CN113220003A - Attitude stabilization hybrid non-fragile control method for non-cooperative flexible assembly spacecraft - Google Patents
Attitude stabilization hybrid non-fragile control method for non-cooperative flexible assembly spacecraft Download PDFInfo
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Abstract
本发明涉及一种非合作柔性组合体航天器姿态稳定混合非脆弱控制方法。本发明是为了解决多源复杂扰动下非合作柔性组合体姿态高精高稳控制问题,多源扰动包括测量误差、执行机构故障、控制器加法式/乘法式增益摄动共存等问题。一、分离未知不确定惯性参数到综合干扰并将姿态动力学模型化为状态空间形式;二、构建含惯性参数、执行机构故障等复杂扰动的综合干扰项,完善一中的状态空间方程;三、考虑加法/乘法式增益摄动共存设计混合非脆弱控制器;四、将三代入二构建闭环姿控系统。五、推导满足系统稳定性的线性矩阵不等式条件并利用工具箱求解;六、在输入受限下实现非合作柔性组合体姿态/模态一体化控制。本发明用于航天器姿态稳定控制领域。
The invention relates to a hybrid non-fragile control method for attitude stability of a non-cooperative flexible composite spacecraft. The invention aims to solve the problem of high-precision and high-stability control of the attitude of a non-cooperative flexible assembly under complex multi-source disturbances, including measurement errors, actuator failures, and controller additive/multiplicative gain perturbations coexisting. 1. Separate unknown and uncertain inertial parameters into synthetic disturbances and model attitude dynamics into state space forms; 2. Construct synthetic disturbance terms including inertial parameters, actuator faults and other complex disturbances, and improve the state space equations in No. 1; 3. . Design a hybrid non-fragile controller considering the coexistence of additive/multiplicative gain perturbation; 4. Substitute three into two to construct a closed-loop attitude control system. 5. Derive the linear matrix inequality conditions that satisfy the stability of the system and use the toolbox to solve it; 6. Realize the attitude/modal integrated control of the non-cooperative flexible assembly under input constraints. The invention is used in the field of spacecraft attitude stability control.
Description
技术领域technical field
本发明涉及空间非合作目标抓捕后柔性组合体航天器姿态稳定混合非脆弱控制方法。The invention relates to a hybrid non-fragile control method for attitude stability of a flexible composite spacecraft after the capture of a space non-cooperative target.
背景技术Background technique
随着人类航天技术的发展和航天活动的增加,空间失效目标和太空垃圾等逐年增加,占据着宝贵的轨道资源,同时威胁其他航天器的正常运行,该类空间目标无法主动提供状态信息及惯性参数信息,且其稳定高精度在轨运行受到复杂扰动影响,是典型的非合作目标,对该类空间目标的捕获处理对航天活动的可持续发展具有重要意义,而抓捕后形成的柔性组合体航天器的姿态高精高稳控制是非常重要的环节。With the development of human spaceflight technology and the increase of space activities, space failure targets and space junk have increased year by year, occupying precious orbital resources and threatening the normal operation of other spacecraft. Such space targets cannot actively provide state information and inertia. parameter information, and its stable and high-precision on-orbit operation is affected by complex disturbances, which is a typical non-cooperative target. The capture and processing of such space targets is of great significance to the sustainable development of space activities, and the flexible combination formed after capture The high-precision and high-stability control of the attitude of the spacecraft is a very important link.
在实际工作条件下,抓捕后组合体航天器的控制不仅面临着状态信息和惯性参数信息未知的问题,还有模型参数不确定性、外界干扰、测量误差、执行机构故障、输入饱和、控制器加法/乘法式摄动共存等不利因素,同时由于物理和安全限制,实际执行机构工作时存在限幅。这些不利因素都会导致针对理想情况设计的控制系统性能下降甚至失稳。Under actual working conditions, the control of the post-capture composite spacecraft not only faces the problem of unknown state information and inertial parameter information, but also the uncertainty of model parameters, external disturbances, measurement errors, actuator failures, input saturation, control However, due to physical and safety constraints, there are limitations in the actual operation of the actuator. These unfavorable factors will lead to the performance degradation or even instability of the control system designed for the ideal situation.
目前尚未出现同时考虑上述不利因素尤其是控制器加法/乘法式摄动共存时非合作柔性组合体航天器的姿态高精高稳混合非脆弱控制方法,且达到稳定的时间和精度也不能保证。At present, there is no hybrid non-fragile control method for non-cooperative flexible composite spacecraft that considers the above disadvantageous factors at the same time, especially when the controllers coexist with additive/multiplicative perturbations, and the time and accuracy to achieve stability cannot be guaranteed.
发明内容SUMMARY OF THE INVENTION
本发明的目的是为了解决存在惯性未知不确定性、模型参数不确定性、外界干扰、测量误差、执行机构故障、输入饱和、控制器加法式/乘法式增益摄动共存等复杂情形下非合作柔性组合体航天器姿态高精高稳控制问题,而提出的一种非合作柔性组合体航天器姿态稳定混合非脆弱控制方法。The purpose of the present invention is to solve the problem of non-cooperation in complex situations such as inertia unknown uncertainty, model parameter uncertainty, external disturbance, measurement error, actuator failure, input saturation, controller additive/multiplicative gain perturbation coexistence, etc. To solve the problem of high-precision and high-stability control of the attitude of a flexible composite spacecraft, a hybrid non-fragile control method for attitude stability of a non-cooperative flexible composite spacecraft is proposed.
