Input energy minimization with acoustic potential energy constraint for active noise control system

In this paper, a performance measure of input energy minimization with acoustic potential energy constraint for active noise control (ANC) system was proposed. Making the control area as “quiet zone” can increase the acoustic energy of the remaining area outside the control area, which are undesirable. By reducing the input energy with a reduction loss in the control area, noise increase in the remaining area can be minimized. Conventional input energy minimization measures, degree of controllability (DOC) and degree of disturbance rejectability (DODR) are defined only for systems that satisfy controllability. Most distributed parameter systems, such as ANC systems, cannot satisfy controllability. Therefore, it is impossible to define the input energy measure for an ANC system using existing methods. Here, a new concept of DODR for an ANC system was proposed. This measure has a physical meaning of minimum input energy under the condition that the acoustic potential energy is less than or equal to a desired acoustic potential energy. The DODR measure can be used to select the sensor and actuator combination with the same noise reduction performance in the control area but with the smallest input energy needed. A numerical example shows the usefulness of the proposed measure of DODR for the ANC system.