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Adaptive Robust Repetitive Control of Piezoelectric Actuators

[+] Author Affiliations
Jinghua Zhong, Bin Yao

Purdue University

Paper No. IMECE2005-81967, pp. 85-92; 8 pages
doi:10.1115/IMECE2005-81967
From:
  • ASME 2005 International Mechanical Engineering Congress and Exposition
  • Dynamic Systems and Control, Parts A and B
  • Orlando, Florida, USA, November 5 – 11, 2005
  • Conference Sponsors: Dynamic Systems and Control Division
  • ISBN: 0-7918-4216-9 | eISBN: 0-7918-3769-6
  • Copyright © 2005 by ASME

abstract

Positioning stages using piezoelectric stack actuators (PEA) possess very high theoretical bandwidth and resolution. However, their tracking performance deteriorates as nonlinear dynamics due to inherent hysteresis starts to dominate when the total length of travel increases. When tracking periodic trajectories, which is common in most industrial applications, the uncertain nonlinearity from hysteresis also becomes periodic. Having identified and separated the fast and slow dynamics of the total stage response, we adopt a simple first-order model assuming the inertial dynamics of the stage is negligible in the low tracking frequency range. By approximating the hysteresis mapping function with simple functions, the overall system model is linearly parameterized for subsequent adaptive robust controller design. Exploiting the periodicity of the uncertain hysteresis nonlinearity, it is further parameterized as finite series of harmonic functions, which eliminates the need for an exact inversion model for hysteresis while achieving high tracking accuracy. Experimental results from tracking control of sinusoidal and typical triangular trajectories show tracking error close to the sensor noise level and demonstrate the effectiveness of the approach.

Copyright © 2005 by ASME

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