近圆参考轨道卫星编队洛仑兹力控制

基于运动电荷在磁场中切割磁力线受到洛仑兹力作用的物理规律,分析了两种带电模式对经典轨道根数长期变化的影响:(1)卫星恒定带电模式;(2)前半个轨道周期卫星带电、后半周期不带电的非恒定带电模式.恒定带电模式可以有效地改变轨道升交点赤经、近地点幅角以及平近点角,对轨道半长轴、偏心率和倾角几乎不产生长期影响;而非恒定带电模式则可以有效地改变轨道偏心率.基于洛仑兹力作用下轨道根数长期变化规律以及轨道根数差描述的带电副星相对于不带电主星的运动,提出了利用洛仑兹力以及两种带电模式实现地球低轨近圆参考轨道卫星编队的控制策略,包括编队绕飞椭圆大小重构与编队中心漂移控制,解析求解了副星所需的带电量,并利用数值仿真验证了洛仑兹力控制的可行性.需要指出的是,洛仑兹力轨道控制无需消耗推进工质.      

Optimal nonlinear feedback control of spacecraft rendezvous with finite low thrust between libration orbits

This paper presents the nonlinear closed-loop feedback control strategy for the spacecraft rendezvous problem with finite low thrust between libration orbits in the Sun–Earth system. The model of spacecraft rendezvous takes the perturbations in initial states, the actuator saturation limits, the measurement errors, and the external disturbance forces into consideration from an engineering point of view. The proposed nonlinear closed-loop feedback control strategy is not analytically explicit; rather, it is implemented by a rapid re-computation of the open-loop optimal control at each update instant. To guarantee the computational efficiency, a novel numerical algorithm for solving the open-loop optimal control is given. With the aid of the quasilinearization method, the open-loop optimal control problem is replaced successfully by a series of sparse symmetrical linear equations coupled with linear complementary problem, and the computational efficiency can be significantly increased. The numerical simulations of spacecraft rendezvous problems in the paper well demonstrate the robustness, high precision, and dominant real-time merits of the proposed closed-loop feedback control strategy.     

Optimal design of near-Earth asteroid sample-return trajectories in the Sun–Earth–Moon system

In the 6th edition of the Chinese Space Trajectory Design Competition held in 2014, a near-Earth asteroid sample-return trajectory design problem was released, in which the motion of the spacecraft is modeled in multi-body dynamics, considering the gravitational forces of the Sun,Earth, and Moon. It is proposed that an electric-propulsion spacecraft initially parking in a circular 200-km-altitude low Earth orbit is expected to rendezvous with an asteroid and carry as much sample as possible back to the Earth in a10-year time frame. The team from the Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences has reported a solution with an asteroid sample mass of 328 tons, which is ranked first in the competition.In this article, we will present our design and optimization methods, primarily including overall analysis, target selection, escape from and capture by the Earth–Moon system,and optimization of impulsive and low-thrust trajectories that are modeled in multi-body dynamics. The orbital resonance concept and lunar gravity assists are considered key techniques employed for trajectory design. The reported solution, preliminarily revealing the feasibility of returning a hundreds-of-tons asteroid or asteroid sample, envisions future space missions relating to near-Earth asteroid exploration.     

控制一类磁性刚体航天器的混沌姿态运动

本文研究一类磁性航天器的混沌姿态运动及其控制,建立了在近地球赤道面圆轨道上运动受万有引力矩、磁力矩作用磁性刚体航天器姿态运动的动力学方程。采用时间历程、Poincare截面、Lyapunov指数和功率谱对系统的动力学行为进行数值识别,结果表明随着磁场参数的增大系统动力学行为由准周期环面破裂而出现混沌。利用输入－输出反馈精确线性化的方法将航天器的混沌姿态控制运动控制为姿态静止和按给定的周期规律运动,数值结果表明该控制方法的有效性。     

Multi-objective transfer to libration-point orbits via the mixed low-thrust and invariant-manifold approach

