This paper proposes a numerical investigation of a controlled loudspeaker designed to absorb acoustic plane waves at a duct termination. More precisely, a nonlinear control for a current-driven loudspeaker is presented, that relies on (i) measurements of velocity and acoustic pressure at the membrane, (ii) a linear electroacoustic loudspeaker model and (iii) a nonlinear finite-time control method. Numerical tests are carried out by a passive-guaranteed simulation of the loudspeaker dynamics in the port-Hamiltonian systems formalism. The sound absorption efficiency is evaluated up to 300Hz by computing the reflected pressure at the membrane. The results are compared with a similar control architecture: the finite-time control for sound absorption proves effective, especially in the low frequency range.

The Doppler effect is a phenomenon inherent to source motion, which introduces a variable propagation time between the source and a listening point. In the case of a vibrating piston, this is responsible for distortion of the radiated sound pressure. This moving-boundary phenomenon is part of the nonlinear effects involved in loudspeaker radiation. The present paper investigates the significance of this distortion, usually considered as neglectible, and addresses its correction. First, the direct problem is solved by: (a) converting the (Lagrangian) position of the moving source into its equivalent (Eulerian) velocity field at a fixed position; (b) deriving the acoustic pressure radiated from this velocity field. A series solution of (a) is derived and timedomain simulations of (b) are built from the truncated series combined with a baffled piston radiation model. Simulations show that Doppler distortion can be significant for realistic loudspeaker diaphragm motion with a wide spectral content. Second, the inverse (anti-Doppler) problem is examined, that is, the derivation of a piston displacement that generates a targeted Eulerian velocity field. The corrected piston velocity solution proves to be an uncentered signal, leading to a diverging displacement. In order to remove this practical problem, a centered approximation is preferred, based on modified inverse Volterra kernels. The anti-Doppler algorithm is reliable in the audio range.