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Research Papers

Simultaneous Optimization of Damping and Tracking Controller Parameters Via Selective Pole Placement for Enhanced Positioning Bandwidth of Nanopositioners

[+] Author and Article Information
Douglas Russell

School of Engineering,
University of Aberdeen,
Aberdeen AB24 3UE, UK
e-mail: r01dr12@abdn.ac.uk

Andrew J. Fleming

Centre for Complex Dynamic
Systems and Control,
School of Electrical Engineering
and Computer Science,
University of Newcastle,
Callaghan NSW 2308, Australia
e-mail: andrew.fleming@newcastle.edu.au

Sumeet S. Aphale

Centre for Applied Dynamics Research,
School of Engineering,
University of Aberdeen,
Aberdeen AB24 3UE, UK
e-mail: s.aphale@abdn.ac.uk

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 18, 2014; final manuscript received April 29, 2015; published online July 10, 2015. Assoc. Editor: Srinivasa M. Salapaka.

J. Dyn. Sys., Meas., Control 137(10), 101004 (Jul 10, 2015) (8 pages) Paper No: DS-14-1539; doi: 10.1115/1.4030723 History: Received December 18, 2014

Positive velocity and position feedback (PVPF) is a widely used control scheme in lightly damped resonant systems with collocated sensor actuator pairs. The popularity of PVPF is due to the ability to achieve a chosen damping ratio by repositioning the poles of the system. The addition of a tracking controller, to reduce the effects of inherent nonlinearities, causes the poles to deviate from the intended location and can be a detriment to the damping achieved. By designing the PVPF and tracking controllers simultaneously, the optimal damping and tracking can be achieved. Simulations show full damping of the first resonance mode and significantly higher bandwidth than that achieved using the traditional PVPF design method, allowing for high-speed scanning with accurate tracking. Experimental results are also provided to verify performance in implementation.

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Figures

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Fig. 1

Interaction of input harmonics and plant dynamics. On the left is a typical input for nanopositioning systems, a high-frequency triangular waveform. The typical magnitude response of a lightly damped resonant system is presented in the center. On the right is the resultant distorted output showing the effects of the lightly damped resonance, creep, and hysteresis. Note: the effects have been exaggerated for illustrative purposes.

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Fig. 2

Block diagram of the damped and tracked PVPF scheme, where G(s) is the plant, Gcc(s) is the frequency response function (FRF) measuring the cross-coupling between the axes, CPVPF(s) is the PVPF damping controller, and Ctrack(s) is the tracking controller

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Fig. 3

Root loci of the tracking loop for the traditional controller design and the proposed controller design for the positive imaginary axis only. The solid (---) arrow indicates the effect of the damping controller, and the dashed (- - -) arrow indicates the effect of the tracking controller. In the traditional PVPF design, the tracking controller displaces the complex poles from the intended location as the tracking gain is increased. The proposed control design places the damped poles at different strategic locations such that when the desired tracking gain is reached, the PVPF-induced poles converge on the desired (damped) location.

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Fig. 4

A two-axis 40 μm serial kinematic nanopositioner designed at the EasyLab, University of Nevada, Reno, Nevada

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Fig. 5

Simulated magnitude response of the closed-loop, damped and tracked system for both the traditional PVPF design and the proposed technique that incorporates simultaneously designed damping and tracking controllers optimized via selective pole placement

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Fig. 6

Measured magnitude response of the nanopositioning platform and the derived second-order model. Higher-order models needed to capture the cross-coupling dynamics are not required for the control design and are not derived. Simulated closed-loop magnitude responses of the nanopositioning platform with PVPF controller are provided for both the second-order model and the full frd-model. As can be seen in the x- (top left) and y-axes (bottom right) FRFs, the response is very similar in the frequency range of interest. The higher-order modes have little effect on the response below the first resonance mode.

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Fig. 7

Experimentally measured open- and closed-loop magnitude response of the nanopositioning platform with PVPF and tracking controllers

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Fig. 8

Plot of the phase-corrected x- and y-axes output (top row) and the error relative to the input (bottom row)

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Fig. 9

Raster scan where the x-axis input is a 20 Hz triangle wave with amplitude of ±1.25 μm, and the y-axis input is 10 Hz stepping function which increases by 0.25 μm each period and the step coincides with the lowest point of the x-axis trajectory. The phase-lag-induced artifacts present in the full scan during the transition between each consecutive increment of the stepping function have been removed, leaving only the usable scan lines.

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