Plurilinear Modeling and discrete μ-Synthesis Control of a Hysteretic and Creeped Unimorph Piezoelectric Cantilever

First, we present a survey on modeling and control of bending piezoelectric microactuators. Second, a simple model for nonlinear piezoelectric actuators (hysteresis and creep) is presented. It is based on the multilinear approximation. This model requires low computing power and is well adapted for embedded systems. Finally, a μ-synthesis controller is implemented. Experiments show that the obtained performances are compatible with the requirements of micromanipulation tasks

[1]  Yassine Haddab,et al.  A microgripper using smart piezoelectric actuators , 2000, Proceedings. 2000 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000) (Cat. No.00CH37113).

[2]  Leonid Mirkin,et al.  On discrete-time H∞ problem with a strictly proper controller , 1997 .

[3]  K. Kuhnen,et al.  COMPENSATION OF THE CREEP AND HYSTERESIS EFFECTS OF PIEZOELECTRIC ACTUATORS WITH INVERSE SYSTEMS , 2000 .

[4]  C.C. Chou,et al.  Electromechanical analysis of an asymmetric piezoelectric/elastic laminate structure: theory and experiment , 1999, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[5]  J.-H. Xu.  Neural network control of a piezo tool positioner , 1993, Proceedings of Canadian Conference on Electrical and Computer Engineering.

[6]  D. Croft,et al.  Creep, Hysteresis, and Vibration Compensation for Piezoactuators: Atomic Force Microscopy Application , 2001 .

[7]  Keith Glover,et al.  μ-analysis and synthesis toolbox: for use with Matlab, user’s guide version 3 , 1998 .

[8]  M. Weinberg.  Working equations for piezoelectric actuators and sensors , 1999 .

[9]  Yoshihiro Ishibashi,et al.  Simulations of Ferroelectric Characteristics Using a One-Dimensional Lattice Model , 1991 .

[10]  K. Glover,et al.  State-space formulae for all stabilizing controllers that satisfy and H ∞ norm bound and relations to risk sensitivity , 1988 .

[11]  V. Hayward,et al.  On the linear compensation of hysteresis , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

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

[13]  G. Stein,et al.  Beyond singular values and loop shapes , 1991 .

[14]  H. Janocha,et al.  Smart actuators with piezoelectric materials , 1996, Other Conferences.

[15]  Yi Guo,et al.  An H∞ almost disturbance decoupling robust controller design for a piezoelectric bimorph actuator with hysteresis , 1999, IEEE Trans. Control. Syst. Technol..

[16]  Hewon Jung,et al.  New open-loop actuating method of piezoelectric actuators for removing hysteresis and creep , 2000 .

[17]  S. Cetinkunt,et al.  CMAC Learning Controller for Servo Control of High Precision Machine Tools , 1993, 1993 American Control Conference.

[18]  Joël Agnus.  Etude, Réalisation, Caractérisation et Commande d'une Micropince Piézoélectrique. , 2003 .

[19]  Dragan Damjanovic,et al.  Preisach distribution function approach to piezoelectric nonlinearity and hysteresis , 2001 .

[20]  Seung-Bok Choi,et al.  Fine motion control of a moving stage using a piezoactuator associated with a displacement amplifier , 2005 .

[21]  S. Li-ning,et al.  Tracking control of piezoelectric actuator based on a new mathematical model , 2004 .

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

[23]  C. J. Li,et al.  On-Line Roundness Error Compensation via P-Integrator Learning Control , 1992 .

[24]  Hartmut Janocha,et al.  Adaptronics and Smart Structures: Basics, Materials, Design, and Applications , 2007 .

[25]  P. Khargonekar,et al.  State-space solutions to standard H2 and H∞ control problems , 1988, 1988 American Control Conference.

[26]  Gary J. Balas,et al.  μ-analysis and synthesis toolbox: for use with Matlab , 1994 .

