IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 19, NO. 4, AUGUST 2014
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Tracking of Triangular Reference Signals Using LQG Controllers for Lateral Positioning of an AFM Scanner Stage H. Habibullah, Student Member, IEEE, H. R. Pota, Ian R. Petersen, Fellow, IEEE, and M. S. Rana, Student Member, IEEE
Abstract—This paper presents the design of an internal reference model-based optimal linear quadratic Gaussian (LQG) controller for the lateral positioning of a piezoelectric tube actuator (PTA) used in an atomic force microscope (AFM). In this control design, internal modeling of the reference signal and system error are considered. As a result, the steady-state tracking error is minimized. In addition to the LQG controller, a vibration compensator is incorporated with the plant to suppress the vibration of the PTA at the resonance frequency. It achieves a high closed-loop bandwidth and significant damping of the resonant mode of the PTA, which enables a reference triangular signal to be tracked. Comparison of performance of the optimal LQG controller augmented with a vibration compensator and a PI controller demonstrates that the proposed controller shows significant improvements over the existing AFM PI controller. Index Terms—Atomic force microscope (AFM), linear quadratic Gaussian controller, piezoelectric tube actuator (PTA), system identification, vibration compensator.
I. INTRODUCTION MOST commonly used tool in nanotechnology is the piezoelectric actuator, which makes it possible to achieve subnanometric precision motion. Nanotechnology allows the attainment of ultrahigh precision and ultrasmall device sizes in the nanometric range [1]. The most common transducers in nanotechnology are piezoelectric materials (PZMs), which enable one to generate nanometer or subnanometer precision motion. The motion generating characteristics of PZMs are not ideal due to various nonlinearities, e.g., hysteresis, creep, and thermal drift. In the last two decades, there has been unprecedented growth in the area of nanoscience and technology [2]. The invention of the scanning tunneling microscope (STM) and scanning probe microscopes (SPMs) such as the atomic force microscope (AFM) has revolutionized research in various areas, such as material science, biology, precision mechanics, optics,
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Manuscript received August 2, 2012; revised December 7, 2012 and April 7, 2013; accepted May 7, 2013. Date of publication July 11, 2013; date of current version April 25, 2014. Recommended by Technical Editor S. O. Reza Moheimani. This work was supported by the Australian Research Council. The authors are with the School of Engineering and Information Technology, University of New South Wales, Canberra, A.C.T. 2600, Australia (e-mail:
[email protected];
[email protected];
[email protected];
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMECH.2013.2270560
Fig. 1.
Basic schematic view of an AFM.
and microelectronics [3], [4]. In spite of its reputation, the STM has some basic limitations, e.g., it can only scan conductive samples or those coated with conductive layers. This limitation has been overcome with the invention of the AFM by Binnig et al. [4]. In recent years, AFMs have been widely used to generate 3-D images of material surfaces, biological specimens, etc., with ultrahigh accuracy [5]. A basic schematic diagram of an AFM is shown in Fig. 1. An AFM works in one of the three modes: contact mode (
