**7. References**


[9] Cavallo, A., Natale, C., Pirozzi, S., Visone, C. & Formisano, A. (2004). Feedback Control Systems for Micropositioning Tasks With Hysteresis Compensation, *IEEE Transactions on Magnetics*, Vol. 40, No. 2, pp. 876-879.

22 Will-be-set-by-IN-TECH

In Sect. 2 a brief description of the phenomena involved in magnetostrictive materials is drawn and the ideas of their modeling are also provided. In this respect, the basic operators describing systems with hysteresis is presented, with a specific attention to the classical Preisach model. Although the most known and applied approach is the one in the 'rotated' system of coordinates, according to Mayergoyz's book, [28], the adopted formalism allover the chapter is that preferred in the books [7] and [26], showing some interesting characteristic from the modeling viewpoint. In any case, the relationship between them is explicitly pointed

In the next section 3 the attention is focused on the main modeling and compensation issues which are normally adopted for control purposes. Here, a specific attention is devoted to the congruency property of Preisach operator, which forces a specific attention in the inversion of the operator. Finally, a basic point is discussed with some detail, that is, the definition of compensation algorithms which doesn't require further computational effort with respect to the 'direct' operator, i.e. the Preisach operator. This specific point becomes crucial when a

In order to put the issues discussed in the chapter in the current framework of smart materials and devices, in section 5 the need to manage two independent variables in controlling the device is emphasized, by proposing a well-behaved procedure to handle the stress and magnetic field simultaneously. The effectiveness of this approach for a more precise description and control of smart devices is also discussed by comparison to measured data. Such discussion paves the way to the last section of the chapter, where some application in *real time* controlling smart materials are presented. In particular, 'standard' and 2-DoF control strategies are presented, all fulfilling the constraint to keep a low computational complexity

[1] Adly, A.A., Mayergoyz, I.D. & Bergqvist, A. (1991). Preisach modeling of

[2] Anton, S.R. & Sodano, H.A. (2007). A review of power harvesting using piezoelectric materials (2003-2006), *IOP Smart Materials and Structures*, vol. 16, 3, pp. R1-R21. [3] Bar-Cohen, Y. (2002). Electro-active polymers: Current capabilities and challenges,

[4] Bellouard, Y. (2008). Shape memory alloys for microsystems: A review from a material research perspective *ELSEVIER Materials Science and Engineering A* 481-482, pp. 582-589. [5] Bergqvist, A. & Engdahl, G. (1991). A stress-dependent magnetic Preisach hysteresis

[6] Brokate, M. (1989). Some mathematical properties of the Preisach model of hysteresis,

[8] Cavallo, A., Natale, C. Pirozzi, S. & Visone, C. (2003). Effects of Hysteresis Compensation in Feedback Control Systems, *IEEE Transactions on Magnetics* Vol. 39, No. 3, pp.1389-1392.

model, *IEEE Transactions on Magnetics*, Vol. 27, No. 6, pt 2, pp. 4796-4798.

[7] Brokate, M. & Sprekels, J. (1996) *Hysteresis and Phase Transitions*,Springer.

of the whole control system, still ensuring good tracking and stability performances.

*University of Sannio - Engineering Department, 82100 Benevento (BN), Italy*

magnetostrictive hysteresis *AIP Journal of Applied Physics* 69, 5777.

*model-based* real time control approach is of concern.

Daniele Davino, Alessandro Giustiniani, Ciro Visone

*Proceedings of SPIE*, San Diego, CA.

*IEEE Transactions on Magnetics*, 25, pp. 2922-24.

out.

