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ALMA MATER STUDIORUM UNIVERSITA’ DI BOLOGNA SECONDA FACOLTA’ DI INGEGNERIA Sede di Forlì TESI DI LAUREA in Dinamica e Controllo d’ Assetto LM Candidato Marco Bosco Relatore Prof. Paolo Tortora Correlatore Ing. Valentino Fabbri Anno Accademico [2011 - 2012] Sessione II

MSc thesis presentation

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Page 1: MSc thesis presentation

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

Page 2: MSc thesis presentation

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

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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.

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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.

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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

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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

Page 7: MSc thesis presentation

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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

Page 8: MSc thesis presentation

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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

Page 9: MSc thesis presentation

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Uncontrolled Tumbling Motion

Filter re-initialization is needed after the eclipse period.

Without filter re-initialization With filter re-initialization

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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

Page 11: MSc thesis presentation

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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

Page 12: MSc thesis presentation

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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

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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.

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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°

Page 15: MSc thesis presentation

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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.

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Angle between the nadir and magnetic field vector Yaw angle error

Σ𝑒𝑟𝑟 = 𝜎12 + 𝜎2

2 + 𝜎32 + 𝜎4

2

Σ𝑒𝑟𝑟 = 𝜎𝜙2 + 𝜎𝜃

2 + 𝜎𝜓2

Page 17: MSc thesis presentation

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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.

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Page 19: MSc thesis presentation

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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.