Active vibration control using minimum actuation power: Multiple primary sources controlled by multiple secondary sources

Minimum Actuation Power (MAP) is a novel active vibration control strategy that minimizes the total input power into the structure by monitoring the input power from the secondary source. In a previous paper, we presented the theory for MAP for a single primary source controlled by a single secondary source and demonstrated the application of MAP for rotorcraft interior noise control. In this paper, we extend the theoretical framework for MAP for multiple primary sources (excitation) controlled by multiple secondary sources (control). We show that the input power from the secondary sources is zero only when the secondary sources are located such that the phase of the cross-mobility term for each primary–secondary pair is same. This condition puts a constraint on the location of the secondary sources with respect to the primary sources so that the input power from the secondary sources is zero. We present simulations for a simply supported plate excited by two primary sources and controlled by a single secondary source that validate the theoretical findings. We also study the effect of phasing between the primary sources on MAP control performance and show that the maximum power reduction is obtained when the phase difference between the primary sources is zero. Experimental results are provided that demonstrate the feasibility of the MAP theory.