Abstract
This paper presents a method to numerically linearise a complex mechanicalsystem. The method is applied to the parameter optimisation of a controlled elastic hydro-mechanical system. The virtual spring damper control concept is used to damp the oscillating system. The system dynamics of the full system are modelled as an interdisciplinary model. From this a mechanical substitution model is derived and linearised at a given operating point. The system matrix of the linearised system is used to efficiently calculate an optimisation criterion that leads to optimal control parameters for rapid oscillation damping. To verify the results a classical, but very time consuming, optimisation is performed. The quality of the optimal parameter sets found is evaluated by comparing simulation results of the complex interdisciplinary model. The system response is almost the same in both cases. The parameters found using the linear model are only slightly different to the parameters found using the non-linear and interdisciplinary model. The performance of the linear model based optimisation is good – it reduces the computational cost by a factor of more than one hundred.
Similar content being viewed by others
References
Bestle, D., Analyse and Optimierung von Mehrkorpersystemen, Springer-Verlag, Berlin, 1994.
Büdding, G., Schneider, M. and Hiller, M., ‘Nichtlineare Approximation mechanischer Modelle’, Zeitschrift für angewandte Mathematik and Mechanik 77, 1997, 531–532.
Kecskemethy, A., Objektorientierte Modellierung der Dynamik von Mehrkörpersystemen mit Hilfe von Ñbertragungselementen, Fortschritt-Berichte VDI, Reihe 20, Nr. 88, VDI Verlag, Düsseldorf, 1993.
Lenord, O., Huber, T., Franitza, D. and Hiller, M., ‘Interdisciplinary modelling of mechatronic systems by coupling simulation tools’, in Proceedings of the IAR 16th Annual Meeting, Illkirch, France, November 22–23, 2001, 91–95.
Müller, P.C. and Schiehllen, W., Lineare Schwingungen, Akademische Verlagsgesellschaft, Wiesbaden, 1976.
Nissing, D., ‘A vibration damped flexible robot: Identification and parameter optimization’, in Proceedings of the American Control Conference, Chicago, IL, 2000, 1715–1719.
Nissing, D., Bernzen, W. and Schwarz, H., ‘On vibration control of a concrete pump’, in Proceedings of ECC, European Control Conference, Karlsruhe, 1999, F1058-2.
Rauh, J., Ein Beitrag zur Modellierung elastischer Balkensysteme, Fortschritt-Berichte VDI, Reihe 18, Nr. 37, VDI Verlag, Düsseldorf, 1987.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lenord, O., Fang, S., Franitza, D. et al. Numerical Linearisation Method to Efficiently Optimise the Oscillation Damping of an Interdisciplinary System Model. Multibody System Dynamics 10, 201–217 (2003). https://doi.org/10.1023/A:1025569425318
Issue Date:
DOI: https://doi.org/10.1023/A:1025569425318