分布式卫星编队构形控制研究
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摘要
分布式卫星系统因其独特的技术优势和广阔的应用前景而备受关注。协同控制技术是实现分布式卫星应用的关键技术,而编队构形控制则是协同控制研究的重要内容,因此对分布式卫星技术的发展具有重要意义。本文在考虑一定任务背景的前提下,对分布式卫星编队构形控制及其相关技术开展了研究。
首先研究了分布式卫星编队构形的构成机理。分别对分布式卫星相对运动的动力学方程和运动学方程进行了推导和简要的分析。在定义编队构形参数的基础上,给出了编队构形确定方程,进而详细分析了编队卫星轨道根数误差对编队构形的影响。
其次,以相对运动的运动学方程为基础,对近地轨道编队构形的受摄稳定性进行了分析。以无量纲化德洛勒变量描述的轨道摄动方程为工具,研究了J 2项摄动造成的编队构形参数变化规律,并推导了补偿J 2项摄动下构形沿航迹漂移的长半轴修正方法。以考虑周日效应的大气密度模型为基础,分析了编队卫星轨道能量耗散差异,进而得到了编队构形的沿航迹漂移规律,然后设计了补偿大气摄动的面质比调整方法。
再次,研究了分布式SAR卫星的编队构形优化设计问题。设计了满足系统总体要求的分布式SAR卫星参考轨道。以分布式SAR卫星系统性能作为优化指标,以遗传算法作为优化工具进行编队构形优化设计。以典型SAR卫星的技术参数为初始条件,设计了几种编队构形,计算结果表明设计构形能够满足任务提出的高程测量精度和可测速比要求。
然后,研究了基于大气阻力的编队构形沿航迹控制问题。在对大气阻力控制基本原理进行详细分析的前提下,提出了相平面控制和模糊控制两种控制方法。分析了构形沿航迹漂移的相轨迹,针对单开关门限控制律不能对初始误差收敛的问题,设计了倾斜开关曲线控制,并分析了相应的极限环参数。提出了沿航迹漂移的模糊控制方法,较好的解决了构形沿航迹漂移不稳定的问题。在对输入输出变量进行模糊化的基础上,设计了模糊控制规则库和控制量解模糊算法,并对控制器进行了稳定性分析。
随后,研究了基于脉冲推力的编队构形控制问题。针对系统对星间基线的具体要求,设计了采用气动阻力板和脉冲推力发动机作为执行器的编队构形控制方案。提出了延长控制周期的编队构形参数偏置策略,使构形控制周期达到任务的要求。研究了编队构形侧向冲量控制和轨道面内绕飞椭圆冲量控制方法,实现了构形的长期控制。对控制方法的能耗进行了分析,仿真结果表明在采用文中提出的编队构形控制方案的条件下,每年用于构形控制的推进剂仅为卫星总质量的1.73%左右。
最后,研究了基于连续微推力的编队构形精密保持控制问题。基于克拉索夫斯基定理推导了编队构形非线性反馈控制律,然后利用数值仿真方法研究了反馈系数、导航误差和推力误差对控制的影响。基于非线性反馈控制律,研究了重力场测量内编队系统的精密保持控制。
Distributed Satellite System (DSS) has been well concerned because of its unique technical advantages and good prospects in applications. Control of formation configuration is an important section of coordinate control, which is the key technique to enable distributed satellite. Therefore, control of formation configuration is of great importance to the development of DSS. Considering some certain missions, control of formation configuration and its correlative techniques were studied in the thesis.
Firstly, the constitution mechanism of formation configuration was studied. The dynamic equations and the kinematic equations of relative motion were derived and analyzed separately. Based on the definition of formation configuration parameters, the determination formulas for formation configuration were given, followed with a detailed analysis on the effect of the orbit elements’errors on the formation configuration.
Secondly, the stability of perturbed configuration in LEO was analyzed on the basis of the kinematic equations of relative motion. The change of the configuration general parameters was studied with the use of perturbed equations described with non-dimensional Delaunay variables, and then the adjustment of semi-major axis was derived to compensate the J 2 perturbation. Using the model of atmosphere density including daily effect, the difference of orbital energy consumption between the formation flying satellites is analyzed, from which the along-track drift law of the formation configuration was derived. And then two methods for the adjustment of area-mass-ratio were designed to compensate the atmosphere perturbation.
