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ALMA MATER STUDIORUM – UNIVERSITA’ DI BOLOGNA
SECONDA FACOLTA’ DI INGEGNERIA Sede di Forlì
TESI DI LAUREAin
Dinamica e Controllo d’ Assetto LM
CandidatoMarco Bosco
RelatoreProf. Paolo Tortora
CorrelatoreIng. Valentino Fabbri
Anno Accademico [2011-2012]Sessione II
2/28226/03/2015Safety Systems for Small Satellites
Uncontrolled Tumbling Motion
ALMASat-EO mission
ALMASat-1 tumbling motion
Mission Simulator
Angular rate damping using hysteresis rods
Angular rate estimation using solar cells output currents
Attitude estimation using a multi-rate Kalman filter
Conclusion and Future work
3/28326/03/2015Safety Systems for Small Satellites
Uncontrolled Tumbling Motion
Mission requirements Earth observation for weather monitoring and
surveillance Images of the Earth’s surface with an area of 150 km² Off-nadir pointing Tray-based structure for the optical payload and the
main on-board equipment
Orbital analysisOrbit definition to have the best light conditions to take images: Low circular orbit: height 686 km Sun-synchronous orbit 10:30 am/10:30 pm
LaunchIt will be placed into orbit by the European launch vehicle, VEGA.
4/28426/03/2015Safety Systems for Small Satellites
Uncontrolled Tumbling Motion
A non-nominal separation of ALMASat-1 from the VEGA launcher led the satellite to tumble with an angular rate of ~102 °/𝑠.
The non-nominal separation waslikely due to a possibledifferential opening time of theADapter and Separation Systemclamps.
The angular velocity wasestimated by using advancedimage pattern matchingtechniques and a virtual modelof ALMASat-1.
5/28526/03/2015Safety Systems for Small Satellites
Uncontrolled Tumbling Motion
The mission simulator is MATLAB/Simulink-based software and several mathematical models are implemented in order to simulate the space environment. Also, a numerical integrator is used to propagate the orbital motion and to predict the ALMASat-EO attitude.
𝑞 =1
2Ω𝑞
𝐽 𝜔 = 𝑀𝑒𝑥𝑡 −𝑑ℎ
𝑑𝑡− 𝜔 × 𝐽𝜔 + ℎ
Quaternion kinematic equation
Rigid body dynamic equation
External torques
Aerodynamic Magnetic Gravity Gradient Solar Radiation Thrusters
6/28626/03/2015Safety Systems for Small Satellites
Uncontrolled Tumbling Motion
MUMETALL Value Unit
Saturation induction 𝐵𝑠 0.8 𝑇
Coercivityforce 𝐻𝑐
1.5 𝐴/𝑚
Remanence 𝐵𝑟 0.35 𝑇
Maximum energy lossper volume over a full
cycle Δ𝐸
1.2 𝐽/𝑚3
Density 𝜌 8.7 𝑔/𝑐𝑚3
Element Ni Cu Mo Fe others
Percentage 76.6% 4.5% 3.3% 14.7% Mn, Si
𝑚ℎ𝑦𝑠𝑡 =𝐵𝑛𝑉
𝜇0
𝑇ℎ𝑦𝑠𝑡 = 𝑚ℎ𝑦𝑠𝑡 × 𝐵𝐵 =
2𝐵𝑠𝜋
tan−1 𝑘 𝐻 ± 𝐻𝑐
Flatley and Henretty empirical model
𝑘 =1
𝐻𝑐tan
𝜋𝐵𝑟2𝐵𝑠
7/28726/03/2015Safety Systems for Small Satellites
Uncontrolled Tumbling Motion
𝐼𝑚𝑒𝑎𝑠,𝑖
𝐼𝑚𝑎𝑥,𝑖= cos𝛼𝑖
𝐼𝑇 = 𝐼 +𝑑𝐼
𝑑𝑇 𝑇 − 𝑇𝑟𝑒𝑓
𝜔 = 𝐽−1 −𝜔 × 𝐽𝜔 + 𝜉 → 𝑥𝑘+1 = Φ𝑘𝑥𝑘 + 𝑢𝑘
𝜕𝑏
𝜕𝑡≈ −𝜔 × 𝑏 → 𝑧𝑘 = 𝐻𝑘𝑥𝑘 + 𝑛𝑘
Solar cells currents cosine law
Temperature correction
Extended Kalman filter (EKF)
Dynamic model
Observation model
28% Triple Junction GaAs Solar Cellby AzurSpace
Projection of the Sun LOS vector measured by solar cells mounted on opposite looking directions along the three orthogonal body axes
Solar cells in short-circuit mode are used as a coarse Sun sensor
8/28826/03/2015Safety Systems for Small Satellites
Uncontrolled Tumbling Motion
To statistically validate the algorithm, 1000 simulations are run randomly varying: Initial angular velocity vector. Right ascension of the ascending node (RAAN). Initial position along the orbit.Each simulation lasts one orbital period.
