Volume 19, Issue 5 (May 2019)                   Modares Mechanical Engineering 2019, 19(5): 1229-1239 | Back to browse issues page

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Ghafarirad H, Rezaei S, Zareinejad M. Hysteretic Constitutive Equations Based Continuous Dynamic Modeling of Bending Piezoelectric Actuators . Modares Mechanical Engineering 2019; 19 (5) :1229-1239
URL: http://mme.modares.ac.ir/article-15-18628-en.html
1- Mechanical Engineering Department, Amirkabir University of Technology, Tehran, Iran, Iran Postal Code: 1591634311 , Ghafarirad@aut.ac.ir
2- Mechanical Engineering Department, Amirkabir University of Technology, Tehran, Iran
3- New Technologies Research Centre, Amirkabir University of Technology, Tehran, Iran
Abstract:   (3347 Views)
Piezoelectric bending actuators have been extensively utilized in recent years. Two major modeling methods, lumped and continuous, have been generally proposed in previous researches for these actuators. The lumped method can only express the transverse vibration of one specified point on the actuator. In addition, the effect of higher vibrational modes has been ignored. Hence, continuous dynamic models have been proposed to rectify the mentioned drawbacks. In this method, linear constitutive equations for low voltage applications are usually applied. But, the main challenge in continuous modeling of piezoelectric actuators is the hysteresis nonlinear phenomenon caused by excitation voltages. In this paper, piezoelectric nonlinear constitutive equations have been employed to carry out the continuous dynamic model for two general types of bending actuators i.e. Series and Parallel. In addition, zero dynamic analysis for nonlinear systems has been applied to clarify the effect of higher vibrational modes the actuator dynamic behavior based on the location of Experimental results show the maximum error 1.44 and 1.2% in the identification of first and second modes, respectively, and the maximum error 2.89% in the modeling of actuator nonlinear behavior by two modes. These results validate the efficiency of the proposed dynamic model to express the actuator nonlinear behavior, dynamic analysis, and its superiority over conventional models with one mode.
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Article Type: Original Research | Subject: Mechatronics
Received: 2018/04/7 | Accepted: 2018/12/12 | Published: 2019/05/1

