Model development and adaptive imbalance vibration control of magnetic suspended system

A system model is developed to describe the translational and rotational motion of an active-magnetic-bearing-suspended rigid rotor of a single-gimbal control moment gyro (SCMG) onboard a rigid satellite. This model closely reflects the motion characteristics of the rotor by considering the dynamic and static imbalance as well as the coupling between the gimbal's and the rotor's motion on a satellite platform. Adaptive autocentering control is strictly constructed for the preceding rotor with unknown dynamic imbalance. The rotor achieves its rotation about the principal axis of inertia by identifying the little rotational angles from the geometric axis to the principal axis and then using the results to tune a stabilizing controller, which is composed of a decentralized PD controller with cross-axis proportional gains and high-pass and low-pass filters. The main disturbance in the wheel spinning can thereby be completely removed and the vibration acting on the satellite can be attenuated.     

Out-of-plane stability analysis of collinear spinning three-craft Coulomb formations

The results of a stability analysis focusing on the out-of-plane motion of collinear three-craft Coulomb formations with set charges are discussed. Such a formation is assumed to be spinning in deep space without relevant gravitational forces present. Assuming in-plane motion only with circular relative trajectories and initial position and velocity perturbations confined to the orbital plane, the previous work analytically proves marginal stability in the linear sense and numerically shows marginal stability in the short term. In this paper, the equations of motion are presented in the cylindrical coordinate frame in order to analyze the out-of-plane motion in more detail. The out-of-plane motion is shown to decouple to first order from the marginally stable in-plane motion. A simple control law is developed and applied, which directly controls the out-of-plane motion only within specified deadbands. For a wide variety of out-of-plane perturbations, the control law succeeds in preserving the in-plane variant shape despite some out-of-plane motion. A trend between the settling time and deadband, which defines the largest out-of-plane errors allowed before the controller is turned on, is determined, which illustrates how large the deadband may be before the in-plane motion is affected.     

航天器机动时DGMSCMG磁悬浮转子干扰补偿控制

双框架磁悬浮控制力矩陀螺（DGMSCMG）具有寿命长、综合效益好等突出优势,但航天器机动时,航天器及DGMSCMG内、外框架系统的转动均导致磁悬浮高速转子产生一定的耦合运动,影响磁悬浮转子系统的稳定性,同时使输出力矩精度下降,从而严重影响航天器姿态控制的精度。本文建立了基于DGMSCMG的航天器动力学模型,分析航天器、外框架、内框架、磁悬浮转子四者之间的动力学耦合关系。针对磁悬浮转子的非线性耦合干扰,提出一种基于复合控制的补偿方法,通过磁轴承产生相应的电磁力,对陀螺耦合力矩和惯性耦合力矩进行补偿控制。仿真结果表明,干扰补偿控制能有效抑制航天器及框架对磁悬浮转子的耦合干扰,也有效提高了磁悬浮转子系统的稳定性。     

Chaos and its avoidance in spinup dynamics of an axial dual-spin spacecraft

Attitude dynamics of a dual-spin spacecraft (DSSC) and a torque-free angular motion of a coaxial bodies system are considered. Some regimes of the heteroclinic chaos are described. The local chaotization of the DSSC is investigated at the presence of polyharmonic perturbations and small nutation restoring/overturning torques on the base of the Melnikov method and Poincaré Maps. Reasons of the chaotic regimes initiation at the spinup maneuver realization are studied. An approach for the local heteroclinic chaos escape/avoidance at the modification of the classical spinup maneuver is suggested.     

Optimal control of reorientation of a spacecraft using free trajectory method

The problem of optimal control over spatial reorientation of a spacecraft is considered. The functional having a sense of propellant consumption is minimized. The analytical solution to the formulated problem is presented. It is shown that the optimal solution can be found in the class of two-impulse control at which the spacecraft’s turn is performed along a free motion trajectory. In order to improve the accuracy of spacecraft guidance into a specified angular position, methods of control are suggested that realize the method of free trajectories. The synthesized controls are invariant with respect to both external perturbations and parametric errors. The results of mathematical modeling are presented that demonstrate high efficiency of developed control algorithms. Propellant consumption for realizing a programmed turn is numerically estimated taking into account considerable gravitational and aerodynamic moments acting upon the spacecraft.     

