One of the major problems occurring in many technical applications is the presence of the hysteretic behavior in sensors and actuators, which causes a nonlinear relationship between input and output variables in such devices. Since the nonlinear phenomenon of hysteresis degrades the performance of the piezoelectric materials and piezoelectric drive mechanisms, for example, in positioning control framework, it has to be characterized in order to mitigate the effect of the nonlinearity in the devices. This paper is aimed to characterize and model the hysteresis in typical piezoelectric actuators under load-free and preloaded circumstances incorporating the inertial effect of the system. For this purpose, the piezoelectric actuator is modeled as a mass-spring-damper system, which is expressed in terms of a stop operator as one of the essential yet efficient hysteresis operators in the Prandtl-Ishlinskii (PI) model. The reason of utilizing the stop operator in this study is for the sake of control purposes, as the stop operator plays as the inverse of the play operator in the PI model and can be used in a feed-forward controller scheme to suppress the effect of hysteresis in general control framework. The results reveal that this model exhibits better correspondence to the measurement output compared to that of the classical PI model. 1. Introduction Hysteresis is a nonlinear phenomenon that occurs in some types of materials such as piezoceramics, shape-memory alloys, and magnetostrictive actuators. The word “hysteresis” refers to systems that have memory such that similar loops are repeated in each cycle of operation in every dynamical system and, after removal of the force or electrical field, the system does not return to its original location. In this phenomenon, the current output depends also on the history of the input. The effect of hysteresis nonlinearity can be neglected in some systems. In contrast, ignoring this phenomenon in other types of systems that possess severe hysteresis might create undesirable consequences such as inaccuracy in open loop system, limit cycle, degradation of the tracking performance, and even instability of closed loop system. To overcome this challenge, some mathematical models, for example, the Preisach model and the PI model, have been proposed to capture the effect of hysteresis in any mechanical systems. Utilization of the PI model is addressed in many works to characterize the hysteresis due to its simplicity compared to the Preisach model. Wang et al. [1] utilized the classical PI model and neural network
References
[1]
Q. Wang, C. Y. Su, and S. S. Ge, “A direct method for robust adaptive nonlinear control with unknown hysteresis,” in Proceedings of the 44th IEEE Conference on Decision and Control, & the European Control Conference (CDC-ECC '05), vol. 1–8, pp. 3578–3583, December 2005.
[2]
M. Al Janaideh, C. Y. Su, and S. Rakehja, “Modeling hysteresis of smart actautors,” in Proceedings of the 5th International Symposium on Mechatronics and Its Applications (ISMA '08), Amman, Jordan, May 2008.
[3]
P. Krejci and K. Kuhnen, “Inverse control of systems with hysteresis and creep,” IEE Proceedings-Control Theory and Applications, vol. 148, no. 3, pp. 185–192, 2001.
[4]
M. Al Janaideh, Y. Feng, S. Rakheja, C. Y. Su, and C. A. Rabbath, “Hysteresis compensation for smart actuators using inverse generalized prandtl-ishlinskii model,” in Proceedings of the American Control Conference (ACC '09), pp. 307–312, St. Louis, Mo, USA, June 2009.
[5]
M. Al Janaideh, Y. Feng, S. Rakheja, Y. Tan, and C. Y. Su, “Generalized Prandtl-Ishlinskii hysteresis: modeling and robust control for smart actuators,” in Proceedings of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, pp. 7279–7284, 2009.
[6]
X. Chen, “High precision control for piezo-actuated positioners,” in Proceedings of the IEEE International Conference on Mechatronics and Automation (ICMA '09), pp. 966–971, Changchun, China, August 2009.
[7]
M. Al Janaideh, S. Rakheja, and C. Y. Su, “Characterization of rate dependent hysteresis of piezoceramic actuators,” in Proceedings of theIEEE International Conference on Mechatronics and Automation (ICMA '07), vol. 5, pp. 550–555, Haerbin, China, August 2007.
[8]
M. A. Janaideh, S. Rakheja, and C. Y. Su, “Experimental characterization and modeling of rate-dependent hysteresis of a piezoceramic actuator,” Mechatronics, vol. 19, no. 5, pp. 656–670, 2009.
[9]
K. Kuhnen and H. Janocha, “Complex hysteresis modeling of a broad class of hysteretic nonlinearities,” in Proceedings of the 8th International Conference on New Actuators, Bremen, Germany, June 2002.
[10]
W. T. Ang, F. A. Garmon, P. K. Khosla, and C. N. Riviere, “Modeling rate-dependent hysteresis in piezoelectric actuators,” in Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1975–1980, Pittsburgh, Pa, USA, October 2003.
[11]
U.-X. Tan, W. T. Latt, C. Y. Shee, C. N. Riviere, and W. T. Ang, “Feedforward controller of ill-conditioned hysteresis using singularity-free Prandtl-Ishlinskii model,” IEEE/ASME Transactions on Mechatronics, vol. 14, no. 5, pp. 598–605, 2009.
[12]
X. Wang, Y. Mao, X. Wang, and C. Su, “Adaptive variable structure control of hysteresis in GMM actuators based on Prandtl-Ishlinskii model,” in Proceedings of the 33rd Annual Conference of the IEEE Industrial Electronics Society (IECON '07), vol. 1–3, pp. 721–726, Taipei, Taiwan, November 2007.
[13]
M. Goldfarb and N. Celanovic, “Modeling piezoelectric stack actuators for control of micromanipulation,” IEEE Control Systems Magazine, vol. 17, no. 3, pp. 69–79, 1997.
[14]
M. Quant, H. Elizalde, A. Flores, R. Ramírez, P. Orta, and G. Song, “A comprehensive model for piezoceramic actuators: modelling, validation and application,” Smart Materials and Structures, vol. 18, no. 12, 2009.
[15]
T. J. Yeh, S. W. Lu, and T. Y. Wu, “Modeling and identification of hysteresis in piezoelectric actuators,” Journal of Dynamic Systems, Measurement and Control-Transactions of the ASME, vol. 128, no. 2, pp. 189–196, 2006.
[16]
J. L. Ha, Y. S. Kung, R. F. Fung, and S. C. Hsien, “A comparison of fitness functions for the identification of a piezoelectric hysteretic actuator based on the real-coded genetic algorithm,” Sensors and Actuators A, vol. 132, no. 2, pp. 643–650, 2006.
[17]
J. L. Ha, R. F. Fung, and C. S. Yang, “Hysteresis identification and dynamic responses of the impact drive mechanism,” Journal of Sound and Vibration, vol. 283, no. 3-5, pp. 943–956, 2005.
[18]
A. Preumont, Vibration Control of Active Structures, An Introduction, Kluwer Academic Publishers, Dodrecht, The Netherlands, 2002.
