Secular evolution of rotary motion of a charged satellite in a decaying orbit

An electrostatically charged Earth satellite whose orbit is decaying due to the Earths oblateness is considered. Secular perturbations of the orbit are taken into account: they are caused by the second zonal harmonic of the geopotential. These perturbations represent deviations of the longitude of the ascending node and perigee argument, the orbit form being invariable and the orbit inclination to the equatorial plane being constant. The attitude rotary motion of the satellite under the action of perturbing moments of the gravitational and Lorentz forces is studied. The magnetic field of the Earth is taken in a quadrupole approximation. The evolution of the satellites rotary motion is investigated on the basis of new differential equations in s-parameters specially constructed for this purpose. Using the method of averaging, basic regularities of the secular evolution of rotary motion of a screened satellite are revealed. It is found that the rotary motion of a charged satellite essentially depends on the quadrupole component of the geomagnetic potential.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 2, 2005, pp. 111–125.Original Russian Text Copyright © 2005 by Tikhonov.     

仅有单个陀螺的Drag—free卫星初始速率阻尼模糊控制研究

研究了在仅有偏航姿态测量陀螺时,利用Drag—free卫星与其内部定向体间的相对状态观测值实现姿态确定的方法。针对Drag—free卫星的特点,建立了定向体的空间姿态观测模型和Drag—free卫星的姿态动力学方程,据此推导了用于姿态确定的Kalman滤波算法。为实现初始速率阻尼阶段Drag—free卫星的三轴姿态稳定,设计了模糊控制律。仿真结果验证了方法的有效性。     

On the stability of spinning satellites

We study the directional stability of rigid and deformable spinning satellites in terms of two attitude angles. The linearized attitude motion of a free system about an assumed uniform-spin reference solution leads to a generic MGK system when the satellite is rigid or deformable. In terms of Lyapunov’s stability theory, we investigate the stability with respect to a subset of the variables. For a rigid body, the MGK system is 6-dimensional, i.e., 3 rotational and 3 translational variables. When flexible parts are present the system can have any arbitrary dimension. The 2×2 McIntyre–Myiagi stability matrix gives sufficient conditions for the attitude stability. A further development of this method has led to the Equivalent Rigid Body method. We propose an alternative practical method to establish sufficiency conditions for directional stability by using the Frobenius–Schur reduction formula. As practical applications we discuss a spinning satellite augmented with a spring–mass system and a rigid body appended with two cables and tip masses. In practice, the attitude stability must also be investigated when the spinning satellite is subject to a constant axial thrust. The generic format becomes MGKN as the thrust is a follower force. For a perfectly aligned thrust along the spin axis, Lyapunov’s indirect method remains valid also when deformable parts are present. We illustrate this case with an apogee motor burn in the presence of slag. When the thrust is not on the spin axis or not pointing parallel to the spin axis, the uniform-spin reference motion does not exist and none of the previous methods is applicable. In this case, the linearization may be performed about the initial state. Even when the linearized system has bounded solutions, the non-linear system can be unstable in general. We illustrate this situation by an instability that actually happened in-flight during a station-keeping maneuver of ESA’s GEOS-I satellite in 1979.     

船载惯性测量单元姿态信息优化方法

随着海洋卫星通信技术的广泛应用，船载通信系统的需求量与日俱增。基于微电子系统的惯性测量单元主要用于测量船体姿态信息，实现姿态反馈与控制补偿，是船载卫星通信设备的核心器件。实际应用中通过卡尔曼滤波处理的惯性测量单元的姿态信息并不完善，经过分析惯性测量单元在运动过程中存在干扰性的有害加速度。分析了有害加速度的产生原因和对测量姿态的影响并提出姿态信息的优化方法。通过此优化方法可提升惯性测量单元的测量精度，增强船载通信系统的控制精度。     

