Nonlinear Analysis: Modelling and Control
Vol. 22, No. 4
Grzegorz Cieplok
A wire transducer in a system with a van der Pol oscillator and velocity feedback
doi:10.15388/NA.2017.4.3
Received  2016-03-20  /   Revised  2017-02-19  /   Accepted   2017-03-15
Published Online  2017-06-19
Abstract

The work concerns wire transducers, which use a system with a van der Pol oscillator, with the aim of maintaining non-decreasing natural vibrations in the wire. As opposed to classical solutions, in which the feedback signal of the oscillator contains the course of displacement and velocity of the vibrating mass, a simple solution based only on the course of velocity is used. Such a solution is more advantageous from a practical perspective as regards to physical systems, because in the case of velocity transducers it eliminates the need to integrate the signal and the problems connected with it.

Particular places for this solution may be found in wire tensometer systems designated for the long-term constant measurement, as well as for the measurement of time-variable courses, including those of a chaotic character.

In the work, analysis was conducted on a modified van der Pol equation adapted for the movement of a discrete mass for the determination conditions of the existence of a limit cycle, the vibration course as well as the definition of the capabilities of adapting the results in the case of a wire transducer.

The results of theoretical analysis were confirmed by the results of the experimental tests conducted on a laboratory model constructed for this purpose.

Keywords:
wire transducer, van der Pol equation, self-oscillation, perturbation method.