三轴稳定卫星姿态确定与控制系统关键技术研究
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摘要
卫星姿态控制系统是卫星的核心部分,一定程度上决定了卫星所能实现的在轨功能。要保证遥感卫星的高精度、高可靠性和高稳定性的在轨长期运行,必须保证足够的指向精度和控制稳定度。论文研究了卫星姿态控制系统中的多个关键技术,包括星敏感器姿态测量算法、基于鲁棒Hoo滤波器的姿态确定算法和基于滑模变结构控制器的姿态跟踪控制算法,实验结果与分析证实了提出的方法能够充分保证卫星上有效载荷的成像精度。论文所作的主要工作如下：
建立卫星姿态控制系统相关数学模型,包括姿态动力学、轨道动力学模型,测量矢量参考模型,执行机构数学模型,空间干扰力矩模型,定义了常用坐标系,姿态描述方法,以及卫星在轨运行的工作模式和逻辑转换关系。
简要介绍了星敏感器的技术指标,工作模式和误差来源,实现了观测星图模拟算法,重点研究了星敏感器的姿态测量方法,采用SAO星表建立导航星库,对观测星图进行预处理及质心定位提取,归纳总结了现有的几类星图识别算法,提出了一种新的基于对数极坐标变换的改进栅格方法,采用对数极坐标变换将二维特征向量降维描述,设计新的特征向量表示规则,采用哈希表建立和查找导航星库,仿真验证该方法能够有效改善和提高星图识别算法的性能指标。
给出矢量确定算法的基本原理,将离散扩展卡尔曼滤波算法应用到“星敏感器+陀螺仪”组合中,推导误差模型,估计姿态参数和其它参数,分析滤波器初始值对结果的影响。建立基于“星敏感器+陀螺仪”的系统模型,将非线性时变系统转换为线性时不变系统,采用鲁棒H∞滤波器估计卫星姿态参数,建立鲁棒滤波器方程,推导增广滤波误差方程,根据有界实引理及Schur补引理,将对传递函数H∞范数的约束条件转换为矩阵不等式,采用变量替换的方式得到关于鲁棒滤波器系数矩阵的线性矩阵不等式,采用LMI工具箱求解线性矩阵不等式的可行解得到滤波器的系数矩阵,迭代求解状态误差量。
引入基于Delta算子离散化系统的鲁棒Hoo滤波器,推导滤波误差方程,根据有界实引理及Riccati不等式推导带采样周期的矩阵不等式,应用Schur补引理推导新的矩阵不等式,联合两个不等式采用ILMI方法迭代求解最小化的扰动衰减因子γ,求解参数γ稳定下的滤波误差方程系数矩阵,推导得到鲁棒滤波器系数矩阵,迭代估计卫星姿态参数,这种方法对于采样周期较小的系统具有较好的效果。
建立误差运动学与误差动力学方程,在卫星姿态跟踪控制中采用滑模变结构控制器,设计控制律,与PD方法对比分析控制效果。设计提出了一种混合参数积分滑模控制器并应用到卫星姿态跟踪中,设计混合参数积分滑模面函数,选择指数趋近律作为切换函数,采用基于李亚普诺夫函数的方法推导了控制量的选取方式,并证明了系统的渐近稳定性,仿真结果表明这种基于混合参数积分滑模控制器收敛、响应速度快,稳态误差小,控制精度高。
为克服趋近运动阶段鲁棒性较弱的缺点,设计了一种全鲁棒变结构控制器,构建非线性切换函数使系统轨线从开始就落在滑模面上,结合改进的指数趋近律函数,减小振颤,推导干扰力矩有界情况下的控制律函数,保证系统的全程鲁棒性,仿真实验证明了这种全鲁棒变结构控制器具有较好的性能指标,能够满足三轴稳定卫星指向精度和控制稳定度的要求。
The attitude control system is the key part of satellite, which determines the realization of in-orbit functions in some degree. To guarantee long-time running with high accuracy, high credibility and high stability of satellite, the pointing precision and stability must satisfy requirements. The thesis researches on several key technologies, including star sensor measuring algorithm, attitude determination algorithm based on robust H∞filter and attitude tracking control algorithm based on sliding mode control. The simulation results and analysis prove that the proposed methods can guarantee imaging precision of payloads on satellite. The main works and results are as follows:
First, relative math models of satellite attitude control system have been built, including attitude dynamics, attitude kinematics, orbit dynamics, measuring vector reference models, actuators math models. And conventional coordinates, attitude description methods have been defined; in-orbit working modes and the transformation relationship also are introduced.
