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

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 the frequencies and damping ratios of the axisymmetric vibration modes of the tom-tom membrane, by altering the cavity volume. By doing so, the active control changes the spectral response of the instrument. The first contribution constitutes the identification of the physical parameters of the tom-tom drum, such as membrane tension (from the modal frequencies) 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 microcontroller (Coala). A chattering phenomenon is observed, caused by the numerical stiffness of the finite-time control law, that can be removed by applying a regularization based on a local softening linear interpolation 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, because of the disparity between model and measurements, it is difficult to quantify the controller performance in achieving a prescribed frequency shift. It is proposed to refine the model, in particular by taking into account the sound propagation inside the cavity.