Since the piezoelectrically actuated system has nonlinear and time-varying behavior, it is difficult to establish an accurate dynamic model for a model-based sensing and control design. Here, a model-free adaptive sliding controller is proposed to improve the small travel and hysteresis defects of piezoelectrically actuated systems. This sensing and control strategy employs the functional approximation technique (FAT) to establish the unknown function for eliminating the model-based requirement of the sliding-mode control. The piezoelectrically actuated system’s nonlinear functions can be approximated by using the combination of a finite number of weighted Fourier series basis functions. The unknown weighted vector can be estimated by an updating rule. The important advantage of this approach is to achieve the sliding-mode controller design without the system dynamic model requirement. The update laws for the coefficients of the Fourier series functions are derived from a Lyapunov function to guarantee the control system stability. This proposed controller is implemented on a piezoelectrically actuated X-Y table. The dynamic experimental result of this proposed FAT controller is compared with that of a traditional model-based sliding-mode controller to show the performance improvement for the motion tracking performance.
References
[1]
Chang, T; Sun, X. Analysis and Control of Monolithic Piezoelectric Nano-Actuator. IEEE Trans Control Syst Techn?2001, 9, 69–75, doi:10.1109/87.896747.
[2]
Choi, SB; Kim, HK; Lim, SC; Park, YP. Position Tracking Control of an Optical Pick-Up Device Using Piezoceramic Actuator. Mechatronics?2001, 11, 691–705, doi:10.1016/S0957-4158(00)00035-0.
[3]
Lin, CJ; Yang, SR. Precise Positioning of Piezo-Actuated Stages Using Hysteresis-Observer Based Control. Mechatronics?2006, 16, 417–426, doi:10.1016/j.mechatronics.2006.03.005.
[4]
Bashash, S; Jalili, N. Robust Multiple Frequency Trajectory Tracking Control of Piezoelectrically Driven Micro/Nanopositioning Systems. IEEE Trans Control Syst Techn?2007, 15, 867–878, doi:10.1109/TCST.2007.902949.
[5]
Liaw, HC; Shirinzadeh, B; Smith, J. Robust Motion Tracking Control of Piezo-Driven Flexure-Based Four-Bar Mechanism for Micro-Nano Manipulation. Mechatronics?2008, 18, 111–120, doi:10.1016/j.mechatronics.2007.09.002.
[6]
Song, G; Zhao, J; Zhou, X; Abreu-García, JAD. Tracking Control of a Piezoceramic Actuator with Hysteresis Compensation Using Inverse Preisach Model. IEEE Trans Mechatron?2005, 10, 198–209, doi:10.1109/TMECH.2005.844708.
[7]
Tzen, JJ; Jeng, SL; Chieng, WH. Modeling of Piezoelectric Actuator for Compensation and Controller Design. Precis Eng?2003, 27, 70–86, doi:10.1016/S0141-6359(02)00183-6.
[8]
Tsai, MS; Chen, JS. Robust Tracking Control of a Piezoactuator Using a New Approximate Hysteresis Model. J Dyn Syst Meas Contr?2003, 125, 96–102, doi:10.1115/1.1540114.
[9]
Xue, X; Tang, J. Robust and High Precision Control Using Piezoelectric Actuator Circuit and Integral Continuous Sliding Mode Control Design. J Sound Vib?2006, 293, 335–359, doi:10.1016/j.jsv.2005.10.009.
[10]
Yeh, TJ; Lu, SW; Wu, TY. Modeling and Identification of Hysteresis in Piezoelectric Actuator. J Dyn Syst Meas Contr?2006, 128, 189–196, doi:10.1115/1.2192819.
[11]
Chen, PC; Huang, AC. Adaptive Sliding Control of Non-Autonomous Active Suspension Systems with Time-Varying Loadings. J Sound Vib?2005, 282, 1119–1135, doi:10.1016/j.jsv.2004.03.055.
[12]
Huang, SJ; Chen, HY. Adaptive Sliding Controller with Self-Tuning Fuzzy Compensation for Vehicle Suspension Control. Mechatronics?2006, 16, 607–622, doi:10.1016/j.mechatronics.2006.06.002.
[13]
Chen, HY; Huang, SJ. A New Model-Free Adaptive Sliding Controller for Active Suspension System. Int J Syst Sci?2008, 39, 57–69, doi:10.1080/00207720701669453.