Discrete-time simulation of air-flow cut-off in pressure-controlled valves

Pressure controlled valves exist in musical instruments such as brasses and woodwinds and are also found in many biological sound producing mechanisms such as the human larynx and the avian syrinx. The behaviour of the differential equation governing volume flow through a pressure-controlled valve is examined with particular attention given to the rather troublesome transition between an open and closed valve. A closed-form solution for the time evolution of volume flow is given and used to derive an update for the volume flow. The result is a smooth, nearly alias free transition between the two states. The form of the update is similar to that of a leaky valve where the leakage decreases as the volume flow decreases. This research was developed while modeling the avian syrinx.