电动力绳系离轨系统的建模与动力学分析
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摘要
电动力绳系是近年来出现的一项新兴技术,在废弃卫星离轨、辅助轨道机动、航天器防护等方面具有广阔的应用前景。电动力绳系具有强非线性且运动过程中存在复杂的多场耦合,现有动力学模型难以满足电动力绳系方案设计、特性分析及展开控制等应用要求。为此本文围绕电动力绳系展开过程和留位状态下动力学建模、展开控制及离轨时间预估等展开研究,取得如下创新性研究成果:
离轨时间是评价电动力绳系离轨策略优劣的一项重要指标,为实现较为精确的离轨时间预估,首先建立了考虑弯曲变形的电动力绳系柔索模型,理论分析和数学仿真表明了该柔索模型与刚性杆模型本质上的一致性,柔索模型具有更高的精度;基于所建立的柔索模型,考虑电动力绳系离轨过程中地磁场强度、环境摄动力等的变化,提出了一种轨道六要素迭代累加离轨时间预估算法;最后,采用数值计算手段,分析了系绳长度、横截面积、末端质量等不同绳系系统参数,以及不同轨道参数对离轨时间的影响,为电动力绳系离轨系统方案设计提供参考。
在各种干扰影响下留位状态电动力绳系系统动力学特性极其复杂,为便于分析需建立其动力学模型。首先,将系绳作为有质量的柔性连续体,考虑系绳所受电动力拉力、重力梯度力、张力等影响,建立了留位状态电动力绳系非线性动力学方程,数值分析结果表明留位状态下系统表现出与两端固定的绳索相类似的振动特性;基于上述结论,研究留位状态绳系短期内振动及张力变化,将系绳简化为两端固定的绳索,并建立了该简化假设下的电动力绳系系统2D和3D振动模型,研究横向振动与纵向振动、面内振动与面外振动的耦合关系。仿真结果显示系绳参数λ与系绳的非线性动力学行为密切相关,横向振动与纵向振动可以互相激发,但不能激发面外振动,面外振动可以激发面内的纵向和横向振动;最后,为降低绳系系统振动,提出在电动力绳系离轨系统中增加阻尼器的方案,并基于上述简化模型建立了具有阻尼器的离轨系统动力学模型,仿真结果表明离轨系统振动振幅得到明显衰减,验证了阻尼器在抑制系绳振动方面的有效性。
针对电动力绳系展开动力学与控制问题,首先利用Hamilton原理建立了包括系绳、末端质量、绕线盘摩擦以及末端球体上推力等作用下的绳系系统展开动力学方程,并分析了绳系自由展开过程中绕线盘出线、系绳振动以及末端质量的运动规律。针对匀速展开和指数展开两种模式,采用极点配置法设计了系绳张力/绕线盘摩擦力/推力器推力混合的展开控制算法,仿真结果表明展开过程中系绳张力变化平稳,微幅振荡抑制效果明显,系绳平稳快速展开,验证了上述控制算法的有效性。
The electrodynamic tether (EDT) is a new technology in recent years, and it has many potential applications in spent or dysfuctional satellites deorbiting, auxiliary orbit maneuver, and spacecrafts protecting. Due to strongly nonlinear dynamics of electrodynamic tether system and complicated multi-fields coupling problems, the dynamic models in existence do not meet the requoments of the electrodynamic tether system design, deorbiting characteristic analysis and tether deployment control. To solve such problems, this dissertation investigates the deorbiting time forecast and the dynamic modeling of EDT in deployment and stationkeeping phase. The main contents of this dissertation are as follows:
The deorbiting time is an important indicator to evaluate the effect of EDT deorbiting system. In order to precise deorbiting time forecast, the flexible cable model of EDT system is established. The flexible cable model is used to discuss effects of flexible deformation on electromotive force and Lorentz force. Theoretical analysis and numerical simulation both indicate that the flexible cable model is the same essence with the rigid bar model, and the flexible cable model improves the veracity of deorbiting time estimate. Based on the flexible cable model, a six-orbit-parameters iterative cumulative algorithm is present to forecast the deorbiting time, in which the variation of magnetic field strength and space environmental perturbation is taken into account. By the flexible cable model, the influence of tether system parameters and orbit parameters to deorbiting time is researched, to discuss the design of electrodynamic tether system and proper satellite orbits suit for EDT deorbiting.