Thirdly, formation optimized design was studied for the distributed SAR. On the research of the coverage performance of the distributed SAR, the reference orbit was designed to meet with the requirement of the integrated design, and the effect of the technical parameters on the mapping duration was analyzed. Taking the system performance as the sufficiency function, genetic algorithm was used to optimize the formation configuration. Based on the parameters of several typical SAR satellites, a number of formation configurations were designed. The result indicated that the configurations can guarantee the accuracy of the height measurement or the ratio of the measurable velocity to fulfill the mission.
Fourthly, the control of the along-track drift of the formation was studied based on atmosphere drag. With a detailed analysis on the principle of the control, phase-plane method and fuzzy control method were presented. According to the phase trajectory of along-track drift, the switching function with the oblique lines was designed in order to converge the initial errors, and the limit cycle was analyzed correspondingly. To deal with the instability of the along-track drift of the configuration, the fuzzy control method was presented. Based on the fuzzification of the inputs and outputs, the fuzzy rules and the defuzzification algorithm were designed, followed with the analysis of the stability of the controller.
Fifthly, the control of the formation was studied based on impulse thrust. According to the limitation of the baselines, the control scheme was designed using the drag panels and impulse thrusters. In order to prolong the control duration to meet the requirement of the mission, the adjustment strategy of the configuration was presented by offsetting the parameters. The cross-track control and co-plane control were studied based on impulse thrust, by which the permanent control of the formation could be enabled. The fuel consumption of the method was analyzed, and the simulation result indicated that the mass of propellant used in the formation control was only 1.73% in proportion to the total mass, on the condition of the control scheme proposed in the thesis.
Finally, precise maintenance of formation was studied based on continuous micro-thrust. Nonlinear feedback control law was derived using Krassowski’s theorem. Then, the effects of the feedback coefficient, navigation error and thrust error were studied with numerical simulation. Based on the nonlinear feedback control law, the precise maintenance of the inner formation for the gravity field observation was studied at the end.
首先研究了分布式卫星编队构形的构成机理。分别对分布式卫星相对运动的动力学方程和运动学方程进行了推导和简要的分析。在定义编队构形参数的基础上,给出了编队构形确定方程,进而详细分析了编队卫星轨道根数误差对编队构形的影响。
其次,以相对运动的运动学方程为基础,对近地轨道编队构形的受摄稳定性进行了分析。以无量纲化德洛勒变量描述的轨道摄动方程为工具,研究了J 2项摄动造成的编队构形参数变化规律,并推导了补偿J 2项摄动下构形沿航迹漂移的长半轴修正方法。以考虑周日效应的大气密度模型为基础,分析了编队卫星轨道能量耗散差异,进而得到了编队构形的沿航迹漂移规律,然后设计了补偿大气摄动的面质比调整方法。
再次,研究了分布式SAR卫星的编队构形优化设计问题。设计了满足系统总体要求的分布式SAR卫星参考轨道。以分布式SAR卫星系统性能作为优化指标,以遗传算法作为优化工具进行编队构形优化设计。以典型SAR卫星的技术参数为初始条件,设计了几种编队构形,计算结果表明设计构形能够满足任务提出的高程测量精度和可测速比要求。
然后,研究了基于大气阻力的编队构形沿航迹控制问题。在对大气阻力控制基本原理进行详细分析的前提下,提出了相平面控制和模糊控制两种控制方法。分析了构形沿航迹漂移的相轨迹,针对单开关门限控制律不能对初始误差收敛的问题,设计了倾斜开关曲线控制,并分析了相应的极限环参数。提出了沿航迹漂移的模糊控制方法,较好的解决了构形沿航迹漂移不稳定的问题。在对输入输出变量进行模糊化的基础上,设计了模糊控制规则库和控制量解模糊算法,并对控制器进行了稳定性分析。
随后,研究了基于脉冲推力的编队构形控制问题。针对系统对星间基线的具体要求,设计了采用气动阻力板和脉冲推力发动机作为执行器的编队构形控制方案。提出了延长控制周期的编队构形参数偏置策略,使构形控制周期达到任务的要求。研究了编队构形侧向冲量控制和轨道面内绕飞椭圆冲量控制方法,实现了构形的长期控制。对控制方法的能耗进行了分析,仿真结果表明在采用文中提出的编队构形控制方案的条件下,每年用于构形控制的推进剂仅为卫星总质量的1.73%左右。
最后,研究了基于连续微推力的编队构形精密保持控制问题。基于克拉索夫斯基定理推导了编队构形非线性反馈控制律,然后利用数值仿真方法研究了反馈系数、导航误差和推力误差对控制的影响。基于非线性反馈控制律,研究了重力场测量内编队系统的精密保持控制。
Distributed Satellite System (DSS) has been well concerned because of its unique technical advantages and good prospects in applications. Control of formation configuration is an important section of coordinate control, which is the key technique to enable distributed satellite. Therefore, control of formation configuration is of great importance to the development of DSS. Considering some certain missions, control of formation configuration and its correlative techniques were studied in the thesis.
