Experimental implementation of a finite-time controller for the axisymmetric vibration modes of a tom-tom drum

Abstract

This paper is concerned with the experimental implementation of a previously derived finite-time observer-regulator controlling the current of a loudspeaker mounted in a tom-tom drum, based on the measurement of its cavity pressure. The control goal is to modify frequency and damping of the axisymmetric vibration modes of the tom-tom membrane. The first contribution constitutes the identification of the physical parameters of the tom-tom drum, such as membrane tension (from its observed Chladni figures) and viscous damping coefficient. Secondly, the testbench for the controller evaluation is developed. It is shown how a reproducible excitation with a drumstick can be achieved. Then, the control law is implemented on a Coala microcontroller. A chattering phenomenon is observed, produced by the numerical stiffness of the control law, that can be removed by applying a regulatization by a local linearization close to the origin. Finally, it is shown that the controller is able to modify frequencies of the axisymmetric vibration modes of the tom-tom membrane. However, there exists a disparity with respect to the frequency shifts predicted by the model used to tune the controller, that could be reduced by refining the model (in particular by taking into account the sound propagation inside the cavity).