Attitude control algorithms for the Russian nanosatellite TNS-1

M.Yu.Ovchinnikov, V.I.Penkov, A.A.Ilyin

Keldysh Institute of Applied Mathematics of Russian Academy of Sciences

Miusskaya Square 4, Moscow 125047, Russia

ovchinni@keldysh.ru

A.S.Selivanov

Russian Research Institute of Space Device Engineering

Aviamotornaya Street 53, Moscow 111024, Russia

selivanov@rniikp.ru

Methods to provide one-axis stabilization of the Russian nano-satellite TNS-1 with respect to the inertial space are presented. It is proposed to use a spin-stabilization technique. The spin axis direction and spin rate are controlled by magnetic coils. To increase an accuracy of orientation at the extremity of the acquisition phase a passive nutation damper is proposed. Two modes of the satellite orientation are considered each as a nominal one. In the first mode the satellite's spin axis is oriented along with the normal to orbital plane, in the second mode the satellite is directed towards the Sun. Algorithms for magnetic coils for the spin-axis and spin-rate control and magnetic nutation dampning in absence of a passive nutation damper are presented. The results of analytical and numerical simulation of the satellite attitude motion under magnetic control are given.

A frequently used method of a satellite orientation is spin-stabilization. Spin-stabilized satellite maintains the orientation of the spin axis direction with respect to the inertial space for a long time. For orientation of the spin axis and to maintain the spin-rate a magnetic attitude control system (MACS) may be used. The system comprises three magnetic coils which develop a magnetic dipole moment. The advantage of the MACS is that the system does not require a fuel consumption. It is especially attractive for small satellites because they are strong restricted in size, mass and power output. MACS does not contain moving parts and, therefore, it is more reliable. Meteorological satellites of "Tiros" series ^љin 60th and 70th were stabilized in the same manner. The spin axis of the eight satellites laid in the orbital plane. The spin axis of two next satellites lies along with the normal to the orbital plane. Owing to the sun-synchronous orbit a given side of the satellite is directed towards the Sun. The satellite is 18-side prism of 50 cm height, about one meter diameter and 130 kg mass. The spin rate is about 9-12 rpm. The similar manner of orientation is now used for the European meteorological satellite "Meteosat".

Usage of the spin stabilization requires inertial satellite configuration to be similar to flywheel's one, that is the spin axis has to be the axis of symmetry and, also, to be the axis of the maximum moment of inertia. After separation from the launcher a satellite chaotically tumbles. Being effected by the magnetic torque developed by coils, the spin axis precesses until it becomes perpendicular to the orbital plane and spin-rate reaches a required magnitude. To control a spin axis direction the coil which is parallel to the axis is used. To control the spin rate the coils lying in a plane which is perpendicular to the spin axis are used.

Advantage of the "flywheel" mode for the satellite equipped with TV cameras is that each satellite orbit TV cameras expose the Earth. At each moment when infrared sensor field of view crosses the visible horizon the pulser is activating the TV camera. Similar approach is accepted and used for the Russian nano-satellite TNS-1 being under development by the Russian Research Institute of Space Device Engineering in cooperation with the Keldysh Institute of Applied Mathematics of RAS.

Because of the strong power limitation of on-board sources of energy another orientation mode is considered. In this case the spin axis has to coincide with the direction towards the Sun in a contrast to first mode when the spin axis directs along with the normal to the orbital plane and the gravity-gradient torque does not disturb spin-stabilization of the satellite. In the second mode the torque disturbs the spin axis. The less spin-rate, the more disturbing effect is due to the gravity-gradient torque. Choosing orientation mode it is important to compare the power output of solar array and the time-schedule for correct of the spin axis direction.

Another problem to be considered is how to maintain the spin axis direction with respect to the inertial space using sensors (sun-sensor and magnetometer) of rather low accuracy. The problem of accuracy becomes critical when satellite is approaching the nominal mode of orientation (either along with the normal to the orbital plane or towards the Sun) and the accuracy of measurements is comparable with required accuracy of orientation. There are two ways to solve the problem. The first one is to use more accurate sensors. The second one is to use a passive nutational damper which permanently decreases the nutational oscillations. The nutational damper principle of operation is based on decreasing the osculation energy due to the friction motion of the small element situated on the satellite. Relative motion of the element is caused by translational forces of inertia applied to the element and appeared due to the nutational motion of the satellite.

To solve these problems a set of control methods are used. As example, the method based on the time averaging is discussed. The control algorithm does not depend on the spin axis direction. In the paper five algorithms were investigated. For a polar orbit the relay algorithm with switching every quarter of orbit was selected. Also another methods: a control algorithm for the polar orbit was developed; the Kalman filter is used for minimization of the angular error and a control algorithm is developed with the minimal power supply; the method of control proposed before is based on analysis the difference between required satellite momentum and the current one. We partially use this approach.

Let us consider two algorithms for coil control. The first algorithm requires an estimation of the angular velocity of the satellite. The latter does not require this information. The nutational damper usage is described here also. Results of computer simulation of the satellite attitude motion under magnetic control are represented.