Feedback control of acoustic musical instruments: Collocated control using physical analogs

Abstract

Traditionally, the average professional musician has owned numerous acoustic musical instruments, many of them having distinctive acoustic qualities. However, a modern musician could prefer to have a single musical instrument whose acoustics are programmable by feedback control, where acoustic variables are estimated from sensor measurements in real time and then fed back in order to influence the controlled variables. In this paper, theory is presented that describes stable feedback control of an acoustic musical instrument. The presentation should be accessible to members of the musical acoustics community who may have limited or no experience with feedback control. First, the only control strategy guaranteed to be stable subject to any musical instrument mobility is described: the sensors and actuators must be collocated, and the controller must emulate a physical analog system. Next, the most fundamental feedback controllers and the corresponding physical analog systems are presented. The effects that these controllers have on acoustic musical instruments are described. Finally, practical design challenges are discussed. A proof explains why changing the resonance frequency of a musical resonance requires much more control power than changing the decay time of the resonance.