balancing of an air-bearing-based acs test bed

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

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

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.

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

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

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]

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

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

BALANCING PLOTS

No balancing mass displacement overrun, max. 0.75 m

Tilt angle tends to 0°

No reaction wheel saturation, max. 4 Nms

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

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

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

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

THANK YOU FOR YOUR ATTENTION