Abstract
Piezoelectric elements (PEMs) are used in a variety of applications. In this paper we developed a full analytical model of a piezoelectric actuator which includes piezostack elements and a three-stage amplification mechanism. The model was derived separately for each unit of the system. Next, the units were combined, while taking into account their coupling. The hysteresis phenomenon, which is significant in piezoelectric materials, was extensively described. A number of hysteresis calculating algorithms were investigated and a new simple method of examining piezoelectric hysteresis was demonstrated. The theoretical model was verified in a laboratory setup. This setup includes a piezoelectric actuator, measuring devices and an acquisition system. The measured results were compared to the theoretical results, while taking into account the nonlinear phenomena of the piezoelectric materials and the three-stage amplification mechanism, and were found to be very similar. Due to its simplicity, this model can easily be modified in order to be applied to other PEMs or other amplification mechanism methods. The main novelty of this work lies in its system-level approach for piezoelectric actuators. All of the system elements include non-linear phenomena, which mutually influence each other. First, each part of the system will be described separately and then, the combined subsystems and the coupling between their parts will be represented. Finally we treat this system as one whole unit.
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References
A. Preumont. (2006) Mechatronics dynamics of electromechanical and piezoelectric systems. Springer, Chapter 4, (95–130).
Li, Y., Xiao, S., Xi, L., & Wu, Z. (2014). Design, modeling, control and experiment for a 2-DOF compliant micro-motion stage. International Journal of Precision Engineering and Manufacturing, 15(4), 735–744.
Kim, C., & Shin, J. W. (2013). Topology optimization of piezoelectric materials and application to the cantilever beams for vibration energy harvesting. International Journal of Precision Engineering and Manufacturing, 14(11), 1925–1931.
Kim, I., Kim, Y. S., & Park, E. C. (2009). Sliding mode control of the inchworm displacement with hysteresis compensation. International Journal of Precision Engineering and Manufacturing, 10(3), 43–49.
Kim, M. S., Park, Y. J., Cho, K. J., Ahn, S. H., Chu, W. S., Lee, K. T., et al. (2012). Review of biomimetic underwater robots using smart actuators. International Journal of Precision Engineering and Manufacturing, 13(7), 1281–1292.
Ghemari, Z., Saad, S., & Khettab, K. (2019). Improvement of the vibratory diagnostic method by evolution of the piezoelectric sensor performances. International Journal of Precision Engineering and Manufacturing, 20, 1361–1369.
Zhang, X., & Xu, Q. (2018). Design and testing of a New 3-DOF spatial flexure parallel micropositioning stage. International Journal of Precision Engineering and Manufacturing, 19(1), 109–118.
McCarty, R., & Mahmoodi, S. N. (2015). Dynamic mulitmode analysis of non-linear piezoelectric microcantilever probe in bistable region of tapping mode atomic force microscopy. International Journal of Non-Linear Mechanics, 74, 25–37.
Dong, W., Chen, F., Li, H., Yang, M., & Du, Z. (2017). A two-dimensional nano-positioner: Design, modelling and experiments. Robotics and Computer-Integrated Manufacturing, 48, 167–173.
Guo, L., Yan, W., Xu, Y., & Chen, Y. (2012). Valveless piezoelectric micropump of parallel double chambers. International Journal of Precision Engineering and Manufacturing, 13(5), 771–776.
Zhenming, L., Pei, J., Guangyao, O., & Jiadong, Z. (2010). Development of an electromechanical model for piezo actuated common rail injectors. International Conference on Intelligent Computation Technology and Automation, 2, 98–101.
Muir, E. R., Liu, L., Friedmann, P. P., & Kumar, D. (2012). Effect of piezoelectric actuator hysteresis on helicopter vibration and noise reduction. Journal of Guidance, Control and Dynamics, 35(4), 1299–1311.
Zanoni, C., & Bortoluzzi, D. (2015). Experimental-analytical qualification of a piezoelectric mechanism for a critical space application. IEEE Transactions on Mechatronics, 20(1), 427–437.