The multi-objective optimization of transfer trajectories from an orbit near Earth to a periodic libration-point orbit in the Sun–Earth system using the mixed low-thrust and invariant-manifold approach is investigated in this paper. A two-objective optimization model is proposed based on the mixed low-thrust and invariant-manifold approach. The circular restricted three-body model (CRTBP) is utilized to represent the motion of a spacecraft in the gravitational field of the Sun and Earth. The transfer trajectory is broken down into several segments; both low-thrust propulsion and stable manifolds are utilized based on the CRTBP in different segments. The fuel cost, which is generated only by the low-thrust trajectory for transferring the spacecraft from an orbit near Earth to a stable manifold, is minimized. The total flight time, which includes the time during which the spacecraft is controlled by the low-thrust trajectory and the time during which the spacecraft is moving on the stable manifold, is also minimized. Using the nondominated sorting genetic algorithm for the resulting multi-objective optimization problem, highly promising Pareto-optimal solutions for the transfer of the spacecraft are found. Via numerical simulations, it is shown that tradeoffs between time of flight and fuel cost can be quickly evaluated using this approach. Furthermore, for the same time of flight, transfer trajectories based on the mixed-transfer method can save a larger amount of fuel than the low-thrust method alone.     

Chaotic attitude motion of a magnetic rigid spacecraft and its control

This paper deals with chaotic attitude motion of a magnetic rigid spacecraft with internal damping in a circular orbit near the equatorial plane of the earth. The dynamical model of the problem is established. The Melnikov analysis is carried out to prove the existence of a complicated non-wandering Cantor set. The dynamical behaviors are numerically investigated by means of time history. Poincare map, power spectrum and Lyapunov exponents. Numerical simulations indicate that the onset of chaos is characterized by the intermittency as the increase of the torque of the magnetic forces and decrease of the damping. The input-output feedback linearization method is applied to control chaotic attitude motions to the given fixed point and periodic motion.     

DYNAMICS AND CONTROL OF SPACECRAFT FORMATION FLYING IN EARTH ORBIT1)

航天器编队飞行被定义为跟踪或维持航天器之间的期望相对间隔、期望指向和相对位置。本文概括介绍了近年来地球轨道飞行编队的动力学和控制方面研究的发展状况,包括传统推进系统和新型无推进剂编队系统的动力学建模方法和控制器设计技术等。在传统推进编队系统中,航天器由使用化学燃料或等离子体的推进器提供推力,可以实现高精度地相对姿态/位置保持或重构,控制简单,灵活性高,但是需要消耗较多的能源。相比之下,在新型无推进剂编队系统中,航天器通过新的推力方式,如大气阻力作用,非接触内力,地磁洛伦兹力,动量交换等,将大大延长编队任务的寿命,并有效地避免羽流污染,但会带来新的控制问题。本文总结了这些领域中动力学与控制方面的研究方法及取得的成果,并提出了相关领域值得深入研究的问题和后续发展的方向。     

Shockwave�Cturbulent boundary layer interaction control using magnetically driven surface discharges

This study demonstrates the potential for shockwave?Cturbulent boundary layer interaction control in air using low current DC constricted surface discharges forced by moderate strength magnetic fields. An analytical model describing the physics of magnetic field forced discharge interaction with boundary layer flow is developed and compared to experiments. Experiments are conducted in a Mach 2.6 indraft air tunnel with discharge currents up to 300?mA and magnetic field strengths up to 5?Tesla. Separation- and non-separation-inducing shocks are generated with diamond-shaped shockwave generators located on the wall opposite to the surface electrodes, and flow properties are measured with schlieren imaging, static wall pressure probes and acetone flow visualization. The effect of plasma control on boundary layer separation depends on the direction of the Lorentz force (j × B). It is observed that by using a Lorentz force that pushes the discharge upstream, separation can be induced or further strengthened even with discharge currents as low as 30?mA in a 3-Tesla magnetic field. If shock-induced separation is present, it is observed that by using Lorentz force that pushes the discharge downstream, separation can be suppressed, but this required higher currents, greater than 80?mA. Acetone planar laser scattering is used to image the flow structure in the test section and the reduction in the size of recirculation bubble and its elimination are observed experimentally as a function of actuation current and magnetic field strength.     