一种非合作柔性组合体航天器姿态稳定混合非脆弱控制方法包括以下步骤:A non-cooperative flexible composite spacecraft attitude stabilization hybrid non-fragile control method includes the following steps:
步骤一、构建并分离惯性参数未知不确定项,同时考虑模型参数不确定性,将存在外界干扰的非合作柔性组合体航天器姿态动力学模型改写成状态空间方程形式。Step 1: Construct and separate the unknown and uncertain terms of inertial parameters, and at the same time consider the uncertainty of model parameters, and rewrite the attitude dynamics model of the non-cooperative flexible composite spacecraft with external interference into the form of state space equation.
步骤二、针对测量误差、执行机构故障,构建执行机构故障干扰项并与步骤一中的惯性参数未知不确定项和外界干扰力矩项组成综合干扰项。Step 2: For the measurement error and actuator fault, construct the actuator fault interference term and form a comprehensive interference term with the unknown uncertainty term of the inertial parameter and the external interference torque term in step 1.
步骤三、针对控制器增益加法/乘法式摄动共存问题,定义控制器参数,设计混合非脆弱控制器。Step 3: Aiming at the coexistence problem of controller gain additive/multiplicative perturbation, define controller parameters and design a hybrid non-fragile controller.
步骤四、将混合非脆弱控制器代入包含综合干扰项的非合作柔性组合体姿态动力学状态空间模型,建立闭环系统状态空间模型。Step 4: Substitute the hybrid non-fragile controller into the attitude dynamics state space model of the non-cooperative flexible assembly including the comprehensive disturbance term, and establish a closed-loop system state space model.
步骤五、根据李雅普诺夫稳定性理论和线性矩阵不等式方法,推导满足系统稳定性的线性矩阵不等式充分条件以求解步骤三中的控制器参数并代入控制器,使步骤四中的状态空间模型完整。
步骤六、在控制力矩限幅的条件下,控制非合作柔性组合体的姿态角、姿态角速度和模态位移快速达到稳定,并且保证一定控制精度。Step 6: Under the condition of controlling the torque limit, the attitude angle, attitude angular velocity and modal displacement of the non-cooperative flexible assembly are controlled to quickly achieve stability, and a certain control accuracy is guaranteed.
本发明的有益效果为:The beneficial effects of the present invention are:
与现有技术相比,本发明的有益效果是在惯性参数未知不确定性、模型参数不确定性、外界干扰、测量误差、执行机构故障、输入饱和、控制器加法式/乘法式增益摄动共存的情况下,能够使非合作柔性组合体航天器快速达到高精高稳状态,并且稳定时间不超过150s,姿态角控制精度小于0.01rad,姿态角速度控制精度小于0.01rad/s,模态位移控制精度小于0.01,在整个控制过程中,控制力矩的大小始终不超过15Nm。Compared with the prior art, the present invention has the beneficial effects of unknown uncertainty of inertial parameters, uncertainty of model parameters, external disturbances, measurement errors, failures of actuators, input saturation, and additive/multiplicative gain perturbation of the controller. In the case of coexistence, the non-cooperative flexible composite spacecraft can quickly reach a high-precision and high-stability state, and the stabilization time does not exceed 150s, the attitude angle control accuracy is less than 0.01rad, the attitude angular velocity control accuracy is less than 0.01rad/s, and the modal displacement The control precision is less than 0.01, and the size of the control torque does not exceed 15Nm throughout the control process.
本发明设计的混合非脆弱控制方法,使空间非合作目标抓捕后柔性组合体航天器在惯性参数未知不确定性、模型参数不确定性、外界干扰、测量误差、执行机构故障、输入饱和、控制器加法式/乘法式增益摄动共存等复杂扰动下快速达到稳定状态,满足任务需求。The hybrid non-fragile control method designed by the invention enables the flexible composite spacecraft to have unknown inertial parameters, model parameter uncertainties, external disturbances, measurement errors, actuator failures, input saturation, etc. The controller can quickly reach a stable state under complex disturbances such as the coexistence of additive/multiplicative gain perturbations to meet mission requirements.
