Bifurcation analysis of a two-DoF system subject to digital position control

Giuseppe Habib, Giuseppe Rega, Gabor Stépán

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper analyzes the stability of a two-DoF system, subject to PD digital position control. In the model the control force is considered piecewise constant. Introducing the nonlinearity related to the saturation of the control force, the bifurcations occurring in the system are analyzed. The system is generally loosing stability through Neimark-Sacker bifurcations, with a relatively simple dynamics. However, the interaction of two different Neimark-Sacker bifurcations steers the system to much more complicated behaviors. About this kind of bifurcation, namely double Neimark-Sacker bifurcation, there are very few studies in the literature. Our analysis is carried out using the method proposed by Kuznetsov. The performed investigation shows the appearance of quasiperiodic motions and the existence of regions with coexisting periodic stable attractors, in the space of the control gains. Numerical simulations validate the results obtained analytically.

Original languageEnglish
Title of host publicationASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2012
Pages1007-1016
Number of pages10
EditionPARTS A AND B
DOIs
Publication statusPublished - Dec 1 2012
EventASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2012 - Chicago, IL, United States
Duration: Aug 12 2012Aug 12 2012

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
NumberPARTS A AND B
Volume1

Other

OtherASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2012
CountryUnited States
CityChicago, IL
Period8/12/128/12/12

Keywords

  • Center manifold reduction
  • Digital position control
  • Discrete time
  • Double Neimark-Sacker bifurcation

ASJC Scopus subject areas

  • Modelling and Simulation
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design

Fingerprint Dive into the research topics of 'Bifurcation analysis of a two-DoF system subject to digital position control'. Together they form a unique fingerprint.

  • Cite this

    Habib, G., Rega, G., & Stépán, G. (2012). Bifurcation analysis of a two-DoF system subject to digital position control. In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2012 (PARTS A AND B ed., pp. 1007-1016). (Proceedings of the ASME Design Engineering Technical Conference; Vol. 1, No. PARTS A AND B). https://doi.org/10.1115/DETC2012-70630