磁悬浮飞轮优化设计与实验

针对在轨磁悬浮飞轮转子系统,考虑发射主动段振动工况,提出一种基于灵敏度分析的多学科优化设计方法。通过比较分析内、外锁紧方案对锁紧状态飞轮转子系统共振频率的影响,得到了较优的抱式外锁紧方案。在此基础上,对飞轮转子进行灵敏度分析,并选择高灵敏度结构参数作为优化设计变量。考虑其结构强度、转动惯量、控制性能、自由状态和锁紧状态一阶共振频率,以飞轮转子质量最小为优化目标,利用序列二次规划法对其进行多学科优化设计。优化结果表明,在满足发射振动工况下,飞轮转子极转动惯量与质量的数值比达到最大为0.0070,比初始值0.0064提高了9.4%。该优化方法提高了飞轮转子设计的可靠性和效率,其首次在轨实验成功对我国磁悬浮飞轮空间应用具有重要意义。     

Inertia-independent generalized dynamic inversion feedback control of spacecraft attitude maneuvers

The generalized dynamic inversion control methodology is applied to the spacecraft attitude trajectory tracking problem. It is shown that the structure of the skew symmetric cross product matrix alleviates the need to include the inertia matrix in the control law. Accordingly, the proposed control law depends solely on attitude and angular velocity measurements, and it neither requires knowledge of the spacecraft's inertia parameters nor it works towards estimating these parameters. A linear time-varying attitude deviation dynamics in the multiplicative error quaternion is inverted for the control variables using the generalized inversion-based Greville formula. The resulting control law is composed of auxiliary and particular parts acting on two orthogonally complement subspaces of the three dimensional Euclidean space. The particular part drives the attitude variables to their desired trajectories. The auxiliary part is affine in a free null-control vector, and is designed by utilizing a semidefinite control Lyapunov function that exploits the geometric structure of the control law to provide closed loop stability. The generalized inversion singularity avoidance is made by augmenting the generalized inverse with an asymptotically stable fast mode that is driven by angular velocity error's norm from reference angular velocity. Asymptotic tracking is achieved for detumbling maneuvers as the stable augmented mode subdues singularity. If the steady state desired quaternion trajectories are time varying, then asymptotic tracking is lost in favor of close ultimately bounded tracking because the stable augmented mode continues to be excited during steady state phase of response. A rest-to-rest slew and a trajectory tracking maneuver examples are provided to illustrate the methodology.     

Maximum Lyapunov Exponents for Chaotic Rotation of Natural Planetary Satellites

Based on the Chirikov approach [1, 2] within the context of the theory of separatrix mappings, we suggest and substantiate a simple method for estimating the maximum Lyapunov characteristic exponent (MLCE) of motion in a chaotic layer in the neighborhood of nonlinear resonance separatrix of a Hamiltonian system under an asymmetric periodic perturbation. For a number of natural planetary satellites, using this method, the estimates are made of the MLCE of chaotic rotation (relative to the center of mass) in the main chaotic layer, i.e., in the chaotic layer in the neighborhood of a synchronous resonance separatrix. The value of the MLCE is determined by an orbital eccentricity and by the parameter of the satellite's dynamic asymmetry. The quantity inverse to the MLCE gives a typical time of predictable rotational motion.     

磁悬浮控制力矩陀螺的动框架效应及其角速率前馈控制方法研究

在磁悬浮控制力矩陀螺中,局限于磁悬浮轴承系统的动态响应速度,框架的转动将使转子轴的角位移和轴心跳动量显著增大(动框架效应),甚至碰撞保护轴承,严重影响磁悬浮系统的稳定性。本文建立框架转动时的磁悬浮转子相对运动模型,分析了框架转动对磁悬浮转子的单方向作用,在Simulink仿真的基础上提出一种抑制动框架效应的角速率前馈控制方法。实验结果表明,磁悬浮轴承采用角速率前馈控制后,转子跳动量被抑制到原来的18％,大大提高了控制力矩陀螺磁悬浮系统的稳定性,同时还改善了控制力矩陀螺的力矩输出特性。     