附图说明Description of drawings
图1为本发明一种非合作柔性组合体航天器姿态稳定混合非脆弱控制方法的流程图;1 is a flowchart of a non-cooperative flexible composite spacecraft attitude stabilization hybrid non-fragile control method of the present invention;
图2为本发明中在混合非脆弱控制器作用下,非合作柔性组合体航天器姿态角大小的变化曲线,θ、ψ分别表示航天器的滚动角、偏航角和俯仰角,rad表示角度的单位为弧度;Fig. 2 is the change curve of the attitude angle of the non-cooperative flexible assembly spacecraft under the action of the hybrid non-fragile controller in the present invention, θ and ψ represent the roll angle, yaw angle and pitch angle of the spacecraft, respectively, and rad represents the unit of the angle in radians;
图3为本发明中在混合非脆弱控制器作用下,非合作柔性组合体航天器姿态角速度大小的变化曲线,ωx,ωy,ωz分别表示角速度在本体坐标系三轴上的分量,rad/s表示角速度的单位为弧度每秒;Fig. 3 is the change curve of the attitude angular velocity of the non-cooperative flexible composite spacecraft under the action of the hybrid non-fragile controller in the present invention, ω x , ω y , ω z respectively represent the components of the angular velocity on the three axes of the body coordinate system, rad/s indicates that the unit of angular velocity is radians per second;
图4为本发明中在混合非脆弱控制器作用下,非合作柔性组合体航天器模态位移的变化曲线,η1,η2,η3,η4分别为模态位移的四个分量;Fig. 4 is the variation curve of the modal displacement of the non-cooperative flexible assembly spacecraft under the action of the hybrid non-fragile controller in the present invention, η 1 , η 2 , η 3 , η 4 are the four components of the modal displacement respectively;
图5为本发明在混合非脆弱控制器作用下,非合作柔性组合体航天器姿态角精度的曲线,精度用姿态角向量的二范数表示;Fig. 5 is the curve of the attitude angle accuracy of the non-cooperative flexible assembly spacecraft under the action of the hybrid non-fragile controller of the present invention, and the accuracy is represented by the two-norm of the attitude angle vector;
图6为本发明在混合非脆弱控制器作用下,非合作柔性组合体航天器姿态角速度精度的曲线,精度用姿态角速度向量的二范数表示;6 is a curve of the attitude angular velocity accuracy of the non-cooperative flexible composite spacecraft under the action of the hybrid non-fragile controller according to the present invention, and the accuracy is represented by the two-norm of the attitude angular velocity vector;
图7为本发明在混合非脆弱控制器作用下,非合作柔性组合体航天器模态位移精度的曲线,精度用模态位移向量的二范数表示;Fig. 7 is the curve of the modal displacement accuracy of the non-cooperative flexible assembly spacecraft under the action of the hybrid non-fragile controller according to the present invention, and the accuracy is represented by the two-norm of the modal displacement vector;
图8为本发明中控制力矩大小的变化曲线,ux,uy,uz分别表示控制力矩在本体坐标系三轴上的分量,Nm表示控制力矩的单位为牛米。Fig. 8 is the change curve of the control torque in the present invention, u x , u y , and u z respectively represent the components of the control torque on the three axes of the body coordinate system, and Nm represents the unit of the control torque is Newton meters.
具体实施方式Detailed ways
具体实施方式一:结合图1说明本实施方式,本实施方式的一种非合作柔性组合体航天器姿态稳定混合非脆弱控制方法,其特征在于,Specific embodiment 1: This embodiment is described with reference to FIG. 1 . A non-cooperative flexible composite spacecraft attitude stability hybrid non-fragile control method of this embodiment is characterized in that:
一种非合作柔性组合体航天器姿态稳定混合非脆弱控制方法包括以下步骤:A non-cooperative flexible composite spacecraft attitude stabilization hybrid non-fragile control method includes the following steps:
步骤一、通过引入标称惯性矩阵的方式,构建并分离惯性参数未知不确定项,同时考虑模型参数不确定性,将存在外界干扰力矩(如空气动力力矩、重力梯度力矩、地磁力矩)的非合作柔性组合体航天器姿态动力学方程改写成状态空间形式;Step 1. Construct and separate the unknown uncertainties of inertial parameters by introducing the nominal inertia matrix. At the same time, considering the uncertainties of model parameters, there will be irregularities of external disturbance moments (such as aerodynamic moments, gravity gradient moments, and geomagnetic moments). The attitude dynamics equation of the cooperative flexible assembly spacecraft is rewritten into the state space form;
步骤二、针对测量误差、执行机构故障,构建执行机构故障干扰项并与步骤一中的惯性参数未知不确定项和外界干扰力矩项组成综合干扰项;Step 2: For the measurement error and the actuator fault, construct the actuator fault interference term and form a comprehensive interference term with the unknown uncertainty term of the inertial parameter and the external interference torque term in step 1;
步骤三、针对控制器同时存在加法/乘法式摄动时,定义控制器参数,设计混合非脆弱控制器;Step 3: Define the controller parameters and design a hybrid non-fragile controller when there is an additive/multiplicative perturbation in the controller at the same time;
步骤四、将控制器模型代入包含综合干扰项的柔性航天器姿态动力学状态空间模型,建立闭环控制状态空间模型;Step 4. Substitute the controller model into the flexible spacecraft attitude dynamics state space model including the comprehensive interference term, and establish a closed-loop control state space model;
步骤五、根据线性矩阵不等式原理和李雅普诺夫稳定性原理,求解步骤三中的控制器参数并代入控制器模型,使步骤四中的状态空间模型完整。Step 5: According to the linear matrix inequality principle and the Lyapunov stability principle, solve the controller parameters in the third step and substitute them into the controller model, so that the state space model in the fourth step is complete.
步骤六、在控制输入限幅为15Nm的条件下,控制非合作柔性组合体航天器的姿态角、姿态角速度和模态位移能够在150s内达到稳定,并且使姿态角的稳定精度小于0.01弧度,姿态角速度的稳定精度小于0.01弧度每秒,模态位移稳定精度小于0.01。Step 6. Under the condition that the control input limit is 15Nm, the attitude angle, attitude angular velocity and modal displacement of the controlled non-cooperative flexible composite spacecraft can be stabilized within 150s, and the stability accuracy of the attitude angle is less than 0.01 radian, The stabilization accuracy of attitude angular velocity is less than 0.01 radians per second, and the stabilization accuracy of modal displacement is less than 0.01.
