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Shock and Vibration
Volume 19 (2012), Issue 5, Pages 947-956

Design of a Nonlinear Controller for a Rigid-Flexible Satellite Using Multi-Objective Generalized Extremal Optimization with Real Codification

I. Mainenti-Lopes, L.C.G. Souza, and F.L. De Sousa

National Institute for Space Research, Space Mechanics and Control Division, São Jose dos Campos, SP, Brazil

Received 25 April 2012; Accepted 25 April 2012

Copyright © 2012 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Attitude Control System (ACS) for Flexible Space Structures (FSS) like rigid-flexible satellite and solar sails demands great reliability, autonomy and robustness. The association of flexible motion and large angle maneuver imply that the FSS dynamics is only captured by complex non-linear mathematical model. As a result, FSS controller performance designed by linear control technique under the hypothesis of rigid dynamic can be degraded. Although vibrations can be suppressed rapidly, the flexibility effect can introduce a tracking error resulting in a minimum attitude acquisition time. On the other hand, faster manoeuvres can excite flexible modes in such a way to make the FSS lose the required pointing accuracy. In the present work, it is shown that a new multi-objective optimization algorithm, called M-GEOreal (Multi-objective Generalized Extremal Optimization with real codification), is a good tool to be used in such kind of problems. The M-GEOreal is a real coded version of the M-GEO evolutionary algorithm. Its performance on finding the gains of a non linear control law is evaluated through its application to the problem of controlling a large angle attitude manoeuvre of a rigid-flexible satellite.. The satellite non-linear model consists of a rigid central hub with a clamped free flexible beam. The multi-objective approach allows optimizing conflicting objective functions like time and energy. As a result, one can find a trade-off solution (non-dominated solutions). These solutions become available to the designer for posterior choice of an individual solution to be implemented. The non-dominated solutions are represented in the design space (Pareto set) and in the objective functions space (Pareto front). Having in mind the complexity of implementing a control algorithm in onboard satellite computer, this preliminary investigation has shown that the non-linear controller based on the M-GEOreal algorithm is a promising technique, since it has satisfied all the ACS requirements. A great advantage of the M-GEOreal procedure is its capacity to deal with non-linear system and designing non-linear controller with constant gains facilitating the on board computer implementation.