Multivariable Negative-Imaginary Controller Design for Damping and Cross Coupling Reduction of Nanopositioners: A Reference Model Matching Approach

Published on Apr 13, 2015in IEEE-ASME Transactions on Mechatronics5.303
路 DOI :10.1109/TMECH.2015.2411995
Sajal K. Das96
Estimated H-index: 96
(UNSW: University of New South Wales),
Hemanshu R. Pota50
Estimated H-index: 50
(UNSW: University of New South Wales),
Ian R. Petersen75
Estimated H-index: 75
(UNSW: University of New South Wales)
Sources
Abstract
This paper presents the design and experimental implementation of a novel multi-input multi-output (MIMO) control structure using two negative-imaginary damping controllers to damp the first resonant mode and attenuate cross coupling effects between the axes of a piezoelectric tube scanner. The dynamics of the scanner in the lateral and longitudinal axes are identified from measured data and the design of the controller using a MIMO framework is done based on a reference model matching approach. The controller proposed in the paper is able to achieve a bandwidth near to the first resonance frequency of the scanner and the proposed controller is robust against changes in resonance frequencies that are due to load changes on the scanner. Experimental results are presented to show the effectiveness of the proposed controller.
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References35
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#1Sajal K. Das (UNSW: University of New South Wales)H-Index: 96
#2Hemanshu R. Pota (UNSW: University of New South Wales)H-Index: 50
Last. Ian R. Petersen (UNSW: University of New South Wales)H-Index: 75
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A design of a double resonant controller to enhance the high-speed nanopositioning performance of a piezoelectric tube scanner (PTS) is presented in this paper. The design of the controller is demonstrated using a multi-input multi-output framework for damping, tracking, and cross coupling control in the PTS. A reference model control technique is applied to design the controller. The controller proposed in this paper achieves a bandwidth near to the first resonance frequency of the PTS. The con...
Source
#1Sajal K. Das (UNSW: University of New South Wales)H-Index: 96
#2Hemanshu R. Pota (UNSW: University of New South Wales)H-Index: 50
Last. Ian R. Petersen (UNSW: University of New South Wales)H-Index: 75
view all 3 authors...
A design of a damping controller to damp the first resonant mode of a piezoelectric tube scanner (PTS) used in most commercial atomic force microscopes (AFMs) is proposed in this study. The design of the controller is carried out by proposing a novel analytical framework. The analytical framework examines the finite-gain stability for a positive feedback interconnection between two stable linear time-invariant systems, where one system has mixed passivity, negative-imaginary, and small-gain prop...
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#1Sachin P. Wadikhaye (University of Newcastle)H-Index: 5
#2Yuen Kuan Yong (University of Newcastle)H-Index: 24
Last. S. O. Reza Moheimani (University of Newcastle)H-Index: 36
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A flexure-guided serial-kinematic XYZ nanopositioner for high-speed Atomic Force Microscopy is presented in this paper. Two aspects influencing the performance of serial-kinematic nanopositioners are studied in this work. First, mass reduction by using tapered flexures is proposed to increased the natural frequency of the nanopositioner. 25% increase in the natural frequency is achieved due to reduced mass with tapered flexures. Second, a study of possible sensor positioning in a serial-kinemati...
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#1Sajal K. Das (UNSW: University of New South Wales)H-Index: 96
#2Obaid Ur Rehman (UNSW: University of New South Wales)H-Index: 16
Last. Ian R. Petersen (UNSW: University of New South Wales)H-Index: 75
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A design and experimental implementation of a minimax linear-quadratic-Gaussian (LQG) controller to damp the resonant modes of a piezoelectric tube scanner (PTS) used in most commercial atomic force microscopes is presented in this paper. The controller design is presented to account two uncertainties in the system which arises due to (a) the spill over dynamics of the PTS at high frequencies and (b) changes in resonance frequency of the scanner which occur due to the various loads on the scanne...
Source
#1Sajal K. Das (UNSW: University of New South Wales)H-Index: 96
#2Hemanshu R. Pota (UNSW: University of New South Wales)H-Index: 50
Last. Ian R. Petersen (UNSW: University of New South Wales)H-Index: 75
view all 3 authors...
This brief presents the design and implementation of a single-input single-output and a multiple-input multiple-output resonant controller to damp the first resonant mode of a piezoelectric tube scanner of an atomic force microscope. The design of the controller is based on a mixed negative-imaginary and small-gain approach and the controller structure is chosen such that closed-loop stability is guaranteed. Experimental results are presented to demonstrate the effectiveness of the resonant cont...
Source
#1Sajal K. Das (UNSW: University of New South Wales)H-Index: 96
#2Hemanshu R. Pota (UNSW: University of New South Wales)H-Index: 50
Last. Ian R. Petersen (UNSW: University of New South Wales)H-Index: 75
view all 3 authors...
An analytical framework to examine the finite-gain stability for a positive feedback interconnection between two stable, linear time-invariant systems where one system has 鈥渕ixed鈥 passivity, negative-imaginary and small-gain properties and the other system has 鈥渕ixed鈥 negative-imaginary, negative-passivity, and small-gain properties is proposed. A classical Nyquist argument is used to examine the stability of the interconnected systems and the usefulness of the proposed framework is illustrated ...
