绳系卫星释放和回收的动力学控制
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摘要
绳系卫星系统是指采用细长系绳将两个或多个人造卫星连在一起飞行的组合体。绳系卫星是一项颇具发展前景的技术,有可能促成太空探索及开发领域的一次技术革命。然而,即便结构形式最简单的绳系卫星系统,其动力学及控制问题也非常复杂。由于系绳具有阻尼小、柔性大的特点,当它被置于空间环境并与卫星耦合时极易产生一系列复杂的天平动及振动。在绳系卫星释放及回收过程中,系绳长度的变化引起Coriolis加速度,可能导致系绳出现大幅摆动及振动。若不施加控制,系绳内的动应力幅值可能会超过材料的强度极限,导致系统失效。
本文考虑绳系卫星系统应用中最关键的释放和回收环节,研究其相关动力学与控制问题。论文的主要研究内容和学术贡献如下:
1.研究非线性最优控制问题的Legendre-Gauss-Lobatto (LGL)伪谱法,提出并证明Bolza型最优控制问题的直接二阶LGL伪谱法的协态映射关系。在此基础上,采用C++语言编写通用非线性最优控制程序包,并通过加入符号数学预处理器和利用矩阵稀疏结构,大大提高了计算效率。
2.针对绳系卫星释放过程的固定及非固定时间区间轨道优化问题,提出基于二阶微分包含的控制律设计方法,使得优化变量数及约束数显著减少。考虑倾斜轨道上电动力绳系卫星的回收过程和轨道面内三体绳系卫星系统的释放过程,分别研究其非线性最优控制问题。利用LGL伪谱法将上述连续时间最优控制问题离散后,通过非线性规划方法进行求解。
3.针对扰动影响下的绳系卫星释放控制问题,基于直接轨道产生方法设计反馈控制器,提出一种在线网格调整算法,使得计算时间大幅减少。考虑倾斜轨道上电动力绳系卫星回收控制问题,设计非线性模型预测控制器,并采用多体动力学模型对控制性能进行检验。
4.通过时间尺度变换,研究绳系卫星回收过程的无限时域最优控制问题,分别利用两种Legendre-Gauss-Radau (LGR)伪谱法进行离散求解,并通过实时轨道产生方法初步设计了反馈控制器。
5.利用气浮装置和喷管来模拟绳系卫星上的重力梯度力和Coriolis加速度作用,提出了新的绳系卫星系统地面模拟实验设计方案,并就卫星仿真器、计算机视觉和系绳控制等关键子系统研制过程中所涉及到的理论和技术问题进行讨论。
The concept of Tethered Satellite System (TSS), that is, two or more satellites connected by thin and long cables, promises to revolutionize many aspects of space exploration and exploitation. However, the dynamics and control of any TSS are quite complex. Because of their overall flexibility, the tethers are strongly susceptible to undergoing a complicated set of librations and vibrations when they are placed into a space environment and coupled with flexible satellites. The problem becomes even more challenging when the deployment and retrieval parts of a TSS mission are taken into consideration because the librations and vibrations of tether can grow dramatically due to the effect of the Coriolis accelerations. If not carefully controlled, motions with large amplitudes may result in an excessively high tensional stress beyond the strength of tether material and may lead to the failure of a whole TSS.
This dissertation focuses on the dynamics and control problems concerning tether deployment and retrieval, which may be the most important but also delicate parts of a TSS mission. The main themes and contributions of the dissertation include:
1. A detailed study is presented on the Legendre-Gauss-Lobatto (LGL) pseudospectral (PS) methods for solving nonlinear optimal control problems. Additionally, a costate estimation scheme is proposed for the Bolza problem of optimal control of a set of dynamic equations of the second order by using the direct LGL PS approach. The presented algorithms are coded into a reusable general optimal control package in C++ language, and the computation efficiency is improved by using a symbolic preprocessor and putting the sparse structures of involved matrices into full use.
2. Optimal schemes are presented for controlling the deployment process of a tethered subsatellite model with fixed and free end-time, in which a second-order differential inclusion formulation is exploited to achieve a significant reduction of the number of optimization variables and constraints. The investigation is later extended to control the retrieval process of an electrodynamic tethered satellite system in an inclined orbit, and to achieve the optimal deployment of a three-body tethered satellite formation in the orbital plane. The optimal control is solved by discretizing the original continuous optimal control problem first, based on the LGL PS algorithm, and numerically solving the resulting large-scale optimization problem.
3. The idea of direct real-time trajectory generation is exploited to design feedback controller for the deployment process of a TSS subject to perturbations with the aid of a grid adaptation scheme, which contributes a significantly reduction of computation burden. In addition, a model predictive control (MPC) scheme is proposed for stabilizing the retrieval process of an electrodynamic TSS in an inclined orbit, and the performance of the MPC scheme is demonstrated by using a multi-body dynamics model.
4. Infinite-horizon optimal control schemes are also explored to stabilize the retrieval process of a TSS. The infinite-horizon optimal control problem is solved individually through two Legendre-Gauss-Radau (LGR) PS algorithms by using a straightforward domain-transformation. A preliminary exploration on feedback controller synthesis is further made about the idea of real-time trajectory generation.
