In this paper, we consider model examples of dynamical systems with only a few degrees of freedom, and with desirable symmetry properties, and explore compensating control strategies for retaining robust symmetric system response even under symmetry-breaking defects. The analysis demonstrates the distinct differences between linear versions of these models, in which fault-compensating strategies are always found, and weakly nonlinear counterparts with varying degrees of asymmetry, for which a multitude of locally optimal solutions may coexist. We further formulate a candidate optimization protocol for fault compensation applied to self-healing systems, which respond to symmetry-breaking defects by a continuous process of fault correction. The analysis shows that such a protocol may exhibit discontinuous changes in the control strategy as the self-healing system successively regains its original symmetry properties. In addition, it is argued that upon return to a symmetric configuration, such a protocol may result in a different control strategy from that applied prior to the occurrence of a fault.
Accounting for Nonlinearities in Open-Loop Protocols for Symmetry Fault Compensation
ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (DETC2012-70387)
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received August 3, 2012; final manuscript received July 28, 2013; published online September 12, 2013. Assoc. Editor: Henryk Flashner.
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DiBerardino, L. A., and Dankowicz, H. (September 12, 2013). "Accounting for Nonlinearities in Open-Loop Protocols for Symmetry Fault Compensation." ASME. J. Comput. Nonlinear Dynam. April 2014; 9(2): 021002. https://doi.org/10.1115/1.4025193
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