具体实施方式二:本方式与具体实施方式一不同的是:Embodiment 2: This mode is different from Embodiment 1 in that:
2.根据权利要求1所述一种非合作柔性组合体航天器姿态稳定混合非脆弱控制方法,其特征在于:所述步骤一构建并分离惯性参数未知不确定项,同时考虑模型参数不确定性,将存在外界干扰力矩(如空气动力力矩、重力梯度力矩、地磁力矩)的柔性组合体姿态动力学方程改写成状态空间形式,具体过程为:2. A kind of non-cooperative flexible composite spacecraft attitude stability hybrid non-fragile control method according to claim 1, it is characterized in that: described step 1 builds and separates the unknown uncertainty item of inertial parameter, considers model parameter uncertainty simultaneously , and rewrite the attitude dynamics equation of the flexible assembly with external disturbance torque (such as aerodynamic torque, gravity gradient torque, geomagnetic torque) into the state space form, and the specific process is as follows:
定义当地水平当地垂直坐标系Fo(Xo,Yo,Zo)(LVLH)作为参考坐标系,该坐标系原点位于非合作组合体质心,滚转轴沿飞行方向,偏航轴指向地心,俯仰轴完成右手坐标系。定义组合体航天器本体坐标系FB(XB,YB,ZB),原点位于非合作组合体质心,三个坐标轴分别与组合体惯性主轴重合。Define the local horizontal and local vertical coordinate system F o (X o , Y o , Z o ) (LVLH) as the reference coordinate system, the origin of the coordinate system is located at the center of mass of the non-cooperative composite body, the roll axis is along the flight direction, and the yaw axis points to the center of the earth , the pitch axis completes the right-handed coordinate system. Define the composite spacecraft body coordinate system FB (X B , Y B , Z B ) , the origin is located at the center of mass of the non-cooperative composite body, and the three coordinate axes coincide with the inertial main axis of the composite body respectively.
则柔性组合体航天器的姿态运动学方程为:Then the attitude kinematics equation of the flexible composite spacecraft is:
其中,θ和ψ分别表示柔性组合体航天器的三个分量,即滚转、俯仰和偏航姿态角,ω0表示柔性组合体所在的轨道角速度。在高轨组合体进行小角度姿态调整时,有:in, θ and ψ represent the three components of the flexible assembly spacecraft, namely roll, pitch and yaw attitude angles, respectively, and ω 0 represents the orbital angular velocity where the flexible assembly is located. When the high-orbit assembly performs small-angle attitude adjustment, there are:
如果将压电驱动器结合到组合体柔性附件的表面以提供输入电压up,从而产生导致控制力矩的变形,则组合体本体及柔性动力学方程可以表示为如下形式:If a piezoelectric actuator is coupled to the surface of the composite flexible attachment to provide an input voltage up , resulting in a deformation that results in a control torque, the composite body and flexibility dynamics equations can be expressed as follows:
其中,表示组合体本体的惯性矩阵,ω=[ωx ωy ωz]表示姿态角速度矢量,包含滚转、俯仰和偏航姿态角变化率,表示刚体与组合体柔性结构之间的耦合系数矩阵,表示相对组合体本体的模态坐标矢量,和表示控制输入力矩和外界干扰力矩;表示模态阻尼矩阵,其中和Ωi,i=1,2,…,m分别表示阻尼比和固有频率,表示刚度矩阵,而m是所考虑的柔性模态的个数。此处,Td包括重力梯度力矩、太阳辐射压力矩和空气动力矩,up表示压电输入电压,而是对应的耦合系数矩阵。in, represents the inertia matrix of the combined body, ω=[ω x ω y ω z ] represents the attitude angular velocity vector, including the roll, pitch and yaw attitude angle change rates, represents the coupling coefficient matrix between rigid body and composite flexible structure, represents the modal coordinate vector relative to the assembly body, and Indicates the control input torque and external disturbance torque; represents the modal damping matrix, where and Ω i , i=1,2,...,m represent damping ratio and natural frequency, respectively, represents the stiffness matrix, and m is the number of flexible modes considered. Here, T d includes gravity gradient moment, solar radiation pressure moment and aerodynamic moment, u p represents the piezoelectric input voltage, and is the corresponding coupling coefficient matrix.
定义辅助变量得到:define auxiliary variables get:
代入非合作柔性组合体姿态动力学方程组中的第二个方程,得到改写后的方程:Substitute into the second equation in the non-cooperative flexible assembly attitude dynamics equations to get the rewritten equation:
采用真实值反馈,压电输入up表示为:Using real value feedback, the piezoelectric input u p is expressed as:
式中Fa,Fb为测量反馈系数。将代入辅助变量导数和改写后的柔性组合体姿态动力学方程,得到:where F a and F b are measurement feedback coefficients. Will Substitute the auxiliary variable derivative and the rewritten attitude dynamics equation of the flexible assembly, we get:
令可将上述两式改写为状态空间形式:make The above two equations can be rewritten in state space form:
其中状态变量输出变量u(t)=Tc为控制力矩,是综合干扰。系数矩阵:where the state variable output variable u(t)=T c is the control torque, is the combined interference. Coefficient matrix:
C=I6+2m C=I6 +2m
未知的惯性参数信息全部归化至下列系数矩阵中:The unknown inertial parameter information is all reduced to the following coefficient matrix:
其中Jn为标称惯量矩阵。in J n is the nominal inertia matrix.
△Ap表示模型参数不确定性(惯性不确定性除外),其具有范数界且满足匹配条件:△A p represents the model parameter uncertainty (except inertial uncertainty), which is norm bound and satisfies the matching condition:
其中M1和N1是具有合适维度的实常数矩阵,F1(t)是勒贝格可测量的矩阵函数。where M 1 and N 1 are real constant matrices of suitable dimensions, and F 1 (t) is a Lebesgue-measurable matrix function.
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 in the first embodiment.
