A guitar string that is rigidly clamped at both the ends is considered. This string is actuated by a supplying current, through it, in the presence of magnetic field. A sensor measuring the string displacement is positioned such that the input, which is the supplied current, and the output, the string displacement, appear collocated. An experiment is performed by exciting the string using sine-sweep and measuring the corresponding output. A model is fit to the input-output data, and is shown to satisfy the negative imaginary property. An integral resonant controller is designed by exploiting negative imaginary property such that it damps the first five resonant modes of the string. This is verified experimentally. © 2012 IEEE.

Bharath Bhikkaji

Department of Electrical Engineering

Input-output data

NEGATIVE IMAGINARY PROPERTY

Resonant controller

RESONANT MODE

Controllers

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

A negative imaginary approach to control the vibrations of a string

Proceedings of the 2012 24th Chinese Control and Decision Conference, CCDC 2012

A feedback control approach to damp the resonances of a guitar string is considered. A guitar string is tightly stretched and fastened at both its ends. This string is placed in a magnetic field and set to vibrations by passing current through it. A displacement sensor is placed such that the actuator and the sensor are collocated. The linear dynamics characterizing the input/output (supplied current/measured displacement) relationship is identified and a model is fit. It is observed that the model satisfies the negative imaginary condition. An Integral Resonant Controller (IRC) is designed, by exploiting the negative imaginary characteristics, to damp the first five modes of the string. Signal conditioning circuitry associated with the sensor could introduce significant time delays that destroy the negative imaginary property. Here, an IRC is designed even when the system does not exhibit negative imaginary characteristics. The effectiveness these control designs are experimentally validated. © 2013 Elsevier Ltd. All rights reserved.

Mechatronics

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Journal	Proceedings of the 2012 24th Chinese Control and Decision Conference, CCDC 2012
Open Access	No