MHD simulation of the distribution of the gasdynamic parameters and magnetic field behind the Earth’s bow shock under sharp variations in the solar wind dynamic pressure

The distributions of the gasdynamic parameters (density, pressure, and velocity) and the magnetic field behind the Earth’s bow shock (on the outer boundary of the magnetosheath) generated under sharp variations in the solar wind dynamic pressure are found in the three-dimensional non-planepolarized formulation with allowance for the interplanetary magnetic field within the framework of the ideal magnetohydrodynamic model using the solution to the MHD Riemann problem of breakdown of an arbitrary discontinuity. Such a discontinuity which depends on the inclination of an element of the bow shock surface arises when a contact discontinuity traveling together with the solar wind and on which the solar wind density and, consequently, the dynamic pressure, increases or decreases suddenly impinges on the Earth’s bow shock and propagates along its surface initiating the development of to six waves or discontinuities (shocks). The general interaction pattern is constructed for the entire bow shock surface as a mosaic of exact solutions to the MHD Riemann problem obtained on computer using an original software (MHD Riemann solver) so that the flow pattern is a function of the angular surface coordinates (latitude and longitude). The calculations are carried out for various jumps in density on the contact discontinuity and characteristics parameters of the solar wind and interplanetary magnetic field at the Earth’s orbit. It is found that there exist horseshoe zones on the bow shock in which the increase in the density and the magnetic field strength in the fast shock waves or their reduced decrease in the fast rarefaction waves penetrating into the magnetosheath and arising as a result of sharp variation in the solar wind dynamic pressure is superposed on significant drop in the density and growth in the magnetic field strength in slow rarefaction waves. The distributions of the hydrodynamic parameters and the magnetic field can be used to interpret measurements carried out on spacecraft in the solar wind at the libration point and orbiters in the neighborhood of the Earth’s magnetosphere.     

Collision of an interplanetary shock wave with the Earth’s bow shock. Hydrodynamic parameters and magnetic field

Hydrodynamic parameters and magnetic field generated in each of the waves in neighborhood of the Earth’s bow shock when an interplanetary shock wave impinges on it and propagates along its surface are found in the three-dimensional non-plane-polarized formulation within the framework of the ideal magnetohydrodynamic model. The interaction pattern is constructed in the quasi-steady-state formulation as a mosaic of exact solutions, obtained by means of a computer, to the Riemann problem of breakdown of a discontinuity between the states downstream of the impinging wave and the bow shock on the traveling line of intersection of their fronts. The calculations are carried out for typical parameters of the quiescent solar wind and the interplanetary magnetic field in the Earth’s orbit when the plane front of a shock wave moves along the Sun-Earth radius with various given velocities. The solutions obtained can be used to interpret measurements carried out by spacecraft in the solar wind and in neighborhood of the Earth’s magnetosphere.     

Impact of the interplanetary magnetic field on thewave flow pattern in the neighborhood of the Earth’s bow shock under sharp variations in the solar wind dynamic pressure

The impact of the interplanetary magnetic field on transformation and disintegration of the Earth’s bow shock into a system of magnetohydrodynamic (MHD) shock waves, rotational discontinuities and rarefaction waves under the action of abrupt variations in the solar wind dynamic pressure is simulated in the three-dimensional non-plane-polarized formulation within the framework of the ideal magnetohydrodynamic model using the solution of the MHD Riemann problem of breakdown of an arbitrary discontinuity. This discontinuity arises when a contact discontinuity, on which the solar wind density increases or decreases suddenly and which travels together with the solar wind, impinges on the Earth’s bow shock and propagates along its surface. The interaction pattern is constructed in the quasisteady- state formulation as a mosaic of exact solutions obtained on computer using an original MHD Riemann solver. The wave flow patterns are found for all elements of the surface of the bow shock as functions of their latitude and longitude for various jumps in the density on the contact discontinuity and characteristics parameters of the solar wind and interplanetary magnetic field at the Earth’s orbit. It is found that when the solar wind dynamic pressure increases, a fast MHD shock wave, that first penetrates into the magnetosheath, is always formed. When the solar wind dynamic pressure decreases, the influence of the interplanetary magnetic field can lead to the development of the leading fast MHD shock wave in certain zones on the surface of the Earth’s bow shock. The solution obtained can be used to interpret measurements on spacecraft in the solar wind at the libration point and in the neighborhood of the Earth’s magnetosphere.     

