复杂太空环境下柔性绳系卫星动力学与控制
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摘要
绳系卫星是人类认知太空的一种新型飞行器，在空间科学、深空探测等领域具有重要价值，受到人们的广泛关注。随着科学技术的日趋进步与成熟，西方国家正争相对绳系卫星系统的理论、地面实验及在轨飞行进行深入研究。众所周知，绳系卫星系绳的柔性、太空环境的复杂性及相应的控制理论等都是当前绳系卫星研究的难点，对这些问题的研究与解决显得十分迫切。本文主要内容如下：
首先，通过将柔性系绳离散为一系列绳结点，在绳结点进/出卫星体时考虑系统自由度变化，建立了时变自由度绳系卫星动力学模型。模型充分考虑了系绳的柔性、粘弹性、“火箭项”、耗散作用以及系绳与卫星本体间摩擦、冲击对Kepler轨道的影响，很好地揭示了绳系卫星运行过程中系绳构形的变化规律。
然后，提出一套改进的有限差分方法来计算时变多自由度系统的动力学响应。算法的核心思想是在每一次迭代循环中对系统自由度变化与否进行判定，一旦自由度发生变化，则通过重新划分系绳单元，添加（或删除）相应结点的信息，重置系统质量、阻尼和刚度矩阵及位移和荷载向量，使得迭代计算可以继续进行直至得出最终响应结果。此算法略去了多余的结点计算，提高了计算效率，可推广至一维连续体系统释放/回收过程的动力学研究中。
随后，研究了各种真实太空环境摄动因素对复杂绳系卫星系统的动力学影响。数值结果表明，热效应与太空碎片撞击对系统作用十分显著；J2摄动与大气阻力对绳系卫星的影响取决于绳系卫星系统所处的轨道倾角与高度；随Kepler轨道偏心率的变化，绳系卫星系统将发生分岔，出现周期运动、概周期运动及混沌运动；而太阳光压力对绳系卫星作用则是非常微小的。
综合考虑以上各种太空摄动因素的存在，提出了柔性绳系卫星系统的有效控制方法。采用子星端喷气控制并设计了一套含约束条件的PID控制器对柔性绳系卫星模型的俯仰姿态进行了有效控制。研究表明，该方法可有效实现任意椭圆轨道下绳系卫星系统的俯仰姿态运动及混沌运动控制。
最后，讨论了电动力绳系卫星以及绳系捕捉等所涉及到的绳系系统的动力学与控制问题。
Tethered satellites, satellites recently innovated for space probe, have become a prominent tool inscientific studies of space and outer space. Researches on theories and experimental methodologies(ground or orbital) regarding tethered satellites have been intensified in Eastern countries, as scienceand technology develop. Among them all, flexibility of the space tether, complexity of the space, andpertinent controlling mechanisms are, without doubt, the most difficult. Solving these issues hastherefore become the most urgent task at hand. This dissertation will focus the following aspects:
First, the flexible tether is modeled as a series of elements with lumped masses. The number ofdegrees-of-freedom of the tethered satellite system is investigated as the discrete lumped mass pointsare transferred from inside (outside) of the satellite to the outside (inside). Flexibility, viscoelasticity,“rocket term”, and dissipation effect of the space tether are taken into proper account within thismodel, as well as the friction between tethers and satellites, and its impact on Keplerian orbit. Themodel is therefore an adequate explanation of changes to the tether configuration within an operatingtethered satellite system.
An improved finite difference method is then presented to calculate the dynamical response ofthe proposed model with a time-varying number of degrees-of-freedom. The core of this method is toidentify changes in the number of degrees-of-freedom of the tethered system within each iteration step.Once the value changes, the tether is re-devided into a different set of units, with properties of eachtether node added or removed, and its lumped mass, damping and stiffness matrices, and displacementand force vectors updated. The calculation continues till a final result can be obtained. Redundantcalculations in this model of node properties are removed, and thus computation efficiency can beobtained. The method can be extended to calculate the dynamics of one-dimensional continuumduring deployment/retrieval.
After that, a dynamics analysis is carried out to study the impact of environment perturbations inthe space on complicated systems of tethered satellites. Simulation results have indicated thatinfluences of heating effect and debris impact on the system are significant. Impacts of J2perturbationand atmospheric drag depend on the inclination and altitude of the orbit where the tethered satellitesystem is located. As the orbital eccentricity changes, the different types of pitch motions such as theperiodic motion, quasi-periodic motion, and chaotic motion will occur in the system. Impact of solarpressure on the tethered satellite appears to be slight.
Taking into account all the space perturbations discussed above, an effective approach ispresented to control the flexible tethered satellite system. Pitch altitude of the satellite system can beregulated through jet force control of satellites within the system. A PID controller subject to a set ofconstraints is designed to achieve the result. Case studies indicate that, with the proposed method,pitch or chaotic motions of the tethered satellites in arbitrary elliptic orbits can be effectivelycontrolled.
