空间快速响应发射转移轨道设计与制导方法研究
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摘要
空间快速响应发射对空间系统的快速部署、重构、扩充和维护等操作具有十分重要的意义,它对发射任务的转移轨道设计和制导方法提出了新的要求。本文以此为背景,对相关理论、技术和方法进行了研究与探讨。
首先研究了空间快速响应发射转移轨道的设计与优化方法,提出了考虑地球扁率影响的转移轨道快速设计方法。(1)分析了同时满足轨道面要求和相位要求的地面等待时间,研究了向前相位调整和向后相位调整的调相轨道设计方法,这种方法能在发射场固定的条件下提高发射的快速响应能力。(2)采用解析分析的方法设计了始末点位置固定的两冲量最短时间转移轨道。根据拉格朗日系数公式和连线速度一致性定理,得到了确定最优解的一元八次代数方程,并在一定假设下对方程进行了简化,得到了对理论分析具有较大意义的结果。(3)采用混合遗传算法设计多约束条件下四冲量最短时间转移轨道。采用一种具有自适应性的退火惩罚函数来处理轨道转移过程中的能量约束条件,设计了串联型、嵌入型两种算法混合结构,成功地解决了遗传算法的收敛结果存在概率性的问题,得到了一种兼具全局和局部搜索能力的优化算法。(4)针对考虑地球扁率的转移轨道快速设计问题,借鉴打靶法及虚拟目标的思想,提出了等时偏差迭代法,对该方法的收敛条件和奇异点存在的原因进行了理论分析。在此基础上,提出了收敛性能更好的改进的等时偏差迭代法。两种方法都采用解析公式计算地球扁率的影响,收敛速度快,设计精度高,能够用于快速任务规划和显式制导需要速度计算等任务。
其次研究了星光/惯性复合制导在空间快速响应发射运载火箭上升段制导中的应用。(1)针对单星星光/平台惯性复合制导系统,分别建立了调平台与不调平台两种方案的数学模型,包括平台的基准偏差与初始误差、惯导工具误差的关系方程,星敏感器的测量方程和星光修正方程。(2)通过对弹道导弹星光/惯性复合制导实现原理的分析,提出了以当地速度倾角和轨道倾角为修正指标、以半长轴和轨道倾角为修正指标的两种运载火箭星光修正方案。研究了修正方程中最佳修正系数的确定方法。数值仿真结果表明,两种方案都能在保证同样的入轨精度下放宽对射前准备条件和惯导系统精度的要求,对空间快速响应发射是很有意义的。(3)针对单星不调平台方案,从信息传递与校验的角度,提出了信息等量压缩的概念,由此分别得到了解析的、半解析的最佳测星方位确定方法。针对单星调平台方案,提出了能够综合不同性质的修正指标性能的整体优化指标,选择单纯形调优法来确定最佳测星方位。针对单纯形法全局搜索能力不足的缺点,提出了通过编制简单条件下的最佳测星方位表来为算法提供良好初值的解决方案。
最后研究了可用于轨道转移段的“速度增益制导+迭代制导”的组合显式制导方法,以达到快速应用空间的目的。(1)研究了速度增益制导方法在航天器转移轨道初制导中的应用。比较了γ制导和关机点需要速度预测制导两种方法的特点和优劣,分析了γ制导方法中推力的最佳施加方向,提出了采用小步长计算和关机时间线性预报的关机控制方法。(2)研究了迭代制导方法在航天器转移轨道末端制导中的应用。在简化轨道运动方程和引力计算的基础上,运用最优控制理论推导了满足终端约束条件的迭代制导方程,通过数值仿真验证了算法的有效性。
随着空间应用的深入和航天技术的发展,空间快速响应发射将成为未来航天运输的发展趋势。本文的研究结果可为我国相关航天装备的发展提供方案参考和技术支持。
The development of responsive space lift could be significant to the rapid deployment, reconfiguration, expansion and maintenance of space systems. Taking that as the background, this thesis makes effort on the technologies of transfer orbit design and vehicle guidance, expecting to meet the new requirements proposed by responsive space lift.
