Wind instruments as time delay systems. Part II: control and estimation*

In this paper, a modal analysis is performed for the slide flute modeled in d'Andréa-N et al. (2009) using the linearized boundary conditions which can also be used to compute the suitable blowing pressure (linked to the mouth delay) and the suitable pipe length (linked to the pipe delay) to obtain a desired fundamental frequency or equivalently a desired note. This will constitute the basis of our control algorithm. Concerning the simplified trumpet-like instrument also described in d'Andréa-N et al. (2009) as a so-called nonlinear neutral state space system, we elaborate a local asymptotic observer of the state, the stability of which being proved using Lyapunov techniques.