Inducing Unusual Dynamics in Acoustic Musical Instruments

The dynamic behavior of an acoustic musical instrument can be drastically modified by closing a feedback loop around even a single sensor and actuator. After reviewing proportional-integral-derivative (PID) control, we analyze RMS level-tracking controllers, which induce a stable limit cycle with specified RMS level when an audio effect is placed in the feedback loop. The space of the RMS level-tracking controllers whose error converges exponentially to zero is succinctly described, and this space is augmented to include controllers that support multiple stable equilibria. Next, an adaptive RMS level-tracking controller is developed that can accommodate changing instrument and audio effect parameters. Finally, several example controllers are tested on a simulated vibrating string to demonstrate 1) creating multiple stable equilibria, 2) driving amplitudes of the string harmonics to various targets (for instance to make the string "sing" vowels), and 3) reducing the dynamic range of resonant ring modulation for time-varying effect parameters.