航天器推进剂晃动的动力学建模与抑制方法研究
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摘要
液体推进剂的晃动问题在现代航天器的总体设计中愈发受到重视。这是由于随着对航天器执行任务能力要求的提高,推进剂在航天器的总重构成中占有的比例亦相应增加。而大量液体推进剂的晃动行为有可能影响航天器整体的动力学性能,对结构的安全性或系统的稳定性构成威胁。本文针对此问题,基于液体晃动模态理论,利用等效力学方法建立了晃动耦合动力学模型,分析研究了推进剂晃动对航天器造成的动力学影响,并从防晃结构设计和前馈控制两种角度探讨了抑制推进剂晃动的实用方法。具体研究内容与主要成果如下:
结合航天应用背景,对以往有关液体晃动的国内外研究从基本理论、研究方法和成果应用三方面进行了综述,确定了研究内容与实现步骤:以模态理论为基础,以等效力学方法为手段,分析推进剂晃动与航天器控制系统的动力学耦合关系,开展关于推进剂晃动抑制策略的研究。
基于流体力学基本理论和变分原理,建立以液体流动速度势为待求函数的晃动问题数学描述。通过分离该函数中的时间变量,将描述方程由原来的偏微分方程组化为关于模态函数的常微分方程组,为之后基于模态理论分析研究晃动的动力学问题奠定了基础。
基于模态响应理论和力学等效原则,推导了以简单机械系统代替液体系统的等效力学模型建模方法。通过在建模过程中,利用固体有限元通用分析手段获取晃动模态特征值和特征向量,提高了建模效率和方法的适用性。方法的有效性和准确性则通过在若干算例中与相关研究数据的对比得到了验证。利用等效模型的动力学开环分析结果,总结了非线性晃动模态被激发的必要条件,为研究推进剂晃动与航天器控制系统动力学耦合效应建立了基础。
从多体动力学的角度出发,以等效力学模型的研究结论为基础,建立了航天器大系统内液-固-控耦合效应的分析模型。建立了可用于晃动动力学闭环分析的实时仿真模块。数值仿真结果表明:以航天器刚体模型设计的控制率,由于推进剂晃动的扰动影响的实际存在,而有可能无法有效地实现控制目的。尤其是当推进剂晃动质量的质心比航天器质心更靠近轴向前端时,系统稳定的必要条件是晃动质量必须满足由航天器转动惯量和推进剂贮箱相对位置确定的限制条件。
以流体力学绕流理论为基础,解析分析了晃动抑制结构的作用机理。建立了结构防晃效能的定量分析模型。通过与实验文献的对比,验证了解析分析的合理性。通过解析方法与计算流体力学模拟技术的结合,实现了对防晃结构设计过程的改进,其方法和结果对航天器贮箱的设计具有参考价值。
将输入成型技术应用到液体推进剂晃动抑制的研究中。依据液体晃动基频,通过对晃动幅度、航天器推力水平、时间或能耗优化等因素的综合考虑,设计了用于前馈控制的输入成型器。数值仿真结果验证了该方法抑制推进剂晃动的有效性。相较于一般的反馈控制器,输入成型器由于设计过程简洁而具有广阔的应用前景。
The problem of liquid fuel sloshing in integrated design of modern large spacecrafts is drawing more and more attention. This is due to the increasing requirements of spacecraft mission executing abilities and thus the increase of fuel portion to overall mass of a spacecraft. Large scale liquid fuel sloshing may interfere overall dynamic characters of a spacecraft, putting structure safety or system stability under threatening. With respect to this problem, this study establishes coupled dynamic sloshing model with mechanic equivalent method and liquid sloshing module theory, and analyzes dynamic affection of fuel sloshing to spacecraft. In addition, practical methods are discussed in terms of anti-sloshing structure design and forward feedback control. Detailed research contents and results are as follows:
Combining aeronautic application backgrounds, such three aspects as basic theories, research methodology, and achievement applications about liquid sloshing both domestic and abroad are reviewed. Research contents and implementation procedure are determined: the foundation of this research is modal theories, implementation means mechanics equivalent method, and the purpose to evaluate coupling effect of propellant sloshing and spacecraft control system and establish methodology for propellant sloshing inhibition.
