火箭上面级导航、中途修正与姿态控制研究
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摘要
本文跟随我国运载火箭先进上面级的研究进展，从工程应用的目的出发，对先进上面级捷联惯导工具误差影响、捷联惯导/星敏感器/地球敏感器组合导航技术、中途修正技术和姿态控制问题进行了研究。
针对发射惯性坐标系下上面级典型MEO转移轨道的飞行过程，基于考虑J2项的地球引力模型，给出了惯性导航的解算方程，推导了惯性导航方程的误差传播方程。给出了工程中应用广泛的捷联惯导测量误差模型。根据标称弹道数据模拟了上面级MEO转移轨道的轨迹发生器，并利用它验证了惯性导航解算方程的正确性。应用算例验证和分析了捷联惯导测量误差模型中的误差项系数和初始基准误差对上面级弹道偏差的影响。基于此，选取误差项系数中的关键元素计算了一条MEO特征偏差弹道，为组合导航研究奠定了基础。
以研究上面级组合导航方案为目的，通过建立GPS导航卫星的空间可见性和导航信号的空间可用性模型，算例分析了上面级MEO转移轨道上GPS导航星可见数量，研究发现GPS导航仅能够在飞行过程中约前3150秒，高度低于7740 km时进行有效导航，而上面级MEO转移轨道最高飞行高度约为25000 km，也就是说在大部分MEO转移轨道上GPS导航是不可用的，同时也因为SINS/GPS组合导航方案姿态信息的估计精度不高，所以本文没有采用。通过分析捷联惯导/星敏感器组合导航方案知道该组合对位置和速度信息的估计精度较差，但是却可以通过其他敏感器来弥补，因此，本文提出了捷联惯导/星敏感器/地球敏感器组合的一种新的SINS/CNS组合导航方案。通过建立星敏感器的姿态测量模型和地球敏感器的地心矢量测量模型，推导了组合导航的观测方程。分别应用Kalman滤波算法和H∞滤波算法验证了SINS/CNS组合导航的有效性。
因为地球非球形引力、大气阻力、日月引力、太阳光压等摄动和变轨时导航误差、发动机推力误差等因素的影响，上面级实际转移轨道会偏离理论计算得到的标称轨道，所以本文研究了上面级转移轨道中途修正问题。基于椭圆轨道Lambert飞行时间定理，推导了修正速度计算公式。通过分析上面级转移轨道初始误差因素来源，设计了误差协方差矩阵迭代算法以计算转移轨道终点位置和速度误差，该算法与传统基于运动方程的精密积分以计算轨道误差的方法相比，具有计算量较小、速度快的优势。利用修正速度计算公式和误差协方差矩阵迭代算法，文中以不加修正、一次修正、两次修正和三次修正为例，研究了中途修正问题中修正次数的选择，通过一次修正的结果发现修正所需的速度脉冲和最终位置误差、速度误差是一个矛盾综合体，需要对三者进行折中以选择合适的修正时间点，通过多次修正的结果确定了采用两次修正的中途修正策略。进而基于两次修正策略，利用多目标优化技术对修正时机进行优化设计。应用较多的方法是将多目标优化问题转化为单目标优化问题求解，容易丢失最优解。文章采用改进的非支配分类遗传算法，不再将以最终位置误差、速度误差和修正速度脉冲最小为目标的两次修正时机优化问题转化成单目标优化问题，得到了修正时机完整的Pareto最优解集，增加了此优化问题的灵活性。
上面级进行多星部署释放有效载荷的过程和燃料消耗会产生较大的转动惯量变化和质心突变以及随之而来的惯性积强耦合，同时，上面级自身携带大型液体燃料贮箱会产生液体晃动。因此系统存在模型不确定性和液体晃动使得上面级姿态控制就变得比较困难。传统解决这类问题的方法多是进行通道解耦控制并设计抑制液体晃动的坎值滤波器。有限频域H∞控制不仅具有很强的鲁棒性，能够解决模型不确定性问题，而且还可以在特定的频域内进行有效的控制。而液体晃动的基频是可以确定的，那么通过给出两个特定频率使得液体晃动基频位于二者之间，进而完成液体晃动的抑制。因此，本文针对带有模型不确定性和液体晃动的上面级姿态模型，设计了有限频域H∞控制器。结合广义KYP引理及其推论、射影定理和反射影定理以及线性矩阵不等式知识，本文给出了有限频域下的状态反馈和输出反馈控制器设计方法。为突出有限频域H∞控制的优越性，给出了全频域下的状态反馈和输出反馈控制器设计方法。针对不同的系统模型
Following the research and development of Chinese launch vehicle upper stage, for the purpose of engineering application, the trajectory errors caused by the instrument coefficients and the initial azimuth bias of SINS, SINS/Star sensor/Earth sensor integrated navigation technology, midcourse correction technology of transfer orbit and attitude control are studied in this paper.
Considering the flight of upper stage in classical MEO transfer orbit described with launch inertial coordinate system, the inertial navigation solution equations are given out and the the errors propagation models are derived. The measurement error models of SINS are given out. A trajectory simulator of MEO transfer orbit is proposed by using the nominal trajectory data. The correctness of the inertial navigation solution equations is verified via the trajectory simulator. The trajectory errors are analyzed and a characteristical trajectory with errors is composed with some key instrument coefficients, which would be a basis for studying integrated navigation.