基于磁力矩定向阻尼特性的卫星姿态磁控制

根据磁力矩在地磁场中的定向阻尼特性，提出了磁控重力梯度和有阻尼器的非重力梯度卫星姿态控制律。给出了卫星姿态运动方程，并证明采用两种方法控制卫星姿态的稳定性。根据地磁场强度变化规律选择控制系数。理论分析和仿真结果表明，基于磁力矩定向阻尼特性的卫星姿态磁控制方法简单、精度较高。     

Lorentz-force-perturbed orbits with application to J2-invariant formation

The Lorentz force acting on an electrostatically charged spacecraft in the Earth's magnetic field provides a new propellantless means for controlling a spacecraft's orbit. Assuming that the Lorentz force is much smaller than the gravitational force, the perturbation of a charged spacecraft's orbit by the Lorentz force in the Earth's magnetic field, which is simplified as a titled rotating dipole, is studied in this article. Our research starts with the derivation of the equations of motion in geocentric equatorial inertial Cartesian coordinates using Lagrange mechanics, and then derives the Gauss variational equations involving Lorentz-force perturbation using a set of nodal inertial coordinates as an intermediate step. Subsequently, the approximate averaged changes in classical orbital elements, including single-orbit-averaged and one-day-averaged changes, are obtained by employing orbital averaging. We have found that the approximate analytic one-day-averaged changes in semi-major axis, eccentricity, and inclination are nearly zero, and those in the other three angular orbital elements are affected by J₂ and Lorentz-force perturbations. This characteristic is applied to model bounded relative orbital motion in the presence of the Lorentz force, which is termed Lorentz-augmented J₂-invariant formation. The necessary condition for J₂-invariant formation is derived when the chief spacecraft's reference orbit is either circular or elliptical. It is shown that J₂-invariant formation is easier to implement if the deputy spacecraft is capable of establishing electric charge. All conclusions drawn from the approximate analytic solutions are verified by numerical simulation.     

一种用于导弹姿态控制系统的直接力非线性控制法

为改善传统导弹姿控系统线性控制法的不足,用相平面法分析了直接力作用下导弹的姿态运动规律和气动力作用对直接力控制的影响,提出了一种综合控制精度、姿控发动机产品特性和推进剂消耗量等指标的直接力非线性控制方法,给出了控制模型。仿真结果表明,该法能在气动力作用或干扰无法忽略的条件下实现导弹姿控发动机的开关工作正常,保证精度及推进剂消耗最省,其控制精度与线性比例微分(PD)控制律相当。     

A Method of Semipassive Attitude Stabilization of a Spacecraft in the Geomagnetic Field

A method is proposed that enables one to accomplish semipassive attitude stabilization of a spacecraft moving in a circular Keplerian orbit in the geomagnetic field. The method is developed on the basis of the electrodynamic effect of the influence of the Lorentz forces acting on the charged spacecraft's surface. It possesses advantages such as control law simplicity, reliability, cost efficiency, small mass, and the possibility of using the basic control system components not only for attitude stabilization of a spacecraft but also for ensuring its electrostatic radiation screening. The possibility of implementing the method for slightly inclined orbits is proved analytically. Two versions of implementation of the method are proposed. The calculations confirmed the possibility of using also these versions for orbits whose inclinations are not small. The advantages of each version are revealed and practical recommendations for their utilization are given.     

三体随动跟踪式重力卫星姿态与无拖曳控制方法

采用非接触洛伦兹力执行器代替微推进系统,提出一种“质量块—载荷舱—平台舱”三体随动跟踪式重力卫星总体架构,避免传统低低跟踪重力场测量卫星设计中的质心波动与执行机构带来的动力学不确定性影响。其次,建立了该架构下的卫星姿轨耦合动力学模型,并在此基础上针对动力学非线性耦合项的影响,构建了一种基于带宽参数化自适应补偿的复合自抗扰控制方法,提升姿态与无拖曳控制性能。最后,采用数学仿真验证了所提出的重力卫星总体架构及其控制方法的有效性。仿真结果表明,该方法有效提升了系统的频域性能。     

