Attitude control system of the first Russian nanosatellite <Emphasis Type="Italic">TNS-0 no. 1</Emphasis>

The results of designing the attitude control system of the first Russian nanosatellite TNS-0 no. 1 providing orientation of its longitudinal axis along the local geomagnetic field induction vector are presented. The system consists of a permanent magnet and two sets of hysteresis rods. The magnetic and geometric parameters of the magnet and rods are calculated. The influence of the permanent magnet field on the hysteresis rods and mutual influence of the rods in the case of compact satellite packaging are analyzed. Examples of calculations of transient processes and steady-state angular satellite motion are presented.     

Nanosatellite <Emphasis Type="Italic">REFLECTOR</Emphasis>: Choice of parameters of the attitude control system

We consider methodological and applied problems of choosing parameters and developing a passive gravity-gradient attitude control system for the REFLECTOR nanosatellite. The attitude control system consists of appropriately distributed satellite mass and additional masses forming the required tensor of inertia, as well as of a set of hysteresis rods manufactured from a magnetically soft material. The combination of these elements allows one, independent of the satellite’s initial angular motion, to maintain its three-axial orientation in the orbital coordinate system with preset performance in precision and fast response. The satellite’s dynamics is investigated using asymptotic and numerical methods. The problems of arrangement of the additional masses and hysteresis rods are discussed, as well as their interaction with magnetizable elements.     

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.     

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.     

Processing the data of measurements of angular velocity and microaccelerations onboard the <Emphasis Type="Italic">Foton-12</Emphasis> satellite

The results of reconstruction of uncontrolled rotational motion of the Foton-12 satellite using the measurement data of onboard sensors are presented. This problem has already been solved successfully several years ago. The satellite motion was reconstructed using the data of measuring the Earth’s magnetic field. The data of measuring the angular velocity and microaccelerations by the QSAM system were actually not used for this purpose, since these data include a clearly seen additional component whose origin was at that time unclear. This component prevented one from using these data directly for reconstruction of the angular motion. Later it became clear that the additional component was caused by the Earth’s magnetic field. Discovery of this fact allowed us to make necessary corrections when processing the QSAM system data and to use them for reconstruction of rotational motion of Foton-12. Below, a modified method of processing the QSAM system data is described together with the results of its application. The main result is obtained by comparing the motion reconstructed from measurements of angular velocity or acceleration with that found by way of processing the measurements of the Earth’s magnetic field. Their coincidence turned out to be rather accurate.     

用地球磁场和重力场成功挽救风云一号（B）卫星的控制技术

风云一号气象卫星是我国最早成功发射的太阳同步三轴稳定对地遥感卫星，由于早期的技术和器件原因，星上计算机因空间辐照而失控，造成星上贮气耗尽、卫星高速翻滚。本文详细介绍了了在卫星面临失败的情况下，作者利用地球磁场和重力场与卫星的相互作用，采用星上的磁力矩器和可用的一切手段而设计的一整套抢救这颗卫星的技术方法，并简述了经过75天的艰苦努力，使这颗濒临失败的卫星重新建立三轴稳定的对地定向姿态的历程。     

The use of refined model of aerodynamic moment in the problem of reconstruction of the <Emphasis Type="Italic">Foton</Emphasis> satellite rotational motion

A new mathematical model of the uncontrolled rotational motion of the Foton satellite is presented. The model is based on the Euler dynamic equations of rigid body motion and takes into account the action upon the satellite of four external mechanical moments: gravitational, restoring aerodynamic, moment with constant components in the satellite-fixed coordinate system, and moment arising due to interaction of the Earth’s magnetic field with the satellite’s proper magnetic moment. To calculate the aerodynamic moment a special geometrical model of the outer satellite shell is used. Detailed form of the formulas giving above-mentioned moments in the equations of satellite motion is agreed with the form of the considered motion. Model testing is performed by determining with its help the rotational motion of the Foton M-2 satellite (it was in orbit from May 31, 2005 to June 16, 2005) using the data of the onboard measurements of the Earth’s magnetic field strength. The use of the new model has led to a relatively small improvement in the accuracy of the motion determination, but allowed us to obtain physically real estimates of some parameters.     

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.     

Determination of <Emphasis Type="Italic">Foton M-2</Emphasis> satellite attitude motion by the data of microacceleration measurements

The results of reconstruction of uncontrolled attitude motion of the Foton M-2 satellite using measurements with the accelerometer TAS-3 are presented. The attitude motion of this satellite has been previously determined by the measurement data of the Earth’s magnetic field and the angular velocity. The TAS-3 data for this purpose are used for the first time. These data contain a well-pronounced additional component which made impossible their direct employment for the reconstruction of the attitude motion and whose origin was unknown several years ago. Later it has become known that the additional component is caused by the influence of the Earth’s magnetic field. The disclosure of this fact allowed us to take into account a necessary correction in processing of TAS-3 data and to use them for the reconstruction of the attitude motion of Foton M-2. Here, a modified method of processing TAS-3 data is described, as well as results of its testing and employing. The testing consisted in the direct comparison of the motion reconstructed by the new method with the motion constructed by the magnetic measurements. The new method allowed us to find the actual motion of Foton M-2 in the period June 9, 2005–June 14, 2005, when no magnetic measurements were carried out.     