Firstly, the constitution mechanism of formation configuration was studied. The dynamic equations and the kinematic equations of relative motion were derived and analyzed separately. Based on the definition of formation configuration parameters, the determination formulas for formation configuration were given, followed with a detailed analysis on the effect of the orbit elements’errors on the formation configuration.
Secondly, the stability of perturbed configuration in LEO was analyzed on the basis of the kinematic equations of relative motion. The change of the configuration general parameters was studied with the use of perturbed equations described with non-dimensional Delaunay variables, and then the adjustment of semi-major axis was derived to compensate the J 2 perturbation. Using the model of atmosphere density including daily effect, the difference of orbital energy consumption between the formation flying satellites is analyzed, from which the along-track drift law of the formation configuration was derived. And then two methods for the adjustment of area-mass-ratio were designed to compensate the atmosphere perturbation.
Thirdly, formation optimized design was studied for the distributed SAR. On the research of the coverage performance of the distributed SAR, the reference orbit was designed to meet with the requirement of the integrated design, and the effect of the technical parameters on the mapping duration was analyzed. Taking the system performance as the sufficiency function, genetic algorithm was used to optimize the formation configuration. Based on the parameters of several typical SAR satellites, a number of formation configurations were designed. The result indicated that the configurations can guarantee the accuracy of the height measurement or the ratio of the measurable velocity to fulfill the mission.
Fourthly, the control of the along-track drift of the formation was studied based on atmosphere drag. With a detailed analysis on the principle of the control, phase-plane method and fuzzy control method were presented. According to the phase trajectory of along-track drift, the switching function with the oblique lines was designed in order to converge the initial errors, and the limit cycle was analyzed correspondingly. To deal with the instability of the along-track drift of the configuration, the fuzzy control method was presented. Based on the fuzzification of the inputs and outputs, the fuzzy rules and the defuzzification algorithm were designed, followed with the analysis of the stability of the controller.
Fifthly, the control of the formation was studied based on impulse thrust. According to the limitation of the baselines, the control scheme was designed using the drag panels and impulse thrusters. In order to prolong the control duration to meet the requirement of the mission, the adjustment strategy of the configuration was presented by offsetting the parameters. The cross-track control and co-plane control were studied based on impulse thrust, by which the permanent control of the formation could be enabled. The fuel consumption of the method was analyzed, and the simulation result indicated that the mass of propellant used in the formation control was only 1.73% in proportion to the total mass, on the condition of the control scheme proposed in the thesis.
Finally, precise maintenance of formation was studied based on continuous micro-thrust. Nonlinear feedback control law was derived using Krassowski’s theorem. Then, the effects of the feedback coefficient, navigation error and thrust error were studied with numerical simulation. Based on the nonlinear feedback control law, the precise maintenance of the inner formation for the gravity field observation was studied at the end.
引文
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