High-bandwidth nanopositioning via active control of system resonance

doi:10.1007/s11465-020-0619-x

Front. Mech. Eng.

2021, Vol. 16

Issue (2) : 331-339 https://doi.org/10.1007/s11465-020-0619-x

RESEARCH ARTICLE

High-bandwidth nanopositioning via active control of system resonance

Linlin LI^1,², Sumeet S. APHALE³(

), Limin ZHU^1,⁴

¹. State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
². State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China
³. The Centre for Applied Dynamics Research, School of Engineering, University of Aberdeen, Aberdeen AB24 3UE, UK
⁴. The Shanghai Key Laboratory of Networked Manufacturing and Enterprise Information, Shanghai 200240, China

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Abstract

Typically, the achievable positioning bandwidth for piezo-actuated nanopositioners is severely limited by the first, lightly-damped resonance. To overcome this issue, a variety of open- and closed-loop control techniques that commonly combine damping and tracking actions, have been reported in literature. However, in almost all these cases, the achievable closed-loop bandwidth is still limited by the original open-loop resonant frequency of the respective positioning axis. Shifting this resonance to a higher frequency would undoubtedly result in a wider bandwidth. However, such a shift typically entails a major mechanical redesign of the nanopositioner. The integral resonant control (IRC) has been reported earlier to demonstrate the significant performance enhancement, robustness to parameter uncertainty, gua-ranteed stability and design flexibility it affords. To further exploit the IRC scheme’s capabilities, this paper presents a method of actively shifting the resonant frequency of a nanopositioner’s axis, thereby delivering a wider closed-loop positioning bandwidth when controlled with the IRC scheme. The IRC damping control is augmented with a standard integral tracking controller to improve positioning accuracy. And both damping and tracking control parameters are analytically optimized to result in a Butterworth Filter mimicking pole-placement—maximally flat passband response. Experiments are conducted on a nanopositioner’s axis with an open-loop resonance at 508 Hz. It is shown that by employing the active resonance shifting, the closed-loop positioning bandwidth is increased from 73 to 576 Hz. Consequently, the root-mean-square tracking errors for a 100 Hz triangular trajectory are reduced by 93%.

Keywords nanopositioning stage high-bandwidth resonant mode control tracking control integral resonant control

Corresponding Author(s): Sumeet S. APHALE

Just Accepted Date: 20 January 2021 Online First Date: 10 March 2021 Issue Date: 15 June 2021

Cite this article:

Linlin LI,Sumeet S. APHALE,Limin ZHU. High-bandwidth nanopositioning via active control of system resonance[J]. Front. Mech. Eng., 2021, 16(2): 331-339.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-020-0619-x
https://academic.hep.com.cn/fme/EN/Y2021/V16/I2/331

Fig.1 Block diagram of the inner loop with unity feedback and feedforward gain (

K s

) to actively shift the Plant’s (

G

) resonance. The ‘Plant’ is the nanopositioner’s axis being controlled.

Fig.2 The overall control diagram with active control of resonance mode.

Fig.3 Experimental setup, including the nanopositioner, the displacement sensor, the voltage amplifier, the data acquisition module and the PC.

Fig.4 Plot of the measured (solid black) and modeled (dashed red) frequency responses demonstrating that the model accurately captures the dynamics of the dominant resonant mode which occurs at 508 Hz.

Fig.5 Nominal open-loop resonant mode (solid blue) at 508 Hz and actively-shifted resonant mode (dashed red) at 908 Hz. Note that the shift in frequency comes at the cost of a reduction in the damping coefficient (sharper/taller resonant peak).

Fig.6 The magnitude responses of the plant, and the closed-loop systems under the proposed active control and the traditional control without the active control of the resonant frequency.

Fig.7 Tracking results of the system under different control schemes with fundamental frequencies of 50 and 100 Hz. Actual displacement with fundamental frequencies of (a) 50 and (b) 100 Hz. For clarity, the traces are offset by 0.5 μm. Furthermore, system-induced phase delay has been eliminated by selecting two full periods of the trajectory for comparison. Tracking errors with fundamental frequencies of (c) 50 and (d) 100 Hz.

Frequency/Hz	Control scheme	$e max ?$ /%	$e rms$ /%	Percentage of tracking within 1% error/%	Percentage of tracking within 5% error/%
50	Without active control of resonant frequency (traditional)	11.40	3.62	64.67	92.01
	With active control of resonant frequency (proposed)	1.83	0.50	97.00	100.00
100	Without active control of resonant frequency (traditional)	33.52	17.79	51.69	58.18
	With active control of resonant frequency (proposed)	4.36	1.09	84.89	100.00

Tab.1 Indices of the tracking results for the system under different control schemes

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