Multi-objective output-feedback control for microsatellite attitude control: An LMI approach

Mixed H₂/H_∞ output-feedback controller with pole placement constraints against the internal uncertainty of moment-of-inertia variation and space environmental disturbances is proposed for mircosatellite attitude control. The multi-objective controller is designed based on linear model of attitude dynamics. The H_∞ performance takes into account both robustness stability against moments-of-inertia uncertainty and the disturbance rejection aspect. H₂ performance takes into account the LQG aspect which avoids the undesirable wheels’ saturation effect. In addition, the closed-loop poles can be forced into some sector of the stable half-plane to obtain well-damped transient responses. The problem is then reduced to a convex optimization involving linear matrix inequalities (LMIs), so it can be efficiently solved. The simulation results demonstrate that the presented mixed H₂/H_∞ control system is robust stable and optimal in the sense of H₂ norm, and has good steady-state and dynamic performances against the parameter uncertainties and various disturbances for the microsatellite attitude control system.     

An inversion approach for lunar regolith layer thickness using optical albedo data and microwave emission simulation

An approach to inversion of the lunar regolith layer thickness by using multi-channel brightness temperature observation in passive microwave remote sensing is developed. To first make simulation of brightness temperature from the lunar layered media, the lunar regolith layer thickness (d) is proposed being constructed by available lunar DEM (digital elevation mapping) and on site measurements. The physical temperature distribution (T) over the lunar surface is also empirically assumed as a monotonic function of the latitude. Optical albedo of the lunar nearside from the telescopic observation is employed to construct the spatial distribution of the FeO+TiO₂ content (S) in the lunar regolith layer. A statistic relationship between the DEM and S of the lunar nearside is further extended to construction of S of the lunar farside. Thus, the dielectric permittivity (ε) of global lunar regolith layer can then be determined. Based on all these conditions (d,T,ε), brightness temperature of the lunar regolith layer in passive microwave remote sensing, which is planned for China's Chang-E lunar project, is numerically simulated by a parallel layering model using the strong fluctuation theory of random media.Then, taking these simulations with random noise as observations, an inversion method of the lunar regolith layer thickness is developed by using three- or two-channels brightness temperatures. When the S is low, and the four channels brightness temperatures in China's Chang-E project are well distinguishable, the regolith layer thickness and physical temperature of the underlying lunar rock media can be inverted by the three-channels approach. When the S becomes high that the brightness temperature at high frequency channels such as 19.35, 37 GHz are saturated, the regolith layer thickness is alternatively inverted only by the two-channels approach.Numerical simulation and inversion approach in this paper make an evaluation of the performance for lunar passive microwave remote sensing, and for future data calibration and validation.     

Orbital stability of planar oscillations of a satellite in a circular orbit

We consider the attitude motion of a satellite with a circular orbit in a central Newtonian gravitational field. The satellite is a solid body whose mass geometry is that of a plate. A nonlinear analysis is made of orbital stability of planar oscillations of the satellite at which its middle or major axis of inertia is perpendicular to the orbit plane. At small amplitudes of oscillations the analysis of stability was made analytically, while for arbitrary amplitudes the numerical analysis was performed.     

Effect of geomagnetic field disturbances on the adaptive stress reaction of cosmonauts

Investigations of the effect of geomagnetic activity factors on the cardiac rhythm regulation and arterial pressure of cosmonauts during the expeditions onboard the Soyuz spacecraft, and the MIR and ISS orbital space stations was carried out for various durations of flight in weightlessness and, under control. Groups of cosmonauts were inspected under flight conditions outside the geomagnetic disturbances and in ground preflight conditions, during disturbances without them. The presence of specific effect of geomagnetic disturbances on the system of vegetative regulation of blood circulation of cosmonauts during the flight was demonstrated for the first time. The response of cosmonauts’ cardiac rhythm on the magnetic storm is definitely revealed; however, it depends on the initial functional background and, in particular, on the state of mechanisms of vegetative regulation (the duration of flight and adaptation to it).     

The use of solutions to problems of spacecraft trajectory optimization in impulse formulation when solving the problems of optimal control of trajectories of a spacecraft with limited thrust engine: I

In this first part of our paper, it is suggested to use solutions to boundary value problems in the optimization problems (in impulse formulation) for spacecraft trajectories in order to obtain the initial approximation, when boundary value problems of the maximum principle are solved numerically by the shooting method. The technique suggested is applied to the problems of optimal control over motion of the center of mass of a spacecraft controlled by the thrust vector of jet engine with limited thrust in an arbitrary gravitational field in a vacuum. The method is based on a modified (in comparison to the classic scheme) shooting method computation together with the method of continuation along a parameter (maximum reactive acceleration, initial thrust-to-weight ratio, or any other parameter equivalent to them). This technique allows one to obtain the initial approximation with a high precision, and it is applicable to a wide range of optimal control problems solved using the maximum principle, if the impulse formulation makes sense for these problems.     

