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Stability‐ and performance‐robustness tradeoffs: MIMO mixed‐µ vs complex‐µ design
Author(s) -
Vasconcelos J. F.,
Athans M.,
Fekri S.,
Silvestre C.,
Oliveira P.
Publication year - 2009
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.1299
Subject(s) - control theory (sociology) , robustness (evolution) , singular value , frequency domain , stability (learning theory) , mimo , singular value decomposition , computer science , mathematics , algorithm , control (management) , channel (broadcasting) , biochemistry , chemistry , eigenvalues and eigenvectors , physics , quantum mechanics , artificial intelligence , machine learning , gene , computer vision , computer network
We present a non‐trivial case study designed to highlight some of the practical issues that arise when using mixed‐µ or complex‐µ robust synthesis methodologies. By considering a multi‐input multi‐output three‐cart mass–spring–dashpot (MSD) with uncertain parameters and dynamics, it is demonstrated that optimized performance (disturbance‐rejection) is reduced as the level of uncertainty in one or two real parameters is increased. Comparisons are made (a) in the frequency domain, (b) by RMS values of key signals and (c) in time‐domain simulations. The mixed‐µ controllers designed are shown to yield superior performance as compared with the classical complex‐µ design. The singular value decomposition analysis shows the directionality changes resulting from different uncertainty levels and from the use of different frequency weights. The nominal and marginal stability regions of the closed‐loop system are studied and discussed, illustrating how stability margins can be extended at the cost of reducing performance. Copyright © 2008 John Wiley & Sons, Ltd.