Active vibration control using minimum actuation power

Minimum actuation power (MAP) is a novel active vibration control strategy whose theoretical framework is introduced. MAP is an optimal control strategy that minimizes the total input power into the structure by only monitoring and controlling the input power going through the control sources. Implementing MAP control without explicit knowledge about the magnitude of the primary excitation is achieved thanks to the key observation that the real part of the input power from the secondary actuator is zero when the total mechanical input power from the primary and secondary sources is minimum. Piezo-electric actuators provide a simple and robust way to estimate the mechanical input power by measuring the electrical power without additional error sensors. The theory of MAP is developed for a simply supported plate excited by a primary piezo-electric patch actuator and controlled by a secondary piezo-electric patch actuator. The MAP theory is also extended to multi-frequency primary excitation where the discrete frequencies are commensurate.