Optimization of passive orbit with the use of gravity maneuver

A high-precision method of calculating gravitational interactions is applied in order to determine optimal trajectories. A number of problems, necessary for determination of optimal parameters at a launch of a spacecraft and during its flyby near celestial bodies, are considered. The spacecraft trajectory was determined by numerical integration of the equations of passive motion of the spacecraft and of the equations of motion for planets, the Sun, and the Moon. The optimal trajectory of the spacecraft approaching the Sun is determined by fitting its initial conditions.     

Determination of two Satellites’ relative motion using tracking measurements

A technique to determine the initial relative velocity of two satellites at the initial time instant, based on the results of NORAD system’s measurements, is presented. The determination of a relative initial position is shown to result in the unsatisfactory accuracy. This technique is applied to determining the initial velocity of separation of the first Russian nanosatellite TNS-0 from the International Space Station.     

About one problem of trajectory optimization

The optimization problem for trajectories of spacecraft flight from the Earth to an asteroid is considered in this paper. The flight is realized in the central Newtonian gravitational field of the Sun with a possibility of gravitational maneuvers near planets. Perturbation maneuvers are taken into account using the method of point area of action with a limitation on the flyby altitude. The spacecraft is controlled by changing the value and direction of the engine thrust. The problem is solved taking into account constraints on the launch time, flight duration, and minimum distance to the Sun.     

Manifestation of configurations of magnetic clouds of the solar wind in geomagnetic activity

On the basis of an analysis of the data of multi-satellite observations of magnetic clouds at the path Venus-Earth, the dependence of their geoeffectiveness on the orientation in the ecliptic plane and position relative to the Sun-Earth line is determined in the paper. The cloud parameters were determined on the basis of the model of a force-free cylindrical flux rope. The search for magnetic clouds in the flow of data from the monitoring space vehicle was performed using a special-purpose computer program.     

Malfunction of satellite navigation systems GPS and GLONASS caused by powerful radio emission of the Sun during solar flares on December 6 and 13, 2006, and October 28, 2003

Poor quality of functioning of GPS during solar flares on December 6 and 13, 2006 is analyzed in this paper. These flares were accompanied by extremely high (unexampled) level of the solar radio emission flux. A comparison is made of these events with the solar flare on October 28, 2003. Statistically reliable experimental evidence is obtained that GPS positioning was partially paralyzed on the sunlit side of the Earth during the strongest bursts of solar radio emission. The obtained results give a serious ground to revise the role played by space weather factors in operation of modern satellite systems and to take these factors into account more carefully, when such systems are designed and exploited.     

Planar inertial motion of an elastic cluster of three bodies

A problem of planar inertial motion of three bodies connected in the form of a triangle by an elastic imponderable filament is considered, as well as a particular case of the problem of motion of a closed chain of n bodies. This configuration can be a basis for extended planar constructions in deep space.The bodies are considered as material points. The paper elaborates a subject of [1]     

Application of a magnetohydrodynamic element in the control loop of a rotating spacecraft with cavities partially filled with liquid

This paper is a continuation of [1–3] and a generalization of the results for a rotating spacecraft with cavities partially filled with liquid and equipped with an operational magnetohydrodynamic (MHD) element in the loop of its attitude control. This element makes possible the creation of hingeless systems of stabilization and orientation that do not require rocket propellant consumption. The application of an MHD element is considered for stabilization in the mode of spin-up of a spacecraft not having gyroscopic stability.     

Proton fluxes measured by low-orbit satellites

In this paper we consider the fluxes of protons in the energy range from 30 keV to 140 MeV recorded by instruments onboard the Russian satellites KORONAS-F and UNIVERSITETSKII and on the American satellites GOES-11 and NOAA-17. In order to estimate the reliability of the obtained data, the comparison of measurements of separate energy channels of these instruments between themselves is performed. Experimental fluxes of trapped protons are compared with the fluxes predicted by the AP8 model.     

