Satellite dynamics under the influence of gravitational and aerodynamic torques. A study of stability of equilibrium positions

The dynamics of the rotational motion of a satellite, moving in the central Newtonian force field under the influence of gravitational and aerodynamic torques, is investigated. The paper proposes a method for determining all equilibrium positions (equilibrium orientations) of a satellite in the orbital coordinate system for specified values of aerodynamic torque and the major central moments of inertia; the sufficient conditions for their existence are obtained. For each equilibrium orientation the sufficient stability conditions are obtained using the generalized energy integral as the Lyapunov function. The detailed numerical analysis of the regions where the stability conditions of the equilibrium positions are satisfied is carried out depending on four dimensionless parameters of the problem. It is shown that, in the general case, the number of satellite’s equilibrium positions, for which the sufficient stability conditions are satisfied, varies from 4 to 2 with an increase in the value of the aerodynamic torque magnitude.     

A novel single thruster control strategy for spacecraft attitude stabilization

Feasibility of achieving three axis attitude stabilization using a single thruster is explored in this paper. Torques are generated using a thruster orientation mechanism with which the thrust vector can be tilted on a two axis gimbal. A robust nonlinear control scheme is developed based on the nonlinear kinematic and dynamic equations of motion of a rigid body spacecraft in the presence of gravity gradient torque and external disturbances. The spacecraft, controlled using the proposed concept, constitutes an underactuated system (a system with fewer independent control inputs than degrees of freedom) with nonlinear dynamics. Moreover, using thruster gimbal angles as control inputs make the system non-affine (control terms appear nonlinearly in the state equation). This necessitates the control algorithms to be developed based on nonlinear control theory since linear control methods are not directly applicable. The stability conditions for the spacecraft attitude motion for robustness against uncertainties and disturbances are derived to establish the regions of asymptotic 3-axis attitude stabilization. Several numerical simulations are presented to demonstrate the efficacy of the proposed controller and validate the theoretical results. The control algorithm is shown to compensate for time-varying external disturbances including solar radiation pressure, aerodynamic forces, and magnetic disturbances; and uncertainties in the spacecraft inertia parameters. The numerical results also establish the robustness of the proposed control scheme to negate disturbances caused by orbit eccentricity.     

Dynamics of an axisymmetric satellite under the action of gravitational and aerodynamic torques

Dynamics of attitude motion of an axisymmetric satellite moving in a circular orbit under the action of gravitational and aerodynamic torques is investigated. All equilibrium positions of the satellite in the orbital coordinate system are determined numerically, and sufficient conditions of stability of the equilibrium positions are derived.     

Attitude dynamics of a pendulum-shaped charged satellite

In this paper, we investigate the possibility of the use of the Lorentz force, which acts on charged satellite when it is moving through the magnetic field, as a means of satellite attitude control. We first derive the equations of attitude motion of charged satellite and then investigate the stability of the motion. Finally we propose an attitude control method using the Lorentz force. Our method requires moderate charge level for future Lorentz-augmented satellite.     

Stochastic control of pitch motion of satellites using stabilizing flaps

The modelling, analysis and synthesis of an attitude control system for low orbit artificial satellites using stabilizing flaps are presented. The function of the system is to maintain the satellite aligned with the local vertical. The aerodynamic forces on the satellite are modelled assuming free molecular flow using the kinetic theory of gases. The control system development is considered through the application of stochastic control concepts. The satellite motion is described by the equations of motion based on Newtonian formulation. Starting from the separation principle, a sequential procedure is developed in which the state estimation and control problems are handled simultaneously. State estimate is provided by Kalman filter using the information about the position of the satellite and of the flaps. The controller acts on satellite in real time, and the stabilizing flaps are the only control elements.     