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:Embodiment 3: The difference between this embodiment and Embodiment 1 or 2 is that:
3.根据权利要求2所述一种非合作柔性组合体航天器姿态稳定混合非脆弱控制方法,其特征在于:所述步骤二中针对存在测量误差、执行机构故障情况下,构建执行机构故障干扰项并与步骤一中的惯性参数未知不确定项和外界干扰力矩项组成综合干扰项;具体过程为:3. A kind of non-cooperative flexible composite spacecraft attitude stability hybrid non-fragile control method according to claim 2, it is characterized in that: in the described step 2, for the existence of measurement error and actuator failure situation, construct actuator failure interference term and together with the unknown uncertainty term of inertial parameters and the external disturbance moment term in step 1 to form a comprehensive disturbance term; the specific process is as follows:
执行机构动作不当会严重影响姿态控制系统的性能,让具有列满秩的E(其结构与B1相似)表示出现在输入中的故障信号f(t)的分布矩阵。如果E≠B1,则表示过程故障;如果E=B1,则表示执行机构故障。Improper action of the actuator will seriously affect the performance of the attitude control system, let E with full rank (its structure is similar to B1) represent the distribution matrix of the fault signal f(t) appearing in the input. If E≠B 1 , it means a process failure; if E=B 1 , it means an actuator failure.
将上述复杂扰动因素构建为综合干扰:The above complex disturbance factors are constructed as synthetic disturbances:
其中矩阵是B2的伪逆,步骤一中状态空间方程改写为:where the matrix is the pseudo-inverse of B 2 , and the state space equation in step 1 is rewritten as:
其中v(t)代表测量误差。where v(t) represents the measurement error.
其他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 in the first or second embodiment.
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:Specific embodiment four: this embodiment is different from one of specific embodiments one to three in that:
4.根据权利要求3所述一种非合作柔性组合体航天器姿态稳定混合非脆弱控制方法,其特征在于:所述步骤三中针对控制器同时存在加法/乘法式摄动时,定义控制器参数,设计混合非脆弱控制器;具体过程为:4. a kind of non-cooperative flexible composite spacecraft attitude stability hybrid non-fragile control method according to claim 3, is characterized in that: in the described step 3, when there is additive/multiplicative perturbation for the controller at the same time, define the controller parameters, design a hybrid non-fragile controller; the specific process is:
在控制器同时存在加法/乘法式摄动时,设计控制器的形式如下:When the controller has additive/multiplicative perturbations at the same time, the form of designing the controller is as follows:
是控制器引入的状态变量,是不考虑测量误差对输出变量的估计值,Ac、Bc是具有合适维度的控制器系数矩阵,K为控制器增益矩阵。控制器错误和未知的执行机构动力学特性会导致摄动问题,当△K是加法式摄动时,其数学表达式为△K=M2F2(t)N2,||F2(t)||≤1,当△K是乘法式摄动时,其数学表达式为△K=M3F3(t)N3K,||F3(t)||≤1。 is the state variable introduced by the controller, is the estimated value of the output variable without considering the measurement error, A c , B c are the controller coefficient matrices with appropriate dimensions, and K is the controller gain matrix. Controller errors and unknown actuator dynamics can lead to perturbation problems. When △K is an additive perturbation, its mathematical expression is △K=M 2 F 2 (t)N 2 ,||F 2 ( t)||≤1, when ΔK is a multiplicative perturbation, its mathematical expression is ΔK=M 3 F 3 (t)N 3 K,||F 3 (t)||≤1.
同时考虑控制器存在上述两种摄动问题,其表达式为:Considering the above two perturbation problems in the controller at the same time, the expressions are:
△K=M2F2(t)N2+M3F3(t)N3K,||F2(t)||≤1,||F3(t)||≤1△K=M 2 F 2 (t)N 2 +M 3 F 3 (t)N 3 K,||F 2 (t)||≤1,||F 3 (t)||≤1
M2、N2、M3、N3是具有合适维度的实常数矩阵,F2(t)、F3(t)是勒贝格可测量的矩阵函数。M 2 , N 2 , M 3 , N 3 are real constant matrices of suitable dimensions, and F 2 (t), F 3 (t) are Lebesgue-measurable matrix functions.
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 one of the first to third embodiments.
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:Embodiment 5: This embodiment is different from one of Embodiments 1 to 4 in that:
5.根据权利要求4所述一种非合作柔性组合体航天器姿态稳定混合非脆弱控制方法,其特征在于:所述步骤四将控制器代入包含综合干扰项的非合作柔性组合体航天器姿态动力学状态空间方程,建立闭环姿态控制系统状态空间模型;具体过程为:5. A kind of non-cooperative flexible composite spacecraft attitude stability hybrid non-fragile control method according to claim 4, it is characterized in that: described step 4 substitutes the controller into the non-cooperative flexible composite spacecraft attitude that includes comprehensive interference term The dynamic state space equation is used to establish the state space model of the closed-loop attitude control system; the specific process is as follows:
将步骤三中得到的控制器代入步骤二中包含综合干扰项的非合作柔性组合体航天器姿态动力学模型得到:Substitute the controller obtained in step 3 into the attitude dynamics model of the non-cooperative flexible composite spacecraft including the comprehensive interference term in step 2 to obtain:
其中B1=B2=B,有:in B 1 =B 2 =B, there are:
y(t)=Cx(t)=[C 0]ζ(t)y(t)=Cx(t)=[C 0]ζ(t)
系数矩阵为:The coefficient matrix is:
当加法式摄动△Kα和乘法式摄动△Km共存时系数矩阵具体数学表达式为:When the additive perturbation △K α and the multiplicative perturbation △K m coexist, the coefficient matrix The specific mathematical expression is:
其中σ∈(0,1)为给定常量。where σ∈(0,1) is a given constant.
将矩阵写成:put the matrix written as:
控制力矩u(t)写成:The control torque u(t) is written as:
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 one of the first to fourth embodiments.