Finally, the dynamics of electrodynamic tethered satellites and tether capturing involving cablesystems and related control methodologies are discussed.
首先，通过将柔性系绳离散为一系列绳结点，在绳结点进/出卫星体时考虑系统自由度变化，建立了时变自由度绳系卫星动力学模型。模型充分考虑了系绳的柔性、粘弹性、“火箭项”、耗散作用以及系绳与卫星本体间摩擦、冲击对Kepler轨道的影响，很好地揭示了绳系卫星运行过程中系绳构形的变化规律。
然后，提出一套改进的有限差分方法来计算时变多自由度系统的动力学响应。算法的核心思想是在每一次迭代循环中对系统自由度变化与否进行判定，一旦自由度发生变化，则通过重新划分系绳单元，添加（或删除）相应结点的信息，重置系统质量、阻尼和刚度矩阵及位移和荷载向量，使得迭代计算可以继续进行直至得出最终响应结果。此算法略去了多余的结点计算，提高了计算效率，可推广至一维连续体系统释放/回收过程的动力学研究中。
随后，研究了各种真实太空环境摄动因素对复杂绳系卫星系统的动力学影响。数值结果表明，热效应与太空碎片撞击对系统作用十分显著；J2摄动与大气阻力对绳系卫星的影响取决于绳系卫星系统所处的轨道倾角与高度；随Kepler轨道偏心率的变化，绳系卫星系统将发生分岔，出现周期运动、概周期运动及混沌运动；而太阳光压力对绳系卫星作用则是非常微小的。
综合考虑以上各种太空摄动因素的存在，提出了柔性绳系卫星系统的有效控制方法。采用子星端喷气控制并设计了一套含约束条件的PID控制器对柔性绳系卫星模型的俯仰姿态进行了有效控制。研究表明，该方法可有效实现任意椭圆轨道下绳系卫星系统的俯仰姿态运动及混沌运动控制。
最后，讨论了电动力绳系卫星以及绳系捕捉等所涉及到的绳系系统的动力学与控制问题。
Tethered satellites, satellites recently innovated for space probe, have become a prominent tool inscientific studies of space and outer space. Researches on theories and experimental methodologies(ground or orbital) regarding tethered satellites have been intensified in Eastern countries, as scienceand technology develop. Among them all, flexibility of the space tether, complexity of the space, andpertinent controlling mechanisms are, without doubt, the most difficult. Solving these issues hastherefore become the most urgent task at hand. This dissertation will focus the following aspects:
First, the flexible tether is modeled as a series of elements with lumped masses. The number ofdegrees-of-freedom of the tethered satellite system is investigated as the discrete lumped mass pointsare transferred from inside (outside) of the satellite to the outside (inside). Flexibility, viscoelasticity,“rocket term”, and dissipation effect of the space tether are taken into proper account within thismodel, as well as the friction between tethers and satellites, and its impact on Keplerian orbit. Themodel is therefore an adequate explanation of changes to the tether configuration within an operatingtethered satellite system.
An improved finite difference method is then presented to calculate the dynamical response ofthe proposed model with a time-varying number of degrees-of-freedom. The core of this method is toidentify changes in the number of degrees-of-freedom of the tethered system within each iteration step.Once the value changes, the tether is re-devided into a different set of units, with properties of eachtether node added or removed, and its lumped mass, damping and stiffness matrices, and displacementand force vectors updated. The calculation continues till a final result can be obtained. Redundantcalculations in this model of node properties are removed, and thus computation efficiency can beobtained. The method can be extended to calculate the dynamics of one-dimensional continuumduring deployment/retrieval.
After that, a dynamics analysis is carried out to study the impact of environment perturbations inthe space on complicated systems of tethered satellites. Simulation results have indicated thatinfluences of heating effect and debris impact on the system are significant. Impacts of J2perturbationand atmospheric drag depend on the inclination and altitude of the orbit where the tethered satellitesystem is located. As the orbital eccentricity changes, the different types of pitch motions such as theperiodic motion, quasi-periodic motion, and chaotic motion will occur in the system. Impact of solarpressure on the tethered satellite appears to be slight.
Taking into account all the space perturbations discussed above, an effective approach ispresented to control the flexible tethered satellite system. Pitch altitude of the satellite system can beregulated through jet force control of satellites within the system. A PID controller subject to a set ofconstraints is designed to achieve the result. Case studies indicate that, with the proposed method,pitch or chaotic motions of the tethered satellites in arbitrary elliptic orbits can be effectivelycontrolled.
Finally, the dynamics of electrodynamic tethered satellites and tether capturing involving cablesystems and related control methodologies are discussed.
引文
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