Realization of modes of satellite attitude motion with a small level of microaccelerations using electromechanical executive devices

Quasi-static microaccelerations are estimated for a satellite specially designed to perform space experiments in the field of microgravity. Three modes of attitude motion of the spacecraft are considered: passive gravitational orientation, orbital orientation, and semi-passive gravitational orientation. In these modes the lengthwise axis of the satellite is directed along the local vertical, while solar arrays lie in the orbit plane. The second and third modes are maintained using electromechanical executive devices: flywheel engines or gyrodynes. Estimations of residual microaccelerations are performed with the help of mathematical modeling of satellite’s attitude motion under the action of gravitational and aerodynamic moments, as well as the moment produced by the gyro system. It is demonstrated that all modes ensure rather low level of quasi-static microaccelerations on the satellite and provide for a fairly narrow region of variation for the vector of residual microacceleration. The semi-passive gravitational orientation ensures also a limited proper angular momentum of the gyro system.     

Modeling of the aerodynamic moment acting upon a satellite

We consider the issues of modeling the moments of aerodynamic forces acting upon a satellite with gravitational system of stabilization. It is assumed that satellite orbits are almost circular with heights in the range 550–750 km. Simplified analytical expressions are suggested for the aerodynamic moment in the case when a satellite moves in the regime of gravitational orientation. Accuracy of the obtained expressions is estimated to be compared with that of expressions derived under the assumption of constant coefficient of frontal resistance. An analysis is made of short-periodic variations of the atmosphere density occurring due to orbital motion of a satellite. It is demonstrated that these variations can result in a substantial change of the aerodynamic moment, and their approximation by a truncated Fourier series is suggested. Estimates of the accuracy of the suggested approximation are given.     

A heuristic design method for attitude stabilization of magnetic actuated satellites

In this paper a heuristic design strategy for stabilizing the satellite attitude has been proposed. It is assumed that the satellite is actuated by a set of mutually perpendicular magnetic coils. Using well-known Lyapunov direct stability method it is shown that the proposed controller causes to a global asymptotic stable system for all near polar orbits. The design procedure is based on analyzing of the conceptual effects of magnetic coils on the satellite attitude motion. Considering these effects lead to some intuitive results which determine the global stabilizing control law. The performance and robustness of the designed controller against actuators saturation and quantization error have been verified using a real-time-hardware–software in-loop (RTHSIL) simulation results. These results show that the global stability can be achieved although some disturbances and restrictions exist. This stabilizing controller can be simply combined with a linear explicit model predictive controller (EMPC) to achieve a full three-axis control law.     

高精度遥感卫星力矩补偿技术

基于建立的卫星姿态动力学模型,对高精度遥感卫星有效载荷工作时载荷运动产生的干扰力矩及其对卫星姿态的影响进行了研究。提出了反馈控制＋力矩补偿的方法,给出了力矩补偿的设计。仿真结果表明：在补偿时延小、补偿精度高条件下利用补偿轮进行力矩补偿,可提高卫星的姿态稳定度,使其满足卫星成像时的姿态控制指标要求。     

绳系太阳能发电卫星姿态机动的主动振动控制

针对绳系太阳能发电卫星大角度回转机动时太阳能板的振动抑制问题,提出了主姿态控制和基于绳中张力的主动振动控制技术相结合的复合控制方法。建立了绳系太阳能发电卫星系统的动力学方程,并基于任务函数控制算法设计了主控制器保证卫星姿态的渐近稳定和挠性结构振动的衰减性;考虑到绳的非线性特性,基于任务函数控制算法设计了绳系卫星系统的主动振动抑制辅助控制器来抑制挠性结构的振动。设计的同时证明了系统的稳定性。将该方法应用于绳系卫星的大角度单轴回转机动的仿真研究,结果表明:该方法不仅能够使绳系卫星完成姿态机动,而且能够有效地抑制太阳能板的振动。     

Stability of large flexible damped spacecraft modeled as elastic continua

Vibrational stability of a large flexible, structurally damped spacecraft subject to large rigid body rotations is analysed modelling the system as an elastic continuum. Using solution of rigid body attitude motion under torque free conditions and modal analysis, the vibrational equations are reduced to ordinary differential equations with time-varying coefficients. Stability analysis is carried out using Floquet theory and Sonin-Polya theorem. The cases of spinning and non-spinning spacecraft idealized as a flexible beam plate undergoing simple structural vibration are analysed in detail. The critical damping required for stabilization is shown to be a function of the spacecraft's inertia ratio and the level of disturbance.     

