An ARX-Based PID-Sliding Mode Control on Velocity Tracking Control of a Stick-Slip Pi-ezoelectric-Driven Actuator
ABSTRACT
Piezoelectric-driven stick slip actuators have been drawn more and more attention in the nano- positioning application due to the high accuracy and theoretical unlimited displacement. However, the hysteresis of piezoelectric actuator (PEA) and the nonlinear friction force between the end- effector and the stage make control of piezoelectric-driven stick slip actuator challenge. This paper presents the development of an autoregressive exogenous (ARX)-based proportional-integral-derive (PID)-sliding mode control (SMC) for the velocity tracking control of the piezoelectric-driven stick slip actuator. Stability is guaranteed by rigorously choosing the appropriate PID parameters and the zero steady state error is achieved. To verify the effectiveness of the proposed method, experiments were carried out on a commercially-available piezoelectric-driven stick slip actuator. The tracking errors were compared with the traditional PID controller, illustrating that in spite of existing of modeling error, the ARX-based PID-SMC is able to better improve the velocity tracking performance of piezoelectric-driven stick slip actuator, compared with the traditional PID controller.
Piezoelectric-driven stick slip actuators have been drawn more and more attention in the nano- positioning application due to the high accuracy and theoretical unlimited displacement. However, the hysteresis of piezoelectric actuator (PEA) and the nonlinear friction force between the end- effector and the stage make control of piezoelectric-driven stick slip actuator challenge. This paper presents the development of an autoregressive exogenous (ARX)-based proportional-integral-derive (PID)-sliding mode control (SMC) for the velocity tracking control of the piezoelectric-driven stick slip actuator. Stability is guaranteed by rigorously choosing the appropriate PID parameters and the zero steady state error is achieved. To verify the effectiveness of the proposed method, experiments were carried out on a commercially-available piezoelectric-driven stick slip actuator. The tracking errors were compared with the traditional PID controller, illustrating that in spite of existing of modeling error, the ARX-based PID-SMC is able to better improve the velocity tracking performance of piezoelectric-driven stick slip actuator, compared with the traditional PID controller.
Cite this paper
Cao, Y. and Chen, X. (2015) An ARX-Based PID-Sliding Mode Control on Velocity Tracking Control of a Stick-Slip Pi-ezoelectric-Driven Actuator. Modern Mechanical Engineering, 5, 10-19. doi: 10.4236/mme.2015.51002.
Cao, Y. and Chen, X. (2015) An ARX-Based PID-Sliding Mode Control on Velocity Tracking Control of a Stick-Slip Pi-ezoelectric-Driven Actuator. Modern Mechanical Engineering, 5, 10-19. doi: 10.4236/mme.2015.51002.
References
[1] Devasia, S. and Moheimani, S.O.R. (2007) A Survey of Control Issues in Nano-Positioning. IEEE Transactions on Control System Technology, 15, 802-823.
http://dx.doi.org/10.1109/TCST.2007.903345 [2] Shiratori, H., Takizawa, M., Irie, Y., Hirata, S. and Aoyama, H. (2012) Development of the Miniature Hemispherical Tilt Stage Driven by Stick-Slip Motion Using Piezoelectric Actuators. Mechatronics-REM, Paris, 21-23 November. [3] Zhang, Q.S., Chen, X.B. Yang, Q. and Zhang, W.J. (2012) Development and Characterization of a Novel Piezoelectric-Driven Stick-Slip Actuator with Anisotropic-Friction Surfaces. International Journal of Advanced Manufacture Technology, 61, 1029-1034.
http://dx.doi.org/10.1007/s00170-011-3771-y [4] Eigoli, A.K. and Vossoughi, G. (2010) Dynamic Modeling of Stick-Slip Motion in a Legged Piezoelectric Driven Microrobot. International Journal of Advanced Robotic Systems, 7, 201-208. [5] Kang, D. (2012) Modeling of the Piezoelectric-Driven Stick-Slip Actuators. Master Thesis, College of Graduate Studies and Research, University of Saskatchewan, Saskatoon. [6] Bergander, A. and Breguet, J.M. (1998) Performance Improvement for Stick-Slip Positioners. International Symposium on Micromechatronics and Human Science, 59-66. [7] Spiller, M. and Hurak, Z. (2011) Hybrid Charge Control for Stick-Slip Piezoelectric Actuators. Mechatronics, 21, 100-108.