The dynamics behavior of EDT system in stationkeeping phase is very complex , resultingly the effection of a series of perturbations. The study on the dynamics character of EDT system in stationkeeping phase, which presents a continuous flexible tether model to capture the gravitational, inertial, tensile forces and electrodynamic drag in the tether, and uses Newton’s laws to derive the dynamic equations of electrodynamic tether system in stationkeeping phase. The simulation results show that the motion of electrodynamic tether in stationkeeping phase is similar to the vibration of cable with two immovable pinned-supports, in which the mid-span has the largest amplitude of vibration. According to this conclusion, the main satellite and the endmass at both ends of tether can be treated as immovable pinned-supports when the tether vibration and tension of electrodynamic tether system in impermanency is investigated. Following the above research, 2D and 3D simplified vibration models of EDT system are presented to study the relationship between vertical and longitudinal vibration, and the relationship between in-plane and out-of-plane vibration. The research results indicate that the nonlinear dynamics of EDT is associated with the tether structure parameterλ. The vertical and longitudinal response of the tether can be excited by each other, but they cannot excite out-of-plane response. The out-of-plane response can cause vertical and longitudinal response in plane. For solving the problem of little damping of EDT system, a damper is presented to add to EDT system. The effects of damping to tether dynamic characteristic is investigated. The simulation results show that the amplitudes are weakened and the vibrations are restrained when a damper is added into EDT system.
For solving the problems of dynamics and control of EDT deployment, a continuous system differential equation model is presented to investigated dynamics of deployment of EDT system.. The dynamic model of space tether deployment provides a way to study motion laws of drum releasing tether, tether vibration and end-mass moving during the tether deployment. According to dynamic characteristics of deployment, uniform deployment and expontial deployment are adopted to control the deployment course. The deployment united control of tether tension/durm torque/thruster force is designed by pole-assignment method. The simulation results show that the deployment united control produces a very fast and stable process for the deployment of EDT system.
离轨时间是评价电动力绳系离轨策略优劣的一项重要指标,为实现较为精确的离轨时间预估,首先建立了考虑弯曲变形的电动力绳系柔索模型,理论分析和数学仿真表明了该柔索模型与刚性杆模型本质上的一致性,柔索模型具有更高的精度;基于所建立的柔索模型,考虑电动力绳系离轨过程中地磁场强度、环境摄动力等的变化,提出了一种轨道六要素迭代累加离轨时间预估算法;最后,采用数值计算手段,分析了系绳长度、横截面积、末端质量等不同绳系系统参数,以及不同轨道参数对离轨时间的影响,为电动力绳系离轨系统方案设计提供参考。
在各种干扰影响下留位状态电动力绳系系统动力学特性极其复杂,为便于分析需建立其动力学模型。首先,将系绳作为有质量的柔性连续体,考虑系绳所受电动力拉力、重力梯度力、张力等影响,建立了留位状态电动力绳系非线性动力学方程,数值分析结果表明留位状态下系统表现出与两端固定的绳索相类似的振动特性;基于上述结论,研究留位状态绳系短期内振动及张力变化,将系绳简化为两端固定的绳索,并建立了该简化假设下的电动力绳系系统2D和3D振动模型,研究横向振动与纵向振动、面内振动与面外振动的耦合关系。仿真结果显示系绳参数λ与系绳的非线性动力学行为密切相关,横向振动与纵向振动可以互相激发,但不能激发面外振动,面外振动可以激发面内的纵向和横向振动;最后,为降低绳系系统振动,提出在电动力绳系离轨系统中增加阻尼器的方案,并基于上述简化模型建立了具有阻尼器的离轨系统动力学模型,仿真结果表明离轨系统振动振幅得到明显衰减,验证了阻尼器在抑制系绳振动方面的有效性。
针对电动力绳系展开动力学与控制问题,首先利用Hamilton原理建立了包括系绳、末端质量、绕线盘摩擦以及末端球体上推力等作用下的绳系系统展开动力学方程,并分析了绳系自由展开过程中绕线盘出线、系绳振动以及末端质量的运动规律。针对匀速展开和指数展开两种模式,采用极点配置法设计了系绳张力/绕线盘摩擦力/推力器推力混合的展开控制算法,仿真结果表明展开过程中系绳张力变化平稳,微幅振荡抑制效果明显,系绳平稳快速展开,验证了上述控制算法的有效性。
The electrodynamic tether (EDT) is a new technology in recent years, and it has many potential applications in spent or dysfuctional satellites deorbiting, auxiliary orbit maneuver, and spacecrafts protecting. Due to strongly nonlinear dynamics of electrodynamic tether system and complicated multi-fields coupling problems, the dynamic models in existence do not meet the requoments of the electrodynamic tether system design, deorbiting characteristic analysis and tether deployment control. To solve such problems, this dissertation investigates the deorbiting time forecast and the dynamic modeling of EDT in deployment and stationkeeping phase. The main contents of this dissertation are as follows:
