Spacecraft Attitude Stabilization using Magnetorquers with Separation between Measurement and Actuation Fabio Celani School of Aerospace Engineering

Outline • 

attitude stabilization problem

• 

model of spacecraft with magnetorquers

• 

separation between measurement and actuation

• 

design of feedback with separation constraint

• 

case study

Fabio Celani AIAA SciTech 2016

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Attitude stabilization problem spacecraft with magnetorquers on a circular Low Earth Orbit Z

GeoCentric Inertial (GCI) frame

body frame X,

Y

objective: stabilize spacecraft’s attitude using only magnetorquers so that body frame is 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 AIAA SciTech 2016

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Spacecraft model attitude kinematics attitude dynamics

magnetorquers = three coils aligned with body axis vector of coils’ magnetic dipole moments geomagnetic field in body frame

spacecraft model

Fabio Celani AIAA SciTech 2016

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Stabilization problem spacecraft model

objective: design control law for

so that

is stabilized PD-like feedback

locally exponentially stable [C., Lovera and Astolfi]

Fabio Celani AIAA SciTech 2016

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Separation between measurement and actuation if magnetometers are close to magnetorquers not measured measure of

objective of the present work: design feedback compatible with separation constraint Fabio Celani AIAA SciTech 2016

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Feedback compatible with separation constraint continuous feedback

feedback compatible with separation constraint

Fabio Celani AIAA SciTech 2016

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Closed-loop system spacecraft model feedback compatible with separation constraint

determined by length of measurement process (not a control design parameter) objective: find algorithm for determining so that is stable for closed-loop dynamics closed-loop dynamics given by sampled-data nonlinear time-varying system Fabio Celani AIAA SciTech 2016

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Stability of closed-loop system stability of sampled-data nonlinear time-varying system principle of stability in the linear approximation [Mancilla Aguilar and Garcia] stability of sampled-data linear time-varying system restrict to sampling times only [Iglesias] stability of discrete-time linear time-varying system averaging theory for discrete-time systems [Bai et al.] stability of discrete-time linear time-invariant system

algorithm for determining Fabio Celani AIAA SciTech 2016

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Case study

circular orbit

inclination 87 deg

altitude 450 km

measurement time

Fabio Celani AIAA SciTech 2016

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Algorithm for feedback’s parameters 1/4 design continuous feedback by trial-and-error initial state

keep Fabio Celani AIAA SciTech 2016

for feedback with separation constraint Page 11

Algorithm for feedback’s parameters 2/4 determine

such that matrix

is stable for all

in case study

Fabio Celani AIAA SciTech 2016

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Algorithm for feedback’s parameters 3/4 determine

for each

= maximum value of fix

for which stability can be achieved

so that

it must be in case study

fix Fabio Celani AIAA SciTech 2016

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Algorithm for feedback’s parameters 4/4 pick

where

in case study pick

Fabio Celani AIAA SciTech 2016

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Simulations 1/2

initial state

Fabio Celani AIAA SciTech 2016

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Simulations 2/2

initial state include gravity gradient and residual magnetization torques

Fabio Celani AIAA SciTech 2016

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Conclusions • 

magnetic attitude stabilizing feedback compatible with separation constraint between measurement and actuation

• 

algorithm for determining feedback’s parameters

• 

feedback design validated through a case study

Fabio Celani AIAA SciTech 2016

Page 17

Spacecraft Attitude Stabilization using Magnetorquers ...

determined by length of measurement process (not a control design parameter) ... closed-loop dynamics given by sampled-data nonlinear time-varying system.

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