Then, technical indexes, working modes and error sources of star sensor have been presented simply, and simulation of observed catalog has been realized. Furthermore, attitude measuring methods have been paid attention to. Navigation star database by SAO catalog is built, then the methods of pretreatment and centroids positioning of observed catalog are given. Several existing star pattern recognition methods are summarized. The thesis has proposed a new improved grid algorithm based on log-polar transformation. By LPT two dimension feature vector has been reduced to one dimension, a new feature vector rule has been designed here, navigation star database has been built and searched by data structure Hash table. Simulation results show that this new method can improve performance indexes of star pattern recognition algorithm.
Third, the principle of vector determination methods is given. Then discrete EKF has been applied to the combination of star sensor and gyro, deriving error models, estimating attitude and other parameters, analyzing the influences of filter intial values. System model of star sensor and gyro which is nonlinear time variable system has been transformed into linear time invariant system. Robust H∞filter is used to estimate attitude parameters, building robust filter equation, deriving augmented filter error equations. According to bounded real lemma and Schur supplement lemma, restricted condition by transfer function of H∞norm is transformed into matrix inequality, by using of variable substitution method the linear matrix inequality of robust filter coefficient matrix can be got. Then, status errors can be resolved iteratively.
Introducing delta operator into robust H∞filter, deriving filter error equation, by bounded real lemma and Riccati inequality matrix inequality with sampling period has been derived. Another new matrix inequality is deduced by Schur supplement lemma. ILMI method is used to resolve these two inequalities, and minimum disturbing attenuation factor y can be solved out. Then robust filter coefficient matrix can be derived by filter error equation coefficient matrix when parameter y reaches stable. And attitude parameters can be estimated iteratively. This algorithm has good effect in short-period system.
Forth, by building error kinematic eqution and error dynamic equation, normal sliding mode controller has been used in attitude tracking control, and control law is designed, which has been compared to PD controller. A new hybrid parameter integar controller has been proposed and applied into attitude tracking control. Designing a hybrid parameter integar sliding surface, using exponential approach law as switching function, deriving control law by Lyapunove function method, and asymptotic stability of the system has been proven. Simulations demonstrate that this controller is good at convergence rate, corresponding velocity, smaller steady-state error and higher control precision.
To overcome the weakness that the reaching process is of bad robustness, a gobal variable structure controller has been designed. System initial point is at sliding mode surface by constructing nonlinear switching function; combining with improved exponential approach law, chattering is weakened. Control law in the situation of bounded interference control torques has been derived, which can satisfy global robustness. Simulation results show that this global robust variable structure controller has good performance indexes, which can satisfy pointing precision and control stability requirements of three stabilized-axis satellite.
建立卫星姿态控制系统相关数学模型,包括姿态动力学、轨道动力学模型,测量矢量参考模型,执行机构数学模型,空间干扰力矩模型,定义了常用坐标系,姿态描述方法,以及卫星在轨运行的工作模式和逻辑转换关系。
简要介绍了星敏感器的技术指标,工作模式和误差来源,实现了观测星图模拟算法,重点研究了星敏感器的姿态测量方法,采用SAO星表建立导航星库,对观测星图进行预处理及质心定位提取,归纳总结了现有的几类星图识别算法,提出了一种新的基于对数极坐标变换的改进栅格方法,采用对数极坐标变换将二维特征向量降维描述,设计新的特征向量表示规则,采用哈希表建立和查找导航星库,仿真验证该方法能够有效改善和提高星图识别算法的性能指标。
给出矢量确定算法的基本原理,将离散扩展卡尔曼滤波算法应用到“星敏感器+陀螺仪”组合中,推导误差模型,估计姿态参数和其它参数,分析滤波器初始值对结果的影响。建立基于“星敏感器+陀螺仪”的系统模型,将非线性时变系统转换为线性时不变系统,采用鲁棒H∞滤波器估计卫星姿态参数,建立鲁棒滤波器方程,推导增广滤波误差方程,根据有界实引理及Schur补引理,将对传递函数H∞范数的约束条件转换为矩阵不等式,采用变量替换的方式得到关于鲁棒滤波器系数矩阵的线性矩阵不等式,采用LMI工具箱求解线性矩阵不等式的可行解得到滤波器的系数矩阵,迭代求解状态误差量。
引入基于Delta算子离散化系统的鲁棒Hoo滤波器,推导滤波误差方程,根据有界实引理及Riccati不等式推导带采样周期的矩阵不等式,应用Schur补引理推导新的矩阵不等式,联合两个不等式采用ILMI方法迭代求解最小化的扰动衰减因子γ,求解参数γ稳定下的滤波误差方程系数矩阵,推导得到鲁棒滤波器系数矩阵,迭代估计卫星姿态参数,这种方法对于采样周期较小的系统具有较好的效果。
建立误差运动学与误差动力学方程,在卫星姿态跟踪控制中采用滑模变结构控制器,设计控制律,与PD方法对比分析控制效果。设计提出了一种混合参数积分滑模控制器并应用到卫星姿态跟踪中,设计混合参数积分滑模面函数,选择指数趋近律作为切换函数,采用基于李亚普诺夫函数的方法推导了控制量的选取方式,并证明了系统的渐近稳定性,仿真结果表明这种基于混合参数积分滑模控制器收敛、响应速度快,稳态误差小,控制精度高。
为克服趋近运动阶段鲁棒性较弱的缺点,设计了一种全鲁棒变结构控制器,构建非线性切换函数使系统轨线从开始就落在滑模面上,结合改进的指数趋近律函数,减小振颤,推导干扰力矩有界情况下的控制律函数,保证系统的全程鲁棒性,仿真实验证明了这种全鲁棒变结构控制器具有较好的性能指标,能够满足三轴稳定卫星指向精度和控制稳定度的要求。
