Active control of Chinese gongs

Active control provides one of the most promising ways of modifying instruments' sound. However, among the various control techniques covered by this discipline, most of the experimental applications have so far been limited to instruments keeping a linear behavior in normal playing conditions. This study explores the possibility of applying active control to Chinese gongs. These instruments exhibit geometric nonlinearities in their dynamical behavior such as a very characteristic pitch glide of the fundamental mode. The implementation of a nonlinear control of this pitch glide is introduced following a two-steps process. First, a reduced nonlinear model of the instrument dynamics is determined from the von Karman and normal form theories. This formulation allows for describing the nonlinear dynamics of the fundamental mode by one single nonlinear mode governed by a Duffing equation. The experimental identification of the Duffing model parameters is performed by measuring the backbone curve of the fundamental mode in forced vibrations. Second, the methodology for the nonlinear control is developed. In particular, the determination of the control law and the overall stability of the control system are discussed. Control simulations results as well as perspectives for experimental applications are finally exposed.