MAGNETIC ATTITUDE CONTROL SYSTEMS OF
THE NANOSATELLITE TNS-SERIES
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
Phone: +7-(095)-250-7813, Fax: +7-(095)-972-0737, [email protected]
S. A.Selivanov
Russian Research Institute of Space Device Engineering
Aviamotornaya Street 53, Moscow 111024, Russia
Phone: +7-(095)-273-97091, Fax: +7-(095)-509-1200, [email protected]
ABSTRACT
The magnetic attitude control systems for TNS-series (Technology Nano Satellite) are
considered. The main attention is given to active magnetic attitude control system for
spin-stabilized nanosatellite TNS-1. The two algorithms are proposed. The first one uses
for its functioning the estimation of satellite orientation and estimation of angular
velocity. These measurements can be obtained by Sun sensor, magnetometer and
angular velocity sensor. The second algorithm uses Sun sensor and magnetometer only
and more suitable for TNS-1. However, the second algorithm is less accurate than first
one.
1. INTRODUCTION
While accuracy and time-response requirements dictated by the aim of a nanosatellite
are not very high, active or, sometimes, even passive magnetic attitude control systems
(MACS) are candidates to provide demanded attitude with intrinsical constrains and
limitations in size, mass and energetic capability. Those satellites considered in the
paper belong to the series of low-cost experimental nanosatellites purposed for middle
resolution remote sensing. Proposed approaches for their miniaturization including “onthe-shelf” technology require preliminary testing in space environment conditions.
Passive MACS provides simple attitude mode without reorientation possibility
during a mission with advantage of simplicity due to no need of sensors, active
actuators, calculator, energy etc. Its usual aim is to prevent the satellite from chaotic
tumbling. The first satellite of the TNS-series which is entitled TNS-0, is purposed to
test a capability of the satellite to use aq global satellite communication network to
transmit commands and to download a telemetry information to on-ground mission
control center. To prevent from chaotic tumbling after launching TNS-0 is equipped by
the passive MACS comprising a permanent magnet and soft-magnetic hystertesis rods.
Active MACS is quite more flexible. Comprising sensors, actuators, source of
energy, calculator with algorithms of attitude determination and control, MACS
provides a required attitude motion so that rather general motion variety requirements
can be satisfied by. The next in the TNS-series nanosatellite TNS-1 is equipped with the
active MACS. More or less standard set of three-axis magnetometer and sun-sensor is
used for attitude determination and three magnetorquers - to develop a control torque.
The satellite is spin-stabilized. Using active MACS we resolve the problems:
orientations with respect to the orbital plane normal, towards the Sun and spatial
reorientation regarding to the current purpose of remote sensing. To solve the problems
a set of controlling methods is usually used. The method based on the time averaging is
discussed in [1]. The control algorithm does not depend on the spin axis direction. For a
polar orbit the relay algorithm with switching every quarter of orbit was selected. In [2,
3] a control algorithm for the polar orbit was developed. The Kalman filter is used [4]
for minimization of the angular error and a control algorithm is developed with the
minimal power supply. The method of control proposed in [5] minimizes the difference
between required and current satellite momentum. We partially use this approach.
Let us consider two algorithms for attitude control. The first one uses, for its
functioning, the estimation of the satellite attitude and estimation of the angular velocity
[6]. The measurements are obtained by Sun sensor, magnetometer and angular velocity
sensor. The second algorithm uses Sun sensor and magnetometer only and it is more
suitable for TNS-1. However, the second algorithm is less accurate than first one.
2. THE FIRST ALGORITHM OF THE ATTITUDE CONTROL
According to the principal equation of attitude dynamics the derivative of the
momentum L is equal to the sum of effecting torques. Let the body be effected by the
magnetic torque only. Therefore, we can write
L& = m × B .
(1)
Assume three magnetorquers perpendicular each other are mounted on the satellite.
Suppose the magnetorquer with dipole moment m3 = m3 a3 alongwith the axis of
symmetry with unit vector a3 governs the spin axis direction. The magnetorquers with
dipole moments m1 = m1 a1 and m = m2 a 2 respectively are used for spin rate control
in spite of the magnetorquers develop the torque which effects the symmetry axis
direction too. The effect is considered as a disturbance of the symmetry axis direction
similarly to the gravity-gradient torque effect.
2.1 Attitude Control
Consider the momentum difference ∆L between the required momentum L f and the
current momentum L of the satellite as
∆L = L f − L .
(2)
Term “required momentum” means the momentum of the nominal (required by the
Customer) attitude motion of the satellite. Derive the control dipole moment m3
followinig the procedure of minimization of the square momentum difference. Consider
the time derivative of the square of momentum difference ∆L . We obtain
d (∆L) 2
d∆L
= 2∆L
= − 2∆L(m3 a3 × B ). Suppose the required momentum L f is a
dt
dt
constant vector in the inertial space. We require d ( ∆L) 2 / dt has to be a negative in
order to minimize a mismatch between required and current momentum. The following
magnitude of the dipole moment m3
m3 = mmax sign (∆L, a 3 , B )
(3)
where m max is a maximum dipole moment developed by magnetorquers ( mmax > 0 )
provides the necessary control. We use a notation for the mixed product of three
vectors (∆L, a 3 , B ) which means scalar product of the vector ∆L by the vector product
of two vectors B and a 3 .
