A unified method for optimal arbitrary pole placement
Abstract
We consider the classic problem of pole placement by state feedback. We offer an eigenstructure assignment algorithm to obtain a novel parametric form for the pole-placing feedback matrix that can deliver any set of desired closed-loop eigenvalues, with any desired multiplicities. This parametric formula is then exploited to introduce an unconstrained nonlinear optimisation algorithm to obtain a feedback matrix that delivers the desired pole placement with optimal robustness and minimum gain. Lastly we compare the performance of our method against several others from the recent literature.
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This is the author’s version of a work that was accepted for publication in the Journal, Automatica. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Automatica, Volume 50, Issue 8, August 2014, Pages 2150–2154. http://doi.org/10.1016/j.automatica.2014.06.006
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Schmid, R.; Ntogramatzidis, Lorenzo; Nguyen, T.; Pandey, A. (2013)We consider the classic problem of pole placement by state feedback. Recently [1] offered an eigenstructure assignment algorithm to obtain a novel parametric form for the pole-placing gain matrix to deliver any set of ...