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:Embodiment 6: This embodiment is different from one of Embodiments 1 to 5 in that:
6.根据权利要求5所述一种非合作柔性组合体航天器姿态稳定混合非脆弱控制方法,其特征在于:所述步骤五中根据李雅普诺夫稳定性理论和线性矩阵不等式方法,推导满足系统稳定性的线性矩阵不等式充分条件以求解步骤三中的控制器参数并代入控制器,使步骤四中的状态空间模型完整;具体过程为:6. A kind of non-cooperative flexible composite spacecraft attitude stability hybrid non-fragile control method according to
当同时存在控制器加法/乘法式摄动时,步骤二中的状态空间模型在步骤三中的控制器作用下具有二次稳定性,则输出y(t)满足H∞性能约束,对给定的常数ξ>0,γ>0,求解线性矩阵不等式:When there are controller additive/multiplicative perturbations at the same time, the state space model in step 2 has quadratic stability under the action of the controller in step 3, then the output y(t) satisfies the H ∞ performance constraint, and for a given The constant ξ>0, γ>0, solve the linear matrix inequality:
其中in
可得正定对称矩阵P11,Q11和矩阵Q21,和进而求得步骤三中的控制器参数矩阵:The positive definite symmetric matrices P 11 , Q 11 and the matrix Q 21 can be obtained, and Then, the controller parameter matrix in step 3 is obtained:
代入步骤四中的闭环系统状态空间方程。Substitute into the closed-loop system state space equation in step 4.
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 one to five.
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:Embodiment 7: The difference between this embodiment and one of Embodiments 1 to 6 is:
7.根据权利要求6所述一种非合作柔性组合体航天器姿态稳定混合非脆弱控制方法,其特征在于:在控制输入限幅的条件下,控制柔性组合体航天器的姿态角、姿态角速度和模态位移快速达到稳定,并保证一定精度;具体过程为:7. a kind of non-cooperative flexible assembly spacecraft attitude stability hybrid non-fragile control method according to claim 6, is characterized in that: under the condition of control input amplitude limit, control the attitude angle, attitude angular velocity of flexible assembly spacecraft and modal displacement quickly reach stability and ensure a certain accuracy; the specific process is:
由于物理和安全限制,执行机构存在约束,控制输入存在饱和,对设计用于“理想”情况的姿态控制系统的稳定性和性能产生负面影响。对于正标量λ:Due to physical and safety constraints, actuator constraints exist and control inputs are saturated, negatively impacting the stability and performance of attitude control systems designed for "ideal" conditions. For a positive scalar λ:
||u||<λ||u||<λ
表示控制输入的二范数饱和值为λ。在步骤五中求得的控制器上加上饱和限幅,即实际控制力矩可以描述为:Indicates that the two-norm saturation value of the control input is λ. Adding saturation limit to the controller obtained in
sat(ui=1,2,3(t))=sign(ui(t))min{|ui(t)|,umi}sat(u i=1,2,3 (t))=sign(u i (t))min{|u i (t)|,u mi }
其中umi是由执行机构提供的控制力矩上限。Where u mi is the upper limit of the control torque provided by the actuator.
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 Embodiments 1 to 6.
采用以下实施例验证本发明的有益效果:Adopt the following examples to verify the beneficial effects of the present invention:
实施例一:Example 1:
本实施例一种非合作柔性组合体航天器姿态稳定混合非脆弱控制方法具体是按照以下步骤制备的:A non-cooperative flexible composite spacecraft attitude stabilization hybrid non-fragile control method of the present embodiment is specifically prepared according to the following steps:
步骤一:构建并分离惯性参数未知不确定项,同时考虑模型参数不确定性,将存在外界干扰的非合作柔性航天器姿态动力学方程改写成状态空间方程形式。Step 1: Construct and separate the unknown and uncertain terms of inertial parameters, and at the same time consider the uncertainty of model parameters, and rewrite the attitude dynamics equation of the non-cooperative flexible spacecraft with external interference into the form of state space equation.
柔性组合体航天器姿态动力学方程可以表示为如下形式:The attitude dynamics equation of the flexible composite spacecraft can be expressed in the following form:
令可将上述两式改写为状态空间形式:make The above two equations can be rewritten in state space form:
其中状态变量输出变量u(t)=Tc为控制力矩,是外界干扰。系数矩阵:where the state variable output variable u(t)=T c is the control torque, outside interference. Coefficient matrix:
C=I6+2m C=I6 +2m
未知不确定的惯性参数信息全部归化至下列系数矩阵中:The unknown and uncertain inertial parameter information is all reduced to the following coefficient matrix:
其中Jn为标称惯性矩阵。in J n is the nominal inertia matrix.
△Ap表示模型参数的不确定性(惯性不确定性除外),其具有范数界且满足匹配条件:△A p represents the uncertainty of the model parameters (except inertial uncertainty), which has norm bounds and satisfies the matching condition:
步骤二:针对存在测量误差、执行机构故障情况下,构建执行机构故障干扰项并与步骤一中的惯性参数未知不确定项和外界干扰力矩项组成综合干扰项。Step 2: In the presence of measurement errors and actuator faults, construct the actuator fault interference term and form a comprehensive interference term with the unknown uncertainty term of the inertial parameter and the external interference torque term in step 1.
将上述复杂扰动构建为综合干扰:The above complex disturbance is constructed as a synthetic disturbance:
代入步骤一中的状态空间模型:Substitute into the state space model in step 1:
v(t)为测量误差。v(t) is the measurement error.