References
1. Bashash S, Saeidpourazar R, Jalili N. Development, analysis and control of a high-speed laser-free atomic force microscope. Review of Scientific Instruments. 2010;81(2):023707. [Link] [DOI:10.1063/1.3302553]
2. Kursu O, Kruusing A, Pudas M, Rahkonen T. Piezoelectric bimorph charge mode force sensor. Sensors and Actuators A Physical. 2009;153(1):42-49. [Link] [DOI:10.1016/j.sna.2009.04.026]
3. Bashash S, Salehi-Khojin A, Jalili N, Thompson GL, Vertegel A, Müller M, et al. Mass detection of elastically distributed ultrathin layers using piezoresponse force microscopy. Journal of Micromechanics and Microengineering. 2009;19(2):025016. [Link] [DOI:10.1088/0960-1317/19/2/025016]
4. Xiaoyan H, Ling SF. A sensing and actuating transducer for measuring point impedance to moment. Measurement. 2010;43(3):363-369. [Link] [DOI:10.1016/j.measurement.2009.12.001]
5. Erturk A, Inman DJ. On mechanical modeling of cantilevered piezoelectric vibration energy harvesters. Journal of Intelligent Material Systems and Structures. 2008;19(11):1311-1325. [Link] [DOI:10.1177/1045389X07085639]
6. Teyssieux D, Euphrasie S, Cretin B. MEMS in-plane motion/vibration measurement system based CCD camera. Measurement. 2011;44(10):2205-2216. [Link] [DOI:10.1016/j.measurement.2011.06.020]
7. Xu Q. Precision position/force interaction control of a piezoelectric multimorph microgripper for microassembly. IEEE Transactions on Automation Science and Engineering. 2013;10(3):503-514. [Link] [DOI:10.1109/TASE.2013.2239288]
8. Shim S, Kim MG, Jo K, Kang YS, Lee B, Yang S, et al. Dynamic characterization of human breast cancer cells using a piezoresistive microcantilever. Journal of Biomechanical Engineering. 2010;132(10):104501. [Link] [DOI:10.1115/1.4002180]
9. Rakotondrabe M. Bouc-Wen modeling and inverse multiplicative structure to compensate hysteresis nonlinearity in piezoelectric actuators. IEEE Transactions on Automation Science and Engineering. 2011;8(2):428-431. [Link] [DOI:10.1109/TASE.2010.2081979]
10. Xu Q. Adaptive discrete-time sliding mode impedance control of a piezoelectric microgripper. IEEE Transactions on Robotics. 2013;29(3):663-673. [Link] [DOI:10.1109/TRO.2013.2239554]
11. Sofla MS, Rezaei SM, Zareinejad M, Saadat M. Trajectory tracking control of a piezoelectric stage for dynamic load applications. Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering. 2010;224(8):983-994. [Link] [DOI:10.1243/09596518JSCE973]
12. Zareinejad M, Rezaei SM, Najafabadi HH, Ghidary SS, Abdullah A, Saadat M. Novel multirate control strategy for piezoelectric actuators. Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering. 2009;223(5):673-682. [Link] [DOI:10.1243/09596518JSCE695]
13. Asghari M, Rezaei SM, Zareinejad M. Robust position control of piezoelectric actuator using self sensing actuation. Modares Mechanical Engineering. 2016;16(8):37-46. [Persian] 19- Chao PCP, Liao PY, Tsai MY, Lin CT. Robust control design for precision positioning of a generic piezoelectric system with consideration of microscopic hysteresis effects. Microsystem Technologies. 2011;17(5-7):1009-1023. [Link]
14. Bilgen O, Karami MA, Inman DJ, Friswell MI. The actuation characterization of cantilevered unimorph beams with single crystal piezoelectric materials. Smart Materials and Structures. 2011;20(5):055024. [Link] [DOI:10.1088/0964-1726/20/5/055024]
15. Chen SN, Wang GJ, Chien MC. Analytical modeling of piezoelectric vibration-induced micro power generator. Mechatronics. 2006;16(7):379-387. [Link] [DOI:10.1016/j.mechatronics.2006.03.003]
16. Shirazi MJ, Salarieh H, Alasty A, Shabani R. Tip tracking control of a micro-cantilever Timoshenko beam via piezoelectric actuator. Journal of Vibration and Control. 2013;19(10):1561-1574. [Link] [DOI:10.1177/1077546312447837]
17. Yi J, Chang S, Shen Y. Disturbance-observer-based hysteresis compensation for piezoelectric actuators. IEEE/ASME Transactions on Mechatronics. 2009;14(4):456-464. [Link] [DOI:10.1109/TMECH.2009.2023986]
18. Hegewald T, Kaltenbacher B, Kaltenbacher M, Lerch R. Efficient modeling of ferroelectric behavior for the analysis of piezoceramic actuators. Journal of Intelligent Material Systems and Structures. 2008;19(10):1117-1129. [Link] [DOI:10.1177/1045389X07083608]
19. Chao PCP, Liao PY, Tsai MY, Lin CT. Robust control design for precision positioning of a generic piezoelectric system with consideration of microscopic hysteresis effects. Microsystem Technologies. 2011;17(5-7):1009-1023. [Link] [DOI:10.1007/s00542-011-1250-x]
20. Cao Y, Yang B. Non-linear modelling of multilayer piezoelectric actuators in non-trivial configurations based on actuator design parameters and piezoelectric material properties. Journal of Intelligent Material Systems and Structures. 2012;23(8):875-884. [Link] [DOI:10.1177/1045389X12441508]
21. Landis CM. Non-linear constitutive modeling of ferroelectrics. Current Opinion in Solid State and Materials Science. 2004;8(1):59-69. [Link] [DOI:10.1016/j.cossms.2004.03.010]
22. Lee SH, Royston TJ, Friedman G. Modeling and compensation of hysteresis in piezoceramic transducers for vibration control. Journal of Intelligent Material Systems and Structures. 2000;11(10):781-790. https://doi.org/10.1106/GQLJ-JGEU-MHG1-7JDF https://doi.org/10.1177/104538900772663829 [Link] [DOI:10.1106/GQLJ-JGEU-MHG1-76DF]
23. Stanton SC, Erturk A, Mann BP, Dowell EH, Inman DJ. Nonlinear nonconservative behavior and modeling of piezoelectric energy harvesters including proof mass effects. Journal of Intelligent Material Systems and Structures. 2012;23(2):183-199. [Link] [DOI:10.1177/1045389X11432656]
24. Asghari M, Rezaei SM, Rezaie AH, Zareinejad M, Ghafarirad H. Self-sensing actuation using online capacitance measurement with application to active vibration control. Journal of Intelligent Material Systems and Structures. 2015;26(2):186-200. [Link] [DOI:10.1177/1045389X14522535]
25. Ghafarirad H, Rezaei SM, Zareinejad M, Hamdi M, Jaberzadeh Ansari R. Robust control with unknown dynamic estimation for multi-axial piezoelectric actuators with coupled dynamics. Comptes Rendus Mécanique. 2012;340(9):646-660. [Link] [DOI:10.1016/j.crme.2012.07.003]
26. Erturk A, Inman DJ. An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations. Smart Materials and Structures. 2009;18(2):025009. [Link] [DOI:10.1088/0964-1726/18/2/025009]
27. Ghafarirad H, Rezaei SM, Zareinejad M, Mardi N. Charge-based hysteresis compensation in low impedance piezoelectric actuators by a modified Prandtl–Ishlinskii model. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering. 2019;233(1):83-93. [Link] [DOI:10.1177/0954408917743391]

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