Forecasting the velocity of quasi-stationary solar wind and the intensity of geomagnetic disturbances produced by it

A brief review is given of contemporary approaches to solving the problem of medium-term forecast of the velocity of quasi-stationary solar wind (SW) and of the intensity of geomagnetic disturbances caused by it. At the present time, two promising models of calculating the velocity of quasi-stationary SW at the Earth’s orbit are realized. One model is the semi-empirical model of Wang-Sheeley-Arge (WSA) which allows one to calculate the dependence V(t) of SW velocity at the Earth’s orbit using measured values of the photospheric magnetic field. This model is based on calculation of the local divergence f _S of magnetic field lines. The second model is semi-empirical model by Eselevich-Fainshtein-Rudenko (EFR). It is based on calculation in a potential approximation of the area of foot points on the solar surface of open magnetic tubes (sources of fast quasistationary SW). The new Bd-technology is used in these calculations, allowing one to calculate instantaneous distributions of the magnetic field above the entire visible surface of the Sun. Using predicted V(t) profiles, one can in EFR model calculate also the intensity of geomagnetic disturbances caused by quasi-stationary SW. This intensity is expressed through the K _p index. In this paper the EFR model is discussed in detail. Some examples of epignosis and real forecast of V(t) and K _p (t) are discussed. A comparison of the results of applying these two models for the SW velocity forecasting is presented.     

Trajectories for missions of low-thrust spacecraft aimed at delivery of soil samples from main belt asteroids and Phobos

Trajectories of spacecraft with electro-jet low-thrust engines are studied for missions planning to deliver samples of matter from small bodies of the Solar System: asteroids Vesta and Fortuna, and Martian moon Phobos. Flight trajectories are analyzed for the mission to Phobos, the limits of optimization of payload spacecraft mass delivered to it are determined, and an estimate is given to losses in the payload mass when a low-thrust engine with constant outflow velocity is used. The model of an engine with ideally regulated low thrust is demonstrated to be convenient for calculations and analysis of flight trajectories of a low-thrust spacecraft.     

Optimization of low-thrust transfers in the three body problem

We consider transfers with low thrust in an arbitrary field of forces. The modified method of transporting trajectory [1–4] is used for optimization of the transfers. The complexity of finding the transporting trajectory of a preset type can be the main obstacle to application of this method. This challenge is solved for the three-body problem in the Hill motion model. Numerical analysis of the method is performed using an example of the transfers to halo-orbits around the solar-terrestrial libration points.     

Studies of the stratosphere aerosol layer based on polarization measurements of the twilight sky

The paper is devoted to an analysis of observational manifestations of the aerosol layer in the Earth’s stratosphere and to a method of determining their optical properties. It is based on polarization measurements of the twilight sky background in the zenith vicinity and in a broad spectral band with an effective wavelength of 5250 Å. An increased abundance of the stratosphere aerosol was found in December 2006 for the first time in several years of observation. The suggested method allows one to determine the ratio of radiation scattering coefficients by the stratosphere aerosol and by air molecules, as well as the degree of polarization of aerosol scattering in the stratosphere. The appearance of the stratosphere aerosol is associated with explosive eruption of Rabaul volcano having occurred in the beginning of October 2006.     

Calculation of quasisynchronous orbits of a spacecraft around Phobos for solving the problem of landing on its surface

The problem of selecting quasi-synchronous orbits of a spacecraft around Phobos is considered. These quasi-synchronous orbits are far (with respect to the Hill’s sphere) quasi-satellite orbits with retrograde rotation in the restricted three body problem. The orbit should pass through a given point at a specified time instant. It should also possess a property of minimum distance from the Phobos surface at every passage above the region of planned landing. The equations of dynamics are represented in the form describing the orbit as a combination of motions in two drifting ellipses, inner and outer ellipses. The center of the outer ellipse is located on the inner ellipse. A formula is derived that relates averaged values of half-axes of the inner and outer ellipses. It is used for construction of the first approximation of numerically designed orbit, which makes it possible to simplify and speed up the computing process. The tables of initial conditions obtained as a result of calculations are presented.     

A mechanism for generating magnetic field by vortex processes in stellar plasma

The difference in viscous properties of proton and electron gases in fully ionized hydrogen plasma is shown to result in a possibility of generation in this plasma of the magnetic field, even if initially there was no field. As an example, a simplified planar stationary model of a magnetohydrodynamic process of the eddy sink type is considered. It is demonstrated that the intensity of the generated magnetic field strongly depends on plasma temperature, so that the range T = 100000–500000 K corresponds to the range of maximum magnetic induction B = 50–2700 G. Such values are frequently observed in ordinary stars, in particular, in solar flares.