Firstly, transfer orbit design and optimization of responsive space lift are investigated, and the rapid design approach of transfer orbit, when the oblateness of the earth is taken into account, is presentd. (1) The ground waiting time during launch to satisfy the constraints of the orbit plane and the phase in the plane is discussed. The approach to design phasing orbit, both forward and backward, is addressed, which could improve the launch responsive capability with regard to an immovable range. (2) The two impulses minimum time transfer orbit design with fixed initial and terminal ends is studied, using an analytical method. Based on the Lagrange coefficient equation and the theorem of chord velocity, a one-unknown algebraic equation of eight degree is deduced to determine the optimum solution. Some assumptions are made to simplify the equation to get an approximate solution which is theoretically instructive. (3) A hybrid genetic algorithm (HGA) is chosen to design the four impulses minimum time transfer orbit with energy constraints. An adaptive annealing penalty function is contrived to deal with the energy constraints during orbit transfer, and two different hybrid algorithms, the serial HGA and the embed HGA, are designed. The HGAs both successfully dispose of the problem that the genetic algorithm usually converges on a probabilistic solution. Consequently, an optimum algorithm that has both local and global search competence is acquired. (4) Inspired by shooting method and virtual target, the equal-time deviation iterating approach is presented to rapidly design the transfer orbit when the oblateness of the earth is taken into account. Subsequently, the convergence conditions and singular points are discussed theoretically, based on which the improved equal-time deviation iterating approach is put forward. The two approaches both use analytical means to compute the influence of the earth’s oblateness, resulting in fast convergence and high precision. Thus, they are both competent for onboard tasks, such as fast mission programming, demanded velocity calculation.
Secondly, the ascending phase guidance scheme of responsive space lift is explored, and stellar/inertial composite guidance technology is selected to conquer the challenge. (1) With regard to the single star/inertial platform composite guidance system, the models with respect to platform leveling and decline are established. Besides the relations between the platform error angles and the inertial errors as well as the inertial instrument errors, the measurement equation of star sensor and the modification equation are also included. (2) Base on the analysis of ballistic missile composite guidance system working principles, two accuracy indices correction policies of the carrier rocket are put forward. One group of the indices is the local slope angle of trajectory and orbit inclination, and the other one is the semi-major axis and orbit inclination. The determination of the best correction coefficients is discussed. The numerical simulation results show that, with the same orbit injection precision, the two policies addressed in the thesis both need fewer requirements on the preparation before launch and the precision of inertial instruments. In other words, the composite guidance technology is fit for the responsive space lift. (3) With respect to the platform leveling scheme, the concept of equivalent information compression is presented, with which analytical and partly analytical approaches are derived to determine the optimum stellar direction. An optimum index that can compromise the performance of accuracy indices which have different properties is proposed, intending to get the best navigation star of the platform decline scheme,. The simplex method is chosen to do the optimization, and a best navigation star table under simple conditions is proposed to reinforce the global optimize capability of simplex method.
Finally, according to the requirements of rapid space application, a combined explicit guidance shceme for orbit transfer phase, including the close-loop guidance and the iterative guidance, is studied. (1) The close-loop guidance approach is selected to steer the initial orbit maneuver. The velocity-to-gain guidance scheme and the cutoff demanded velocity prediction guidance scheme are discussed and compared. The best thrust direction of velocity-to-gain guidance scheme is surveyed, and a cutoff concept with smaller integral step and cutoff time linear forecasting is proposed. (2) The iterative guidance scheme is selected to steer the terminal orbit maneuver. With the simplification of motion equations and gravitation calculation, the iterative guidance equation is derived, using optimal control theory. The guidance algorithm is verified by numerical simulations finally.
