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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 365141, 19 pages
Research Article

On Synergistic Integration of Adaptive Dithering Based Internal Model Control for Hysteresis Compensation in Piezoactuated Nanopositioner

1Electronics & Instrumentation Group, CSIR-CMERI, Durgapur 713209, India
2Department of Electrical Engineering, University of Minnesota, Minneapolis, MN 55455, USA

Received 17 September 2014; Accepted 1 December 2014

Academic Editor: Xinggang Yan

Copyright © 2015 Saikat Kumar Shome et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Piezoelectric-stack actuated platforms are very popular in the parlance of nanopositioning with myriad applications like micro/nanofactory, atomic force microscopy, scanning probe microscopy, wafer design, biological cell manipulation, and so forth. Motivated by the necessity to improve trajectory tracking in such applications, this paper addresses the problem of rate dependent hysteretic nonlinearity in piezoelectric actuators (PEA). The classical second order Dahl model for hysteresis encapsulation is introduced first, followed by the identification of parameters through particle swarm optimization. A novel inversion based feedforward mechanism in combination with a feedback compensator is proposed to achieve high-precision tracking wherein the paradoxical concept of noise as a performance enhancer is introduced in the realm of PZAs. Having observed that dither induced stochastic resonance in the presence of periodic forcing reduces tracking error, dither capability is further explored in conjunction with a novel output harmonics based adaptive control scheme. The proposed adaptive controller is then augmented with an internal model control based approach to impart robustness against parametric variations and external disturbances. The proposed control law has been employed to track multifrequency signals with consistent compensation of rate dependent hysteresis of the PEA. The results indicate a greatly improved positioning accuracy along with considerable robustness achieved with the proposed integrated approach even for dual axis tracking applications.