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

Abstract

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-todisplacement 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.

Computationally Efficient Formulation of Relay Operator for Preisach Hysteresis Modeling

“…Another thinkable application is an online (recursive) identification of hysteresis behavior in a process, see e.g. [21]. Here the proposed method is easily extendable for a recursive scheme of parameter adaption.…”

“…( 4) allows equally for further advanced features of the Preisach hysteresis model, like e.g. the direct recursive identification [20], [21]. These are, however, out of scope of the recent communication and will be addressed in the future works.…”

Discrete-Time Adaptive Hysteresis Filter for Parallel Computing and Recursive Identification of Preisach Model

“…2) has been evaluated on the experimental data collected from a standard piezoelectric stage with one translational degree of freedom. For more details on the system hardware configuration we refer to [12], [13]. The principal structure of the experimental setup is schematically shown in Fig.…”

“…It is also worth noting that the piezoelectric stage is subject to the process noise as well. However, this remains unconsidered as evident from (13). The most obvious sources of the process noise are the inherent creeping effects in the piezoelectric structures, see e.g.…”