Chaotic attitude motion of a magnetic rigid spacecraft in an elliptic orbit and its control

This paper deals with the chaotic attitude motion of a magnetic rigid spacecraft with internal damping in an elliptic orbit. The dynamical model of the spacecraft is established. The Melnikov analysis is carried out to prove the existence of a complicated nonwandering Cantor set. The dynamical behaviors are numerically investigated by means of time history, Poincaré map, Lyapunov exponents and power spectrum. Numerical simulations demonstrate the chaotic motion of the system. The input-output feedback linearization method and its modified version are applied, respectively, to control the chaotic attitude motions to the given fixed point or periodic motion. The project supported by the National Natural Science Foundation of Chine (10082003)     

Specific features of propagation of unsteady waves in a rotating spherical layer of an ideal incompressible stratified electroconducting fluid in the equatorial latitude belt

Three-dimensional large-scale motions of a rotating inviscid incompressible stratified ideal electroconducting fluid in a spherical equatorial latitude belt are studied. The mathematical model of this physical process is a closed system of partial differential equations consisting of hydrodynamic equations, which take into account the Earth rotation and the Lorentz force, and corresponding equations of magnetic dynamics with appropriate boundary conditions. An analytical solution of the system is constructed in the approximation of an equatorial β-plane, which describes propagation of lowamplitude waves.     

Influence of velocity profile on calibration function of Lorentz force flowmeter

A Lorentz force flowmeter is a noncontact electromagnetic flow-measuring device based on exposing a flowing electrically conducting liquid to a magnetic field and measuring the force acting on the magnet system. The measured Lorentz force is proportional to the flow rate via a calibration coefficient which depends on the velocity distribution and magnetic field in liquid. In this paper, the influence of different velocity profiles on the calibration coefficient is investigated by using numerical simulations. The Lorentz forces are computed for laminar flows in closed and open rectangular channels, and the results are compared with the simplified case of a solid conductor moving at a constant velocity. The numerical computations demonstrate that calibration coefficients for solid bodies are always higher than for liquid metals. Moreover, it can be found that for some parameters the solid-body calibration coefficient is almost twice as high as for a liquid metal. These differences are explained by analyzing the patterns of the induced eddy currents and the spatial distributions of the Lorentz force density. The result provides a first step for evaluating the influence of the laminar velocity profiles on the calibration function of a Lorentz force flowmeter.     

Chaotic attitude motion of a magnetic rigid spacecraft

IntroductionAttitudedynamicsofspacecraftisascientificresearchsubjectwithgreatsignificance[1,2 ].Aschaosiswidelyanddeeplyinvestigated ,muchattentionhasbeenpaidonchaoticattitudemotionofspacecraft.Itnotonlyprovidesadefiniteengineeringbackgroundforexploringchaos,butalsooffersanewviewpointfordesigningspacecraft.Ithasbeenshownthatthereexistschaoticattitudemotioninsomemodelsofspacecraft,suchasspinningsatellitesinacircularorbit,gyrostatsatellitesinthegravitationalfield ,andtetheredsatellites[3 ,4].Ho…     

Adaptive control for autonomous rendezvous of spacecraft on elliptical orbit

A strategy for spacecraft autonomous rendezvous on an elliptical orbit in situation of no orbit information is developed. Lawden equation is used to describe relative motion of two spacecraft. Then an adaptive gain factor is introduced, and an adaptive control law for auton- omous rendezvous on the elliptical orbit is designed using Lyapunov approach. The relative motion is proved to be ultimately bounded under this control law, and the final relative position error can achieve the expected magnitude. Simulation results indicate that the adaptive control law can realize autonomous rendezvous on the elliptical orbit with relative state information only.     

