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Spacecraft Formation Control for the Next Generation Gravity Mission
No full textThe expression ‘formation flying’ refers to a group of satellites performing their mission
objectives in a cooperative and coordinated way, to achieve an increased scientific return,
with respect to single-satellite systems. Formation flying concepts have been applied to
several classes of space missions, in the last decade.
In this thesis, we devoted our attention to the European next-generation space gravimetric
missions. After the successful European gravity mission GOCE, which provided a static
global map of the Earth’s gravity field, the European Space Agency has proposed several
preparatory studies for a Next Generation Gravity Mission (NGGM). It aims to measure the
temporal variations of the Earth’s gravity field, over a long time span, with an unprecedented
level of accuracy. NGGM will consist of a two-satellite long-distance drag-free formation, flying
in a polar orbit at a low-Earth altitude. Satellite-to-satellite distance variations, encoding
gravity anomalies, will be measured by laser interferometry.
This thesis explores the design, implementation, and simulation of the guidance, navigation,
and control system for the science phase of the NGGM mission; with a focus on
two baseline formation configurations: (i) in-line, and (ii) pendulum (slightly separated but
intersecting orbits). The control unit was designed according to the Embedded Model Control
methodology (EMC). EMC encompasses three model classes of the system to be controlled,
by means of the uncertainty description, which lead to the definition of the so-called Embedded
Model (EM). The EM is the core of the control unit, and its states drive the model-based
control law. The NGGM overall control architecture is organized in a hierarchical way, where
drag-free control plays the role of a wide-band inner loop, while the orbit/formation and the
attitude/pointing are narrow band outer loops. Such hierarchical control pursues a frequency
coordination among the several control tasks, to prevent inner/outer loops interference.
The drag-free control uses ultra-fine accelerometers to counteract the atmospheric drag,
making the satellite orbit ideally determined by the local gravity only. Thus, the EMC dragfree
architecture of the GOCE satellite was extended to accomplish the demanding NGGM
control performances. Further, the long-term formation stability requires an attitude, and an orbit and formation control counteracting bias and drift of the residual drag-free accelerations.
A pointing control was designed to reach the inter-satellite mutual alignment, via specific
optical sensors. As shown in this dissertation, since the drag-free control constrains the
pointing control, the attitude and the accelerometer measurements must be wisely coordinated.
Such hybridization, leading to a proper pointing performance, highlighted some criticality in
the preliminary scientific requirements. On the other side, the orbit and formation control
was addressed through an innovative control strategy, admitting large fluctuations around
the reference values due to the gravity effect (loose control), and with a continuous control
action, to respect the drag-free requirements. Further, the orbit and formation dynamics were
integrated into a unique model, through the formation triangle concept. A multi-rate and
hierarchical control law, designed with care to reduce as much as possible the demanded
thrust, completes the formation controller, actuated by millinewton-range electric thrusters.
Concerning the pendulum formation configuration, an effort has been spent to demonstrate
that it can be affected by some peculiar dynamic effects, coherently with the semi-aperture
angle. This analysis led to an on-purpose designed roll compensation control law.
Simulated results, from a long-run campaign via a high-fidelity simulator, prove the
concept validity and show that the control strategy is capable of keeping the attitude and
formation variables stable, through a few millinewton thrust authority.
Finally, in this thesis, an optimisation-based worst-case analysis framework was applied to
the drag-free formation, finalized at the verification and validation of the control performance.
Specifically, this preliminary study tried to evaluate the optimization-based methods and
tools for enhancing the performance verification process, in a complex and highly uncertain
mission scenario. The first preliminary simulated results indicate that it could be possible to
improve the controller performance according to the worst-case expected behaviour, due to
possible system uncertainties and environmental condition variations.