Investigation of the effectiveness of an algorithm of active magnetic damping

We consider the rapid rotation of a satellite equipped with an active magnetic attitude control system with the -Bdot algorithm designed to damp the initial angular velocity. The time-response of the algorithm is analytically studied as a function of orbit inclination.     

模块化卫星的多螺杆连接分析

相对于单螺栓连接或平均受力的多螺栓连接,模块化卫星的多根螺杆连接涉及被连接件的非均匀连接刚度,各螺杆处的不同连接刚度的耦合作用与影响还有待深入分析。本文基于单螺栓的载荷分析方法,通过计算被连接件的连接刚度矩阵参数,并融入到螺杆载荷分析中,从而得到计算螺杆直径与预紧力的公式。最后,给出一个模块化卫星多螺杆连接分析的算例,计算结果显示,使用M3钛螺杆、每个螺杆施加最小1Nm拧紧力矩,可以满足此模块化卫星的使用要求。     

CRYOGENIC TECHNOLOGY TO IMPROVE ELECTRIC THRUSTERS

This paper analyzes superconducting (SC) coils technology to improve satellite electric propulsion. SC magnets can generate very high magnetic fields with extremely low ohmic losses, low electric power and PCU weight. Moreover, the weight of SC magnet coils is quite low compared with conventional or permanent magnets capable of producing the same field strength. For instance, to obtain a 0.4 T magnetic field strength, typical of applied field magnetoplasmadynamic thrusters (AF-MPD), based on the Lorentz force, and with thrust in the range of 1 N, this paper shows that only a 40 g coil SC weight is needed, whereas an equivalent field copper winding would weigh about 36 kg. Using SC technology it is shown that the limited magnetic induction provided by a permanent magnet may be raised and also that it is possible to obtain high magnetic fields (of order of several Tesla) with fewer turns, drastically reducing coil volume, weight and complexity compared to conventional winding.

Superconductivity at low temperature (LTSC) requires liquid helium at 4.2 K to produce very high current densities: the thermal analysis in this paper shows that, depending on satellite and thruster, high temperature superconductors (HTSC) wires are sometimes better than LTSC because these can support lower current densities but with a critical superconductivity temperature higher than for LHe, requiring LN₂ at 77 K, easier to maintain during the whole mission.

Finally, this paper shows that implementing SC cryogenic technology on a satellite can be achieved with current active coolers technology.     

Rotational motion of <Emphasis Type="Italic">Foton M-4</Emphasis>

The actual controlled rotational motion of the Foton M-4 satellite is reconstructed for the mode of single-axis solar orientation. The reconstruction was carried out using data of onboard measurements of vectors of angular velocity and the strength of the Earth’s magnetic field. The reconstruction method is based on the reconstruction of the kinematic equations of the rotational motion of a solid body. According to the method, measurement data of both types collected at a certain time interval are processed together. Measurements of the angular velocity are interpolated by piecewise-linear functions, which are substituted in kinematic differential equations for a quaternion that defines the transition from the satellite instrument coordinate system to the inertial coordinate system. The obtained equations represent the kinematic model of the satellite rotational motion. A solution of these equations that approximates the actual motion is derived from the condition of the best (in the sense of the least squares method) match between the measurement data of the strength vector of the Earth’s magnetic field and its calculated values. The described method makes it possible to reconstruct the actual rotational satellite motion using one solution of kinematic equations over time intervals longer than 10 h. The found reconstructions have been used to calculate the residual microaccelerations.     

Elimination of relative secular drift of orbits of two satellites caused by polar oblateness of the Earth

A method of elimination of relative secular drifts in satellite formations is suggested for the case of influence of a perturbation due to polar oblateness of the Earth. The method is applied to eliminate relative secular drifts in the case when a satellite is controlled using an engine mounted along its orientation axis (the satellite is supplied with a passive magnetic attitude control system) and with the help of a solar sail installed on one of the satellites. Analytical results are confirmed by numerical simulation.     

