Abstract
A key factor in developing and assessing any vibration attenuation technique for elastic systems is the measure that quantifies the occurring vibrations. In this paper, we propose a general and instantaneous vibration measure which allows for more subtle methods of localized vibration attenuation techniques. This measure is based on extracting the vibrational part from the conventional tracking error signal using wavelet technique. The paper also provides a method for constructing a wavelet function based on the system impulse response. This wavelet outperforms the existing ones in representing the system behavior while guaranteeing admissibility and providing sufficient smoothness and rate of decay in both time and frequency domains.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Barre, P.-J., Bearee, R., Borne, P., Dumetz, E.: Influence of a Jerk Controlled Movement Law on the Vibratory Behaviour of High-Dynamics Systems. J. of Intell. Robot. Systems 42, 275–293 (2005)
Junsheng, C., Dejie, Y., Yu, Y.: Application of an Impulse Response Wavelet to Fault Diagnosis of Rolling Bearings. Mechanical Systems and Signal Processing 21, 920–929 (2007)
Kozak, K., Singhose, W., Ebert-Uphoff, I.: Performance Measures For Input Shaping and Command Generation. J. Dyn. Syst., Meas., Control 128, 731–736 (2006)
Krantz, S.G.: 4.1.5 The Riemann Removable Singularity Theorem. In: Handbook of Complex Variables, pp. 42–43. Birkhäuser, Boston (1999)
Alkafafi, L., Hamm, C., Sauer, T.: A Strategy for Suppressing Residual Vibrations in Motion Control. In: Proc. PCIM, Nuremberg, pp. 76–82 (2012)
Mallat, S.: A Wavelet Tour of Signal Processing The Sparse Way, pp. 102–112. Academic Press, San Diego (2009)
Polge, R.J., Bhagavan, B.K.: Fourier Transform and Ambiguity Function of Piecewise Polynomial Functions. IEEE Trans. Aerospace Electron. Systems 13, 403–408 (1977)
Sauer, T.: Time–frequency analysis, wavelets and why things (can) go wrong. Human Congnitive Neurophysiology 4, 38–64 (2011)
Sauer, T.: Transformations, implementations, and pitfalls. Proc. Appl. Math. Mech. 11, 863–866 (2011)
Singer, N.C., Seering, W.P.: Preshaping Command Inputs to Reduce System Vibration. J. Dyn. Syst., Meas., Control 112(1), 76–82 (1990)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Alkafafi, L., Hamm, C., Sauer, T. (2014). Vibrational Error Extraction Method Based on Wavelet Technique. In: Floater, M., Lyche, T., Mazure, ML., Mørken, K., Schumaker, L.L. (eds) Mathematical Methods for Curves and Surfaces. MMCS 2012. Lecture Notes in Computer Science, vol 8177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54382-1_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-54382-1_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-54381-4
Online ISBN: 978-3-642-54382-1
eBook Packages: Computer ScienceComputer Science (R0)