High frequency bandwidth polarization and strain control using a fractional derivative inverse model

Abstract

The present paper proposes an inverse dynamical model based on fractional derivatives in order to simulate the electrical field versus the polarization field E(P) as well as the electrical field versus the mechanical strain E(S) of ferroelectric hysteresis. By considering a fractional derivative term, the frequency bandwidth of the inverse model is greatly increased. As a consequence, the model became suited for the usual inverse model applications, such as adaptive inverse control of piezoelectric actuators, high-speed positioning or high precision positioning. The proposed high-accuracy inverse model rendered it possible to avoid standard feedback mechanisms that usually exhibit restrain frequency bandwidths due mainly to high frequency noise. Starting from a quasi-static inverse model, and based on a simple mechanism related to the dry-friction concept, a polarization fractional derivative term was added in order to take into account the dynamical effects. The order of the fractional derivative was, using a direct model P(E) and experimental data on a large frequency bandwidth (10 −3 Hz < f < 10 2 Hz), found to be equal to 0.5. A quadratic relation was used to link the ferroelectric strain and the polarization field. Moreover, a dynamical strain control based on an inverse dynamic polarization field contribution was proposed. Experimental procedures were developed to verify the accuracy of the polarization as well as of the strain control. Good results were obtained and exposed for sinus and triangular polarization-imposed waveforms. Various frequencies and amplitudes were tested in both cases.

Simulation of Synchronized-Switching Method Energy Harvester Including Accurate Piezoceramic Nonlinear Behavior

“…The experiment loop was obtained using the experiment setup described in [33]. Because of space limitation, this comparison is the only one displayed here, but a large number of further numerical simulation validations on the same material can be found elsewhere [32][33][34][35][36]. All these already published results confirm the validation of the piezoceramic ferroelectric behavior as demonstrated in the simulation results in this work.…”

“…Figure 3 shows a comparison of simulated/measured major dielectric hysteresis cycle P(E) while the branching point probability µ(E α , E β ) is shown in Figure 4. The experiment loop was obtained using the experiment setup described in [33]. Because of space limitation, this comparison is the only one displayed here, but a large number of further numerical simulation validations on the same material can be found elsewhere [32][33][34][35][36].…”

Modeling energy losses in power ultrasound transducers

“…In prior investigations (Guyomar et al, 2008(Guyomar et al, , 2009b(Guyomar et al, , 2010Sebald et al, 2004), a theoretical development based on the above-mentioned relation (1) has been proposed to introduce a specific relation between the polarization field and the mechanical strain. In prior investigations (Guyomar et al, 2008(Guyomar et al, , 2009b(Guyomar et al, , 2010Sebald et al, 2004), a theoretical development based on the above-mentioned relation (1) has been proposed to introduce a specific relation between the polarization field and the mechanical strain.…”

High nonlinearities in Langevin transducer: A comprehensive model

“…In prior investigations [40][41][42][43][44], a theoretical development based on the above-mentioned relation (1) has been proposed to introduce a specific relation between the polarization field and the mechanical strain. S is described as a linear function of P 2 .…”

“…In Ref. [40], the scaling law may be understood as a consequence of electrostriction. Experimental tests have demonstrated that relation (2) is particularly well adapted, regardless of the frequency [41].…”