空间飞行器非线性姿态控制与最优制导
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摘要
本文主要研究了空间飞行器非线性姿态控制方法和月球探测器燃耗最优软着陆的最优轨道及最优制导律设计。研究内容主要分为两部分，一部分是研究分别以剪式陀螺系统和双框架控制力矩陀螺系统为执行机构的空间飞行器姿态控制方法，另一部分是研究月球探测器燃耗最优软着陆段三维动力学建模及最优轨道、最优制导律设计。具体内容如下：
由一对可以同步进动的陀螺转子组成的剪式陀螺系统，当两个陀螺转子同步进动时，可以与星体产生动量交换，进行姿态控制。我们的目的是设计一个控制律保证两个陀螺转子可以同步进动。在工程中，系统经常受到时变未知扰动的影响，针对这些扰动，我们利用反馈线性化理论和递推李亚普诺夫方法设计了一种非线性闭环反馈控制律。可以证明，若系统中时变不确定项是有界的，则所设计的控制器可以保证系统跟踪误差和同步误差都是有界收敛的。并且证明了若给出合适的回转角指令，则系统的跟踪动力学也是有界的。
针对由剪式陀螺驱动的空间飞行器回转运动控制中系统存在不确定参数及未知扰动的情况，我们利用反馈线性化理论和递推李亚普诺夫方法，结合tuningfunction方法设计了非线性自适应控制器。通过对系统中不确定项的估计，我们所设计的控制器可以使系统跟踪误差和同步误差随时间收敛至零。我们所设计的基于剪式陀螺的空间飞行器非线性姿态控制律可以用于完成月球探测器轨道舱的姿态控制任务，也可以应用于空间站或空间机动平台等其它空间飞行器的大角度快速姿态机动控制任务。
针对空间飞行器三轴大角度快速姿态机动问题，我们推导得到了由双框架控制力矩陀螺系统操纵空间飞行器姿态机动的精确数学模型，并在此基础上基于李亚普诺夫第二法设计了空间飞行器三轴大角度姿态机动非线性控制律，在设计的同时证明了系统的稳定性。比较了在不同操纵律下系统回避和退出奇异状态的能力。并给出了双框架控制力矩陀螺系统奇异性定理，对三个双框架陀螺垂直安装及四个双框架陀螺平行安装两种构形方式进行了奇异性分析。并仿真验证了在这两种安装构形下系统大角度姿态机动的能力及当有陀螺失效时系统重构和恢复控制的能力。我们推导的基于双框架陀螺的空间飞行器动力学模型及所设计的控制律和操纵律不但可以用于进行月球探测器轨道舱、空间站等空间飞行器的姿态控制，而且也可以考虑应用于月球探测器着陆舱的姿态控制以及小型敏捷卫星、空间机器人等小型空间飞行器的姿态控制任务。
针对月球探测器月面软着陆问题，首先在不考虑月球自转的情况下，通过建立月心惯性坐标系、探测器轨道坐标系及其转换关系，推导得到了月球探测器在三维空间飞行的动力学模型。在实际工程中，探测器的轨控发动机一般采用开关控制工作方式，其推力大小不能连续调节，并假设姿控系统可以实现快速准确姿态指令跟踪。因此，在轨控发动机推力为开关控制情况下，我们以软着陆过程中燃耗最优为指标，利用Pontryagin极大值原理，得到了发动机推力开关曲线和推力方向角的开环最优制导律。通过约束软着陆终端速度求解两点边值问题，得到了探测器软着陆的最优轨线。
由于月球是一个自旋体，其自转会对探测器落点精度产生一定影响。为了提高制导精度，在考虑月球自转的基础上，通过引入月固坐标系，我们推导出了月球探测器在三维空间飞行的精确动力学模型。同样以燃耗最优为指标，利用Pontryagin极大值原理，得到了发动机推力开关曲线和推力方向角的开环最优制导律。综合考虑落点位置和速度约束求解两点边值问题，得到了探测器软着陆的最优轨线。
通过引入两个新的状态方程，对推导得到的月球探测器软着陆三维精确动力学模型进行变换，使其具有仿射非线性系统的表达形式。并基于此新系统方程设计了具有闭环形式的非线性状态反馈最优控制器，其控制参数矩阵K是一个黎卡提类微分方程的解。针对矩阵K的求解，我们提出了一种较为实用的设计方法，即通过使闭环控制器在整个运行时间段上逼近开环计算得到的最优数值解来直接求解系数矩阵K，而避免了求解复杂的黎卡提类微分方程，显著降低了计算量。
This dissertation includes research of nonlinear attitude control of spacecraftand optimal guidance for soft landing of lunar module. It can be divided into twoparts: in the first part nonlinear attitude controls of spacecraft based on scissored pairof control moment gyros or double gimbal control moment gyros are studied; in thesecond part precise modeling, the optimal guidance and optimal trajectory design forlunar module soft landing are studied.
