer can realize the attitude tracking of the spacecraft, with high precision and small modal vibration amplitude of the flexible sail . In addition, the nonlinear disturbance observer is used to estimate and suppress the uncertain disturbance, and the ideal effect is achieved.
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510874918.3ACN105468007B (en) | 2015-12-02 | 2015-12-02 | A kind of flexible satellite track linearisation attitude control method based on interference observer |
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510874918.3ACN105468007B (en) | 2015-12-02 | 2015-12-02 | A kind of flexible satellite track linearisation attitude control method based on interference observer |
| Publication Number | Publication Date |
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| CN105468007Atrue CN105468007A (en) | 2016-04-06 |
| CN105468007B CN105468007B (en) | 2018-07-06 |
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201510874918.3AActiveCN105468007B (en) | 2015-12-02 | 2015-12-02 | A kind of flexible satellite track linearisation attitude control method based on interference observer |
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