A fault-tolerant magnetic spin stabilizing controller for the JC2Sat-FF mission

This paper presents a spin-stabilization algorithm for the Japan Canada Joint Collaboration Satellite-Formation Flying (JC2Sat-FF) mission using magnetic actuation only. It is shown that under a reasonable assumption on the Earth’s magnetic field, the resulting control law is asymptotically stabilizing for an axisymmetric spacecraft, even under the failure of up to two magnetic torque rods and magnetic torque rod saturation. It is also stabilizing under quantization. The satellite motion remains stable under control outages, meaning that the error can be reduced by implementing the control intermittently. The effectiveness of the control law is demonstrated using a high fidelity attitude control system simulator for the JC2Sat-FF satellite.     

A heuristic design method for attitude stabilization of magnetic actuated satellites

In this paper a heuristic design strategy for stabilizing the satellite attitude has been proposed. It is assumed that the satellite is actuated by a set of mutually perpendicular magnetic coils. Using well-known Lyapunov direct stability method it is shown that the proposed controller causes to a global asymptotic stable system for all near polar orbits. The design procedure is based on analyzing of the conceptual effects of magnetic coils on the satellite attitude motion. Considering these effects lead to some intuitive results which determine the global stabilizing control law. The performance and robustness of the designed controller against actuators saturation and quantization error have been verified using a real-time-hardware–software in-loop (RTHSIL) simulation results. These results show that the global stability can be achieved although some disturbances and restrictions exist. This stabilizing controller can be simply combined with a linear explicit model predictive controller (EMPC) to achieve a full three-axis control law.     

Determination of the Attitude Motion of a Satellite Based on a Kinematical Model of Motion and Using Data of Measurements of Its Angular Velocity and the Earth’s Magnetic Field Strength

An integral statistical procedure of determination of the attitude motion of a satellite using the data of onboard measurements of angular velocity vectors and the strength of the Earth’s magnetic field (EMF) is suggested. The procedure uses only the equations of kinematics of a solid body and is applicable to determining both controlled and uncontrollable motions of a satellite at any external mechanical moments acting upon it. When applying this procedure, the data of measurements of both types, accumulated during a certain interval of time, are processed jointly. The data of measuring the angular velocity are smoothed by discrete Fourier series, and these series are substituted into kinematical Poisson equations for elements of the matrix of transition from a satellite-fixed coordinate system to the orbital coordinate system. The equations thus obtained represent a kinematical model of the satellite motion. The solution to these equations (which approximate the actual motion of a satellite) is found from the condition of the best (in the sense of the least squares method) fit of the data of measuring the EMF strength vector to its calculated values. The results of testing the suggested procedure using the data of measurements of the angular velocity vectors onboard the Foton-12 satellite and measurements of EMF strengths are presented.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 4, 2005, pp. 295–305.Original Russian Text Copyright © 2005 by Abrashkin, Volkov, Voronov, Egorov, Kazakova, Pankratov, Sazonov, Semkin.     

A hybrid attitude controller consisting of electromagnetic torque rods and an active fluid ring

In this paper, a novel hybrid actuation system for satellite attitude stabilization is proposed along with its feasibility analysis. The system considered consists of two magnetic torque rods and one fluid ring to produce the control torque required in the direction in which magnetic torque rods cannot produce torque. A mathematical model of the system dynamics is derived first. Then a controller is developed to stabilize the attitude angles of a satellite equipped with the abovementioned set of actuators. The effect of failure of the fluid ring or a magnetic torque rod is examined as well. It is noted that the case of failure of the magnetic torque rod whose torque is along the pitch axis is the most critical, since the coupling between the roll or yaw motion and the pitch motion is quite weak. The simulation results show that the control system proposed is quite fault tolerant.     

