An experimental method to estimate the electro-mechanical coupling for active vibration control of a non-collocated free-edge sandwich plate

Positive Position Feedback (PPF) is one of the leading algorithms for the active suppression of the mechanical vibrations of thin-walled structures. The ease of integration with piezoelectric patches and its modal characteristics are among its main assets. In Multi-Input Multi-Output (MIMO) architectures, however, the passage from the physical signals of piezoelectric transducers to modal coordinates is required; this is achieved by placing participation matrices between sensors, controllers and actuators. The determination of these matrices is non-trivial, especially when the number of actuators is different from the number of modes to be controlled. Usually, the construction of an electromechanical Finite Element (FE) or reduced-order model is required to estimate the participation matrices. In this work, a method for the estimation of the participation matrices based on experimental measurements only is proposed. For the sake of generality, a bidimensional structure – a composite plate – with free edges (and thus with rigid body motions) was considered, and the vibration of eight vibration modes was suppressed by using four sensors and four actuators, in a non-collocated configuration. The simplified experimental identification of the electromechanical coupling allowed the numerical simulation of the uncontrolled and controlled vibrations of the plate when the latter was subjected to an external disturbance. The resulting PPF AVC achieved a reduction of several decibels in the vibration amplitude of all the eight modes under consideration, with negligible spillover over the following normal modes in laboratory experiments. The vibration reduction was verified in correspondence of several points across the surface of the plate in presence of a pseudo-random excitation. The proposed experimental identification technique simplifies considerably the design of PPF controls, eliminating the need for electromechanical modeling and opening the door to a more widespread use of Active Vibration Control (AVC) techniques.