Based on fluid dynamic basics and variation principles, a mathematic description is established of fuel sloshing with liquid flow velocity potential as undermined functions. Via separating time variable of the function, description equation can be transformed from original partial differential equations to ordinary differential equations about modal functions. This transformation lays foundation for research of sloshing dynamics utilizing modal theories.
Applying modal response theories and mechanical equivalent principles, models are built to replace liquid system equivalent mechanic modeling with simple mechanical system. Modeling efficiency and feasibility are improved during modeling process where solid finite element universal computation program is used. Several computational cases and comparison to corresponding research data validate the accuracy of this method. Open-looped analyzing results of equivalent model are used to summarize necessary exciting conditions of non-linear sloshing modules. These conclusions are research foundation of research on coupling effects between propellant sloshing and spacecraft control system dynamics.
From the view of multi-body dynamics, based on equivalent mechanic model research results, analyzing model of liquid-solid-control of a spacecraft large system is established and a real-time simulation module is constructed. The numerical simulation results indicate that the control algorithm, which was designed based on rigid model of spacecraft, may be unable to achieve the control objective due to the sloshing disturbance. Especially when the centroid of the sloshing mass above the centroid of the spacecraft, the necessary condition for a stable system is that the sloshing mass must satisfy the constraint depends on moment of inertia of spacecraft and location of propellant vessel.
Analytically, the sloshing inhibition structure mechanism is analyzed applying the circumferential flow theory in fluid dynamics. Quantity analysis model of the sloshing inhibition effect is founded. Comparison to experiments in literature validates the analytical results. Also, sloshing inhibiting structure improved was realized with combination of analytical methods and CFD simulation technology. This work has positive value to assist overall design of spacecraft.
Finally, input shaping technique is adopted in this liquid propellant sloshing inhibition research. In specific, considering liquid sloshing primary frequency and inclusive factors as sloshing amplitudes, spacecraft thrust levels, time or energy optimization, input shaper for forward feedback control is designed. Numerical simulation validates the efficiency of inhibiting propellant sloshing of this method. Compare to common feedback controller, input shaper is simple in design process, and has a broad and promising application foreground.
结合航天应用背景,对以往有关液体晃动的国内外研究从基本理论、研究方法和成果应用三方面进行了综述,确定了研究内容与实现步骤:以模态理论为基础,以等效力学方法为手段,分析推进剂晃动与航天器控制系统的动力学耦合关系,开展关于推进剂晃动抑制策略的研究。
基于流体力学基本理论和变分原理,建立以液体流动速度势为待求函数的晃动问题数学描述。通过分离该函数中的时间变量,将描述方程由原来的偏微分方程组化为关于模态函数的常微分方程组,为之后基于模态理论分析研究晃动的动力学问题奠定了基础。
基于模态响应理论和力学等效原则,推导了以简单机械系统代替液体系统的等效力学模型建模方法。通过在建模过程中,利用固体有限元通用分析手段获取晃动模态特征值和特征向量,提高了建模效率和方法的适用性。方法的有效性和准确性则通过在若干算例中与相关研究数据的对比得到了验证。利用等效模型的动力学开环分析结果,总结了非线性晃动模态被激发的必要条件,为研究推进剂晃动与航天器控制系统动力学耦合效应建立了基础。
从多体动力学的角度出发,以等效力学模型的研究结论为基础,建立了航天器大系统内液-固-控耦合效应的分析模型。建立了可用于晃动动力学闭环分析的实时仿真模块。数值仿真结果表明:以航天器刚体模型设计的控制率,由于推进剂晃动的扰动影响的实际存在,而有可能无法有效地实现控制目的。尤其是当推进剂晃动质量的质心比航天器质心更靠近轴向前端时,系统稳定的必要条件是晃动质量必须满足由航天器转动惯量和推进剂贮箱相对位置确定的限制条件。
以流体力学绕流理论为基础,解析分析了晃动抑制结构的作用机理。建立了结构防晃效能的定量分析模型。通过与实验文献的对比,验证了解析分析的合理性。通过解析方法与计算流体力学模拟技术的结合,实现了对防晃结构设计过程的改进,其方法和结果对航天器贮箱的设计具有参考价值。
将输入成型技术应用到液体推进剂晃动抑制的研究中。依据液体晃动基频,通过对晃动幅度、航天器推力水平、时间或能耗优化等因素的综合考虑,设计了用于前馈控制的输入成型器。数值仿真结果验证了该方法抑制推进剂晃动的有效性。相较于一般的反馈控制器,输入成型器由于设计过程简洁而具有广阔的应用前景。
