State-space realization of a describing function
Springer Science and Business Media LLC
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Ghirardo, G., Ćosić, B., Juniper, M., & Moeck, J. (2015). State-space realization of a describing function. Nonlinear Dynamics, 82 9-28. https://doi.org/10.1007/s11071-015-2134-x
The describing function is a powerful tool for characterizing nonlinear dynamical systems in the frequency domain. In some cases, it is the only available description of a nonlinear operator characterizing a certain subcomponent of the system. This paper presents a methodology to provide a state-space realization of one given describing function, in order to allow the study of the system in the time domain as well. The realization is based on Hammerstein models and Fourier–Bessel series. It can be embedded in time domain simulations of complex configurations with many nonlinear elements interacting, accurately describing the nonlinear saturation of the system. The technique is applied to an example application in the field of combustion instability, featuring self-excited thermoacoustic oscillations. We benchmark the performance of the tool comparing the results with a frequency domain analysis of the same system, obtaining good agreement between the two formulations.
This work was supported by the European Research Council through project ALORS N.259620 and by the German Research Association for Combustion Engines (Forschungsvereinigung Verbrennungskraftmaschinen e.V. FVV).
European Research Council (259620)
External DOI: https://doi.org/10.1007/s11071-015-2134-x
This record's URL: https://www.repository.cam.ac.uk/handle/1810/248287