The deorbiting time is an important indicator to evaluate the effect of EDT deorbiting system. In order to precise deorbiting time forecast, the flexible cable model of EDT system is established. The flexible cable model is used to discuss effects of flexible deformation on electromotive force and Lorentz force. Theoretical analysis and numerical simulation both indicate that the flexible cable model is the same essence with the rigid bar model, and the flexible cable model improves the veracity of deorbiting time estimate. Based on the flexible cable model, a six-orbit-parameters iterative cumulative algorithm is present to forecast the deorbiting time, in which the variation of magnetic field strength and space environmental perturbation is taken into account. By the flexible cable model, the influence of tether system parameters and orbit parameters to deorbiting time is researched, to discuss the design of electrodynamic tether system and proper satellite orbits suit for EDT deorbiting.
The dynamics behavior of EDT system in stationkeeping phase is very complex , resultingly the effection of a series of perturbations. The study on the dynamics character of EDT system in stationkeeping phase, which presents a continuous flexible tether model to capture the gravitational, inertial, tensile forces and electrodynamic drag in the tether, and uses Newton’s laws to derive the dynamic equations of electrodynamic tether system in stationkeeping phase. The simulation results show that the motion of electrodynamic tether in stationkeeping phase is similar to the vibration of cable with two immovable pinned-supports, in which the mid-span has the largest amplitude of vibration. According to this conclusion, the main satellite and the endmass at both ends of tether can be treated as immovable pinned-supports when the tether vibration and tension of electrodynamic tether system in impermanency is investigated. Following the above research, 2D and 3D simplified vibration models of EDT system are presented to study the relationship between vertical and longitudinal vibration, and the relationship between in-plane and out-of-plane vibration. The research results indicate that the nonlinear dynamics of EDT is associated with the tether structure parameterλ. The vertical and longitudinal response of the tether can be excited by each other, but they cannot excite out-of-plane response. The out-of-plane response can cause vertical and longitudinal response in plane. For solving the problem of little damping of EDT system, a damper is presented to add to EDT system. The effects of damping to tether dynamic characteristic is investigated. The simulation results show that the amplitudes are weakened and the vibrations are restrained when a damper is added into EDT system.
For solving the problems of dynamics and control of EDT deployment, a continuous system differential equation model is presented to investigated dynamics of deployment of EDT system.. The dynamic model of space tether deployment provides a way to study motion laws of drum releasing tether, tether vibration and end-mass moving during the tether deployment. According to dynamic characteristics of deployment, uniform deployment and expontial deployment are adopted to control the deployment course. The deployment united control of tether tension/durm torque/thruster force is designed by pole-assignment method. The simulation results show that the deployment united control produces a very fast and stable process for the deployment of EDT system.
引文
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