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
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.
Jan 5, 2016 - Let Bi be the geomagnetic field at spacecraft expressed in inertial frame Fi. .... In order to simplify forthcoming expressions let us define â.
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 R
The book documents the development of the important ... determination and control systems. It provides ... Spacecraft Systems Engineering (Aerospace Series).
Sapienza University of Rome â DyCoSS 2014. Page 2. ⢠three-axis inertial pointing. ⢠model for spacecraft and geomagnetic field. ⢠spacecraft controllability.
verse directional unit vectors expressed in the body frame. Thus, ..... u D W QT .QWQT /¡1 Lrp ... Note that according to the condition number of the matrix C, the.
signed for spacecraft attitude tracking using Variable Speed Control Moment Gyros ... (2). (3). (4) where the 's denote the values of at . The symbol denotes the ..... are not physically meaningful since they may not preserve the orthogonality of ...
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Administration/ Goddard Space Flight Center Extensiye work has been done for ... this book, prepared by the Computer Sciences Corporation under the able direction of Dr. James Wertz, ... who need information on spacecraft orientation and how it is de
GeoCentric Inertial (GCI) frame body frame parametrize attitude of ... spacecraft with magnetorquers on a circular Low Earth Orbit body frame aligned with GCI ...
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Date: August, 2009. Key words and phrases. groupoids, stabilization, G-Hilbert modules, G-Hilbert ... any Hilbert (H, C0(Y ))-module P, there is an equivariant isomorphism of. Hilbert (H, C0(Y ))- ...... ãbi,biã converges in C0(Y ). By (3) and (4
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