Inversion algorithms for the homogenized energy model for hysteresis in ferroelectric and shape memory alloy compounds

Abstract

Ferroelectric and ferromagnetic materials have the advantage of broadband and dual actuator and sensor capabilities. Ferroelastic compounds such as shape memory alloys have large energy densities and are biocompatible. However, to take full advantage of these properties, it is necessary to employ models and control designs that account for the rate-dependent hysteresis, creep, and constitutive nonlinearities inherent to the materials. Inverse compensation is one technique that achieves this purpose. We present an inversion algorithm based on a binary search of a discretized input grid and apply this to the homogenized energy model for modeling hysteresis. The inversion algorithm is shown to provide a reasonable balance between accuracy and computational speed. Numerical examples are presented for three specific cases of the homogenized energy model.

Quantification of parameter uncertainty for robust control of shape memory alloy bending actuators

“…The phase fraction evolution equation is evaluated numerically using an implicit Euler scheme resulting in a 2 × 2 matrix-vector multiplication at each grid point. For systems where the calculation of transition rates used to construct the 2 × 2 matrix for the Euler scheme at each grid point proves to be an obstacle to real-time computation, look-up tables for the rates can be used to improve the computational efficiency [18].…”

“…However, the hysteretic, nonlinear nature of the relationship between θ r (t) and input temperature complicates the task of computing the appropriate input. The approach in this paper is to use the algorithm presented in [18] to construct an approximate inverse. Regarding temperature as the input to the homogenized energy model, representing the inverse model as ε −1 , and applying it in (1), we obtain…”

“…It has been applied to ferroelectric [15], ferromagnetic [15,16], and shape memory alloy materials [17]. Additionally, an inverse algorithm for the HEM is used for hysteresis compensation [18]. Whereas, SMA is the focus here, the methods and results can be directly extended to other smart materials using the generalized framework of the HEM.…”

“…The remainder of this paper is organized as follows. The forward and inverse homogenized energy models for SMA bending actuators are briefly summarized, as they are described in greater detail in [12,17,18]. The DRAM algorithm is briefly motivated and the reader is referred to [21] for details.…”

Εφαρμογές Και Έλεγχος Έξυπνων Υλικών Με Έμφαση Στην Χρησιμοποίησή Τους Ως Επενεργητές

“…Αντίθετα από την λειτουργία των πιεζοκρυσταλλικών επενεργητών, τα ΜΚ περιορίζονται γενικότερα σε εύρος συχνοτήτων μικρότερο του 1Hz. Η τιμή του ορίζεται από τον συντελεστή απαγωγής θερμότητας, για φυσική (συνήθως) απαγωγή και εξαρτάται από την γεωμετρία του επενεργητή ( [20,21] Μεγαλύτερη ακρίβεια παρέχεται από την χρήση μαθηματικών/ φαινομενολογικών μοντέλων, αλλά τόσο ο συντονισμός των παραμέτρων τους, όσο και η αντιστροφή τους μπορεί να αποδειχθούν δύσκολες διαδικασίες ( [38]). Επιπρόσθετα, η απαίτηση για άμεση πρόσβαση στην θερμοκρασία του υλικού μπορεί να είναι περιοριστική κατά τον σχεδιασμό, ειδικότερα για δυναμικά φαινόμενα σε μη ελεγχόμενο περιβάλλον ( [39]).…”