Eigenvalue Assignment of a Nonlinear Electromagnetic System by the Receptance Method: Theory and Experiment

Mahshad Farzannasab*, Maryam GhandchiTehrani

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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Abstract

This paper presents experimental and numerical active vibration control of a nonlinear system for eigenvalue assignment and active damping, using receptance method. A nonlinear electromagnetic setup consist of two identical coils, two magnets and a cantilever beam has been built for this purpose. By varying the electrical current and distance between the two coils, nonlinear cubic stiffness with various strengths obtained. Active damping control performed experimentally in order to validate the performance of control method on the designed nonlinear setup. For eigenvalue assignment, first, receptance of the open loop system is experimentally measured by varying electrical currents and the coil distance to define the effect of parameter variations on the system’s FRF. Next step involved developing an iterative Sherman-Morrison formula to obtain the feedback control gains for the eigenvalue assignment. This step was challenging due to the amplitude dependence and also instability and jump phenomena that exist in the nonlinear FRFs. Increasing excitation level causes strong nonlinear effects in closed loop receptance, as shown by simulation. In the end, a stability analysis is conducted and discussed to prevent instability during the eigenvalue assignment process. Considered method effectively assigned poles and ensured the stability of the system under different conditions.
Original languageEnglish
Title of host publicationProceedings of the 10th Convention of the European Acoustics Association Forum Acusticum 2023
PublisherEAA
Pages5237-5244
Number of pages8
DOIs
Publication statusPublished - 2023
Event10th Convention of the European Acoustics Association Forum Acusticum 2023 - Politecnico di Torino, Turin, Italy
Duration: 11-Sept-202315-Sept-2023
http://dael.euracoustics.org

Conference

Conference10th Convention of the European Acoustics Association Forum Acusticum 2023
Abbreviated titleForum Acusticum 2023
Country/TerritoryItaly
CityTurin
Period11/09/202315/09/2023
Internet address

Keywords

  • experimental pole placement
  • active vibration control
  • nonlinear electromagnetic system

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