含固定转速驱动电机的挠性卫星自旋稳定性分析

分析一类含驱动电机挠性卫星的自旋稳定性,应用不变集定理证明了系统轨迹收敛于系统平衡点集,并通过构造正定的单调递减的类能量函数来判断各平衡点的稳定性质。获得的结论包括：由于挠性振动阻尼特性,在无外扰力矩作用时,含固定转速驱动电机的挠性卫星存在稳定的自旋;不含驱动电机的挠性卫星,稳定的自旋轴为其最大主惯量轴;驱动电机可改变挠性卫星的自旋轴,给出了稳定的自旋轴与电机转速方向夹角公式,该夹角为锐角;当电机转动角动量幅值远小于系统角动量时,稳定自旋轴接近最大主惯量轴;电机转动角动量幅值越接近系统角动量,稳定自旋轴越接近电机转动方向。文中也给出了稳定自旋轴平行电机转轴的条件。     

Unmodeled perturbation effect on the orbit determination accuracy

The dependence of the estimates of an orbital parameter from unmodeled perturbations is considered that affect a space object but are not taken into account in the mathematical model of motion used in the paper. The expressions for Ensured characteristics of the accuracy in the estimate of the given parameter is obtained under the condition that there are known restrictions on mathematical expectations and the correlation function of these perturbations. The calculated results for the specific problem are given.     

基于磁悬浮控制力矩陀螺的航天器姿态高精度高带宽测量方法

针对航天器姿态测量精度和带宽之间相互制约问题,提出一种基于磁悬浮陀螺的航天器姿态高精度、高带宽测量方法。根据刚体动力学和坐标变换原理建立磁悬浮转子径向转动合外力矩模型。在框架静止条件下,通过实时检测磁悬浮控制力矩陀螺（MSCMG）中的磁轴承电流、磁悬浮转子位移,计算出磁悬浮转子径向转动所受合外力矩以及磁悬浮转子径向偏转信息,间接得到航天器运动对磁悬浮转子径向转动作用力矩,进而求出航天器单轴姿态角速度和姿态角加速度。不同带宽下的仿真结果表明,本测量方法能同时检测出航天器单方向的姿态角速度和角加速度,并且满足高精度高带宽要求。     

近距离航天器相对轨道的鲁棒自适应控制

针对近距离航天器的相对轨道提出了一种鲁棒自适应控制律。在追踪星本体坐标系中考虑航天器的相对运动。首先,在转动惯量未知的情形下提出了自适应控制律,保证系统的全局渐近稳定性。其次,将两星地心引力加速度之差作为干扰加速度,并假设干扰有未知上界,对自适应控制律进行修正,提出了鲁棒自适应律,使得系统是全局一致最终有界稳定的。控制律的设计不需要绝对轨道信息,适用于任意轨道。对航天器编队飞行和空间交会两种情形分别进行了仿真分析,结果表明所设计的控制律是合理有效的。     

Translational–Rotational Motion of a Viscoelastic Sphere in Gravitational Field of an Attracting Center and a Satellite

We study the translational–rotational motion of a planet modeled by a viscoelastic sphere in the gravitational fields of an immovable attracting center and a satellite modeled as material points. The satellite and the planet move with respect to their common center of mass that, in turn, moves with respect to the attracting center. The exact system of equations of motion of the considered mechanical system is deduced from the D'Alembert–Lagrange variational principle. The method of separation of motions is applied to the obtained system of equations and an approximate system of ordinary differential equations is deduced which describes the translational–rotational motion of the planet and its satellite, taking into account the perturbations caused by elasticity and dissipation. An analysis of the deformed state of the viscoelastic planet under the action of gravitational forces and forces of inertia is carried out. It is demonstrated that in the steady-state motion, when energy dissipation vanishes, the planet's center of mass and the satellite move along circular orbits with respect to the attracting center, being located on a single line with it. The viscoelastic planet in its steady-state motion is immovable in the orbital frame of reference. It is demonstrated that this steady-state motion is unstable.     

