Online identification of piezoelectric hysteresis by direct recursive algorithm of Preisach model

A direct recursive identification method for determining online the Preisach hysteresis density function has been recently proposed in [1]; its convergence was rigorously proved in [2]. One of the possible application areas relates to the identification of large-scale hysteresis effects in smartmaterial systems. This paper discusses an application of the direct recursive identification method to the input-output voltage-to-displacement measurements of piezoelectric hysteresis in a standard piezo-actuated stage. We excite the piezoelectric actuator in an open-loop manner through an appropriate notch-filter, designed beforehand, so as to suppress two dominant harmonics of mechanical domain and obtain the hysteresis response without dynamical by-effects. The applied input sequence is a simple (memoryless) Bernoulli process which is easy to generate in practice. This input does not impose any special requirements on the experimental design and control/accuracy of the input signal. The experimental evaluation is provided along with a discussion of an envisaged application.