For the integrated navigations system, a mathematical model of the visibility of GPS satellites and the availability of navigation signals is built. GPS navigation can be effective in the flight under the conditons of 3150 seconds afore or the height of less than 7740 km. On the contrary, the highest altitude of the trajectory is about 25000 km and the total flight time is 15800 s, which means the GPS navigation is not available within the most of the trajectory. Because attitude errors of SINS/GPS navigation and position errors and velocity errors of SINS/Star sensor are not accurate, a novel SINS/Star sensor/Earth sensor integrated navigation system is proposed. The observation equations are derived from attitude measurement model and the geocentric vector measurement model. The effectiveness of the novel SINS/CNS integrated navigation is verified by using the estimation errors obtained via Kalman filter and H filter.
By the influence of non-spherical earth gravity, atmospheric drag, sun and moon gravity, solar radiation pressure and other perturbations, there are large errors between the real and the ideal transfer orbit. So the midcourse correction is studied. By the solution method of Lambert problem, the calculation method of correction velocity is derived. Considering the resourse of initial errors, an iterative algorithm with the error covariance matrix is designed, which has a superiority of small computation load and quickness compareing with the traditional calculation method of trajectory errors. Taking zero, one, two and three correction scheme as example, the choice of correction number is analyzed. The correction velocity impulse, the terminal position and velocity errors are contradictory through one correction result, which indicates that there needs to carry on a compromise. A two correction scheme is determined through multi-corrections. Then a multi-objective evolution algorithm is introduced to optimize the two correction timings. Tansforming the multi-objective optimization problem to a single objective optimization problem is a commonly used method, which can lose optimal solutions. So a modified non- dominated sorting genetic algorithm (NSGA-II) is introduced to the correction timing optimization problem, which obtains complete Pareto optimal solution set and increased flexibility of this optimization problem.
Considering the model uncertainty and the liquid sloshing, a finite frequency domain H control algorithm is presented for the upper stage attitude control. The finite frequency omain H control not only has strong robustness for solving the uncertainty problem, but also has effective control ability in specific frequency range. Based on the generalized KYP lemma and its inference, Projection lemma, Reciprocal Projection lemma and linear matrix inequality knowledge, state feedback and output feedback controllers in finite frequency domain are designed. And to highlight the advantagesof finite frequency domain H control, design methods of state feedback and output feedback controllers in entire frequency domain are presented. The effeciveness and feasibility of finite frequency domain control are verified through the results of four examples with different model parameters and the availability of jet attitude control system.
针对发射惯性坐标系下上面级典型MEO转移轨道的飞行过程，基于考虑J2项的地球引力模型，给出了惯性导航的解算方程，推导了惯性导航方程的误差传播方程。给出了工程中应用广泛的捷联惯导测量误差模型。根据标称弹道数据模拟了上面级MEO转移轨道的轨迹发生器，并利用它验证了惯性导航解算方程的正确性。应用算例验证和分析了捷联惯导测量误差模型中的误差项系数和初始基准误差对上面级弹道偏差的影响。基于此，选取误差项系数中的关键元素计算了一条MEO特征偏差弹道，为组合导航研究奠定了基础。
以研究上面级组合导航方案为目的，通过建立GPS导航卫星的空间可见性和导航信号的空间可用性模型，算例分析了上面级MEO转移轨道上GPS导航星可见数量，研究发现GPS导航仅能够在飞行过程中约前3150秒，高度低于7740 km时进行有效导航，而上面级MEO转移轨道最高飞行高度约为25000 km，也就是说在大部分MEO转移轨道上GPS导航是不可用的，同时也因为SINS/GPS组合导航方案姿态信息的估计精度不高，所以本文没有采用。通过分析捷联惯导/星敏感器组合导航方案知道该组合对位置和速度信息的估计精度较差，但是却可以通过其他敏感器来弥补，因此，本文提出了捷联惯导/星敏感器/地球敏感器组合的一种新的SINS/CNS组合导航方案。通过建立星敏感器的姿态测量模型和地球敏感器的地心矢量测量模型，推导了组合导航的观测方程。分别应用Kalman滤波算法和H∞滤波算法验证了SINS/CNS组合导航的有效性。
因为地球非球形引力、大气阻力、日月引力、太阳光压等摄动和变轨时导航误差、发动机推力误差等因素的影响，上面级实际转移轨道会偏离理论计算得到的标称轨道，所以本文研究了上面级转移轨道中途修正问题。基于椭圆轨道Lambert飞行时间定理，推导了修正速度计算公式。通过分析上面级转移轨道初始误差因素来源，设计了误差协方差矩阵迭代算法以计算转移轨道终点位置和速度误差，该算法与传统基于运动方程的精密积分以计算轨道误差的方法相比，具有计算量较小、速度快的优势。利用修正速度计算公式和误差协方差矩阵迭代算法，文中以不加修正、一次修正、两次修正和三次修正为例，研究了中途修正问题中修正次数的选择，通过一次修正的结果发现修正所需的速度脉冲和最终位置误差、速度误差是一个矛盾综合体，需要对三者进行折中以选择合适的修正时间点，通过多次修正的结果确定了采用两次修正的中途修正策略。进而基于两次修正策略，利用多目标优化技术对修正时机进行优化设计。应用较多的方法是将多目标优化问题转化为单目标优化问题求解，容易丢失最优解。文章采用改进的非支配分类遗传算法，不再将以最终位置误差、速度误差和修正速度脉冲最小为目标的两次修正时机优化问题转化成单目标优化问题，得到了修正时机完整的Pareto最优解集，增加了此优化问题的灵活性。