步骤三:针对控制器同时存在加法/乘法式摄动时,定义控制器参数,设计混合非脆弱控制器。Step 3: Define the controller parameters and design a hybrid non-fragile controller when there are additive/multiplicative perturbations in the controller at the same time.
在控制器同时存在加法/乘法式摄动时,设计控制器的形式如下:When the controller has additive/multiplicative perturbations at the same time, the form of designing the controller is as follows:
是控制器引入的状态变量,是不考虑测量误差对输出变量的估计值,Ac、Bc是具有合适维度的控制器参数矩阵,K为控制器增益矩阵。同时考虑控制器存在上述两种摄动,其表达式为: is the state variable introduced by the controller, is the estimated value of the output variable without considering the measurement error, A c , B c are the controller parameter matrices with appropriate dimensions, and K is the controller gain matrix. Considering the existence of the above two kinds of perturbation in the controller at the same time, its expression is:
△K=M2F2(t)N2+M3F3(t)N3K,||F2(t)||≤1,||F3(t)||≤1△K=M 2 F 2 (t)N 2 +M 3 F 3 (t)N 3 K,||F 2 (t)||≤1,||F 3 (t)||≤1
M2、N2、M3、N3是具有合适维度的实常数矩阵,F2(t)、F3(t)是勒贝格可测量的矩阵函数。M 2 , N 2 , M 3 , N 3 are real constant matrices of suitable dimensions, and F 2 (t), F 3 (t) are Lebesgue-measurable matrix functions.
步骤四:将控制器代入包含综合干扰项的非合作柔性组合体航天器姿态动力学状态空间方程,建立闭环姿态控制系统状态空间方程。Step 4: Substitute the controller into the state space equation of the attitude dynamics of the non-cooperative flexible composite spacecraft including the comprehensive interference term, and establish the state space equation of the closed-loop attitude control system.
将步骤三中得到的控制器代入步骤二中包含综合干扰项的柔性组合体姿态动力学方程中得到:Substitute the controller obtained in step 3 into the attitude dynamics equation of the flexible assembly including the comprehensive interference term in step 2, and obtain:
其中:in:
系数矩阵为:The coefficient matrix is:
当加法式摄动△Kα和乘法式摄动△Km共存时不确定系数矩阵具体数学表达式为:Uncertainty coefficient matrix when additive perturbation △K α and multiplicative perturbation △K m coexist The specific mathematical expression is:
其中σ∈(0,1)为给定常量。where σ∈(0,1) is a given constant.
步骤五:根据李雅普诺夫稳定性理论和线性矩阵不等式方法,推导满足系统稳定性的线性矩阵不等式充分条件以求解步骤三中的控制器参数并代入控制器,使步骤四中的状态空间模型完整。Step 5: According to the Lyapunov stability theory and the linear matrix inequality method, deduce the sufficient conditions of the linear matrix inequality satisfying the system stability to solve the controller parameters in step 3 and substitute them into the controller, so that the state space model in step 4 is complete. .
当同时存在加法/乘法式摄动时,步骤二中的状态空间模型在步骤三中的控制器作用下具有二次稳定性,则输出y(t)满足H∞性能约束,对给定的常数ξ>0,γ>0,求解线性矩阵不等式:When there are additive/multiplicative perturbations at the same time, the state space model in step 2 has quadratic stability under the action of the controller in step 3, then the output y(t) satisfies the H ∞ performance constraint, and for a given constant ξ>0, γ>0, solve the linear matrix inequality:
其中in
可得正定对称矩阵P11,Q11和矩阵Q21,和进而求得步骤三中的控制器参数矩阵:The positive definite symmetric matrices P 11 , Q 11 and the matrix Q 21 can be obtained, and Then, the controller parameter matrix in step 3 is obtained:
步骤六:在控制输入限幅的条件下,控制非合作柔性组合体航天器的姿态角、姿态角速度和模态位移快速达到稳定,并保证一定精度。Step 6: Control the attitude angle, attitude angular velocity and modal displacement of the non-cooperative flexible composite spacecraft under the condition of limiting the control input to quickly achieve stability and ensure a certain accuracy.
在步骤五中求得的控制器上加入限幅,即实际控制力矩可以描述为:Adding a limiter to the controller obtained in
sat(ui=1,2,3(t))=sign(ui(t))min{|ui(t)|,umi}sat(u i=1,2,3 (t))=sign(u i (t))min{|u i (t)|,u mi }
其中umi是由执行机构提供的控制力矩上限。Where u mi is the upper limit of the control torque provided by the actuator.