Future work should address the suggested theoretical developments of the integrated
formation model, while the highlighted critical points of the current design should be tackled,
also considering the devised strategies and system reassessments. Yet, the current preliminary
worst-case analysis should be extended to the entire AOCS
Angular drag-free control and fine satellite-to-satellite pointing for the Next Generation Gravity Missions
No full textThe paper presents the design and the simulated results of the attitude control of a two-satellite formation under study by the European Space Agency for the Next Generation Gravity Mission. The formation spacecrafts, distant more than 200 km and Earth orbiting at about 300 km altitude, must align their axis to the satellite-to-satellite line (SSL) with a microradian accuracy (pointing control). This is made possible by specific optical sensors accompanying the inter-satellite laser interferometer, capable of materializing the SSL. Such sensors allow each satellite to autonomously align after an acquisition procedure. Pointing control is severely constrained by the angular drag-free control, which is imposed by Earth gravimetry (science), and must zero the spacecraft angular acceleration vector below 0.01 microradian/s2 in the science bandwidth. This is made possible by the ultrafine accelerometers whose measurements must be coordinated with attitude sensors to meet drag-free and pointing requirements. Embedded Model Control shows how naturally coordination can be implemented around the embedded model of the spacecraft attitude and of the formation frame quaternion
Embedded model control: Reconciling modern control theory and error-based control design
No full textThe paper addresses the problem of reconciling the modern control paradigm developed by R. Kalman in the sixties of the past century, and the centenary error-based design of the proportional, integrative and derivative (PID) controllers. This is done with the help of the error loop, whose stability is proved to be necessary and sufficient for the close-loop plant stability. The error loop is built by cascading the uncertain plant-to-model discrepancies (causal, parametric, initial state, neglected dynamics), which are driven by the design model output and by arbitrary bounded signals, with the control unit transfer functions. The embedded model control takes advantage of the error loop and its equations to design appropriate algorithms of the modern control theory (state predictor, control law, reference generator), which guarantee the error loop stability and performance. A simulated multivariate case study shows modeling and control design steps and the coherence of the predicted and simulated performance
ORBIT AND FORMATION CONTROL FOR LOW-EARTH-ORBIT GRAVIMETRY DRAG-FREE SATELLITES
Full text linkThe paper outlines orbit and formation control of a long-distance (>100 km) two-satellite formation for the Earth gravity monitoring. Modeling and control design follows the Embedded Model Control methodology. We distinguishe be-tween orbit and formation control: orbit control applies to a single satellite and performs altitude control. Formation control is formulated as a control capable of altitude and distance control at the same time. The satellites being placed in a low Earth orbit, orbit and formation control employ the measurements of a global navigation system. Formation control is imposed by long-distance laser interferometry, which is the key instrument together with GOCE-class accelerometers for gravity measurement. Orbit and formation control are low-frequency control systems in charge of cancelling the bias and drift of the residual drag-free accelerations. Drag-free control is the core of orbit/formation control since it makes the formation to fly drag-free only subject to gravity. Drag-free is demanded by the low-Earth orbit and by the accelerometer systematic errors. Drag-free control being required to have a bandwidth close to 1 Hz, is designed as the inner loop of the formation control, but formation control must not destroy drag-free performance, which is obtained by restricting formation control to be effective only below orbital frequency. A control of this kind appears to be original: an appropriate orbit and formation dynamics is derived, discussed and compared with the classical Hill-Clohessy-Wiltshire equations. The derived dynamics is the first step to build the embedded model which is sampled at the orbit rate. Embedded model derivation is explained only for the orbit control, and briefly mentioned for the formation control. Control design is explained in some details, pointing out reference generation, state predictor, control law and main design steps. Simulated results are provided. Drag free results are compared to GOCE data
Satellite-to-satellite attitude control of a long-distance spacecraft formation for the Next Generation Gravity Mission
Full text linkThe paperpresentsthedesignandsomesimulatedresultsoftheattitudecontrolofasatelliteformation
under studybytheEuropeanSpaceAgencyfortheNextGenerationGravityMission.Theformation
consists oftwospacecraftswhich fly morethan200kmapartatanaltitudefromtheEarth'sgroundof
between 300and400km.Theattitudecontrolmustkeeptheopticalaxesofthetwospacecraftaligned
with amicroradianaccuracy(pointingcontrol).Thisismadepossiblebyspecific opticalsensors
accompanyingtheinter-satellitelaserinterferometer,whichisthemainpayloadofthemission.These
sensors alloweachspacecrafttoactuateautonomousalignmentafterasuitableacquisitionprocedure.
Pointing controlisconstrainedbytheangulardrag-freecontrol,whichisimposedbymissionscience
(Earth gravimetryatalowEarthorbit),andmustzerotheangularaccelerationvectorbelow0.01 μrad/s2
in thesciencefrequencyband.Thisismadepossiblebyultrafine accelerometersfromtheGOCE-class,
whose measurementsmustbecoordinatedwithattitudesensorstoachievedrag-freeandpointing
requirements.EmbeddedModelControlshowshowcoordinationcanbeimplementedaroundthe
embedded modelsofthespacecraftattitudeandoftheformationframequaternion.Evidenceand
discussion aboutsomecriticalrequirementsarealsoincludedtogetherwithextensivesimulatedresults
of twodifferentformationtypes
Model Description and Simulated Mission Performance of the Next Generation Gravity Mission E2E Simulator
No full textIn the years to come, Earth observation via remote sensing will enter into a new era, characterized by a
growing number of advanced and sophisticated satellite missions. They will provide scientists with an
unprecedented capacity to observe and monitor the Earth’s mass transport and its inner physical phenomena.