The combination of a pair of gyros which could precess synchronously withinone gimbal is called scissored pair of control moment gyros, where the two gyrosmust synchronously precess for proper momentum exchange with the spacecraft. Soour aim is to design a controller which could guarantee the two gyros to precesssynchronously. To suppress external disturbances to the system, we design anonlinear feedback controller by using the method of feedback linearization,backstepping Lyapunov theory and young’s inequality. It can be proved that if theunknown disturbances are bounded, then the tracking error and the synchronizationerror are all bounded. Furthermore, the nonlinear tracking dynamics of the system areproved to be bounded in the case of a bounded command.
Concerning both unknown inertia properties and unknown constant disturbances,we propose an adaptive control law for the closed-loop slewing motion controlutilizing the methods of feedback linearization, backstepping tuning function andLyapunov theory. Under this design the system tracking error and thesynchronization error converge to zero. The proposed nonlinear control law based onscissored pair of control moment gyros can be applied to many kinds of spacecraftssuch as lunar orbit module, space station and space platform.
Concerning the attitude control of three axis large angle maneuver of spacecraft,we derived an exact mathematical description for the angular motion driven bydouble gimbal control moment gyros. A nonlinear control law is designed based onthe second method of Lyapunov. System capabilities to avoid or withdraw from thesingularity are studied under different steering laws. Moreover, a theorem about thesingularity of double gimbal control moment gyros’ system is proposed. Based onthis theorem the singularities of two configurations of double gimbal control momentgyros system are detailed. The first configuration consists of three orthogonally mounted double gimbal control moment gyros and the second configuration consistsof four parallel mounted double gimbal control moment gyros. Simulation resultsshow that both the two configurations can effectively fulfill tasks of trackingconstant torque commands and driving large angle attitude maneuvers, even some ofthe gyros fail in both the two configuration. The system dynamics and nonlinearcontrol law proposed for double gimbal control moment gyros can be applied toattitude control of lunar orbit module, lunar descent module and some other kinds ofspacecrafts.
Three dimensional dynamics for lunar module soft landing were presented byintroducing two sets of coordinate without consideration of the moon rotation. Inpractice, the thrust of the module always works in switching mode which can not beadjusted smoothly. We assume that the attitude commands can be followed precisely.To realize the minimal fuel strategy, an optimal open loop guidance law is proposedbased on the maximum principle. By solving the two-point boundary value problemwith the constraints of final velocities, the optimal trajectory of the lunar soft landingis obtained.
To enhance the precision of soft landing which would be influenced by themoon rotation, we introduce another coordinate, Lunar Centered Fixed Coordinate,and a precise three dimensional dynamic model with consideration of the rotation ofmoon is then derived. Using the minimal fuel consumption as an index, we present anopen loop optimal guidance law based on Pontryagin’s maximum principle. Optimaltrajectories are obtained by solving the two-point boundary value problem withconstraints of final velocities and locations.