以下通过数值仿真对本实施例的一种非合作柔性组合体航天器姿态稳定混合非脆弱控制方法进行验证:A non-cooperative flexible composite spacecraft attitude stability hybrid non-fragile control method of the present embodiment is verified by numerical simulation as follows:
非合作柔性组合体航天器的标称惯性参数: Nominal inertial parameters of the non-cooperative flexible composite spacecraft:
未知不确定惯性矩阵为:△J=(0.05+0.01sin(πt))Jn The unknown uncertain inertia matrix is: △J=(0.05+0.01sin(πt))J n
所考虑的柔性模态的个数:m=4Number of flexible modes considered: m=4
刚体与柔性结构之间的耦合系数矩阵:Coupling coefficient matrix between rigid body and flexible structure:
阻尼比:[ξ1 ξ2 ξ3 ξ4]=[0.005607 0.008620 0.01283 0.02516]Damping ratio: [ξ 1 ξ 2 ξ 3 ξ 4 ]=[0.005607 0.008620 0.01283 0.02516]
固有频率:[Ω1 Ω2 Ω3 Ω4]=[0.7681 1.1038 1.8733 2.5496]Natural frequency: [Ω 1 Ω 2 Ω 3 Ω 4 ]=[0.7681 1.1038 1.8733 2.5496]
耦合矩阵: Coupling matrix:
反馈系数矩阵:Fa=[3.1533 -0.5714 5.3674 9.3389],Fb=[1.0976 0.19651.8086 3.0873]Feedback coefficient matrix: F a = [3.1533 -0.5714 5.3674 9.3389], F b = [1.0976 0.19651.8086 3.0873]
外界环境力矩: External environment torque:
勒贝格矩阵函数及其对应的实常数矩阵:Lebesgue matrix functions and their corresponding real constant matrices:
M1=0.01×[8 11 13 15 16 -18 8 11 13 15 16 18 8 11]T,M 1 =0.01×[8 11 13 15 16 -18 8 11 13 15 16 18 8 11] T ,
N1=0.01×[1 2 3 4 2 10 1 2 3 4 2 10 1 2],F1(t)=sin(0.11πt)N 1 =0.01×[1 2 3 4 2 10 1 2 3 4 2 10 1 2], F 1 (t)=sin(0.11πt)
M2=0.1×ones(3,1)N2=0.01×ones(1,14),F2(t)=sin(0.11πt+π/4)M 2 =0.1×ones(3,1) N 2 =0.01×ones(1,14), F 2 (t)=sin(0.11πt+π/4)
M3=0.1×ones(3,1)N3=0.01×ones(1,3),F3(t)=cos(0.11πt)M 3 =0.1×ones(3,1) N 3 =0.01×ones(1,3), F 3 (t)=cos(0.11πt)
角度初始值:Θ(0)=[0.18,0.15,-0.15]TradAngle initial value: Θ(0)=[0.18,0.15,-0.15] T rad
角速度初始值:ω(0)=[-0.02,-0.02,0.02]Trad/sInitial value of angular velocity: ω(0)=[-0.02,-0.02,0.02] T rad/s
模态位移初始值: Modal displacement initial value:
模态位移导数的初始值: Initial value of the modal displacement derivative:
执行机构故障信号: Actuator failure signal:
相关正常数:ξ1=0.025,ξ2=0.025,γ=3.2,σ=0.5.Relevant normals: ξ 1 =0.025,ξ 2 =0.025,γ=3.2,σ=0.5.
测量误差:Measurement error:
v(t)=10-4×[4 5 6 0.2 0.2 0.2 0.2 0.1 0.2 0.2 0.2 0.2 0.1 0.2]sin(0.01πt)v(t)=10 -4 ×[4 5 6 0.2 0.2 0.2 0.2 0.1 0.2 0.2 0.2 0.2 0.1 0.2]sin(0.01πt)
控制力矩限幅:um1=um2=um3=15NmControl torque limiter: u m1 =u m2 =u m3 =15Nm
用LMI工具箱求解线性矩阵不等式可得:Solving the linear matrix inequalities with the LMI toolbox gives:
在设计的混合非脆弱控制器下,图2至图8为相应的仿真结果,其中图2为非合作柔性组合体航天器的姿态角变化曲线,图3为非合作柔性组合体航天器姿态角速度的变化曲线,图4为非合作柔性组合体航天器模态位移的变化曲线,图5为非合作柔性组合体航天器姿态角精度的曲线,图6为非合作柔性组合体航天器姿态角速度精度的曲线,图7为非合作柔性组合体航天器模态位移精度的曲线,图8为整个姿态稳定控制过程中控制力矩的变化曲线。观察可知,非合作柔性组合体航天器的姿态角、姿态角速度和模态位移的收敛时间都小于150s,精度分别小于0.01rad、0.01rad/s和0.01,控制力矩大小始终在限幅15Nm范围内。Under the designed hybrid non-fragile controller, Figures 2 to 8 are the corresponding simulation results, in which Figure 2 is the attitude angle change curve of the non-cooperative flexible composite spacecraft, and Figure 3 is the attitude angular velocity of the non-cooperative flexible composite spacecraft. Figure 4 is the change curve of the modal displacement of the non-cooperative flexible composite spacecraft, Figure 5 is the attitude angle accuracy curve of the non-cooperative flexible composite spacecraft, and Figure 6 is the attitude angular velocity accuracy of the non-cooperative flexible composite spacecraft. Figure 7 is the curve of the modal displacement accuracy of the non-cooperative flexible composite spacecraft, and Figure 8 is the change curve of the control torque during the entire attitude stabilization control process. It can be seen from the observation that the convergence time of the attitude angle, attitude angular velocity and modal displacement of the non-cooperative flexible composite spacecraft are all less than 150s, the accuracy is less than 0.01rad, 0.01rad/s and 0.01 respectively, and the control torque is always within the limit of 15Nm. .
可见,本发明的一种非合作柔性组合体航天器姿态稳定混合非脆弱控制方法能够在惯性参数未知不确定性、模型参数不确定性、外界干扰、测量误差、执行机构故障、输入饱和、控制器加法/乘法式摄动共存等复杂扰动影响下成功使非合作柔性组合体航天器姿态达到高精高稳控制。It can be seen that a non-cooperative flexible composite spacecraft attitude stability hybrid non-fragile control method of the present invention can be used in the unknown uncertainty of inertial parameters, model parameter uncertainty, external disturbance, measurement error, actuator failure, input saturation, control Under the influence of complex disturbances such as additive/multiplicative perturbation coexistence, the attitude of the non-cooperative flexible composite spacecraft has been successfully controlled with high precision and high stability.
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 can also have other various 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 are all It should belong to the protection scope of the appended claims of the present invention.
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