Following the two successful missions GOCE and GRACE, gravity missions have acquired a great importance
within the ESA Earth Observation Programmes directorate. Indeed, a Next Generation Gravity Mission
(NGGM) concept for measuring the variability of the Earth’s gravity field is proposed, whose objectives will be
very challenging in terms of spatial and temporal resolution. The baseline measurement technique will be a
laser interferometry system via low-low satellite-to-satellite tracking. This space segment will be based on two
drag-free satellites, flying in loose formation in LEO, equipped with a very accurate accelerometer-based
sensing system. The mission concepts and architectures have been implemented in an End-to-End (E2E) multimissions
simulation tool, an evolving simulator platform for the NGGM concept. The paper presents a
description of the main subsystem models of the software simulating a typical NGGM mission scenario, giving
particular attention to the mathematical expression of the relevant embedded models. Considered the specific
thorny points of the mission (the 10 years duration, above all), particular attention is given to the environmental
models, the ion thrusters’ assembly and the drag-free, attitude and orbit control algorithms. In addition, for a
complete validation of the software, series of sensitivity tests have been carried out, mostly involving the
gradiometer, the optical metrology and ion thrusters’ models. These tests have pointed out the different levels of
compliance of the simulated NGGM scenarios against the preliminary mission requirements. Therefore, in the
last part of the paper, a set of guidelines for the enhancement of the control algorithms will be provided, in
order to allow an optimal fitting of the E2E simulator with the latest mission concepts of NGGM
The LISA DFACS: A nonlinear model for the spacecraft dynamics
Full text linkIn the last few years, the observation of gravitational waves by means of LIGO and Virgo interferometers and the success of LISA Pathfinder, gave a significant boost to the development of space-based gravitational wave observatories. The European Space Agency confirmed LISA as the third large class mission of the Cosmic Vision program. The present work is part of the Drag Free and Attitude Control System (DFACS) preliminary prototyping study, which aims at the development of mathematical models and advanced controllers for the science phases of the LISA mission. Nonlinear modelling is a fundamental step for the derivation of linearized and decoupled models as well as for the development of suitable linear and nonlinear controllers. In this paper, an analytical nonlinear model is derived, which describes all the relevant dynamics of a LISA spacecraft, representing an effective compromise between accuracy and complexity. The model is extensively validated through linearization analysis and Monte Carlo simulations
Long-distance, low-Earth-orbit, drag-free integrated orbit and formation control for the Next Generation Gravity Mission
No full textThe Next Generation Gravity Mission (NGGM) under study by the European Space Agency, will take advantage of the previous gravimetry missions GOCE [1] and GRACE [2], and will consists of a two-satellite long-distance formation like GRACE where each satellite will be controlled to be drag-free like GOCE [3]. As a significant advancement, satellite-to-satellite distance variations, encoding gravity anomalies, will be measured by laser interferometry with an accuracy improvement of at least three orders of magnitude with respect to GRACE radiometric measurements [4]. The formation will fly in a polar orbit at an Earth altitude between 300 and 400 km, which requires drag cancellation (drag-free control) and orbit/formation control. Drag-free control uses the ultrafine accelerometers of the GOCE mission. Orbit and formation control use the receivers of a Global Navigation System (GNS) mounted on each satellite and a suitable satellite interlink. Orbit and formation actuators have been selected among millinewton electric thrusters. Two kinds of formation have been studied: in line formation where the two satellites move on the same polar orbit, and pendulum formation where the satellites move on RAAN separated orbits.
The paper focuses on the orbit and formation control, whose aim is the orbit and formation long-term stability (> 10 years) though admitting large 'natural' fluctuations around the reference values. Drag-free control by itself, being an acceleration control, is not capable of achieving orbit and formation stability, although the non-gravitational acceleration residuals must be very small and bounded. The reason is that Hill's perturbation equations (orbit and formation) are not bounded-input-bounded-output (BIBO) stable (longitudinal and radial components), and position/velocity feedback becomes mandatory.
The design of the control loop presented here appears not conventional for different reasons. Firstly it must not alter the zero-mean near-periodical free response of the local gravity field, but it must only zero the 'secular' free response components (bias, drift) and stabilize the perturbed dynamics to achieve BIBO stability. Stabilization programs of this sort are implemented by ground stations through impulsive commands and aim to stabilize orbit altitude (as for GOCE [5]) and to achieve and stabilize formations. Secondly we look for a 'continuous' control with the aim of respecting drag-free residuals above 1 mHz, where gravity anomalies should be detected. A stepwise command changing each orbit has been proved being capable of stabilizing orbit and formation without degrading drag-free residuals. The relevant perturbed dynamics sampled at the orbit period has been proved to allow controllability of the required variables. Third, orbit and formation con-trol have been integrated in a unique three degrees-of-freedom (DoF) control system, aiming at stabilizing the 'formation triangle' consisting of the satellite CoMs and of the Earth CoM. The three degrees are the formation distance, the formation radius and the non orthogonality (it expresses the difference between the satellite orbit altitudes). Other degrees to be controlled, but not treated here are yaw and roll rates.
Control has been designed using the Embedded Model control methodology [6] and is organized in a hierarchical way where drag-free plays the role of wide-band inner loop, and orbit/formation control plays the role of narrow band, under-sampled outer loop. The paper will start with the formation triangle dynamic model, which is credited to be a new set of formation perturbation equations. They will be converted to discrete time to obtain the embedded model part of the control unit. State predictor, control law and reference generator are built on and interface to the embedded model. Simulated results proving the control performance are provided
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