Model-based control for second-order piezo actuator system with hysteresis in time-delay environment
Model-based control for second-order piezo actuator system with hysteresis in time-delay environment
Piezo actuated systems are promising solutions for precision positioning applications. In this paper, a piezoelectric actuator is modeled as a second-order system using the Dahl hysteresis model and the system parameters have been identified from experimental data. The modified internal model control (M-IMC) approach is presented, which not only improves control performance but also reduces associated controller hardware resources. System dead time is approximated using first-order Padé expansion and the proposed Smith predictor-based M-IMC for piezoelectric actuators is seen to offer satisfactory stable control response even for plants with large dead time. The control performance of the M-IMC has been examined for the piezo actuator system against different set point tracking inputs in the presence of a wide range of external disturbances such as plant parameter mismatch, white noise perturbation, and time delay. Simulation results depict the efficacy and versatility of M-IMC in terms of decreased overshoot and settling time compared to traditional IMC and PID designs.
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- [1] Binnig G, Rohrer H. Scanning tunneling microscopy. Helvetica Physica Acta 1983; 55: 726-735.
- [2] Binnig G, Quate CF, Gerber C. Atomic force microscope. Physics Review Letters 1986; 56: 930-933.
- [3] Devasia S, Eleftheriou E, Moheimani R. A survey of control issues in nanopositioning. IEEE Transactions on Control Systems Technology 2007; 15 (5): 205-213. doi: 10.1109/TCST.2007.903345
- [4] Song G, Zhao J, Zhou X, de Abreu-García JA. Tracking control of a piezoceramic actuator with hysteresis compensation using inverse Preisach model. IEEE/ASME Transactions on Mechatronics 2005; 10 (2): 198-209. doi: 10.1109/TMECH.2005.844708
- [5] Ge P, Jouaneh M. Modeling hysteresis in piezoceramic actuators. Precision Engineering; 1995; 17 (3): 211-221. doi: 10.1016/0141-6359(95)00002-U
- [6] Weibel F, Michellod Y, Mullhaupt P, Gillet D. Real-time compensation of hysteresis in a piezoelectric-stack actuator tracking a stochastic reference. In: Proceedings of the American Control Conference; Seattle, WA, USA; 2008. pp. 2939-2944.
- [7] Kuhnen K. Modeling identification and compensation of complex hysteretic non-linearities: a modified Prandtl– Ishlinskii approach. European Journal of Control 2003; 9 (4): 407-418. doi: 10.3166/ejc
- [8] Shome SK, Prakash M, Pradhan S. Mukherjee A. On synergistic integration of adaptive dithering based internal model control for hysteresis compensation in piezoactuated nanopositioner. Mathematical Problems in Engineering 2015; 2015: 1-19. doi: 10.1155/2015/365141
- [9] Hou G, Huang Y, Du H, Zhang J, Zheng X. Design of internal model controller based on ITAE index and its application in boiler combustion control system. In: 12th IEEE Conference on Industrial Electronics and Applications; Siem Reap, Cambodia; 2017. pp. 2078-2083.
- [10] Liu T, Gao F. Enhanced IMC design of load disturbance rejection for integrating and unstable processes with slow dynamics. ISA Transactions 2011; 50 (2): 239-248. doi: 10.1016/j.isatra
- [11] Xu Q, Li Y. Robust Process Control. Hoboken, NJ, USA: Prentice Hall, 1989.
- [12] Naik K, Srikanth P, Negi P. IMC tuned PID governor controller for hydro power plant with water hammer effect. Procedia Technology 2012; 4 (2012): 845-853. doi: 10.1016/j.protcy
- [13] Negi P. Frequency domain analysis of optimal tuned IMC-PID controller for continuous stirred tank reactor. International Journal of Electronics 2014; 2: 34-39.
- [14] Shome SK, Jana S, Mukherjee A, Bhattacharjee P, Datta U. Improved internal model control based closed loop controller design for second order piezoelectric system with dead time. In: Proceedings of 2018 8th IEEE India International Conference on Power Electronics; Jaipur, India; 2018. pp. 1-6.
- [15] Bahill A. A simple adaptive Smith-predictor for controlling time-delay systems. IEEE Control Systems Magazine 1983; 3 (2): 16-22. doi: 10.1109/MCS.1983.1104748
- [16] Shome SK, Pradhan S, Mukherjee A, Datta U. Dither based precise position control of piezo actuated micro-nano manipulator. In: Proceedings of the 39th Annual Conference of the IEEE Industrial Electronics Society; Vienna, Austria; 2013. pp. 3486-3491.
- [17] Xu Q, Li Y. Dahl model-based hysteresis compensation and precise positioning control of an XY parallel micromanipulator with piezoelectric actuation. Journal of Dynamic System, Measurement and Control 2010; 132 (4): 41011. doi: 10.1115/1.400171