A generalized Prandtl–Ishlinskii model for characterizing the hysteresis and saturation nonlinearities of smart actuators

Smart actuators, such as shape memory alloy (SMA) and magnetostrictive actuators, exhibit saturation nonlinearity and hysteresis that may be symmetric or asymmetric. The Prandtl–Ishlinskii model employing classical play operators has been used to describe the hysteresis properties of smart actuators that are symmetric in nature. In this study, the application of a generalized play operator capable of characterizing symmetric as well as asymmetric hysteresis properties with output saturation is explored in formulating a generalized Prandtl–Ishlinskii model. The generalized play operator employs different envelope functions under increasing and decreasing inputs to describe asymmetric and saturated output–input hysteresis loops. The validity of the proposed generalized model to characterize symmetric and asymmetric hysteresis properties is demonstrated by comparing the model responses with the measured major and minor hysteresis loops of three different types of actuator, namely SMA, magnetostrictive, and piezoceramic actuators. The simulation results suggest that the proposed generalized Prandtl–Ishlinskii model can be directly applied for modeling the hysteresis loops of different smart actuators together with the output saturation.

[1]  Hartmut Janocha,et al.  Real-time compensation of hysteresis and creep in piezoelectric actuators , 2000 .

[2]  I. Mayergoyz Mathematical models of hysteresis and their applications , 2003 .

[3]  D.R. Walker,et al.  Hybrid Monolithic SMA Actuators , 2007, 2007 IEEE/ASME international conference on advanced intelligent mechatronics.

[4]  M. Brokate,et al.  Hysteresis and Phase Transitions , 1996 .

[5]  J. Wen,et al.  Preisach modeling of piezoceramic and shape memory alloy hysteresis , 1995, Proceedings of International Conference on Control Applications.

[6]  Klaus Kuhnen,et al.  Modeling, Identification and Compensation of Complex Hysteretic Nonlinearities: A Modified Prandtl - Ishlinskii Approach , 2003, Eur. J. Control.

[7]  A. Visintin Differential models of hysteresis , 1994 .

[8]  W. Galinaitis Two Methods for Modeling Scalar Hysteresis and their use in Controlling Actuators with Hysteresis , 1999 .

[9]  Mohammad Al Janaideh,et al.  Modelling rate-dependent symmetric and asymmetric hysteresis loops of smart actuators , 2008 .

[10]  H. Banks,et al.  Identification of Hysteretic Control Influence Operators Representing Smart Actuators, Part II: Convergent Approximations , 1997 .

[11]  M. Krasnosel’skiǐ,et al.  Systems with Hysteresis , 1989 .

[12]  Gangbing Song,et al.  Vibration control of civil structures using piezoceramic smart materials: A review , 2006 .

[13]  Ralph C. Smith,et al.  Nonlinear Optimal Control Techniques for Vibration Attenuation Using Magnetostrictive Actuators , 2008 .

[14]  Joshua R. Smith,et al.  A Free Energy Model for Hysteresis in Ferroelectric Materials , 2003, Journal of Intelligent Material Systems and Structures.

[15]  John S. Baras,et al.  Adaptive identification and control of hysteresis in smart materials , 2005, IEEE Transactions on Automatic Control.

[16]  Chun-Yi Su,et al.  Development of the rate-dependent Prandtl–Ishlinskii model for smart actuators , 2008 .

[17]  Musa Jouaneh,et al.  Modeling hysteresis in piezoceramic actuators , 1995 .

[18]  S. Hirose,et al.  Mathematical model and experimental verification of shape memory alloy for designing micro actuator , 1991, [1991] Proceedings. IEEE Micro Electro Mechanical Systems.

[19]  Ralph C. Smith,et al.  Smart material systems - model development , 2005, Frontiers in applied mathematics.

[20]  Harvey Thomas Banks,et al.  Identification of Hysteretic Control Influence Operators Representing Smart Actuators Part I: Formulation , 1997 .

[21]  Gang Tao,et al.  Adaptive control of plants with unknown hystereses , 1995 .

[22]  K. Kuhnen,et al.  Inverse control of systems with hysteresis and creep , 2001 .

[23]  Ralph C. Smith,et al.  A Domain Wall Model for Hysteresis in Piezoelectric Materials , 1999 .

[24]  David W. L. Wang,et al.  Preisach model identification of a two-wire SMA actuator , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[25]  Rob Gorbet,et al.  A LOW COST MACRO-MICRO POSITIONING SYSTEM WITH SMA-ACTUATED MICRO STAGE , 2007 .

[26]  Yun-Jung Lee,et al.  Fast Preisach modeling method for shape memory alloy actuators using major hysteresis loops , 2004 .