Controlling chaotic oscillations in a symmetric two-mass model of the vocal folds

Abstract

Human phonation is a highly non-linear process in which subglottal flow emanating from the lungs induces self-oscillations of the vocal folds. In normal conditions, this results in the generation of a regularly pulsating volume velocity that becomes the source of acoustic waves, which once modulated by the vocal tract, get emitted outwards as voice. However, vocal fold oscillations can become chaotic under many circumstances. For instance, even in the case of healthy symmetric vocal folds, an excess value of the subglottal pressure can trigger chaotic motion. In this paper, we derive a chaos control strategy for a two-mass model of the vocal cords to revert the situation and render the motion regular again. The approach relies on slightly altering the system energy to move it to a stable state. Given that no external control forces can be applied to the vocal cords, it is proposed to add a third mass to the original two-mass model, which is assumed to be made of an ideal smart material. The mass of the smart material is presumed negligible in comparison to the two masses of the vocal folds model, but its damping and stiffness can be tuned to evolve with time. For a fixed subglottal pressure for which the motion is chaotic, it is shown how periodicity can be recovered using adequate damping laws, by either attaching the smart material onto the larger vocal fold mass or onto the smaller one. For the latter, chaos control turns to be more difficult and the damping of the smart material has to quickly vary with time. On the other hand, given that the subglottal pressure would rarely be constant in a real situation, we also introduce a damping law to avoid chaotic motion as the subglottal pressure augments or diminishes. Finally, it is shown that control can not only be achieved by acting on the damping of the smart material but also on its stiffness. A stiffness law to prevent chaotic oscillations and get a healthy pulsating volume velocity is therefore implemented. A brief discussion on the mid-long term potential of the presented solution for practical cases is included.