Uncontrollable Rotational Motion of the Mir Orbital Station

The results of determining the rotational motion of the Mir orbital station are presented for four long segments of its unmanned uncontrolled flight in 1999–2000. The determination was carried out using the data of onboard measurements of the Earth's magnetic field intensity. These data, taken for a time interval of several hours, were jointly processed by the least squares method with the help of integration of the equations of station motion relative to its center of mass. As a result of this processing, the initial conditions of motion and the parameters of the mathematical model used were evaluated. The technique of processing is verified using the telemetry data on angular velocity of the station and its attitude parameters. Two types of motion were applied on the investigated segments. One of them (three segments) presents a rotation around the axis of the minimum moment of inertia. This axis executes small oscillations with respect to a normal to the orbit plane. Such a motion was used for the first time on domestic manned orbital complexes. The second type of motion begins with a biaxial rotation which, in a few weeks, goes over into a motion very similar to the rotation around the normal to the orbit plane, but around the axis of the maximum moment of inertia.     

Orbital and angular motion construction for low thrust interplanetary flight

Low thrust interplanetary flight is considered. Firstly, the fuel-optimal control is found. Then the angular motion is synthesized. This motion provides the thruster tracking of the required by optimal control direction. And, finally, reaction wheel control law for tracking this angular motion is proposed and implemented. The numerical example is given and total operation time for thrusters is found. Disturbances from solar pressure, thrust eccentricity, inaccuracy of reaction wheels installation and errors of inertia tensor are taken into account.     

弹道式飞行器惯性制导机电式方法的研究历史

以分析最初的资料和报告为基础,介绍了前苏联进行的弹道式飞行器沿“刚性”和“柔韧”(自适应)轨迹惯性制导机电方法数学论证和研制方面的历史,叙述了以著名惯导专家伊什林斯基为首的学派研究出的飞行器惯性制导方案在3个方面的实现情况:1)在被称作λ,μ惯性制导泛函形式下,使用视加速度积分陀螺仪,可以不用积分计算仪表而在飞行器本体上构成主要的制导方程;2)主要的制导方程可以转换成被称作α,β惯性制导泛函的形式,在飞行器本体上构成该泛函时完全不需要复杂的计算装置;3)所研究的机电方法不仅能够通过修正所设计的主动段的距离实现在垂直平面内对飞行器质心运动轨迹的单参数修正,也即沿被称作“刚性的”轨迹制导,而且还能对所设计的俯仰转弯角进行修正,也即实现双参数修正,沿着被称作“柔韧性的”轨迹制导.对于使用固体火箭发动机,推力调节有困难的情况,后者具有重要的意义.给出了某些方法的方块图,其中包括最简单的一种一按α,β泛函制导的情况.     

椭圆轨道航天器自主接近的制导律研究

椭圆轨道自主交会接近制导律问题是当今空间技术领域中的一个研究不足。基于T\|H方程 ,设计了两种仅利用相对运动信息、控制力定常的椭圆轨道自主接近制导律：滑模制导律和 势函数制导律。从两种制导律的特性分析,滑模制导律对系统的运行轨迹更加苛刻,而势函 数制导律更加充分地利用了系统的自由运动,具有更好的控制性能。数值仿真结果也表明： 对 于相同的制导目标、制导时间和制导精度,势函数制导律所需的喷气开关次数和速度增量均较少。     

Evolution of the out-of-plane amplitude for quasi-periodic trajectories in the Earth–Moon system

The out-of-plane amplitude along quasi-periodic trajectories in the Earth–Moon system is highly sensitive to perturbations in position and/or velocity as underscored recently by the ARTEMIS spacecraft. Controlling the evolution of the out-of-plane amplitude is non-trivial, but can be critical to satisfying mission requirements. The sensitivity of the out-of-plane amplitude evolution to perturbations due to lunar eccentricity, solar gravity, and solar radiation pressure is explored and a strategy for designing low-cost deterministic maneuvers to control the amplitude history is also examined. The method is sufficiently general and is applied to the L₁ quasi-periodic orbit that serves as a baseline for the ARTEMIS P2 trajectory.