面向空间近距离操作的机械臂与服务卫星协同控制

针对航天器在轨服务任务中涉及的空间近距离操作需求，提出一种机械臂与服务卫星协同控制方法。首先建立了机械臂和服务卫星组合体动力学模型以及服务卫星和目标卫星相对位姿耦合动力学模型。然后采用全局终端滑模控制设计了机械臂轨迹跟踪控制方法，采用PD控制设计了服务卫星相对位姿耦合控制方法，并将机械臂反作用力和力矩作为前馈补偿叠加到服务卫星控制系统中，实现了两者的协同控制。最后通过数值仿真验证了控制方法的有效性。仿真结果表明，该方法能够满足空间近距离操作任务对机械臂和服务卫星的控制精度、稳定性和误差收敛时间的要求，具有工程实用性。     

FY—1C卫星姿态控制系统

针对FY－1C卫星姿态控制系统，给出了系统方案、系统设计、系统特点和飞行试验的结果；对一些新的技术设计和新颖特殊的方案特点，从理论分析和技术实现给出了设计思路和工程实现的方法；分析了FY－1C卫星姿态控制系统在轨运行的结果；对长寿命、低成本和稳定连续运行的工程实现进行了研究；给出了FY－1C卫星姿态控制系统的水平能力和应用发展方向。     

超低轨卫星气动力辅助轨道控制研究

针对超低轨卫星所受气动力显著的特点,提出一种利用气动舵的气动力辅助轨道控制方法。通过分析大气旋转、卫星所处空间位置以及气动舵偏转角度对气动力的影响,对提出的轨道控制方法进行了优化。该方法通过调整气动舵产生连续微小的气动力对卫星轨道进行控制,使各轨道要素均保持在误差容限范围内。将其应用于太阳同步轨道上的对地观测卫星,仿真结果表明,该方法可以在卫星姿态保持三轴对地稳定的前提下,实现轨道保持控制,保证任意纬度下卫星实际位置与标称轨道位置偏差在给定范围内。     

空间太阳能电站的准对日定向姿态

针对空间太阳能电站的俯仰姿态运动，提出一种能追踪太阳运动的准对日定向(QSP)姿态方案。此方案的太阳能电池阵列在万有引力梯度力矩的作用下，始终在垂直于太阳光的方向附近作幅值约为18.8°的振动，且几乎不需要姿态控制力矩。准对日定向姿态方案解决了大型太阳能电池阵列对日定向所需的巨大俯仰姿态控制力矩问题。准对日定向姿态的发电效率为对日定向姿态的97.3%，对Abacus空间太阳能电站而言每年可节省燃料约36791 kg。通过数值方法得到了准对日定向姿态的精确初始条件。随后，设计了比例-微分控制器，保证了系统存在初始姿态误差的条件下收敛到准对日定向姿态。最后研究了轨道、姿态和结构振动对准对日定向姿态的影响，并发现准对日定向姿态下的结构振动幅值比对日定向姿态减小约40倍。     

Variation of the Satellite Orbit Altitude by the Light Pressure Force

The possibility of the uncontrolled increase of the altitude of an almost circular satellite orbit by the force of the light pressure is investigated. The satellite is equipped with a damper and a system of mirrors (solar batteries can serve as such a system). The flight of the satellite takes place in the mode of a single-axis gravitational orientation, the axis of its minimum principal central moment of inertia makes a small angle with the local vertical and the motion of the satellite around this axis constitutes forced oscillations under the impact of the moment of force of the light pressure. The form of the oscillations and the initial orbit are chosen so that the transverse component of the force of the light pressure acting upon the satellite be positive and the semimajor axis of the orbit would continuously increase. As this takes place, the orbit remains almost circular. We investigate the evolution of the orbit over an extended time interval by the method which employs separate integration of the equations of the orbital and rotational motions of the satellite. The method includes outer and inner cycles. The outer cycle involves the numerical integration of the averaged equations of motion of the satellite center of mass. The inner cycle serves to calculate the right-hand sides of these equations. It amounts to constructing an asymptotically stable periodic motion of the satellite in the mode of a single-axis gravitational orientation for current values of the orbit elements and to averaging the equations of the orbital motion along it. It is demonstrated that the monotone increase of the semimajor axis takes place during the first 15 years of motion. In actuality, the semimajor axis oscillates with a period of about 60 years. The eccentricity and inclination of the orbit remain close to their initial values.     

