Theoretical modeling issue in active noise control for a one-dimensional acoustic duct system

The theoretical modeling of active noise control for an acoustic duct system is discussed. A partial differential equation (PDE) model with external inputs for the acoustic duct is first developed by following the physical acoustic propagation principles. Then this PDE model is converted into an infinite dimensional complex-valued state space model using the variable separation technique under the assumption that the acoustic terminal impedance is constant. The assumed acoustic impedance can be estimated using the experimental system identification method. By combining the acoustic duct model with the model of the canceling loudspeaker module, in which the acoustic coupling between the acoustic duct and the loudspeaker is also explicitly modeled, a mathematical model for the entire one-dimensional active duct noise control system is obtained and validated. The developed model provides a solid and sufficient platform for design of active noise control using advanced filtering technique, advanced control techniques and development of virtual sensors as well.