The attitude control system is the key part of satellite, which determines the realization of in-orbit functions in some degree. To guarantee long-time running with high accuracy, high credibility and high stability of satellite, the pointing precision and stability must satisfy requirements. The thesis researches on several key technologies, including star sensor measuring algorithm, attitude determination algorithm based on robust H∞filter and attitude tracking control algorithm based on sliding mode control. The simulation results and analysis prove that the proposed methods can guarantee imaging precision of payloads on satellite. The main works and results are as follows:
First, relative math models of satellite attitude control system have been built, including attitude dynamics, attitude kinematics, orbit dynamics, measuring vector reference models, actuators math models. And conventional coordinates, attitude description methods have been defined; in-orbit working modes and the transformation relationship also are introduced.
Then, technical indexes, working modes and error sources of star sensor have been presented simply, and simulation of observed catalog has been realized. Furthermore, attitude measuring methods have been paid attention to. Navigation star database by SAO catalog is built, then the methods of pretreatment and centroids positioning of observed catalog are given. Several existing star pattern recognition methods are summarized. The thesis has proposed a new improved grid algorithm based on log-polar transformation. By LPT two dimension feature vector has been reduced to one dimension, a new feature vector rule has been designed here, navigation star database has been built and searched by data structure Hash table. Simulation results show that this new method can improve performance indexes of star pattern recognition algorithm.
Third, the principle of vector determination methods is given. Then discrete EKF has been applied to the combination of star sensor and gyro, deriving error models, estimating attitude and other parameters, analyzing the influences of filter intial values. System model of star sensor and gyro which is nonlinear time variable system has been transformed into linear time invariant system. Robust H∞filter is used to estimate attitude parameters, building robust filter equation, deriving augmented filter error equations. According to bounded real lemma and Schur supplement lemma, restricted condition by transfer function of H∞norm is transformed into matrix inequality, by using of variable substitution method the linear matrix inequality of robust filter coefficient matrix can be got. Then, status errors can be resolved iteratively.
Introducing delta operator into robust H∞filter, deriving filter error equation, by bounded real lemma and Riccati inequality matrix inequality with sampling period has been derived. Another new matrix inequality is deduced by Schur supplement lemma. ILMI method is used to resolve these two inequalities, and minimum disturbing attenuation factor y can be solved out. Then robust filter coefficient matrix can be derived by filter error equation coefficient matrix when parameter y reaches stable. And attitude parameters can be estimated iteratively. This algorithm has good effect in short-period system.
Forth, by building error kinematic eqution and error dynamic equation, normal sliding mode controller has been used in attitude tracking control, and control law is designed, which has been compared to PD controller. A new hybrid parameter integar controller has been proposed and applied into attitude tracking control. Designing a hybrid parameter integar sliding surface, using exponential approach law as switching function, deriving control law by Lyapunove function method, and asymptotic stability of the system has been proven. Simulations demonstrate that this controller is good at convergence rate, corresponding velocity, smaller steady-state error and higher control precision.
To overcome the weakness that the reaching process is of bad robustness, a gobal variable structure controller has been designed. System initial point is at sliding mode surface by constructing nonlinear switching function; combining with improved exponential approach law, chattering is weakened. Control law in the situation of bounded interference control torques has been derived, which can satisfy global robustness. Simulation results show that this global robust variable structure controller has good performance indexes, which can satisfy pointing precision and control stability requirements of three stabilized-axis satellite.
引文
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