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.

Bharath Bhikkaji

Department of Electrical Engineering

Control design

Displacement sensor

INTEGRAL RESONANT CONTROLLER (IRC)

Linear dynamics

NEGATIVE-IMAGINARY SYSTEMS

Resonant controller

SIGNAL CONDITIONING CIRCUITRY

SUB-SPACE METHODS

Identification (control systems)

Resonance

Sensors

Musical instruments

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IIT Madras

Mechatronics

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.

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

A negative imaginary approach to control the vibrations of a string

A transfer-function is said to be negative imaginary if the corresponding frequency response function has a negative definite imaginary part (on the positively increasing imaginary axis). Negative imaginary transfer-functions can be stabilized using negative imaginary feedback controllers. Flexible structures with compatible collocated sensor/actuator pairs have transfer-functions that are negative imaginary. In this paper a model structure that typically represents a collocated structure is considered. An identification algorithm which enforces the negative imaginary constraint is proposed for estimating the model parameters. A feedback control technique, known as integral resonant control (IRC), is proposed for damping vibrations in collocated flexible structures. Conditions for the stability of the proposed controller are derived, and shown that the set of stabilizing IRCs is convex. Finally, a flexible beam with two pairs of collocated piezoelectric actuators/sensors is considered. The proposed identification scheme is used determining the transfer-function and an IRC is designed for damping the vibrations. The experimental results obtained are reported. © 1996-2012 IEEE.

Fulltext

IEEE/ASME Transactions on Mechatronics

A negative imaginary approach to modeling and control of a collocated structure

IEEE Transactions on Automatic Control

Stability Analysis of Interconnected Systems With “Mixed” Negative-Imaginary and Small-Gain Properties

A Negative Imaginary Lemma and the Stability of Interconnections of Linear Negative Imaginary Systems

Integral Resonant Control of a Piezoelectric Tube Actuator for Fast Nanoscale Positioning

A negative imaginary approach to the actuation of a guitar string

Journal	Mechatronics
ISSN	09574158
Open Access	No