A negative imaginary approach to the actuation of a guitar string

• A string placed in a magnetic field and actuated by regulating a current through it.
• A laser vibration sensor is placed such that the sensing/actuation are collocated.
• A model is estimated and shown to be negative imaginary with resonant peaks.
• Signal conditioners (for vibration sensors) causes considerable time delays.
• Controllers are designed for situations with and without the signal conditioners.

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.