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Tomas Tuma, Angeliki Pantazi,John Lygeros, Abu Sebastian
Mechatronics, Volume 22, Issue 3, April 2012
Abstract
Non-linear approaches to feedback control for nanopositioning have recently attracted renewed interest thanks to their superior performance in the presence of measurement noise. In this article, we investigate two recent non-linear control schemes, namely signal transformation and impulsive control, and show that in the context of triangular waveform tracking, they are inherently related. This rather surprising result not only fosters further theoretical studies but also has a significant impact on implementation. We demonstrate that for the tracking of triangular reference signals, impulsive control drastically improves the transient tracking error while providing the same steady state performance. Both methods are compared in theory, simulation and experiments.
Description:
In science and engineering on the nanometer and sub-nanometer scale, position control with precision down to the size of a single atom is of key importance. To that end, feedback control is an essential tool used to compensate for the dynamics of the mechanical scanning devices and for environmental disturbances such as building vibrations and ambient temperature changes. The performance of conventional linear feedback controllers is inherently constrained, but novel non-linear and, in particular, hybrid control techniques have shown great promise towards overcoming the traditional trade-offs of linear feedback control. Specifically, in the field of nanopositioning, two hybrid control techniques have recently been introduced: the so-called signal transformation approach and the concept of impulsive control. The paper presents some rather surprising connections between these two control concepts which significantly advance the theoretical understanding and the implementation aspects. Also, the paper shows that by using impulsive control to track triangular waveforms, significant improvements in performance can be obtained compared with the signal transformation approach.
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