Spacecraft Attitude Stabilization with Piecewise-constant Magnetic Dipole Moment Fabio Celani School of Aerospace Engineering

Outline •  •  •  •  • 

attitude control problem model of spacecraft with magnetorquers separation between measurement and actuation design of piecewise-constant control case study

Fabio Celani Sapienza University of Rome – RAST 2015

Page 2

Attitude control problem Z

spacecraft on a circular Low Earth Orbit

Geocentric Inertial (GCI) frame

body frame Y

X, !

objective: body frame aligned with GCI frame parametrize attitude of body frame with respect to GCI frame using quaternion vector part of body frame aligned with GCI frame Fabio Celani Sapienza University of Rome – RAST 2015

Page 3

Model of spacecraft with magnetorquers relative kinematics dynamics

spacecraft is equipped with three coils aligned with body axis vector of coils’ magnetic dipole moments geomagnetic field in body frame

spacecraft model

Fabio Celani Sapienza University of Rome – RAST 2015

Page 4

Control problem spacecraft model objective: design control law for

so that

and

PD-like feedback

locally exponentially stable [C., Lovera-Astolfi]

Fabio Celani Sapienza University of Rome – RAST 2015

Page 5

Separation between measurement and actuation not measurable measure of

set

Fabio Celani Sapienza University of Rome – RAST 2015

Page 6

Piecewise-constant control continuous control

piecewise-constant control

objective: design parameters

Fabio Celani Sapienza University of Rome – RAST 2015

so that

and

Page 7

Case study

circular orbit

inclination 87°

•  initial state

altitude 450 km



•  desired final state

Fabio Celani Sapienza University of Rome – RAST 2015

Page 8

Design of piece-wise constant control – step 1/3 design continuous control by trial-and-error

keep Fabio Celani Sapienza University of Rome – RAST 2015

for piecewise-constant control Page 9

Design of piece-wise constant control - step 2/3 determine

such that matrix

is stable for all

and fix

in case study pick

Fabio Celani Sapienza University of Rome – RAST 2015

Page 10

Design of piece-wise constant control - step 3/3 pick

sufficiently small where

in case study pick

Fabio Celani Sapienza University of Rome – RAST 2015

Page 11

Simulation

Fabio Celani Sapienza University of Rome – RAST 2015

Page 12

Conclusions •  attitude stabilization method for spacecraft using piecewise-constant magnetic dipole moment •  piecewise-constant attitude and attitude rate feedback •  piecewise-constant attitude only feedback (no rategyros) in conference proceedings

Fabio Celani Sapienza University of Rome – RAST 2015

Page 13

Spacecraft Attitude Stabilization with Piecewise ...

attitude control problem. • model of spacecraft with magnetorquers. • separation between measurement and actuation. • design of piecewise-constant control. • case study. Page 3. Attitude control problem. Fabio Celani. Sapienza University of Rome – RAST 2015. Page 3. X,. Y. Z. Geocentric Inertial (GCI) frame body frame.

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