电磁流变效应微磨头抛光加工电磁协同作用机理

将磨料混入以Fe3O4为分散粒子的电磁流变液作为抛光液,在电磁场耦合作用下形成电磁流变效应微磨头对玻璃材料进行抛光加工试验,通过考察不同电磁场耦合条件下玻璃材料的去除量,揭示了电磁流变效应微磨头抛光规律,建立了分散粒子的力学模型,深入研究了电磁流变效应微磨头抛光的电磁协同作用机理.结果表明:励磁电压为5V、电场电压3kV时,电磁流变效应微磨头材料去除量达到电流变效应微磨头的1.74倍和磁流变效应微磨头的5.71倍,产生了显著的电磁流变协同效应;电磁流变液分散粒子所受的电场力、磁场力和洛伦兹力产生的自旋力偶的综合作用决定了电磁流变效应微磨头链串的稳定性及其加工性能,在适当的电场和磁场耦合状态下能获得良好的电磁流变协同效应.     

OPTIMAL CONTROL OF NONLINEAR VIBRATION RESONANCES OF SINGLE-WALLED NANOTUBE BEAMS

An optimal time-delay feedback control method is provided to mitigate the primary resonance of a single-walled carbon nanotube （SWCNT） subjected to a Lorentz force excited by a longitudinal magnetic field. The nonlinear governing equations of motion for the SWCNT under longitudinal magnetic field are derived and the modulation equations are obtained by using the method of multiple scales. The regions of the stable feedback gain are worked out by using the stability conditions of eigenvalue equation. Taking the attenuation ratio as the objective function and the stable vibration regions as constrained conditions, the optimal control parameters are worked out by using minimum optimal method. The optimal controllers are designed to control the dynamic behaviors of tile nonlinear vibration systems. It is found that the optimal feedback gain obtained by the optimal method can enhance the control performance of the primary resonance of SWCNT devices.     

Determination of a magnetic field with rotational symmetry about a given line of magnetic force

In certain technical applications when a magnetic field with rotational symmetry has to be calculated, it is often a principal requirement that a given line should be a magnetic line of force (or more accurately, that a given surface of rotation should coincide with a surface of magnetic force).An exact particular solution of the problem is found in the case when the given line of force is straight. This solution is subsequently generalized to the case of an arbitrary smooth line, approximating it by a broken line. A method is also proposed for producing and calculating a magnetic field satisfying the above conditions.The solution of this problem may be used in questions of magneto-hydrodynamics and plasmadynamics as the first approximation for the magnetic field in the case of small magnetic Reynolds numbers, when it is required that a certain line of fluid flow should coincide with a magnetic line of force.The authors would like to mention that it was due to the constant interest of E. S. Kuznetsov and his valuable advice that the present paper was completed.     

Stationary cylindrical vortex in a viscous electrically conducting fluid

An exact solution of the magnetohydrodynamic equations is constructed which describes steady vortex flow in a stationary cylinder on the axis of which a conductor carrying a known current is located. The solution is obtained under the assumption that the fluid is viscous and has finite electrical conductivity and that the magnetic field has only the axial and azimuthal components in a cylindrical coordinate system. It is found that the action of the Lorentz force is compensated by changing the pressure. Fluid flow occurs from the periphery to the axis of the cylinder under a pressure gradient, with flow rotation and swirling. The fluid flow causes a concentration of the magnetic lines near the axis of the cylinder, providing an exponential decrease in the magnetic field strength with distance from the axis. This flow can be considered as a model of a local increase in the magnetic field strength due to the transfer of its force lines by the flow of the electrically conducting fluid.