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What is Small Gain Theorem

Chapter 3
Handbook of Research on Advanced Intelligent Control Engineering and Automation
The small-gain theorem states that, the feedback interconnection between two stable linear systems is stable if the loop-gain between the two systems is strictly less than one.
Published in Chapter:
Advanced Vibration Control of Atomic Force Microscope Scanner
Sajal K. Das (University of New South Wales, Australia), Hemanshu R. Pota (University of New South Wales, Australia), and Ian R. Petersen (University of New South Wales, Australia)
Copyright: © 2015 |Pages: 23
DOI: 10.4018/978-1-4666-7248-2.ch003
Abstract
Atomic Force Microscopes (AFMs) are used in many nanopositioning applications in order to measure the topography of various specimens at an atomic level through surface imaging. The imaging of the samples in AFMs is carried out by using a three degree-of-freedom positioning unit called Piezoelectric Tube Scanner (PTS). The performance of the AFM mostly depends on the performance of the PTS. However, the PTS of the AFM suffers from the problem of vibration. This chapter presents a design of a damping controller to compensate the induced vibration of the scanner. Experimental results are presented to show the effectiveness of the proposed controller. The experimental results show that the proposed controller is able to compensate 90% of the vibration of the PTS.
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