Frequency domain based performance optimization of systems with static nonlinearities

Frequency Domain Based Performance Optimization of Systems with Static Nonlinearities The widespread acceptance and applicability of frequency domain techniques for linear and time invariant systems has been an impetus for the extension of these methodologies towards nonlinear systems. However, although the application of fre¬quencydomain methodsforthe analysis, modelingand control of nonlinear systems can beadvantageous it isgenerallynotstraightforward. Thiswork contributestothis ?eld by providing connections between di?erent frequency domain methods for nonlinear systems using new analytical results with an application to spectral analysis of block structured systems. Furthermore, practically applicable results that allow frequency domain based performance optimization of nonlinear systems are presented. The ?rst part of the thesis deals with the analysis of nonlinear e?ects in the frequencydomain. Thecontributionof thispartistwofold:First,acomparative litera¬ture review and new analytical results are used to connect di?erent, existing frequency domain methods for nonlinear systems. Second, new analytical results are presented that allow spectral analysis ofparallelpolynomialWiener-Hammerstein systems. This yields insight inthemechanismthatgeneratesnonlineare?ects inthefrequencydomain and provides a numerically e?cient method to compute these e?ects. In the second part of the thesis, a novel frequency domain based approach for detection,quanti?cation andoptimal compensation ofperformancedegrading nonlinear e?ects is presented. It is shown that a frequency domain representation of the input-output dynamics yields a well de?ned notion of performance for a class of nonlinear systems. This allows to detect nonlinear e?ects and optimally design static nonlinear compensators that minimize the e?ects of such performance degrading nonlinearities. For convergent Lur’e systems, necessary and su?cient conditions for optimal perfor¬manceareprovided,based onaspectral representationof the input-outputdynamics. Moreover, for non convergent systems, the approach is shown to be e?ective in an industrial case study of frequency domain based optimal friction compensation in a transmission electron microscope.

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