Source
Jul 26, 2013 in CCC (Chinese Control Conference)
#1Sajal K. Das (UNSW: University of New South Wales)H-Index: 96
#2Hemanshu R. Pota (UNSW: University of New South Wales)H-Index: 50
Last. Ian R. Petersen (UNSW: University of New South Wales)H-Index: 75
view all 3 authors...
This paper presents the design and implementation of a multi-input multi-output (MIMO) velocity feedback controller (VFC) based on a recent theoretical results on 鈥渕ixed鈥 negative-imaginary and small-gain approach to damp the first resonant mode of a piezoelectric tube scanner (PTS) used in atomic force microscopes (AFMs). The identification of the MIMO dynamics of the PTS is done by using the measured data and the 鈥渕ixed鈥 negative-imaginary and small-gain approach is used to establish the inter...
Jul 26, 2013 in CCC (Chinese Control Conference)
#1Sajal K. Das (UNSW: University of New South Wales)H-Index: 96
#2Hemanshu R. Pota (UNSW: University of New South Wales)H-Index: 50
Last. Ian R. Petersen (UNSW: University of New South Wales)H-Index: 75
view all 3 authors...
This paper presents the design and implementation of a velocity feedback controller for the piezoelectric tube scanner (PTS) of an atomic force microscope (AFM) to damp its first resonant mode. The dynamics of the PTS is identified by using the measured data and the 鈥渕ixed鈥 negative-imaginary and small-gain approach is used to establish the internal stability of the interconnected systems. The experimental results demonstrate the performance improvement achieved by the proposed controller.
Jul 9, 2013 in AIM (International Conference on Advanced Intelligent Mechatronics)
#1Sajal K. Das (UNSW: University of New South Wales)H-Index: 96
#2Hemanshu R. Pota (UNSW: University of New South Wales)H-Index: 50
Last. Ian R. Petersen (UNSW: University of New South Wales)H-Index: 75
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This paper presents the design and implementation of a multi-variable combined resonant and integral resonant controller for the piezoelectric tube scanner (PTS) of an atomic force microscope (AFM) to damp the resonant mode of the scanner, reduce the cross coupling effect between the axes of the scanner, increase the bandwidth of the overall closed-loop system, and improve the high speed imaging performance of the AFM. The lateral and longitudinal positioning system of the PTS is treated as a tw...
Source
Atomic Force Microscopes (AFM) are used for generating surface topography of samples at micro to atomic resolutions. Many commercial AFMs use piezoelectric tube nanopositioners for scanning. Scanning rates of these microscopes are hampered by the presence of low frequency resonant modes. When inadvertently excited, these modes lead to high amplitude mechanical vibrations causing the loss of accuracy, while scanning, and eventually to break down of the tube. Feedback control has been used to damp...
Source
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In this paper, we present necessary and sufficient conditions under which a linear time-invariant (LTI) system is state feedback equivalent to a negative imaginary (NI) system. More precisely, we show that a minimal LTI strictly proper system can be rendered NI using full state feedback if and only if it can be output transformed into a system, which has relative degree less than or equal to two and is weakly minimum phase. We also considered the problems of state feedback equivalence to output ...
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Multiple-axis nanopositioning stages are widely used in nanotechnology, which suffer not only from hysteresis nonlinearity but also from cross-coupling effect. A vast body of literature have been proposed to model the hysteresis nonlinearity. However, few efforts have been made to describe the cross-coupling effect due to its complexity, and most of the presented works considered only the effect of the motion of the other axis from the aspect of lumped system. Actually, the cross-coupling effect...
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This paper presents necessary and sufficient conditions under which a linear system of relative degree either one or two is state feedback equivalent to a negative imaginary (NI) system. More precisely, we show for a class of linear time-invariant strictly proper systems, that such a system can be rendered minimal and negative imaginary using full state feedback if and only if it is controllable and weakly minimum phase. A strongly strict negative imaginary (SSNI) state feedback equivalence resu...
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This paper demonstrates the design of robust proportional resonant (PR) controller using negative imaginary (NI) theorem for voltage control of three-phase islanded microgrid (MG) application. While operating MG as the islanded mode, different types of random and unknown load dynamics affect the MG. These loads eventually deteriorate the proper execution of MG-inducing disturbances in voltage and current. Therefore, to improve the performance of the three-phase MG, a simple, second-order control...
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A robust output feedback consensus problem for networked identical nonlinear negative-imaginary (NI) systems is investigated in this paper. Output consensus is achieved by applying identical linear output strictly negative-imaginary (OSNI) controllers to all the nonlinear NI plants in positive feedback through the network topology. First, we extend the definition of nonlinear NI systems from single-input single-output (SISO) systems to multiple-input multiple-output (MIMO) systems and also exten...
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#1Kanghong Shi (ANU: Australian National University)H-Index: 2
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This paper surveys the recent advances on the modeling and control of hysteresis of piezoelectric actuators (PTAs) in the context of high precision applications of atomic force microscopes (AFMs). The current states, findings, and outcomes on hysteresis modeling and control in terms of achievable bandwidth and accuracy are discussed in detailed. Future challenges and the scope of possible research are presented to pave the way to video rate atomic force microscopy.
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Parameter uncertainty is a key challenge in the real-time control of nanopositioners employed in scanning probe microscopy. Changes in the sample to be scanned introduces changes in system resonances, requiring instantaneous online tuning of controller parameters to ensure stable, optimal scanning performance. This paper presents a method based on the frequency-domain algebraic derivative approach for the accurate online identification of the nanopositioner's parameters. The parameter estimates ...
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