By introducing two new state equations, the system dynamics obtainedpreviously can be changed which would have the form of affine nonlinear systems.Based on the new equations, a closed loop optimal guidance law is designed with aparameter matrix K to be determined which is the solution of a riccati likedifferential equation. Here we propose a more practical method to calculate thematrix K that is to let the closed loop controller approximate the numerical solutionsobtained by an open loop optimization, such that it is avoided to solve the complexriccati like differential equation.
由一对可以同步进动的陀螺转子组成的剪式陀螺系统，当两个陀螺转子同步进动时，可以与星体产生动量交换，进行姿态控制。我们的目的是设计一个控制律保证两个陀螺转子可以同步进动。在工程中，系统经常受到时变未知扰动的影响，针对这些扰动，我们利用反馈线性化理论和递推李亚普诺夫方法设计了一种非线性闭环反馈控制律。可以证明，若系统中时变不确定项是有界的，则所设计的控制器可以保证系统跟踪误差和同步误差都是有界收敛的。并且证明了若给出合适的回转角指令，则系统的跟踪动力学也是有界的。
针对由剪式陀螺驱动的空间飞行器回转运动控制中系统存在不确定参数及未知扰动的情况，我们利用反馈线性化理论和递推李亚普诺夫方法，结合tuningfunction方法设计了非线性自适应控制器。通过对系统中不确定项的估计，我们所设计的控制器可以使系统跟踪误差和同步误差随时间收敛至零。我们所设计的基于剪式陀螺的空间飞行器非线性姿态控制律可以用于完成月球探测器轨道舱的姿态控制任务，也可以应用于空间站或空间机动平台等其它空间飞行器的大角度快速姿态机动控制任务。
针对空间飞行器三轴大角度快速姿态机动问题，我们推导得到了由双框架控制力矩陀螺系统操纵空间飞行器姿态机动的精确数学模型，并在此基础上基于李亚普诺夫第二法设计了空间飞行器三轴大角度姿态机动非线性控制律，在设计的同时证明了系统的稳定性。比较了在不同操纵律下系统回避和退出奇异状态的能力。并给出了双框架控制力矩陀螺系统奇异性定理，对三个双框架陀螺垂直安装及四个双框架陀螺平行安装两种构形方式进行了奇异性分析。并仿真验证了在这两种安装构形下系统大角度姿态机动的能力及当有陀螺失效时系统重构和恢复控制的能力。我们推导的基于双框架陀螺的空间飞行器动力学模型及所设计的控制律和操纵律不但可以用于进行月球探测器轨道舱、空间站等空间飞行器的姿态控制，而且也可以考虑应用于月球探测器着陆舱的姿态控制以及小型敏捷卫星、空间机器人等小型空间飞行器的姿态控制任务。
针对月球探测器月面软着陆问题，首先在不考虑月球自转的情况下，通过建立月心惯性坐标系、探测器轨道坐标系及其转换关系，推导得到了月球探测器在三维空间飞行的动力学模型。在实际工程中，探测器的轨控发动机一般采用开关控制工作方式，其推力大小不能连续调节，并假设姿控系统可以实现快速准确姿态指令跟踪。因此，在轨控发动机推力为开关控制情况下，我们以软着陆过程中燃耗最优为指标，利用Pontryagin极大值原理，得到了发动机推力开关曲线和推力方向角的开环最优制导律。通过约束软着陆终端速度求解两点边值问题，得到了探测器软着陆的最优轨线。
由于月球是一个自旋体，其自转会对探测器落点精度产生一定影响。为了提高制导精度，在考虑月球自转的基础上，通过引入月固坐标系，我们推导出了月球探测器在三维空间飞行的精确动力学模型。同样以燃耗最优为指标，利用Pontryagin极大值原理，得到了发动机推力开关曲线和推力方向角的开环最优制导律。综合考虑落点位置和速度约束求解两点边值问题，得到了探测器软着陆的最优轨线。
通过引入两个新的状态方程，对推导得到的月球探测器软着陆三维精确动力学模型进行变换，使其具有仿射非线性系统的表达形式。并基于此新系统方程设计了具有闭环形式的非线性状态反馈最优控制器，其控制参数矩阵K是一个黎卡提类微分方程的解。针对矩阵K的求解，我们提出了一种较为实用的设计方法，即通过使闭环控制器在整个运行时间段上逼近开环计算得到的最优数值解来直接求解系数矩阵K，而避免了求解复杂的黎卡提类微分方程，显著降低了计算量。
This dissertation includes research of nonlinear attitude control of spacecraftand optimal guidance for soft landing of lunar module. It can be divided into twoparts: in the first part nonlinear attitude controls of spacecraft based on scissored pairof control moment gyros or double gimbal control moment gyros are studied; in thesecond part precise modeling, the optimal guidance and optimal trajectory design forlunar module soft landing are studied.
