Two-dimensional dynamics of a quasi-static legged piezoelectric actuator

Piezoelectric actuators are becoming a viable alternative to electrodrives in terms of size, speed and stall force characteristics. In this paper, a novel dynamic model of a contemporary linear piezoelectric actuator is presented. The model is based on physically meaningful parameters and macroscopically measured data for the fully assembled state. The model describes the frictional interaction between multiple piezoelectric legs and a ceramic rod. It consists of two orthogonal dynamics which are coupled together by means of preload and frictional forces. Linearity of the model is maintained through most of the modelling stages with a clear indication of nonlinear effects due to hysteresis, friction and impact dynamics of the legs. Unknown model parameters are estimated within a global optimization procedure and bounds on parameter values are indicated. The model presented explains the linear drive frequency/velocity as well as the nonlinear load force/velocity characteristics of the actuator within its full operational range. The insights gained throughout the modelling process indicate the possibilities of design improvements. Moreover, the model can be used to explain the resonance phenomena limiting the range of actuator operation and is used to anticipate an alternative drive strategy.

[1]  Zdeněk Hurák,et al.  Hybrid charge control for stick–slip piezoelectric actuators , 2011 .

[2]  James Friend,et al.  Modelling and testing of a piezoelectric ultrasonic micro-motor suitable for in vivo micro-robotic applications , 2010 .

[3]  J. Wallaschek.  Contact mechanics of piezoelectric ultrasonic motors , 1998 .

[4]  Kenji Uchino,et al.  Piezoelectric actuators 2006 , 2008 .

[5]  C. Newcomb,et al.  Improving the linearity of piezoelectric ceramic actuators , 1982 .

[6]  Urban Simu,et al.  Analysis of quasi-static and dynamic motion mechanisms for piezoelectric miniature robots , 2006 .

[7]  Urban Simu,et al.  MICRON: Small Autonomous Robot for Cell Manipulation Applications , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[8]  Xinliang Zhang,et al.  A hybrid model for rate-dependent hysteresis in piezoelectric actuators , 2010 .

[9]  Branislav Borovac,et al.  A platform for micropositioning based on piezo legs , 2001 .

[10]  Jean-Marc Breguet,et al.  Unified mechanical approach to piezoelectric bender modeling , 2007 .

[11]  J. G. Smits,et al.  Dynamic admittance matrix of piezoelectric cantilever bimorphs , 1994 .

[12]  Carlos Canudas de Wit,et al.  A survey of models, analysis tools and compensation methods for the control of machines with friction , 1994, Autom..

[13]  J. Bareisis,et al.  Influence of Different Factors on the Stiffness and Strength of Multilayer Composite Elements , 2003 .

[14]  C. Caroli,et al.  Solid friction from stick–slip down to pinning and aging , 2005, cond-mat/0506657.

[15]  Hewon Jung,et al.  Creep characteristics of piezoelectric actuators , 2000 .

[16]  A. Pisano,et al.  Modeling and optimal design of piezoelectric cantilever microactuators , 1997 .

[17]  Mustafa Arafa,et al.  Modeling and Characterization of a Linear Piezomotor , 2009 .

[18]  R. Ben Mrad,et al.  On the classical Preisach model for hysteresis in piezoceramic actuators , 2003 .

[19]  Giancarlo Ferrigno,et al.  Force feedback in a piezoelectric linear actuator for neurosurgery , 2011, The international journal of medical robotics + computer assisted surgery : MRCAS.

[20]  J. C. Cain,et al.  Summary and future work , 1973 .

[21]  Filip Szufnarowski,et al.  Force control of a piezoelectric actuator based on a statistical system model and dynamic compensation , 2011 .

[22]  K.J. Astrom,et al.  Revisiting the LuGre friction model , 2008, IEEE Control Systems.

[23]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[24]  Branislav Borovac,et al.  Parameter identification and hysteresis compensation of embedded piezoelectric stack actuators , 2011 .

[25]  Qingsong Xu,et al.  Dahl Model-Based Hysteresis Compensation and Precise Positioning Control of an XY Parallel Micromanipulator With Piezoelectric Actuation , 2010 .

[26]  Carlos Canudas de Wit,et al.  A new model for control of systems with friction , 1995, IEEE Trans. Autom. Control..

[27]  Sung Kyu Ha,et al.  ANALYSIS OF A PIEZOELECTRIC MULTIMORPH IN EXTENSIONAL AND FLEXURAL MOTIONS , 2002 .

[28]  Seung-Yop Lee,et al.  Theoretical modeling, experiments and optimization of piezoelectric multimorph , 2005 .

[29]  Jan G. Smits,et al.  The constituent equations of piezoelectric bimorphs , 1991 .

[30]  Axel Schneider,et al.  Compliant piezo-flexdrives for muscle-like, antagonistic actuation of robot joints , 2010, 2010 3rd IEEE RAS & EMBS International Conference on Biomedical Robotics and Biomechatronics.

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

[32]  Arne Burisch,et al.  APIS — A miniaturized robot for precision assembly with low-cost piezoelectric motors , 2011 .

[33]  Joseph Horn.  Aircraft and Rotorcraft System Identification: Engineering Methods with Flight Test Examples (M.B. Tischler et al.; 2006) [Bookshelf] , 2008, IEEE Control Systems.

[34]  T. Baumberger,et al.  Physical analysis of the state- and rate-dependent friction law: Static friction , 1999 .

[35]  Kenji Uchino,et al.  Advanced piezoelectric materials , 2010 .

[36]  Urban Simu,et al.  Fabrication of monolithic piezoelectric drive units for a miniature robot , 2002 .

[37]  M Steinbuch,et al.  Modeling and Waveform Optimization of a Nano-motion Piezo Stage , 2011, IEEE/ASME Transactions on Mechatronics.

[38]  S. Y. Wang,et al.  A finite element model for the static and dynamic analysis of a piezoelectric bimorph , 2004 .

[39]  Kentaro Nakamura,et al.  A robot finger joint driven by hybrid multi-DOF piezoelectric ultrasonic motor , 2011 .

[40]  Yonghong Tan,et al.  Modeling hysteresis in piezoelectric actuators using NARMAX models , 2009 .

[41]  R. Merry,et al.  Using a Walking Piezo Actuator to Drive and Control a High-Precision Stage , 2009, IEEE/ASME Transactions on Mechatronics.

[42]  Stefan Johansson,et al.  Microassembly of a Piezoelectric Miniature Motor , 1999 .