Kurniawan, R., Ali, S., Park, K. M., Li, C. P., & Ko, T. J. (2019). Development of a three-dimensional ultrasonic elliptical vibration transducer (3D-UEVT) based on sandwiched piezoelectric actuator for micro-grooving. International Journal of Precision Engineering and Manufacturing, 20, 1229–1240.
Kim, J., Lee, H., & Kim, H. S. (2010). Beam vibration control using cellulose-based electro-active paper sensor. International Journal of Precision Engineering and Manufacturing, 11(6), 823–827.
Yun, J. N., Sun, J. B., & Kim, Y. C. (2013). Robust disturbance observer for twoinertia system. IEEE Transactions on Industrial Electronics, 60(7), 2700–2710.
Kanno, I., Kunisawa, T., Suzuki, T., & Kotera, H. (2007). Development of deformable mirror composed of piezoelectric thin films for adaptive optics. IEEE Journal of Selected Topics in Quantum Electronics, 13(2), 155–161.
S.E. NIV, D.A. Levy, D. Oster. (2013). Integrated model and analysis of a pneumatic piezoelectric actuator. in 53th Israel Annual Conference on Aerospace Science.
Ben-Yaakov, S., & Lineykin, S. (2004). Maximum power tracking of piezoelectric transformer HV converters under load variations. IEEE Transactions on Power Electronics, 21(1), 73–78.
Lineykin, S., & Ben-Yaakov, S. (2005). Feedback isolation by piezoelectric transformers: comparison of amplitude to frequency modulation. HAIT Journal of Science and Engineering, 2(5–6), 830–847.
T. Jordan, Z. Ounaies, J. Tripp, P. Tcheng. (2000). Electrical properties and power considerations of a piezoelectric actuator. ICASE Report. no. 2000–8.
Rakotondrabe, M., Haddab, Y., & Lutz, P. (2009). Quadrilateral modelling and robust control of a nonlinear piezoelectric cantilever. IEEE Transactions on control systems technology, 17(3), 528–539.
Q. Zhou, P. Kallio, H. N. Koivo. (1999) Modeling of piezohydraulic actuator for control of a parallel micromanipulator. in Proceedings of the 1999 IEEE International conference on robotics and automation. Michigan.
Zupan, M., Ashby, M. F., & Fleck, N. A. (2002). Actuator classification and selection-the development of a database. Advanced Engineering Materials, 4(12), 933–940.
Richter, H., Misawa, E. A., Lucca, D. A., & Lu, H. (2001). Modeling nonlinear behavior in a piezoelectric actuator. Journal of the International Societies for Precision Engineering and Nanotechnology, 25, 128–137.
Pozzi, M., & King, T. (2003). Piezoelectric modelling for an impact actuator. Mechatronics, 13(6), 553–570.
Karunanidhi, S., & Singaperumal, M. (2010). Mathematical modelling and experimental characterization of a high dynamic servo valve integrated with piezoelectric actuator. Proceedings of The Institution of Mechanical Engineers Part I-journal of Systems and Control Engineering, 224(4), 419–435.
Boukari, A. F., Carmona, J. C., Moraru, G., Malburet, F., Chaaba, A., & Douimi, M. (2011). Piezo-actuators modeling for smart applications. Mechatronics, 21, 339–349.
Ch, S. H. (2009). Trajectory tracking control of a pneumatic XY table using neural network based PID control. International Journal of Precision Engineering and Manufacturing, 10(5), 37–44.
Huang, D., Xu, J. X., Venkataramanan, V., & Huynh, T. C. T. (2014). High-performance tracking of piezoelectric positioning stage using current-cycle iterative learning control with gain scheduling. IEEE Transactions on Industrial Electronics, 61(2), 1085–1098.
Campolo, D., Sitti, M., & Fearing, R. S. (2003). Efficient charge recovery method for driving piezoelectric actuators with quasi-square waves. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 50(3), 237–244.
