### Abstract

For high precision motion systems, modeling and control design specifically oriented at friction effects is instrumental. The Sinusoidal Input Describing Function theory represents an approximative mathematical framework for analyzing nonlinear system behavior. This theory however limits the description of the nonlinear system behavior to a quasi linear amplitude dependent relation between sinusoidal excitation and sinusoidal response. In this paper an extension to Higher Order Describing Functions is realized by introducing the concept of the harmonics generator. The resulting Higher Order Sinusoidal Input Describing Functions (HOSIDFs) relate the magnitude and phase of the higher harmonics of the periodic response of the system to the magnitude and phase of a sinusoidal excitation. Based on this extension two techniques to measure HOSIDFs are presented. The first technique is FFT based. The second technique is based on IQ (in-phase/quadrature-phase) demodulation. In a simulation the measurement techniques have been tested by comparing the simulation results to analytically derived results from a known (backlash) non-linearity. In a subsequent practical case study both techniques are used to measure the changes in dynamic behavior as function of drive level due to friction in an electric motor. Both methodes prove successful for measuring HOSIDFs.

Original language | English |
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Title of host publication | Proceedings of the 5th EUROMECH Nonlinear Dynamics Conference (ENOC 2005) 7 - 12 August 2008, Eindhoven, The Netherlands |

Pages | 1893-1902 |

Publication status | Published - 2005 |

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## Cite this

Nuij, P. W. J. M., & Steinbuch, M. (2005). Two techniques for measuring Higher Order Sinusoidal Input Describing Functions. In

*Proceedings of the 5th EUROMECH Nonlinear Dynamics Conference (ENOC 2005) 7 - 12 August 2008, Eindhoven, The Netherlands*(pp. 1893-1902)