The problem of liquid fuel sloshing in integrated design of modern large spacecrafts is drawing more and more attention. This is due to the increasing requirements of spacecraft mission executing abilities and thus the increase of fuel portion to overall mass of a spacecraft. Large scale liquid fuel sloshing may interfere overall dynamic characters of a spacecraft, putting structure safety or system stability under threatening. With respect to this problem, this study establishes coupled dynamic sloshing model with mechanic equivalent method and liquid sloshing module theory, and analyzes dynamic affection of fuel sloshing to spacecraft. In addition, practical methods are discussed in terms of anti-sloshing structure design and forward feedback control. Detailed research contents and results are as follows:
Combining aeronautic application backgrounds, such three aspects as basic theories, research methodology, and achievement applications about liquid sloshing both domestic and abroad are reviewed. Research contents and implementation procedure are determined: the foundation of this research is modal theories, implementation means mechanics equivalent method, and the purpose to evaluate coupling effect of propellant sloshing and spacecraft control system and establish methodology for propellant sloshing inhibition.
Based on fluid dynamic basics and variation principles, a mathematic description is established of fuel sloshing with liquid flow velocity potential as undermined functions. Via separating time variable of the function, description equation can be transformed from original partial differential equations to ordinary differential equations about modal functions. This transformation lays foundation for research of sloshing dynamics utilizing modal theories.
Applying modal response theories and mechanical equivalent principles, models are built to replace liquid system equivalent mechanic modeling with simple mechanical system. Modeling efficiency and feasibility are improved during modeling process where solid finite element universal computation program is used. Several computational cases and comparison to corresponding research data validate the accuracy of this method. Open-looped analyzing results of equivalent model are used to summarize necessary exciting conditions of non-linear sloshing modules. These conclusions are research foundation of research on coupling effects between propellant sloshing and spacecraft control system dynamics.
From the view of multi-body dynamics, based on equivalent mechanic model research results, analyzing model of liquid-solid-control of a spacecraft large system is established and a real-time simulation module is constructed. The numerical simulation results indicate that the control algorithm, which was designed based on rigid model of spacecraft, may be unable to achieve the control objective due to the sloshing disturbance. Especially when the centroid of the sloshing mass above the centroid of the spacecraft, the necessary condition for a stable system is that the sloshing mass must satisfy the constraint depends on moment of inertia of spacecraft and location of propellant vessel.
Analytically, the sloshing inhibition structure mechanism is analyzed applying the circumferential flow theory in fluid dynamics. Quantity analysis model of the sloshing inhibition effect is founded. Comparison to experiments in literature validates the analytical results. Also, sloshing inhibiting structure improved was realized with combination of analytical methods and CFD simulation technology. This work has positive value to assist overall design of spacecraft.
Finally, input shaping technique is adopted in this liquid propellant sloshing inhibition research. In specific, considering liquid sloshing primary frequency and inclusive factors as sloshing amplitudes, spacecraft thrust levels, time or energy optimization, input shaper for forward feedback control is designed. Numerical simulation validates the efficiency of inhibiting propellant sloshing of this method. Compare to common feedback controller, input shaper is simple in design process, and has a broad and promising application foreground.
引文
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