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Using LMIs to optimize robustness of observer‐based state‐feedback for a synchrotron
Author(s) -
Gering Stefan,
Grieser Jochen,
Wahrburg Arne
Publication year - 2014
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3066
Subject(s) - control theory (sociology) , robustness (evolution) , observer (physics) , constant (computer programming) , state observer , output feedback , computer science , feedback control , mathematics , control engineering , control (management) , physics , nonlinear system , engineering , biochemistry , chemistry , quantum mechanics , artificial intelligence , gene , programming language
SUMMARY In this article, a synthesis method for linear systems subject to uncertain time‐varying parameters is proposed. Starting with the given values for the nominal parameters, the first objective is to find a constant state feedback such that the controlled system is stabilized and given dynamic specifications, such as a minimal decay rate, are met. In a second step, the constant feedback is then locally optimized such that the uncertain system parameters are allowed to vary around their nominal point as much as possible, whereas stabilization and dynamic specifications still hold. In addition, the procedure is extended toward observer‐based state feedback. Finally, this approach is applied to a synchrotron example, where the particle beam in longitudinal direction is to be stabilized and the coherent synchrotron frequency as well as the damping rate are uncertain. Copyright © 2013 John Wiley & Sons, Ltd.