1. Balancing of air-bearing-based
ACS Test Bed
Facoltà di Ingegneria Civile e Industriale
Corso di Laurea in Ingegneria Spaziale e
Astronautica
Candidato:
Cesare Pepponi
Relatore:
Prof. Luciano Iess
Correlatore:
Ing. Mirco Junior Mariani
A.A. 2015/2016
2. 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 platform
mass balancing
3. 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.
4. PLATFORM MASS DISTRIBUTION
The 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
5. SENSORS
Sensors that have to be implemented on the platform are:
• 2 inclinometers;
• 1 triaxial gyroscope.
Resolution Noise Output data rate
3.125·10-5 [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
6. ACTUATORS
Actuators 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 torque
4 [Nms] 0.06 [Nm]
7. MASS BALANCING PROCEDURE
GROSS 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
8. INITIAL CONDITIONS
• ωx = ωy = ωz = 0
• αx = αx0
• αy = αy0
• Unbalanced
• Stable equilibrium
TARGET
αx=αY=0
PD SYSTEM
INCLINOMETER
αx , αy
FINAL MASS DISPLACEMENT
Xmass_x = A Ymass_y = B
EVALUATION OF Zmass_z
DISPLACEMENT
BALANCE
Tres < 10-4 Nm
FINE BALANCING PROCEDURE
STEPPER
NO
END
YES
PROPORTIONAL CONTROL DERIVATIVE CONTROL
Kyp= kxp = 0.02 Kyd =Kxd= 4
9. BALANCING PLOTS
No balancing mass displacement overrun,
max. 0.75 m
Tilt angle tends to 0°
No reaction wheel saturation, max. 4
Nms
10. 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
11. 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
12. 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 samples
Real Mean Std
Jxx [kgm2] 38.600 38.600 3.07E-03
Jyy [kgm2] 38.571 38.571 4.28E-03
Jzz [kgm2] 45.489 45.489 1.29E-03
Jxy [kgm2] -11.436 -11.436 2.93E-03
Jxz [kgm2] 11.212 11.212 1.52E-03
Jyz [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
13. CONCLUSIONS
By 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