5. Furthermore, an innovative experiment design is presented for the ground-based experiments of TSS, where a combination of air-bearing facilities and on-board thrusts are proposed to simulate the microgravity field and the Coriolis forces experienced by a TSS. Additionally, a detailed discussion is presented on the theoretical and technical issues related to the development of some key subsystems, such as satellite simulator, computer vision module, tether reel device, etc.
本文考虑绳系卫星系统应用中最关键的释放和回收环节,研究其相关动力学与控制问题。论文的主要研究内容和学术贡献如下:
1.研究非线性最优控制问题的Legendre-Gauss-Lobatto (LGL)伪谱法,提出并证明Bolza型最优控制问题的直接二阶LGL伪谱法的协态映射关系。在此基础上,采用C++语言编写通用非线性最优控制程序包,并通过加入符号数学预处理器和利用矩阵稀疏结构,大大提高了计算效率。
2.针对绳系卫星释放过程的固定及非固定时间区间轨道优化问题,提出基于二阶微分包含的控制律设计方法,使得优化变量数及约束数显著减少。考虑倾斜轨道上电动力绳系卫星的回收过程和轨道面内三体绳系卫星系统的释放过程,分别研究其非线性最优控制问题。利用LGL伪谱法将上述连续时间最优控制问题离散后,通过非线性规划方法进行求解。
3.针对扰动影响下的绳系卫星释放控制问题,基于直接轨道产生方法设计反馈控制器,提出一种在线网格调整算法,使得计算时间大幅减少。考虑倾斜轨道上电动力绳系卫星回收控制问题,设计非线性模型预测控制器,并采用多体动力学模型对控制性能进行检验。
4.通过时间尺度变换,研究绳系卫星回收过程的无限时域最优控制问题,分别利用两种Legendre-Gauss-Radau (LGR)伪谱法进行离散求解,并通过实时轨道产生方法初步设计了反馈控制器。
5.利用气浮装置和喷管来模拟绳系卫星上的重力梯度力和Coriolis加速度作用,提出了新的绳系卫星系统地面模拟实验设计方案,并就卫星仿真器、计算机视觉和系绳控制等关键子系统研制过程中所涉及到的理论和技术问题进行讨论。
The concept of Tethered Satellite System (TSS), that is, two or more satellites connected by thin and long cables, promises to revolutionize many aspects of space exploration and exploitation. However, the dynamics and control of any TSS are quite complex. Because of their overall flexibility, the tethers are strongly susceptible to undergoing a complicated set of librations and vibrations when they are placed into a space environment and coupled with flexible satellites. The problem becomes even more challenging when the deployment and retrieval parts of a TSS mission are taken into consideration because the librations and vibrations of tether can grow dramatically due to the effect of the Coriolis accelerations. If not carefully controlled, motions with large amplitudes may result in an excessively high tensional stress beyond the strength of tether material and may lead to the failure of a whole TSS.
This dissertation focuses on the dynamics and control problems concerning tether deployment and retrieval, which may be the most important but also delicate parts of a TSS mission. The main themes and contributions of the dissertation include:
1. A detailed study is presented on the Legendre-Gauss-Lobatto (LGL) pseudospectral (PS) methods for solving nonlinear optimal control problems. Additionally, a costate estimation scheme is proposed for the Bolza problem of optimal control of a set of dynamic equations of the second order by using the direct LGL PS approach. The presented algorithms are coded into a reusable general optimal control package in C++ language, and the computation efficiency is improved by using a symbolic preprocessor and putting the sparse structures of involved matrices into full use.
2. Optimal schemes are presented for controlling the deployment process of a tethered subsatellite model with fixed and free end-time, in which a second-order differential inclusion formulation is exploited to achieve a significant reduction of the number of optimization variables and constraints. The investigation is later extended to control the retrieval process of an electrodynamic tethered satellite system in an inclined orbit, and to achieve the optimal deployment of a three-body tethered satellite formation in the orbital plane. The optimal control is solved by discretizing the original continuous optimal control problem first, based on the LGL PS algorithm, and numerically solving the resulting large-scale optimization problem.
3. The idea of direct real-time trajectory generation is exploited to design feedback controller for the deployment process of a TSS subject to perturbations with the aid of a grid adaptation scheme, which contributes a significantly reduction of computation burden. In addition, a model predictive control (MPC) scheme is proposed for stabilizing the retrieval process of an electrodynamic TSS in an inclined orbit, and the performance of the MPC scheme is demonstrated by using a multi-body dynamics model.
4. Infinite-horizon optimal control schemes are also explored to stabilize the retrieval process of a TSS. The infinite-horizon optimal control problem is solved individually through two Legendre-Gauss-Radau (LGR) PS algorithms by using a straightforward domain-transformation. A preliminary exploration on feedback controller synthesis is further made about the idea of real-time trajectory generation.
5. Furthermore, an innovative experiment design is presented for the ground-based experiments of TSS, where a combination of air-bearing facilities and on-board thrusts are proposed to simulate the microgravity field and the Coriolis forces experienced by a TSS. Additionally, a detailed discussion is presented on the theoretical and technical issues related to the development of some key subsystems, such as satellite simulator, computer vision module, tether reel device, etc.
引文
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