2.2 Spin Rate Control
Similarly let us consider the momentum difference ∆L between the required
momentum L f and the current momentum L of the satellite. The required momentum
is defined by the following formula
L f = Ω3С a 3
(4)
where Ω3 is a required spin rate, С is a moment of inertia about the axis of symmetry
of the satellite. Consider the time derivative of the square of momentum difference ∆L
d (∆L) 2
d∆L
= 2∆L
= 2Ω f С∆L(ω × a3 ) − 2∆L(m1 a1 × B ) − 2∆L(m2 a 2 × B ).
(5)
dt
dt
We require the time derivative of the square of the momentum difference has to be
minimum. Using (5) we obtain the following control magnitudes for the magnetorquers
m1 = mmax sign (∆L, a1 , B ) ,
m2 = mmax sign (∆L, a 2 , B ) .
(6)
3. THE SECOND ALGORITHM OF ATTITUDE CONTROL
Similarly we suppose the magnetorquer with dipole moment m 3 = m3 a3 alongwith the
axis of symmetry with the unit vector a3 governs the spin axis direction and the
magnetorquers with dipole moments m1 = m1 a1 and m = m2 a 2 are used for the spin
rate control. Method which is described in the section does not require measurements of
a value of the angular velocity vector of the satellite. However, this method can be
applied for a satellite with high spin rate only, that is, for a, so called, satellitegyroscope. Momentum L of the axisymmetrical satellite can be written as follows
L = ω1 A a1 + ω2 Aa 2 + ω3 Ca3 where ω1 , ω2 , ω3 are projections of the angular velocity
vector in the body-fixed reference system, A , C are principle moments of inertia of the
satellite. We suppose ω3 >> ω1 , ω2 and write the approximate satellite momentum
L = ω3 Ca3 .
(7)
where a 3 is a unit vector along with the satellite symmetry axis.
3.1 Attitude Control
Let the required momentum L f be defined as
L f = ω 3 Ca 03
(8)
where unit vector a03 determines a required direction of the satellite’s axis of
symmetry. Substituting the expressions (7) and (8) in expression (3), we get control low
for the satellite-gyroscope m3 = mmax sign(ω 3 ) sign (a 03 , a 3 , B ) .
3.2 Spin Rate Control
Let the current satellite momentum L be defined by formula (7) and the required
momentum L f be defined as (4). Substitute these expressions into expressions (6) we
get control laws m1 = mmax sign(Ω 3 − ω 3 ) sign( B2 ) , m2 = −mmax sign(Ω 3 − ω 3 ) sign( B1 ) ,
where Ω 3 is required spin rate, and ω 3 is current satellite spin rate.
4. SUMMARY
Passive and active MACS described above are realized for the first two TNS-series
nanosatellites which are developped by the Russian Research Institute of Space
Device Engineering (RNII KP) in collaboration with the Keldysh Institute of Applied
Mathematics of RAS. The TNS-0 with passive MACS (Fig.1) is already prepared for
launching from ISS in 2005. Mock-up of TNS-1 with active MACS is shown in Fig.2.
Fig.1. TNS-0 (courtesy RNII KP)
Fig.2. TNS-1 (courtesy RNII KP)
5. REFERENCES
[1] Renard M.L., Command Laws for Magnetic Attitude Control of Spin-Stabilized Earth Satellites. J.
of Spacecraft and Rockets, Feb. 1967, v.4, N2, pp. 156-163.
[2] Wheeler P.C. Spinning Spacecraft Attitude Control via the Environmental Magnetic Field. J. of
Spacecraft and Rockets, Dec. 1967, v.4, N12, pp 1631-1637.
[3] Ergin E.I., Wheeler P.C., Magnetic Attitude Control of a Spinning Satellite. Journal of Spacecraft
and Rockets, 1965, v.2, N 6, pp.846-850.
[4] Sorensen J.A., A Magnetic Three-Degree of Freedom Attitude Control System for an Axisymmetric
Spinning Spacecraft, Journal of Spacecraft and Rockets, 1971 v.8, N5, pp 441-448.
[5] Shigehara M, Geomagnetic Attitude Control of an Axisymmetric Spinning Satellite, J. of Spacecraft
and Rocket, June 1972, v.9, N6, pp 391-398.
[6] Ilyin A.A., Ovchinnikov M.Yu. and Penkov V.I., Orientation Maintenance of the Small SpinStabilized Satellite, , Preprint of KIAM RAS, 2004, 28p.