**Author details**

**7. References**

	- [26] Krejci, P. (1996). Hysteresis, convexity and dissipation in hyperbolic equations, *Gakuto Int. Series Math. Sci. & Appl.*, 8, Gakkotosho, Tokyo.
	- [27] Krejci, P. & Kuhnen, K. (2001). Inverse control of systems with hysteresis and creeps, *Proceedings of Control Theory and Applications*, Vol. 148, No. 3, pp. 185-192.
	- [28] Mayergoyz, I. D. (1991) *Mathematical Models of Hysteresis*, Springer.
	- [29] Miano, G., Serpico, C. & Visone, C. (1997). A new model of magnetic hysteresis, based on Stop hysterons: an application to magnetic field discussion, *IEEE Transactions on Magnetics*, Vol. 32, No. 3, pp. 1132-1135.
	- [30] Natale, C., Velardi, F. & Visone, C. (2001). Identification and compensation of Preisach hysteresis models for magnetostrictive actuators, *ELSEVIER Physica B*, 306, pp. 161-165.
	- [31] Otsuka, K. & Wayman, C.M. (1998) *Shape Memory Materials*, Cambridge University Press.
	- [32] Panda, P. K. (2009). Review: environmental friendly lead-free piezoelectric materials, *SPRINGER Journals of Matererials Science*, 44, pp. 5049-5062, DOI 10.1007/s10853-009-3643-0.
	- [33] Pecharsky, V.K. & Gschneidner, K.A. (2006). Advanced magnetocaloric materials: What does the future hold? *International Journal of Refrigeration* 29 pp. 1239-1249.
	- [34] Polla, D.L. & Francis, L.F. (1998). Processing And Characterization Of Piezoelectric Materials And Integration Into Microelectromechanical Systems, *Annual Review Matererials Science*, 28, pp. 563-597.
	- [35] Schafer, J. & Janocha, H. (1995). Compensation Of Hysteresis In Solid-State Actuators, *ELSEVIER Sensors And Actuators A* 49, pp. 97-102.
	- [36] Skogestad, S. & Postlethwaite, I. (2005). Multivariable Feedback Control: Analysis and Design, *Wiley-Interscience*.
	- [37] Söderberg, O., Ge, Y., Sozinov, A., Hannula, S.P. & Lindroos, V.K. (2005). Recent breakthrough development of the magnetic shape memory effect in Ni-Mn-Ga alloys *IOP Smart Materials and Structures* 14, 5.
	- [38] Sugie, T. & Yoshikawa, T. (1986). General solution of robust tracking problem in two-degree-of-freedom control systems *IEEE Transactions on Automatic Control*, Vol. 31 (6), pp. 552-554.
	- [39] Tan, X., Venkataraman, R. & Krishnaprasad, P.S. (2001). Control of hysteresis: Theory and experimental results, SPIE Modeling, Signal Processing, and Control in Smart Structures (Rao V. S., Ed.), 4326, pp. 101-112.
	- [40] Tellinen, J., et al., (2002). Basic properties of magnetic shape memory actuators, *Proceedings of 8th ACTUATOR Conference*, Bremen, Germany.
	- [41] Visintin, A. (1991) *Differential Models of Hysteresis*, Springer.
	- [42] Visone, C. & Serpico, C. (2001). Hysteresis operators for the modeling of magnetostrictive materials, *ELSEVIER Physica B: Condensed Matter*, 306 (1-4) , pp. 78-83.
	- [43] Visone, C. & Sjostrom, M. (2004). Exact invertible hysteresis models based on play operators, 2004, *ELSEVIER Physica B: Condensed Matter*, 343, pp. 148Ð52.
	- [44] Visone, C. (2008). Hysteresis Modelling and Compensation for Smart Sensors and Actuators, *IOP Journal of Physics Conference Series*.
	- [45] Webb, G.V., Lagoudas, D.C. & Kurdila, J. (1998). Hysteresis modeling of SMA actuators for control applications, *SAGE Journal of Intelligent Material Systems and Structures*, Vol. 9, No. 6, pp. 432-48.
	- [46] Webb, G., Lagoudas, D. & Kurdila, A. (1999). Adaptive hysteresis compensation for SMA actuators with stress-induced variations in hysteresis, *SAGE Journal of Intelligent Material Systems and Structures*, Vol. 10, No. 11, pp. 845-854.