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.     

Analytical solutions for the relative motion of spacecraft subject to Lorentz-force perturbations

A spacecraft capable of producing higher-than-natural electrostatic charges may achieve propellantless orbital maneuvering via the Lorentz-force interaction with a planetary magnetic field. Development of maneuver strategies for these propellantless vehicles is complicated by the fact that the perturbative Lorentz force acts along only a single line of action at any instant. Relative-motion dynamical models are developed that lead to approximate analytical solutions for the motion of charged spacecraft subject to the Lorentz force. These solutions indicate that the principal effects of the Lorentz force on a spacecraft in a circular orbit are to change the intrack position and to change the orbit plane. A rendezvous example is presented in which a spacecraft with a specific charge of ?3.81 $\times$ 10^?4 C/kg reaches a target vehicle initially 10 km away (on the same equatorial low-Earth orbit) in 1 day. Fly-around maneuvers may be achieved in low-Earth orbit with specific charges on the order of 0.001 C/kg.     

Variable structure control for satellite attitude stabilization in elliptic orbits using solar radiation pressure

The paper proposes the use of solar radiation pressure for satellite attitude control in elliptic orbits based on variable structure control. The system comprises of a satellite with two-oppositely placed solar flaps. Sliding mode control and terminal sliding mode control techniques have been adopted to develop nonlinear control laws for suitably rotating the control solar flaps to neutralize the adverse effect of eccentricity normally responsible for a considerable deterioration in the attitude control performance. The detailed numerical simulation of the governing nonlinear equation of the motion including the effects of various system parameters on the controller performance, establishes the feasibility of the proposed control strategy. The proposed controller is found to be robust against parameter uncertainties and external disturbances and thereby, the control strategy presented in the paper may be applicable to future satellite missions.     

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.     

冗余空间机械臂抓捕自旋卫星后的消旋控制

旨在提出一种运动学冗余空间机器人抓捕自旋卫星后的消旋策略和协调控制方法。首先，给出运动学冗余空间机器人捕获目标后的动力学模型，作为协调控制器设计基础。然后，基于四阶Bézier曲线和满足特定约束的自适应微分进化(Differential Evolution, DE)算法提出抓捕后的最优消旋与路径规划策略，最优消旋策略中同时考虑对消旋时间和控制力矩进行优化。提出一种跟踪所设计参考轨迹的协调控制方法，调整基座的姿态达到期望值。所提方法有效地衰减了自旋卫星的初始角速度，同时实现对基座姿态的控制。文末给出利用7 DOF冗余空间机械臂消除目标自旋运动的仿真结果，表明所提方法的有效性。     

基于RO-NUIO/LMI的挠性卫星轨控期间姿控系统故障诊断

卫星轨控期间,由于推力偏心,会产生较大的干扰力矩,直接影响卫星姿态。针对轨道控制期间的挠性卫星姿态控制系统,设计了干扰解耦的降阶非线性未知输入观测器(RO-NUIO),用于故障检测与故障隔离。在设计过程中,首先通过坐标变换,使得不可观的状态及部分可观状态不受干扰影响,然后针对不可观的子系统利用可观状态的信息设计观测器,观测器中的部分参数利用LMI方法获得,可以弱化非线性部分对观测器的影响。所设计观测器的存在条件仅依赖于系统本身特性,无需在线验证。观测器采用降阶设计,同时借助LMI思想,结构简单,适合于非线性卫星姿态控制系统。仿真结果验证了降阶非线性未知输入观测器实现卫星姿态控制故障诊断的可行性与有效性。