Hysteresis Modeling of Amplified Piezoelectric Stack Actuator for the Control of the Microgripper
Keywords:
Hysteresis modeling, amplified piezoelectric actuator (APA), Bouc-Wen model, tracking control.Abstract
This paper presents Bouc-Wen hysteresis modelling and tracking control of piezoelectric stack APA120S. The actuator is used to control a microgripper. A modified Bouc-Wen non-symmetric model is applied to study the behaviour of the system in static and dynamic state. The good agreement between predicted and measured curve showed that the Bouc-Wen model is an effective mean for modelling the hysteresis of piezoelectric actuator system. Subsequently, the inverse Bouc-Wen model is formulated and applied to cancel the non-linear hysteresis. In perspective of a control design, it is desirable to linearize the non-linear Bouc-Wen model to produce a static system. Finally, in order to increase damping of the actuator system and to improve the control accuracy, a cascaded PID controller is designed with consideration of the dynamics and static behaviour of the actuator. Experiment result shows that error is of only 5% if PID is cascaded with hysteresis compensation. Therefore, hysteresis compensation with PID controller greatly improves the micromanipulation accuracy of the microgripper actuated by piezoelectric stack.
References
[2] Pluta, J.; Sibielak, M., “The application of a piezoelectric stack for control of small flow intensity hydraulic fluid Carpathian”, 13th International Control Conference (ICCC), 2012, 573 – 577.
[3]. S. Zhao, A. Erturk “Deterministic and band-limited stochastic energy harvesting from uniaxial excitation of a multilayer piezoelectric stack”, Sensors and Actuators A: Physical, Volume 214, 1 August 2014, Pages 58-65.
[4] G. M?boungui, K. Adendorff, R. Naidoo, A.A. Jimoh, D.E. Okojie, “A hybrid piezoelectric micro-power generator for use in low power applications”, Renewable and Sustainable Energy Reviews, Volume 49, September 2015, Pages 1136-1144.
[5] Wang, C.; Gachagan, A.; O'Leary, R.; Mackersie, J. “High inensity focused ultrasound array treansducers using a 2-2 stacked piezoelectric composite appropriate for sonochemistry applications”, IEEE International Ultrasonics Symposium (IUS), 2012, Pages: 2497 – 2500.
[6]. M. Goldfarb and N. Celanovic, “Modeling piezoelectric stack actuators for control of micromanipulation,” IEEE Contr. Syst. Mag., vol. 17, no. 3, Mar. 1997, pp. 69–79.
[7]. S. Salapaka, A. Sebastian, J. P. Cleveland, and M. V. Salapaka, “High bandwidth nano-positioner: A robust control approach,” Rev. Sci. Instr., vol. 73, no. 9, pp. 3232–41, 2002.
[8]. P. Ge and M. Jouaneh, “Tracking control of a piezoceramic actuator,” IEEE Trans. Control Syst. Technol., May 1996, vol. 4, no. 3, pp. 209–216.
[9]. M. Goldfard and N. Celanovic, “A lumped parameter electromechanical model for describing the nonlinear behavior of piezoelectric actuators,” ASME J. Dyn. Syst., Meas. Contr., vol. 119, pp. 478–485, 1997.
[10]. M.-S. Tsai and J.-S. Chen, “Robust tracking control of a piezoactuator using a new approximate hysteresis model,” ASME J. Dyn. Syst., Meas. Contr., vol. 125, pp. 96–102, 2003.
[11]. L. Dupre, R. van Keer, and J. A. A. Melkebeek, “Identi?cation of the relation between the material parameters in the Presach model and in the Jiles-Atherton hysteresis model,” J. Appl. Phys., vol. 85, pp. 4376–4378, au- 1999.
[12]. Habineza, D.; Rakotondrabe, M.; Le Gorrec, Y. “Modeling, identification and feedforward control of multivariable hysteresisby combining Bouc-Wen equations and the inverse multiplicative structure”, American Control Conference (ACC), 2014, Pages: 4771 - 4777, IEEE Conference Publications.
[13]. Kozlov, D.V., “Approximate analytical solution of the Bouc-Wen hysteresis model by the Fourier transform”, International Siberian Conference on Control and Communications (SIBCON), 2011, Pages: 76 – 80, IEEE Conference Publications.
[14]. Qiao Zhi; Gan Minggang; Wang Chenyi, “Sliding Mode Control Using linear extended state observer(LESO) andhysteresis compensator based on Bouc-Wen model in sinusoidal position control of a piezoelectric actuator” 33rd Chinese Control Conference (CCC), 2014 , Pages: 3840 – 3845.
[15]. Zhi Liu; Guanyu Lai; Yun Zhang; Chen, C.L.P. “Adaptive Neural Output Feedback Control of Output-Constrained Nonlinear Systems With Unknown Output Nonlinearity”, IEEE Transactions on Neural Networks and Learning Systems, 2015, Vol. 26(8), Pages: 1789 – 1802, IEEE Journals & Magazines.
[16]. Habineza, D.; Rakotondrabe, M.; Le Gorrec, Y. “Bouc–Wen Modeling and Feedforward Control of Multivariable Hysteresis in Piezoelectric Systems: Application to a 3-DoF Piezotube Scanner”, IEEE Transactions on Control Systems Technology, 2015, Volume: 23, Issue: 5 Pages: 1797 – 1806.
[17]. Laudani, A.; Fulginei, F.R.; Salvini, A. “Bouc–Wen Hysteresis Model Identification by the Metric-Topological Evolutionary Optimization” IEEE Transactions on Magnetics, Year: 2014, Volume: 50, Issue: 2, IEEE Journals & Magazines.
[18]. Zhi Liu; Guanyu Lai; Yun Zhang; Xin Chen; Chen, C.L.P., "Adaptive Neural Control for a Class of Nonlinear Time-Varying Delay Systems With Unknown Hysteresis”, IEEE Transactions on Neural Networks and Learning Systems, Year: 2014, Volume: 25, Issue: 12 Pages: 2129 – 2140, IEEE Journals & Magazines.
[19]. Rakotondrabe, M., “Bouc–Wen Modeling and Inverse multiplicative structure to Compensate Hysteresis Nonlinearity in Piezoelectric Actuators, IEEE Transactions on Automation Science and Engineering, Year: 2011, Volume: 8, Issue: 2, Pages: 428 – 431.
[20] Wei Zhu, Dai-hua Wang “Non-symmetrical Bouc–Wen model for piezoelectric ceramic actuators” Sensors and Actuators A: Physical, Volume 181, July 2012, Pages 51–60.
[21] Jayawardhana, Bayu, Hartmut Logemann, and Eugene P. Ryan. "PID control of second-order systems with hysteresis." International Journal of Control 81.8 (2008): 1331-1342.
Downloads
Published
How to Cite
Issue
Section
License
Authors who submit papers with this journal agree to the following terms.