Abstract
In this chapter, the control without sensors, also called feedforward control, of piezoelectric actuators is proposed. Typified by hysteresis and creep nonlinearities and by badly damped vibration, the design of the controller (compensator) is based on precise models and on the inversion of the latter. For that, the hysteresis is first modeled and compensated by using the Prandtl–Ishlinskii technique. Then, the creep is treated. Finally, the badly damped vibration is modeled and controlled. Experimental results along the chapter demonstrate the efficiency of the approach.
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J. Agnus, N. Chaillet, C. Clévy, S. Dembélé, M. Gauthier, Y. Haddab, G. Laurent, P. Lutz, N. Piat, K. Rabenorosoa, M. Rakotondrabe, B. Tamadazte, Robotic microassembly and micromanipulation at FEMTO-ST. J. Micro. Bio. Robot. (JMBR), 8(2), 91–106 (2013)
M. Rakotondrabe, C. Clévy, P. Lutz, Modelling and robust position/force control of a piezoelectric microgripper, in IEEE - International Conference on Automation Science and Engineering (CASE), Scottsdale, AZ, USA, 2007, pp. 39–44
M. Rakotondrabe, Y. Haddab, P. Lutz, Quadrilateral modelling and robust control of a nonlinear piezoelectric cantilever. IEEE - Trans. Contr. Syst. Technol. (T-CST) 17(3), 528–539 (2009)
M. Rakotondrabe, K. Rabenorosoa, J. Agnus, N. Chaillet, Robust feedforward-feedback control of a nonlinear and oscillating 2-dof piezocantilever. IEEE - Trans. Autom. Sci. Eng. (T-ASE) 8(3), 506–519 (2011)
S. Khadraoui, M. Rakotondrabe, P. Lutz, Interval modeling and robust control of piezoelectric microactuators. IEEE - Trans. Contr. Syst. Technol. (T-CST) 20(2), 486–494 (2012)
Y. Shan, K.K. Leang, Accounting for hysteresis in repetitive control design. Automatica 48(8), 1751–1758 (2012)
A. Sebastian, A. Gannepalli, M.V. Salapaka, A review of the systems approach to teh analysis of dynamic-mode atomic force microscopy. IEEE Trans. Contr. Syst. Technol. 15(5), 952–959 (2007)
Q. Xu, Y. Li, Model predictive discrete-time sliding mode control of a nanopositioning piezostage without modeling hysteresis. IEEE Trans. Contr. Syst. Technol. 20(4), 983–994 (2012)
A. Bazaei, Y.K. Yong, S.O.R. Moheimani, A. Sebastian, Tracking of triangular references using signal transformation for control of a novel AFM scanner stage. IEEE Trans. Contr. Syst. Technol. 20(2), 453–464 (2012)
S. Devasia, E.E. Eleftheriou, R. Moheimani, A survey of control issues in nanopositioning. IEEE Trans. Contr. Syst. Technol. 15(5), 802–823 (2007)
D. Croft, G. Shed, S. Devasia, Creep, hysteresis and vibration compensation for piezoactuators: atomic force microscopy application. ASME J. Dyn. Syst. Meas. Contr. 123(1), 35–43 (2001)
A. Dubra, J. Massa, C.l. Paterson, Preisach classical and nonlinear modeling of hysteresis in piezoceramic deformable mirrors. Optic. Express 13(22), 9062–9070 (2005)
M. Rakotondrabe, C. Clévy, P. Lutz, Complete open loop control of hysteretic, creeped and oscillating piezoelectric cantilever. IEEE Trans. Autom. Sci. Eng. (TASE) 7(3), 440–450 (2010)
W.T. Ang, P.K. Kholsa, C.N. Riviere, Feedforward controller with inverse rate-dependent model for piezoelectric actuators in trajectory-tracking applications. IEEE/ASME Trans. Mechatron. 12(2), 134–142 (2007)
B. Mokaberi, A.A.G. Requicha, Compensation of scanner creep and hysteresis for AFM nanomanipulation. IEEE Trans. ASE 5(2), 197–0208 (2008)
M. Al Janaideh, P. Krejci, Inverse rate-dependent Prandtl–Ishlinskii model for feedforward compensation of hysteresis in a piezomicropositioning actuator. IEEE/ASME Trans. Mechatron. (2012). doi:10.1109/TMECH.2012.2205265
M. Rakotondrabe, Classical Prandtl–Ishlinskii modeling and inverse multiplicative structure to compensate hysteresis in piezoactuators, in ACC (American Control Conference), Montréal, Canada, June 2012, pp. 1646–1651
M. Rakotondrabe, Bouc–Wen modeling and inverse multiplicative structure to compensate hysteresis nonlinearity in piezoelectric actuators. IEEE Trans. ASE 8(2), 428–431 (2011)
H. Jung, J.Y. Shim, D. Gweon, New open-loop actuating method of piezoelectric actuators for removing hysteresis and creep. Rev. Sci. Instrum. 71(9), 3436–3440 (2000)
G.M. Clayton, S. Tien, S. Devasia, A.J. Fleming, S.O.R. Moheimani, Inverse-feedforward of charge-controlled piezopositioners. Mechatronics 18, 273–281 (2008)
M. Rakotondrabe, C. Clévy, P. Lutz, Hysteresis and vibration compensation in a nonlinear unimorph piezocantilever, in IEEE/RSJ - IROS, (International Conference on Intelligent Robots and Systems), Nice, France, Sept 2008, pp. 558–563
M. Rakotondrabe, Piezoelectric Cantilevered Structures: Modeling Control and Measurement/Estimation Aspects (Springer, Berlin, 2013)
R. Bouc, Forced vibration of mechanical systems with hysteresis, in Conference on Nonlinear Oscillation, Prague, 1967
Y.K. Wen, Method for random vibration of hysteresis systems. J. Eng. Mech. Div. 102(2), 249–263 (1976)
M. Jouaneh, H. Tian, Accuracy enhancement of a piezoelectric actuators with hysteresis, in ASME Japan/USA Symp. Flexible Automation, Proceedings of the Japan-USA Symposium on Flexible Automation, A Pacific Rim Conference, San Francisco, California, USA, ASME/ISCIE, ISBN 0-7918-0765-8, 1992, pp. 631–637
T.S. Low, W. Guo, Modeling of a three-layer piezoelectric bimorph beam with hysteresis. J. Microelectromech. Syst. 4(4), 230–237 (1995)
L. Ljung, System identification toolbox, for use with Matlab. The Matworks (1995)
T. Singh, W. Singhose, Tutorial on input shaping/time delay control of maneuvering flexible structures, in American Control Conference, Proceedings of the American Control Conference, Anchorage Alaska USA, 2002, pp. 1717–1731
N.C. Singer, W.P. Seering, K.A. Pasch, Shaping command inputs to minimize unwanted dynamics. Patent No. US-4.916.635, 1990
Acknowledgements
This work is supported by the national ANR-JCJC C-MUMS-project (National young investigator project ANR-12-JS03007.01: Control of Multivariable Piezoelectric Microsystems with Minimization of Sensors).
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Rakotondrabe, M. (2013). Feedforward Control of Flexible and Nonlinear Piezoelectric Actuators. In: Rakotondrabe, M. (eds) Smart Materials-Based Actuators at the Micro/Nano-Scale. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6684-0_10
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DOI: https://doi.org/10.1007/978-1-4614-6684-0_10
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