Along with the extension of space system application and development of astro- nautical technology, the responsive space lift will be the trends of space entrance and space application. The research conclusions of this thesis could be helpful in the development of our country’s related space vehicles, theoretically and technically.
首先研究了空间快速响应发射转移轨道的设计与优化方法,提出了考虑地球扁率影响的转移轨道快速设计方法。(1)分析了同时满足轨道面要求和相位要求的地面等待时间,研究了向前相位调整和向后相位调整的调相轨道设计方法,这种方法能在发射场固定的条件下提高发射的快速响应能力。(2)采用解析分析的方法设计了始末点位置固定的两冲量最短时间转移轨道。根据拉格朗日系数公式和连线速度一致性定理,得到了确定最优解的一元八次代数方程,并在一定假设下对方程进行了简化,得到了对理论分析具有较大意义的结果。(3)采用混合遗传算法设计多约束条件下四冲量最短时间转移轨道。采用一种具有自适应性的退火惩罚函数来处理轨道转移过程中的能量约束条件,设计了串联型、嵌入型两种算法混合结构,成功地解决了遗传算法的收敛结果存在概率性的问题,得到了一种兼具全局和局部搜索能力的优化算法。(4)针对考虑地球扁率的转移轨道快速设计问题,借鉴打靶法及虚拟目标的思想,提出了等时偏差迭代法,对该方法的收敛条件和奇异点存在的原因进行了理论分析。在此基础上,提出了收敛性能更好的改进的等时偏差迭代法。两种方法都采用解析公式计算地球扁率的影响,收敛速度快,设计精度高,能够用于快速任务规划和显式制导需要速度计算等任务。
其次研究了星光/惯性复合制导在空间快速响应发射运载火箭上升段制导中的应用。(1)针对单星星光/平台惯性复合制导系统,分别建立了调平台与不调平台两种方案的数学模型,包括平台的基准偏差与初始误差、惯导工具误差的关系方程,星敏感器的测量方程和星光修正方程。(2)通过对弹道导弹星光/惯性复合制导实现原理的分析,提出了以当地速度倾角和轨道倾角为修正指标、以半长轴和轨道倾角为修正指标的两种运载火箭星光修正方案。研究了修正方程中最佳修正系数的确定方法。数值仿真结果表明,两种方案都能在保证同样的入轨精度下放宽对射前准备条件和惯导系统精度的要求,对空间快速响应发射是很有意义的。(3)针对单星不调平台方案,从信息传递与校验的角度,提出了信息等量压缩的概念,由此分别得到了解析的、半解析的最佳测星方位确定方法。针对单星调平台方案,提出了能够综合不同性质的修正指标性能的整体优化指标,选择单纯形调优法来确定最佳测星方位。针对单纯形法全局搜索能力不足的缺点,提出了通过编制简单条件下的最佳测星方位表来为算法提供良好初值的解决方案。
最后研究了可用于轨道转移段的“速度增益制导+迭代制导”的组合显式制导方法,以达到快速应用空间的目的。(1)研究了速度增益制导方法在航天器转移轨道初制导中的应用。比较了γ制导和关机点需要速度预测制导两种方法的特点和优劣,分析了γ制导方法中推力的最佳施加方向,提出了采用小步长计算和关机时间线性预报的关机控制方法。(2)研究了迭代制导方法在航天器转移轨道末端制导中的应用。在简化轨道运动方程和引力计算的基础上,运用最优控制理论推导了满足终端约束条件的迭代制导方程,通过数值仿真验证了算法的有效性。
随着空间应用的深入和航天技术的发展,空间快速响应发射将成为未来航天运输的发展趋势。本文的研究结果可为我国相关航天装备的发展提供方案参考和技术支持。
The development of responsive space lift could be significant to the rapid deployment, reconfiguration, expansion and maintenance of space systems. Taking that as the background, this thesis makes effort on the technologies of transfer orbit design and vehicle guidance, expecting to meet the new requirements proposed by responsive space lift.
