System properties of flexible structures with self-sensing piezoelectric transducers

Active and passive implementations of self-sensing readout networks are studied in terms of system properties such as the poles and the zeros of their transfer functions. The location of the zeros is shown to be dependent on two non-dimensional parameters related to the balancing condition of the readout bridge and to the compensation of its losses, while it is not affected by the active or passive implementation of the readout bridge. In the case of ideal “loss compensation” a graphical procedure is employed to describe the migration of the zeros. Even if the self-sensing arrangement guarantees the colocation of the sensing and actuating functions, the graphical procedure shows the possibility of non-minimum phase zero coupls for balancing conditions close to the so-called “electrical balancing”. The effects of model reduction techniques such as truncation or residualization is then studied, starting from a model of the system in terms of modal coordinates. Truncation is shown to be better suited to determine the “electrical balancing” condition while residualization gives a better approximation of the system zeros. The conditions of electrical balancing and loss compensation are then related to a condition of minimum dependance of the self-sensing bridge output from the driving electrical input. This property can be practically exploited to devise an adaptive readout bridge which can automatically reach the balancing conditions and the loss compensation or to identify the electrical parameters of the piezoelectric transducer. Experimental tests performed on a beam and a plate structures provided with self-sensing piezoelectric transducers are used to validate the analytical models.