上面级进行多星部署释放有效载荷的过程和燃料消耗会产生较大的转动惯量变化和质心突变以及随之而来的惯性积强耦合，同时，上面级自身携带大型液体燃料贮箱会产生液体晃动。因此系统存在模型不确定性和液体晃动使得上面级姿态控制就变得比较困难。传统解决这类问题的方法多是进行通道解耦控制并设计抑制液体晃动的坎值滤波器。有限频域H∞控制不仅具有很强的鲁棒性，能够解决模型不确定性问题，而且还可以在特定的频域内进行有效的控制。而液体晃动的基频是可以确定的，那么通过给出两个特定频率使得液体晃动基频位于二者之间，进而完成液体晃动的抑制。因此，本文针对带有模型不确定性和液体晃动的上面级姿态模型，设计了有限频域H∞控制器。结合广义KYP引理及其推论、射影定理和反射影定理以及线性矩阵不等式知识，本文给出了有限频域下的状态反馈和输出反馈控制器设计方法。为突出有限频域H∞控制的优越性，给出了全频域下的状态反馈和输出反馈控制器设计方法。针对不同的系统模型
Following the research and development of Chinese launch vehicle upper stage, for the purpose of engineering application, the trajectory errors caused by the instrument coefficients and the initial azimuth bias of SINS, SINS/Star sensor/Earth sensor integrated navigation technology, midcourse correction technology of transfer orbit and attitude control are studied in this paper.
Considering the flight of upper stage in classical MEO transfer orbit described with launch inertial coordinate system, the inertial navigation solution equations are given out and the the errors propagation models are derived. The measurement error models of SINS are given out. A trajectory simulator of MEO transfer orbit is proposed by using the nominal trajectory data. The correctness of the inertial navigation solution equations is verified via the trajectory simulator. The trajectory errors are analyzed and a characteristical trajectory with errors is composed with some key instrument coefficients, which would be a basis for studying integrated navigation.
For the integrated navigations system, a mathematical model of the visibility of GPS satellites and the availability of navigation signals is built. GPS navigation can be effective in the flight under the conditons of 3150 seconds afore or the height of less than 7740 km. On the contrary, the highest altitude of the trajectory is about 25000 km and the total flight time is 15800 s, which means the GPS navigation is not available within the most of the trajectory. Because attitude errors of SINS/GPS navigation and position errors and velocity errors of SINS/Star sensor are not accurate, a novel SINS/Star sensor/Earth sensor integrated navigation system is proposed. The observation equations are derived from attitude measurement model and the geocentric vector measurement model. The effectiveness of the novel SINS/CNS integrated navigation is verified by using the estimation errors obtained via Kalman filter and H filter.
By the influence of non-spherical earth gravity, atmospheric drag, sun and moon gravity, solar radiation pressure and other perturbations, there are large errors between the real and the ideal transfer orbit. So the midcourse correction is studied. By the solution method of Lambert problem, the calculation method of correction velocity is derived. Considering the resourse of initial errors, an iterative algorithm with the error covariance matrix is designed, which has a superiority of small computation load and quickness compareing with the traditional calculation method of trajectory errors. Taking zero, one, two and three correction scheme as example, the choice of correction number is analyzed. The correction velocity impulse, the terminal position and velocity errors are contradictory through one correction result, which indicates that there needs to carry on a compromise. A two correction scheme is determined through multi-corrections. Then a multi-objective evolution algorithm is introduced to optimize the two correction timings. Tansforming the multi-objective optimization problem to a single objective optimization problem is a commonly used method, which can lose optimal solutions. So a modified non- dominated sorting genetic algorithm (NSGA-II) is introduced to the correction timing optimization problem, which obtains complete Pareto optimal solution set and increased flexibility of this optimization problem.
Considering the model uncertainty and the liquid sloshing, a finite frequency domain H control algorithm is presented for the upper stage attitude control. The finite frequency omain H control not only has strong robustness for solving the uncertainty problem, but also has effective control ability in specific frequency range. Based on the generalized KYP lemma and its inference, Projection lemma, Reciprocal Projection lemma and linear matrix inequality knowledge, state feedback and output feedback controllers in finite frequency domain are designed. And to highlight the advantagesof finite frequency domain H control, design methods of state feedback and output feedback controllers in entire frequency domain are presented. The effeciveness and feasibility of finite frequency domain control are verified through the results of four examples with different model parameters and the availability of jet attitude control system.
引文
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