Firstly, transfer orbit design and optimization of responsive space lift are investigated, and the rapid design approach of transfer orbit, when the oblateness of the earth is taken into account, is presentd. (1) The ground waiting time during launch to satisfy the constraints of the orbit plane and the phase in the plane is discussed. The approach to design phasing orbit, both forward and backward, is addressed, which could improve the launch responsive capability with regard to an immovable range. (2) The two impulses minimum time transfer orbit design with fixed initial and terminal ends is studied, using an analytical method. Based on the Lagrange coefficient equation and the theorem of chord velocity, a one-unknown algebraic equation of eight degree is deduced to determine the optimum solution. Some assumptions are made to simplify the equation to get an approximate solution which is theoretically instructive. (3) A hybrid genetic algorithm (HGA) is chosen to design the four impulses minimum time transfer orbit with energy constraints. An adaptive annealing penalty function is contrived to deal with the energy constraints during orbit transfer, and two different hybrid algorithms, the serial HGA and the embed HGA, are designed. The HGAs both successfully dispose of the problem that the genetic algorithm usually converges on a probabilistic solution. Consequently, an optimum algorithm that has both local and global search competence is acquired. (4) Inspired by shooting method and virtual target, the equal-time deviation iterating approach is presented to rapidly design the transfer orbit when the oblateness of the earth is taken into account. Subsequently, the convergence conditions and singular points are discussed theoretically, based on which the improved equal-time deviation iterating approach is put forward. The two approaches both use analytical means to compute the influence of the earth’s oblateness, resulting in fast convergence and high precision. Thus, they are both competent for onboard tasks, such as fast mission programming, demanded velocity calculation.
Secondly, the ascending phase guidance scheme of responsive space lift is explored, and stellar/inertial composite guidance technology is selected to conquer the challenge. (1) With regard to the single star/inertial platform composite guidance system, the models with respect to platform leveling and decline are established. Besides the relations between the platform error angles and the inertial errors as well as the inertial instrument errors, the measurement equation of star sensor and the modification equation are also included. (2) Base on the analysis of ballistic missile composite guidance system working principles, two accuracy indices correction policies of the carrier rocket are put forward. One group of the indices is the local slope angle of trajectory and orbit inclination, and the other one is the semi-major axis and orbit inclination. The determination of the best correction coefficients is discussed. The numerical simulation results show that, with the same orbit injection precision, the two policies addressed in the thesis both need fewer requirements on the preparation before launch and the precision of inertial instruments. In other words, the composite guidance technology is fit for the responsive space lift. (3) With respect to the platform leveling scheme, the concept of equivalent information compression is presented, with which analytical and partly analytical approaches are derived to determine the optimum stellar direction. An optimum index that can compromise the performance of accuracy indices which have different properties is proposed, intending to get the best navigation star of the platform decline scheme,. The simplex method is chosen to do the optimization, and a best navigation star table under simple conditions is proposed to reinforce the global optimize capability of simplex method.
Finally, according to the requirements of rapid space application, a combined explicit guidance shceme for orbit transfer phase, including the close-loop guidance and the iterative guidance, is studied. (1) The close-loop guidance approach is selected to steer the initial orbit maneuver. The velocity-to-gain guidance scheme and the cutoff demanded velocity prediction guidance scheme are discussed and compared. The best thrust direction of velocity-to-gain guidance scheme is surveyed, and a cutoff concept with smaller integral step and cutoff time linear forecasting is proposed. (2) The iterative guidance scheme is selected to steer the terminal orbit maneuver. With the simplification of motion equations and gravitation calculation, the iterative guidance equation is derived, using optimal control theory. The guidance algorithm is verified by numerical simulations finally.
Along with the extension of space system application and development of astro- nautical technology, the responsive space lift will be the trends of space entrance and space application. The research conclusions of this thesis could be helpful in the development of our country’s related space vehicles, theoretically and technically.
引文
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