Balancing of an air-bearing-based Acs Test Bed
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Balancing of air-bearing-based ACS Test Bed
Facoltà di Ingegneria Civile e IndustrialeCorso di Laurea in Ingegneria Spaziale e
Astronautica
Candidato:Cesare Pepponi
Relatore:Prof. Luciano IessCorrelatore:Ing. Mirco Junior Mariani
A.A. 2015/2016
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ACS TEST BED GENERAL DESCRIPTION
• It is a test bed for satellite ACS testing, with the goal of reproducing the space environment.
• It is composed by:– HELMHOLTZ COILS: to reproduce the Earth magnetic field the
satellite will meet along its orbit.
– MOVING SOLAR LAMP: to reproduce the Sun position WRT the satellite during its orbit.
– PLATFORM: to reproduce a frictionless environment with no external torques
This thesis focuses on the platformmass balancing
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MOTIVATIONS:My thesis aims at determine a mass balancing technique for an ACS test Bed with the following features: • The platform shall host satellites up to 50 kg.• Maximum tilt angle allowed: 40°.
GOALS:• Reduce, by a suitable balancing technique, the residual gravitational torque to a value lower than 10-4 Nm.
The residual gravitational torque is due to the offset between the CM and CR:
• Estimate the inertia (platform + S/C) matrix elements with an accuracy lower than 10-2 kgm2.
• Validate the model through Monte Carlo simulations.
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PLATFORM MASS DISTRIBUTIONThe elements composing the platform have been modeled as discrete, point-shaped, masses.
mass [kg] X [m] Y[m] Z[m]
Platform 20 0 0 0
Mx 20 XMx -0.75 0
My 20 -0.75 YMy 0
Mz 20 0.75 0.75 ZMz
mx 0.2 Xmx 0.75 0
my 0.2 0.75 Ymy 0
mz 0.2 -0.75 -0.75 Zmz
DUT 50 XDUT YDUT ZDUT
EQUATIONS OF MOTION
Quaternions are not affected by trigonometric singularities.
Mz
My
Mx
mx
mz
my
DUT
Platform
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SENSORSSensors that have to be implemented on the platform are:• 2 inclinometers;
• 1 triaxial gyroscope.
Resolution Noise Output data rate3.125·10-5 [rad] 10-4 [rad] RMS Up to 125 [Hz]
Resolution Random walk, σu White noise, σv
3.125·10-3 [rad/s] 10-4 [rad/s] 10-5 [rad/s2]
Farrenkopf model
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ACTUATORSActuators that have to be implemented on the platform are:• 3 Step motors, reduced, and connected to a 1mm pitch (p) threaded rod;
The mass displacement resolution is:
• 3 Reaction wheels.
Angular step size, αst
Max rotational speed Reduction, Red
1.8 [°] 2000 [rpm] 100
Max stored momentum Max torque4 [Nms] 0.06 [Nm]
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MASS BALANCING PROCEDUREGROSS MASS BALANCING
• Made by a manual adjustment of 20 kg masses• Masses adjustments are made upon a spacecraft CAD model and
platform properties• It aims at reducing the CM-CR distance to allow a correct fine
balancing
FINE MASS BALANCING
• It is driven by a PD control law fed by inclinometers readings• The mass displacement actuation is made by stepper motors
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INITIAL CONDITIONS• ωx = ωy = ωz = 0• αx = αx0
• αy = αy0
• Unbalanced• Stable equilibrium
TARGET αx=αY=0
PD SYSTEM
INCLINOMETER
αx , αy
FINAL MASS DISPLACEMENTXmass_x = A Ymass_y = B
EVALUATION OF Zmass_z DISPLACEMENT
BALANCETres < 10-4 Nm
FINE BALANCING PROCEDURE
STEPPER
NO
END
YES
PROPORTIONAL CONTROL DERIVATIVE CONTROL
Kyp= kxp = 0.02 Kyd =Kxd= 4
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BALANCING PLOTS
No balancing mass displacement overrun, max. 0.75 m
Tilt angle tends to 0°
No reaction wheel saturation, max. 4 Nms
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MONTECARLO SIMULATION FOR BALANCING METHOD VALIDATION
Two Monte Carlo simulations have been made to validate the method:
• MC simulation for overall method characterization, different initial conditions for every sample.
120 samples Mean Standard deviation
Residual torque [Nm] 2.91E-05 2.81E-05
Total balancing time [s] 1476 203
• MC simulation for method repeatability characterization, same initial conditions for every sample.
200 samples Mean Standard deviation
Residual torque [Nm] 7.52E-05 7.56E-06
Total balancing time [s] 1856 3.5
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LSE FOR INERTIA MATRIX DETERMINATION
The solution was obtained by a rearrangment of the system equations
• Π is the state vector:• Ψ is a function of gyroscopes’ readings• W is the weight matrix• P is a function of the torque applied
The system is observed for 30 s, no need for a gyroscope correction.
Problems arose:• Define a suitable torque waveform• Define a suitable weight matrix
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SIMULATION AND RESULTS
• The method was validated by a Monte Carlo simulation.• Monte Carlo results have been compared to those obtained by the covariance matrix corresponding to a singular simulation.
Monte Carlo 200 samplesReal Mean Std
Jxx [kgm2] 38.600 38.600 3.07E-03Jyy [kgm2] 38.571 38.571 4.28E-03Jzz [kgm2] 45.489 45.489 1.29E-03Jxy [kgm2] -11.436 -11.436 2.93E-03Jxz [kgm2] 11.212 11.212 1.52E-03Jyz [kgm2] 11.382 11.382 2.13E-03
Correlation matrix
1.00E+00 1.87E-01 1.20E-01 -5.02E-01 4.11E-01 -1.95E-01
1.87E-01 1.00E+00 1.33E-01 -5.01E-01 -2.07E-01 4.29E-01
1.20E-01 1.33E-01 1.00E+00 1.64E-01 4.29E-01 4.49E-01
-5.02E-01 -5.01E-01 1.64E-01 1.00E+00 1.51E-01 1.28E-01
4.11E-01 -2.07E-01 4.29E-01 1.51E-01 1.00E+00 -2.45E-01
-1.95E-01 4.29E-01 4.49E-01 1.28E-01 -2.45E-01 1.00E+00
Std from covariance matrix
Jxx [kgm2] 4.31E-03
Jyy [kgm2] 4.25E-03
Jzz [kgm2] 5.10E-03
Jxy [kgm2] 3.29E-03
Jxz [kgm2] 3.50E-03
Jyz [kgm2] 3.50E-03
• True value inside ±1σ• Std from LSE compliant to Std from Monte Carlo simulation• No correlation between estimated values
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CONCLUSIONSBy the balancing algorithm and the inertia matrix determination procedure have been obtained the following results:
• Residual torque lower than 10-4 Nm over 90% of the times.• Balancing time of 1450s ± 600s(3σ)• Inertia matrix determination accuracy lower than 1.5·10-2
kgm2 (3σ)
FUTURE WORK• Test the balancing procedure and the LSE technique on a
real ACS Test Bed
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THANK YOU FOR YOUR ATTENTION