Zero Control Power Phenomena in the Minimization of Sound Power Using Multiple Control Sources

In active noise control, if total acoustic power is minimized, absorption and blowout of acoustic energy around the control source are balanced and a zero control power phenomenon occurs in which the time average of control power becomes zero. In this research, we focus on this phenomenon, and the main objective of this chapter is to derive the analytical solution of optimal control law. First, the zero control power phenomenon in the case of one control sound source (CSS) is discussed. Next, the zero control power phenomenon in the case of multiple CSSs is discussed. Furthermore, the analytical solution of the zero control power law in the case of multiple CSSs is derived. Finally, it is numerically shown that as the number of CSSs increases, the control effect of the total acoustic power is improved.