The combination of a pair of gyros which could precess synchronously withinone gimbal is called scissored pair of control moment gyros, where the two gyrosmust synchronously precess for proper momentum exchange with the spacecraft. Soour aim is to design a controller which could guarantee the two gyros to precesssynchronously. To suppress external disturbances to the system, we design anonlinear feedback controller by using the method of feedback linearization,backstepping Lyapunov theory and young’s inequality. It can be proved that if theunknown disturbances are bounded, then the tracking error and the synchronizationerror are all bounded. Furthermore, the nonlinear tracking dynamics of the system areproved to be bounded in the case of a bounded command.
Concerning both unknown inertia properties and unknown constant disturbances,we propose an adaptive control law for the closed-loop slewing motion controlutilizing the methods of feedback linearization, backstepping tuning function andLyapunov theory. Under this design the system tracking error and thesynchronization error converge to zero. The proposed nonlinear control law based onscissored pair of control moment gyros can be applied to many kinds of spacecraftssuch as lunar orbit module, space station and space platform.
Concerning the attitude control of three axis large angle maneuver of spacecraft,we derived an exact mathematical description for the angular motion driven bydouble gimbal control moment gyros. A nonlinear control law is designed based onthe second method of Lyapunov. System capabilities to avoid or withdraw from thesingularity are studied under different steering laws. Moreover, a theorem about thesingularity of double gimbal control moment gyros’ system is proposed. Based onthis theorem the singularities of two configurations of double gimbal control momentgyros system are detailed. The first configuration consists of three orthogonally mounted double gimbal control moment gyros and the second configuration consistsof four parallel mounted double gimbal control moment gyros. Simulation resultsshow that both the two configurations can effectively fulfill tasks of trackingconstant torque commands and driving large angle attitude maneuvers, even some ofthe gyros fail in both the two configuration. The system dynamics and nonlinearcontrol law proposed for double gimbal control moment gyros can be applied toattitude control of lunar orbit module, lunar descent module and some other kinds ofspacecrafts.
Three dimensional dynamics for lunar module soft landing were presented byintroducing two sets of coordinate without consideration of the moon rotation. Inpractice, the thrust of the module always works in switching mode which can not beadjusted smoothly. We assume that the attitude commands can be followed precisely.To realize the minimal fuel strategy, an optimal open loop guidance law is proposedbased on the maximum principle. By solving the two-point boundary value problemwith the constraints of final velocities, the optimal trajectory of the lunar soft landingis obtained.
To enhance the precision of soft landing which would be influenced by themoon rotation, we introduce another coordinate, Lunar Centered Fixed Coordinate,and a precise three dimensional dynamic model with consideration of the rotation ofmoon is then derived. Using the minimal fuel consumption as an index, we present anopen loop optimal guidance law based on Pontryagin’s maximum principle. Optimaltrajectories are obtained by solving the two-point boundary value problem withconstraints of final velocities and locations.
By introducing two new state equations, the system dynamics obtainedpreviously can be changed which would have the form of affine nonlinear systems.Based on the new equations, a closed loop optimal guidance law is designed with aparameter matrix K to be determined which is the solution of a riccati likedifferential equation. Here we propose a more practical method to calculate thematrix K that is to let the closed loop controller approximate the numerical solutionsobtained by an open loop optimization, such that it is avoided to solve the complexriccati like differential equation.
引文
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