An Analysis of the Low-Frequency Component in Measurements of Angular Velocity and Microacceleration onboard the Foton-12 Satellite

We compare the results of two methods used to determine the angular velocity of the Foton-12 satellite and the low-frequency component of microaccelerations onboard it. The first method is based on reconstruction of the satellite's rotational motion using the data of onboard measurements of the strength of the Earth's magnetic field. The motion (time dependence of the orientation parameters and angular velocity) was found from the condition of best approximation of the measurement data by the functions calculated along the solutions to equations of attitude motion of the satellite. The solutions found were used to calculate the quasistatic component of microaccelerations at certain points of the satellite, in particular, at the point of location of an accelerometer of the QSAM system. Filtration of the low-frequency component of the angular velocity and microacceleration from the data of measurements by a sensor of angular velocity and by the accelerometer of this system served as a second method. The filtration was made using the discrete Fourier series. A spectral analysis of the functions representing the results of determining the angular velocity and microacceleration by both methods is performed. Comparing the frequencies and amplitudes of the harmonic component of these functions allowed us to estimate the accuracy of measurements made by the QSAM system in the low-frequency range.     

高精度飞轮控制系统方案分析研究

卫星姿态控制是卫星控制领域里的最重要的一个方面 ,用于保证卫星的正常工作。一般的卫星姿态控制都采用飞轮控制方案 ,所采用的飞轮有磁悬浮飞轮和普通飞轮两种。虽然磁悬浮飞轮能克服飞轮自身摩擦力对卫星姿态的影响 ,但是磁悬浮飞轮在制造、工艺等方面要求高 ,而且成本昂贵。本文讨论了采用直流无刷电机控制普通飞轮的方案中关于转速和电流这两个关键参数的高精度控制问题 ,并给出了实际可行的解决方法。这些方法已在某型卫星上得到了部分应用。     

利用地磁场测量的小卫星自主导航设计

地磁场矢量是卫星所在位置的函数 ,通过对地磁场的测量 ,即可实现对近地小卫星的自主导航。本文采用卡尔曼滤波技术设计了小卫星基于地磁场测量的导航方法 ,在采用地磁场模型时选取磁偶极子模型 ,以此使设计算法的计算量大大减少。最后利用数字仿真验证了系统性能。     

Dual attitude and parameter estimation of passively magnetically stabilized nano satellites

The attitude determination capability of a nano satellite is limited by a lack of traditional high performance attitude sensors, a result of having small budgets for mass and power. Attitude determination can still be performed on a nano satellite with low fidelity sensors, but an accurate model of the spacecraft attitude dynamics is required. The passive magnetic stabilization systems commonly employed in nano satellites are known to introduce uncertainties in the parameters of the attitude dynamics model that cannot easily be resolved prior to launch. In this paper, a batch estimation problem is formulated that simultaneously solves for the attitude of the spacecraft and performs parameter estimation on the magnetic properties of the magnetic materials using only a measurement of the solar vector. The estimation technique is applied to data from NASA Ames Research Center's O/OREOS nano satellite and the University of Michigan's RAX-1 nano satellite, where clear differences are detected between the magnetic properties as measured before launch and those that fit the observed data. To date this is the first known on-orbit verification of the attitude dynamics model of a passively magnetically stabilized spacecraft.     

Determination of attitude motion of the <Emphasis Type="Italic">Foton M-3</Emphasis> satellite according to the data of onboard measurements of the Earth’s magnetic field

The results of reconstruction of rotational motion of the Foton M-3 satellite during its uncontrolled flight in September 2007 are presented. The reconstruction was performed by processing the data of onboard measurements of the Earth’s magnetic field obtained by the DIMAC instruments. The measurements were carried out continuously throughout the flight, but the processing technique dealt with the data portions covering time intervals of a few orbital revolutions. The data obtained on each such interval were processed jointly by the least squares method with using integration of the equations of satellite motion relative to its center of mass. When processing, the initial conditions of motion and the used mathematical model’s parameters were estimated. The results of processing 16 data sets gave us complete information about the satellite motion. This motion, which began at a low angular velocity, had gradually accelerated and in five days became close to the regular Euler precession of an axisymmetric solid body. At the end of uncontrolled flight the angular velocity of the satellite relative to its lengthwise axis was 0.5 deg/s; the angular velocity projection onto the plane perpendicular to this axis had a magnitude of about 0.18 deg/s.     

Asymptotic study of a complete magnetic attitude control cycle providing a single-axis orientation

The angular motion of an axisymmetrical satellite equipped with the active magnetic attitude control system is examined. Attitude control system has to ensure necessary orientation of the axis of symmetry in the inertial space. It implements the following strategy: coarse reorientation of the axis of symmetry with nutation damping or “-Bdot” without initial detumbling; spinning-up about the axis of symmetry to achieve the property of a gyro; fine reorientation of the axis in the inertial space. Dynamics of the satellite is analytically studied using averaging technique on the complete control loop consisting of five algorithms. Solutions of the equations of motion are obtained in terms of quadratures for most cases or even in closed-form. The latter allowed to study the dependence of motion parameters including time-response with respect to the orbit inclination and other parameters for all algorithms.