http://dx.doi.org/10.1016/j.mechatronics.2010.09.002 [8] Rakotondrabe, M., Haddab, Y. and Lutz, P. (2008) Voltage/Frequency Proportional Control of Stick-Slip Micropositioning Systems. IEEE Transactions on Control System Technology, 16, 1316-1322.
http://dx.doi.org/10.1109/TCST.2008.917232 [9] Rakotondrabe, M., Haddab, Y. and Lutz, P. (2009) Development of Modeling and Control of Mircro/Nano-Positioning 2-DOF Stick-Slip Device. IEEE Transactions on Mechatronics, 14. [10] Breguet, J.M. and Clavel, R. (1998) Stick and Slip Actuators: Design, Control, Performances and Applications. International Symposium on Micromechatronics and Human Sciences, Nagoya, 25-28 November 1998, 89-95. [11] Young, K.D., Utkin, V.I. and Özgüner, ü. (1999) A Control Engineer’s Guide to Sliding Mode Control. IEEE Transactions on Control System Technology, 17, 328-342.
http://dx.doi.org/10.1109/87.761053 [12] Edwards, C. and Spurgeon, S.K. (1998) Sliding Mode Control. Taylor & Francis Ltd, London. [13] Liawa, H.C., Shirinzadeh, B. and Smith, J. (2007) Enhanced Sliding Mode Motion Tracking Control of Piezoelectric Actuators. Sensors and Actuators, A138, 194-202.
http://dx.doi.org/10.1016/j.sna.2007.04.062 [14] Wang, S., Habibi, S., Burton, R. and Sampson, E. (2006) Sliding Mode Control of an Electrohydraulic Actuator System with Discontinuous Nonlinear Friction. Proceedings of the Institution of Mechanical Engineers, 222, Part I:J, Systems and Control Engineering. [15] Peng, J.Y. and Chen, X.B. (2014) Integrated PID-Based Sliding Mode State Estimation and Control for Piezoelectric Actuators. IEEE/ASME Transactions on Mechatronics, 19, 88-99.
http://dx.doi.org/10.1109/TMECH.2012.2222428 [16] Cao, Y. and Chen, X.B. (2014) Disturbance Observer Based Sliding Mode Control for a Three-DOF Nano-Positioning Stage. IEEE/ASME Transactions on Mechatronics, 19, 924-931.
http://dx.doi.org/10.1109/TMECH.2013.2262802 [17] Cao, Y. and Chen, X.B. (2012) Integrated Inversion-Feedforward and PID-Based Sliding Mode Control for Piezoelectric Actuators. American Control Conference, Montreal, 27-29 June 2012. [18] Peng, J.Y. and Chen, X.B. (2011) Modeling of Piezoelectric-Driven Stick-Slip Actuators. IEEE/ASME Transactions on Mechatronics, 16, 394-399.
http://dx.doi.org/10.1109/TMECH.2010.2043849 [19] Cao, Y. and Chen, X.B. (2012) A Novel Discrete ARMA-Based Model for Piezoelectric Actuator Hysteresis. IEEE/ ASME Transactions on Mechatronics, 17, 737-744.
http://dx.doi.org/10.1109/TMECH.2011.2128339 [20] Chen, X.B., Zhang, Q.S., Kang, D. and Zhang, W.J. (2008) On the Dynamics of Piezoelectric Positioning Systems. Review of Scientific Instrument, 79, Article ID: 116101.
http://dx.doi.org/10.1063/1.2982238
[1] Devasia, S. and Moheimani, S.O.R. (2007) A Survey of Control Issues in Nano-Positioning. IEEE Transactions on Control System Technology, 15, 802-823.
http://dx.doi.org/10.1109/TCST.2007.903345 [2] Shiratori, H., Takizawa, M., Irie, Y., Hirata, S. and Aoyama, H. (2012) Development of the Miniature Hemispherical Tilt Stage Driven by Stick-Slip Motion Using Piezoelectric Actuators. Mechatronics-REM, Paris, 21-23 November. [3] Zhang, Q.S., Chen, X.B. Yang, Q. and Zhang, W.J. (2012) Development and Characterization of a Novel Piezoelectric-Driven Stick-Slip Actuator with Anisotropic-Friction Surfaces. International Journal of Advanced Manufacture Technology, 61, 1029-1034.