Mean of the error Standard deviation of the error
9/28926/03/2015Safety Systems for Small Satellites
Uncontrolled Tumbling Motion
Filter re-initialization is needed after the eclipse period.
Without filter re-initialization With filter re-initialization
10/281026/03/2015Safety Systems for Small Satellites
Uncontrolled Tumbling Motion
Angular rate estimation in the worst-case scenario
For very low elevation angles (< 5°) of the Sun rays on the solar cells the current cannot be disentangled from noise → If the angular velocity vector is nearly parallel to the Sun LOS vector the angular rate cannot be accurately estimated.
Angle between the angular velocity vector and the Sun LOS vector
11/281126/03/2015Safety Systems for Small Satellites
Uncontrolled Tumbling Motion
The new arrangement consists of solar cellsmounted on inclined planes ≅ 10° to ensure
an accurate Sun position estimation.
Solar cells arrangement on ALMASat-EO
Cone intersections on the unity celestial sphere to estimate the Sun
LOS vector
𝑆𝑏 ∙ 𝑛𝑖 = 𝛼𝑖
𝑆𝑏 ∙ 𝑛𝑗 = 𝛼𝑗
𝑆𝑏𝑇∙ 𝑆𝑏 = 1
12/281226/03/2015Safety Systems for Small Satellites
Uncontrolled Tumbling Motion
Comparison between the standard and the new solution in terms of
Angular velocity estimation using the new solution for the worst-case scenario.
Standard solution New solution
𝛴𝑒𝑟𝑟𝑜𝑟 = 𝜎𝑥2 + 𝜎𝑦
2 + 𝜎𝑧2
13/281326/03/2015Safety Systems for Small Satellites
Uncontrolled Tumbling Motion
Multi – rate Fault detection and isolation Better precision and faster convergence speed than F.E.K.F.
An accurate attitude estimation is necessary to guarantee the spacecraft pointing accuracy as prescribed by the mission requirements.
14/281426/03/2015Safety Systems for Small Satellites
Uncontrolled Tumbling Motion
ALMASat-EO is three-axis stabilized Attitude quaternion error
Euler angles error
The yaw angle error is larger since the Earth horizon sensor is poor in yaw.
Euler angles Roll 𝜙 Pitch 𝜃 Yaw 𝜓
Mean of the error 0.0003° −0.0560° −0.0149°
Std of the error 0.1066° 0.1013° 0.2404°
15/281526/03/2015Safety Systems for Small Satellites
Uncontrolled Tumbling Motion
To fully validate the F.U.K.F., Monte Carlo simulations are performed. Each simulation lasts two orbital period once the satellite is 3-axis stabilized.
16/281626/03/2015Safety Systems for Small Satellites
Uncontrolled Tumbling Motion
Angle between the nadir and magnetic field vector Yaw angle error
Σ𝑒𝑟𝑟 = 𝜎12 + 𝜎2
2 + 𝜎32 + 𝜎4
2
Σ𝑒𝑟𝑟 = 𝜎𝜙2 + 𝜎𝜃
2 + 𝜎𝜓2
17/281726/03/2015Safety Systems for Small Satellites
Uncontrolled Tumbling Motion
New solutions for the attitude determination and control subsystem (ADCS) have been studied, implemented and statistically validated by Monte Carlo simulations:
The hysteresis rods can be used as a passive magnetic angular rate damping system.
The angular rate estimation using solar cells output currents can be used in tumbling motion.
The attitude is accurately computed in nominal conditions by a F.U.K.F.
The hysteresis rods, solar cells and the gyroscope require an experimental characterization.
The angular rate and attitude estimation algorithms need to be run in hardware-in-the-loop simulations to have more realistic performance information.
19/281926/03/2015Safety Systems for Small Satellites
Uncontrolled Tumbling Motion
The filter is less accurate for high angular velocities.
A satellite can tumble with a predominant high angular velocity around its
maximum and minimum principal axis of inertia.