dc.contributor.author | Blanchard, Antoine | |
dc.contributor.author | Mowlavi, Saviz | |
dc.contributor.author | Sapsis, Themistoklis P | |
dc.date.accessioned | 2021-09-20T17:30:15Z | |
dc.date.available | 2021-09-20T17:30:15Z | |
dc.date.issued | 2018-12-17 | |
dc.identifier.uri | https://hdl.handle.net/1721.1/131784 | |
dc.description.abstract | Abstract
Identification and control of transient instabilities in high-dimensional dynamical systems remain a challenge because transient (non-normal) growth cannot be accurately captured by reduced-order modal analysis. Eigenvalue-based methods classify systems as stable or unstable on the sole basis of the asymptotic behavior of perturbations and therefore fail to predict any short-term characteristics of disturbances, including transient growth. In this paper, we leverage the power of the optimally time-dependent (OTD) modes, a set of time-evolving, orthonormal modes that capture directions in phase space associated with transient and persistent instabilities, to formulate a control law capable of suppressing transient and asymptotic growth around any fixed point of the governing equations. The control law is derived from a reduced-order system resulting from projecting the evolving linearized dynamics onto the OTD modes and enforces that the instantaneous growth of perturbations in the OTD-reduced tangent space be nil. We apply the proposed reduced-order control algorithm to several infinite-dimensional systems, including fluid flows dominated by normal and non-normal instabilities, and demonstrate unequivocal superiority of OTD control over classical modal control. | en_US |
dc.publisher | Springer Netherlands | en_US |
dc.relation.isversionof | https://doi.org/10.1007/s11071-018-4720-1 | en_US |
dc.rights | Creative Commons Attribution-Noncommercial-Share Alike | en_US |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | en_US |
dc.source | Springer Netherlands | en_US |
dc.title | Control of linear instabilities by dynamically consistent order reduction on optimally time-dependent modes | en_US |
dc.type | Article | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mechanical Engineering | |
dc.eprint.version | Author's final manuscript | en_US |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
dc.date.updated | 2020-09-24T20:38:48Z | |
dc.language.rfc3066 | en | |
dc.rights.holder | Springer Nature B.V. | |
dspace.embargo.terms | Y | |
dspace.date.submission | 2020-09-24T20:38:48Z | |
mit.license | OPEN_ACCESS_POLICY | |
mit.metadata.status | Authority Work and Publication Information Needed | |