http://dx.doi.org/10.1007/s00170-011-3771-y [4] Eigoli, A.K. and Vossoughi, G. (2010) Dynamic Modeling of Stick-Slip Motion in a Legged Piezoelectric Driven Microrobot. International Journal of Advanced Robotic Systems, 7, 201-208. [5] Kang, D. (2012) Modeling of the Piezoelectric-Driven Stick-Slip Actuators. Master Thesis, College of Graduate Studies and Research, University of Saskatchewan, Saskatoon. [6] Bergander, A. and Breguet, J.M. (1998) Performance Improvement for Stick-Slip Positioners. International Symposium on Micromechatronics and Human Science, 59-66. [7] Spiller, M. and Hurak, Z. (2011) Hybrid Charge Control for Stick-Slip Piezoelectric Actuators. Mechatronics, 21, 100-108.
http://dx.doi.org/10.1016/j.mechatronics.2010.09.002 [8] Rakotondrabe, M., Haddab, Y. and Lutz, P. (2008) Voltage/Frequency Proportional Control of Stick-Slip Micropositioning Systems. IEEE Transactions on Control System Technology, 16, 1316-1322.
http://dx.doi.org/10.1109/TCST.2008.917232 [9] Rakotondrabe, M., Haddab, Y. and Lutz, P. (2009) Development of Modeling and Control of Mircro/Nano-Positioning 2-DOF Stick-Slip Device. IEEE Transactions on Mechatronics, 14. [10] Breguet, J.M. and Clavel, R. (1998) Stick and Slip Actuators: Design, Control, Performances and Applications. International Symposium on Micromechatronics and Human Sciences, Nagoya, 25-28 November 1998, 89-95. [11] Young, K.D., Utkin, V.I. and Özgüner, ü. (1999) A Control Engineer’s Guide to Sliding Mode Control. IEEE Transactions on Control System Technology, 17, 328-342.
http://dx.doi.org/10.1109/87.761053 [12] Edwards, C. and Spurgeon, S.K. (1998) Sliding Mode Control. Taylor & Francis Ltd, London. [13] Liawa, H.C., Shirinzadeh, B. and Smith, J. (2007) Enhanced Sliding Mode Motion Tracking Control of Piezoelectric Actuators. Sensors and Actuators, A138, 194-202.
http://dx.doi.org/10.1016/j.sna.2007.04.062 [14] Wang, S., Habibi, S., Burton, R. and Sampson, E. (2006) Sliding Mode Control of an Electrohydraulic Actuator System with Discontinuous Nonlinear Friction. Proceedings of the Institution of Mechanical Engineers, 222, Part I:J, Systems and Control Engineering. [15] Peng, J.Y. and Chen, X.B. (2014) Integrated PID-Based Sliding Mode State Estimation and Control for Piezoelectric Actuators. IEEE/ASME Transactions on Mechatronics, 19, 88-99.
http://dx.doi.org/10.1109/TMECH.2012.2222428 [16] Cao, Y. and Chen, X.B. (2014) Disturbance Observer Based Sliding Mode Control for a Three-DOF Nano-Positioning Stage. IEEE/ASME Transactions on Mechatronics, 19, 924-931.
http://dx.doi.org/10.1109/TMECH.2013.2262802 [17] Cao, Y. and Chen, X.B. (2012) Integrated Inversion-Feedforward and PID-Based Sliding Mode Control for Piezoelectric Actuators. American Control Conference, Montreal, 27-29 June 2012. [18] Peng, J.Y. and Chen, X.B. (2011) Modeling of Piezoelectric-Driven Stick-Slip Actuators. IEEE/ASME Transactions on Mechatronics, 16, 394-399.
http://dx.doi.org/10.1109/TMECH.2010.2043849 [19] Cao, Y. and Chen, X.B. (2012) A Novel Discrete ARMA-Based Model for Piezoelectric Actuator Hysteresis. IEEE/ ASME Transactions on Mechatronics, 17, 737-744.
http://dx.doi.org/10.1109/TMECH.2011.2128339 [20] Chen, X.B., Zhang, Q.S., Kang, D. and Zhang, W.J. (2008) On the Dynamics of Piezoelectric Positioning Systems. Review of Scientific Instrument, 79, Article ID: 116101.
http://dx.doi.org/10.1063/1.2982238