[27]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[28]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[29]  J.-M. Breguet,et al.  A smart microrobot on chip: design, identification and modeling , 2003, Proceedings 2003 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM 2003).

[30]  Ephrahim Garcia,et al.  Piezoelectric actuation systems: optimization of driving electronics , 1996, Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[31]  Hewon Jung,et al.  Tracking control of piezoelectric actuators , 2001 .

[32]  Michael Goldfarb,et al.  A Lumped Parameter Electromechanical Model for Describing the Nonlinear Behavior of Piezoelectric Actuators , 1997 .

[33]  T. Low,et al.  Modeling of a three-layer piezoelectric bimorph beam with hysteresis , 1995 .

[34]  Ping Ge,et al.  Tracking control of a piezoceramic actuator , 1996, IEEE Trans. Control. Syst. Technol..

[35]  C. Rogers,et al.  A Macroscopic Phenomenological Formulation for Coupled Electromechanical Effects in Piezoelectricity , 1993 .

[36]  J.G. Smits,et al.  The constituent equations of piezoelectric heterogeneous bimorphs , 1991, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[37]  Michael Goldfarb,et al.  Modeling Piezoelectric Stack Actuators for Control of Mlcromanlpulatlon , 2022 .

[38]  Ounaies Zoubeida,et al.  A model for rate-dependent hysteresis in piezoceramic materials operating at low frequencies , 2001 .

[39]  Musa Jouaneh,et al.  Generalized preisach model for hysteresis nonlinearity of piezoceramic actuators , 1997 .

[40]  Philippe Lutz,et al.  Specification of technical information system dedicated to a reorganizable and reconfigurable microfactory. , 2004 .

[41]  Sabri Cetinkunt,et al.  Design, fabrication and real-time neural network control of a piezo-electric actuated toolpost , 1995 .

[42]  R. Ben Mrad,et al.  A discrete-time compensation algorithm for hysteresis in piezoceramic actuators , 2004 .

[43]  John Doyle,et al.  Structured uncertainty in control system design , 1985, 1985 24th IEEE Conference on Decision and Control.

[44]  Tsu-Chin Tsao,et al.  Dynamic variable depth of cut machining using piezoelectric actuators , 1994 .

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

[46]  Robert C. Rogers,et al.  Compensation for hysteresis using bivariate Preisach models , 1997, Smart Structures.

[47]  Hong Hu,et al.  Discrete-time compensation algorithm for hysteresis in piezoceramic actuators , 2001, Optics East.

[48]  R. Ben Mrad,et al.  A model for voltage-to-displacement dynamics in piezoceramic actuators subject to dynamic-voltage excitations , 2002 .

[49]  A. Dubra,et al.  Preisach classical and nonlinear modeling of hysteresis in piezoceramic deformable mirrors. , 2005, Optics express.

[50]  N. Rogacheva,et al.  Electromechanical analysis of a symmetric piezoelectric/elastic laminate structure: theory and experiment , 1998, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[51]  Bruce A. Francis,et al.  Optimal Sampled-Data Control Systems , 1996, Communications and Control Engineering Series.

[52]  David W. L. Wang,et al.  Passivity-based stability and control of hysteresis in smart actuators , 2001, IEEE Trans. Control. Syst. Technol..

[53]  Vincent Hayward,et al.  An approach to reduction of hysteresis in smart materials , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[54]  Ephrahim Garcia,et al.  Precision position control of piezoelectric actuators using charge feedback , 1995 .

[55]  Jan G. Smits,et al.  Equations of state including the thermal domain of piezoelectric and pyroelectric heterogeneous bimorphs , 1993 .

[56]  Zoubeida Ounaies,et al.  A hysteresis model for piezoceramic materials , 1999 .

[57]  Philippe Lutz,et al.  Modular and re-organizable micromanipulation station , 2004 .

[58]  Stefan Seelecke,et al.  Optimal control of piezoceramic actuators , 2003, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.