Goldfarb, M., & Celanovic, N. (1997). Modeling piezoelectric stack actuators for control of micromanipulation. IEEE Transactions on Control Systems, 17(3), 69–79.
https://www.pi-usa.us/en/products/piezo-motors-stages-actuators/piezo-motion-control-tutorial/tutorial-4-16. Accessed 10 June 2020.
(2005). “Designing with Piezoelectric Transducers: Nanopositioning Fundamentals”. Available http://www.pi.ws. Accessed 10 June 2020.
Kuhnen, K., & Krejci, P. (2009). Compensation of complex hysteresis and creep effects in piezoelectrically actuated systems—A new Preisach modeling approach. IEEE Transactions on Automation Control, 54(3), 537–550.
Nguyen, P. B., & Choi, S. B. (2011). Micro-position control of a piezostack actuator using rate-dependent hysteretic compensator. International Journal of Precision Engineering and Manufacturing, 12(5), 885–891.
Villegas, F., Hecker, R. L., & Peña, M. (2016). Two-state GMS-based friction model for precise control applications. International Journal of Precision Engineering and Manufacturing, 17(5), 553–564.
K. Kuhnen, H. Janocha. (1999). Adaptive inverse control of piezoelectric actuators with hysteresis operators. in Proceedings of the European control conference ECC99, Karlsruhe, Germany, 1–6.
Rosenbaum, S., Ruderman, M., Strohla, T., & Bertram, T. (2010). Use of Jiles-Atherton and Preisach hysteresis models for inverse feed-forward control. IEEE Transactions on Magnetics, 46(12), 3984–3989.
Song, G., Zhao, J. Q., Zhou, X. Q., & de Abreu-Garcia, J. A. (2005). Tracking control of a piezoceramic actuator with hysteresis compensation using inverse Preisach model. IEEE/ASME Transactions on Mechatronics, 10(2), 198–209.
Iyer, R., & Tan, X. (2009). Control of hysteretic systems through inverse compensation. IEEE Control Systems Magnetics, 29(1), 83–99.
Sivaselvan, M. V. (2013). Hysteretic models with stiffness and strength degradation in a mathematical programming format. International Journal of Non-Linear Mechanics, 51, 10–27.
Ming, M., Ling, J., Feng, Z., & Xiao, X. (2018). A model prediction control design for inverse multiplicative structure based feedforward hysteresis compensation of a piezo nanopositioning stage. International Journal of Precision Engineering and Manufacturing, 19(11), 1699–1708.
Dong, R., & Tan, Y. (2009). A modified Prandtl-Ishlinskii modeling method for hysteresis. Physica B: Condensed Matter, 404(8–11), 1336–1342.
Jiang, H., Ji, H., Qiu, J., & Chen, Y. (2010). A modified Prandtl-Ishlinskii model for modeling asymmetric hysteresis of piezoelectric actuators. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 57(5), 1200–1210.
Pickelmann, L. (2006). “Low voltage co-fired multilayer stacks, rings and chips for actuation”. Piezomechanik GmbH., p. 23. Available https://www.piezomechanik.com/en/products/. Accessed 10 June 2020.
Lining, S., Changhai, R., Weibin, R., Liguo, C., & Minxiu, K. (2004). Tracking control of piezoelectric actuator based on a new mathematical model. Journal of Micromechanics and Microengineering, 12, 1439–1444.
S. Eliahou-Niv, M. Tsabari, D. Bar-Anan, D. Oster. (2010). Design validation and testing of a piezoelectric mechanism. in Proceedings of the 50th Israel Annual Conference on Aerospace Sciences, Tel-Aviv, Israel.
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Levy, D.A., Shapiro, A. Model and Analysis of Piezoelectric Actuator in Practical Three-Stage Mechanism. Int. J. Precis. Eng. Manuf. 21, 1717–1728 (2020). https://doi.org/10.1007/s12541-020-00369-x
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DOI: https://doi.org/10.1007/s12541-020-00369-x