Spin-stabilized satellite magnetic attitude control scheme without initial detumbling

The angular motion of an axisymmetrical satellite equipped with an active magnetic attitude control system is considered. The dynamics of the satellite are analytically studied on the whole control loop. The control loop is as follows: preliminary reorientation along with nutation damping, spinning about the axis of symmetry, then precise reorientation of the axis of symmetry in inertial space. Reorientation starts right after separation from the launch vehicle. Active magnetic attitude control system time-response with respect to its parameters is analyzed. It is proven that low-inclined orbit forces low control system time-response. Comparison with the common control scheme shows the time-response gain. Numerical analysis of the disturbances effect is carried out and good pointing accuracy is proved.     

星载大型空间天线的一种解耦控制方法

针对星载大型空间可展开天线与卫星平台之间的动力学耦合问题提出一种三自由度驱动与测量机构用于连接天线臂与卫星平台。该机构以驱动电机来控制天线臂转动,通过角度传感器对天线臂转角的测量来实现反馈控制,同时在卫星姿态控制系统中引入前馈控制进行反作用力矩补偿,实现卫星平台与天线之间的解耦控制、抑制天线的振动、提高卫星姿态控制系统的性能。通过姿态稳定状态下卫星-天线系统解耦动力学模型的建立、控制系统的设计、姿态控制的仿真分析,表明解耦机构能大幅增加天线振动的阻尼,有效提高卫星稳定性和天线指向精度。     

A study of evolution of spin-up mode of a satellite in the plane of its orbit

We investigate the mode of spinning up a low-orbit satellite in the plane of its orbit. In this mode the satellite rotates around its principal central axis of the minimum moment of inertia which executes small oscillations with respect to the normal to the orbit plane; the angular velocity of the rotation around this axis several times exceeds the mean orbital motion. Gravitational and restoring aerodynamic moments are taken into account in the satellite’s equations of motion. A small parameter characterizing deviation of the satellite from a dynamically symmetric shape is introduced into the equations. A two-dimensional integral surface of the equations of motion, describing quasi-steady-state rotations of the satellite close to cylindrical precession of the corresponding symmetrical satellite in a gravitational field, has been studied by the method of small parameter and numerically. Such quasi-steady-state rotations are suggested to be considered as unperturbed motions of the satellite in the spin-up mode. Investigation of the integral surface is reduced to numerical solution of a periodic boundary value problem of a certain auxiliary system of differential equations and to calculation of quasi-steady-state rotations by the two-cycle method. A possibility is demonstrated to construct quasi-steady rotations by way of minimization of a special quadratic functional.     

帆板驱动影响下的卫星姿态高精度高稳定度控制

受步进电机驱动作用,太阳帆板对日定向时卫星姿态受到影响。本文针对帆板驱动不平稳引起的同卫星姿态耦合干扰,提出了一种卫星姿态稳定和太阳帆板对日定向的复合控制方法。卫星姿态稳定采用自抗扰控制器,以估计补偿由帆板驱动和系统不确定性引起的干扰,并在此基础上,设计了步进电机自适应电流补偿驱动器,以克服帆板驱动机构摩擦力矩和谐波力矩影响。仿真结果表明,该方法能大大提高卫星姿态控制精度和稳定度,同时还改善了帆板对日定向的精度。
     

基于Fluent计算的火箭离轨姿态运动仿真与分析

在航天器姿态运动分析中常遇到液体的流动、晃动及流/固耦合等问题,针对这类问题建立精确的数学模型是很困难的,通常需要利用数值计算和仿真手段进行分析。利用用户互动功能(UDF),引入自定义的变量源函数,应用Fluent对运载火箭离轨姿态控制进行剩余燃料的流场数据分析。通过在流体运动方程中加入相关的牵连运动,得到在轨运行状态下贮箱内剩余液体的运动参数和对贮箱的干扰力矩,为运载火箭系统的姿态运动分析和仿真提供运算参数,使得流场的变化与运载火箭的姿态运动相关联,分析各个时刻流场运动状态对箭体姿态的影响。