Low-order continuous-time robust repetitive control: Application in nanopositioning

Eielsen, Arnfinn A.; Gravdahl, Jan Tommy; Leang, Kam K.

doi:10.1016/j.mechatronics.2015.07.006

Cited by 22 publications

(11 citation statements)

References 48 publications

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“…The stability margin of the system is increased by using k s = 1.5. Due to the hysteresis in the piezoelectric actuator, the effective gain of the actuator is known to change by up to 80% , hence a constant margin should capture this uncertainty well. The frequency response of the filter and the stability criterion () are shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

Improving Robustness Filter Bandwidth in Repetitive Control by Considering Model Mismatch

Eielsen

Teo

Fleming

2016

Asian Journal of Control

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Repetitive control (RC) is used to track and reject periodic signals by including a model of a periodic signal in the feedback path. The performance of RC can be improved by including an inverse plant response filter, but due to modeling uncertainty at high frequencies, a low-pass robustness filter is also required to limit the bandwidth of the signal model and ensure stability. The design of robustness filters is presently ad-hoc, which may result in excessively conservative performance. This article proposes a new automatic method for designing the robustness filter based on convex optimization and an uncertainty model. Experimental results on a nanopositioning system demonstrate that the proposed method outperforms the traditional brick-wall filter approach.

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Section: Resultsmentioning

confidence: 99%

Improving Robustness Filter Bandwidth in Repetitive Control by Considering Model Mismatch

Eielsen

Teo

Fleming

2016

Asian Journal of Control

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“…Additionally, they cannot provide asymptotic tracking either. Though tracking triangular trajectories can be tracked via the internal 5model principle using repetitive control [11] or iterative learning control [30], these techniques have several drawbacks: a) they are complicated to design, b) they require several cycles of the signal in order to reduce the tracking error, which deems them inapplicable for non-periodic signals, c) they require perfect knowledge of all the parameters of the system, or in the case of uncertainties, they must be combined with robust control schemes [11] [30]. A simpler approach would be extremely beneficial for such applications.…”

Section: Dof-pi 2 D Desginmentioning

confidence: 99%

“…Among the different actuation methods available, piezoelectric actuators (PEAs) [5,6] have been extensively adopted in micro-/nanopositioning applications mainly due to their nanometer-scale resolution, high bandwidth, high force density and, absence of backlash and stick-slip [7]. The early models of piezoelectric tube scanners have been replaced by various PEA-driven nanopositioners capable of providing multi-DOF motions [8][9][10][11]. Flexurebased nanopositioners are popular due to several key advantages viz: low cross-coupling between motion axes, robust mechanical construction, large motion range and high mechanical bandwidth [12].…”

Section: Introductionmentioning

confidence: 99%

“…Controllers that provide asymptotic tracking of periodic signals have also been proposed. These are based on the internal model principle (IMP) and use variations of either repetitive control (RC) or iterative learning control (ILC) [11] [21]. It should also be emphasized that in RC, the enhanced performance at the desired periodic frequencies commonly results in deteriorated loop shapes at other frequencies [22], which from a practical point of view means that either the time-period must be constant (±0.1%), or an on-line accurate measurement of the period of the signal is necessary in order to adaptively tune the controller -thereby increasing complexity.…”

Section: Introductionmentioning

confidence: 99%

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Two-degrees-of-freedom PI2D controller for precise nanopositioning in the presence of hardware-induced constant time delay

2019

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The fast and accurate tracking of periodic and arbitrary reference trajectories is the principal goal in many nanopositioning applications. Flexure-based piezoelectric stack driven nanopositioners are widely employed in applications where accurate mechanical displacements at these nanometer scales are required. The performance of these nanopositioners is limited by the presence of lightly damped resonances in their dynamic response and actuator nonlinearities. Closed-loop control techniques incorporating both damping and tracking are typically used to address these limitations. However, most tracking schemes employed use a first-order integrator where a triangular trajectory commonly used in nanopositioning applications necessitates a double integral for zero-error tracking. The phase margin of the damped system combined with the hardware-induced delay deem the implementation of a double-integrator unstable. To overcome this limitation, this paper presents the design, analysis and application of a new control scheme based on the structure of the traditional Two-Degrees-of-Freedom PID controller (2DOF-PID). The proposed controller replaces the integral action of the traditional 2DOF-PID with a double integral action (2DOF-PI 2 D). Despite its simplicity, the proposed controller delivers superior tracking performance compared to traditional combined damping and tracking control schemes based on well-reported designs such as positive position feedback (PPF), Integral resonant control (IRC), and Positive Velocity and Position Feedback (PVPF). The stability of the control system is analyzed in the presence of a time delay in the system. Experimental results validating the efficacy of the proposed chattering-free control of a piezo-driven nanopositioning system are included.

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“…In addition, an approach based on modified repetitive control is proposed for high-speed tracking control of piezo-actuated nanopositioning stages in [11]. A low-order repetitive control design in continuous-time for piezo-based nanopositioning system was proposed in [12]. The authors in [13] introduced a novel modeling and identification for approach for piezoelectric-actuated stages by cascading hysteresis nonlinearity with linear dynamics, which is described as a Hammerstein-like structure.…”

Section: Introductionmentioning

confidence: 99%

Force control of piezoelectric walker

Uzunović

Golubovic²,

Şabanoviç

2016

IECON 2016 - 42nd Annual Conference of the IEEE Industrial Electronics Society

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Abstract-This paper is concerned with the force control of a walking piezoelectric motor, a commercially available Piezo LEGS motor. The motor is capable of providing high precision positioning control on nanometer scale, but also relatively high forces up to 6 N. The proposed force control algorithm is very simple, but effective, and it is based on a recently presented coordinate transformation. The transformation allows definition of the driving waveforms for the motor according to a desired motion of the motor legs in the plane of motion. Such a possibility opens a path for creating the y-direction interaction force between the motor legs and the rod which is enough to ensure no relative motion between the legs and the rod. Once that is achieved, one can control the x-direction force imposed by the motor rod on its environment. The presented force control scheme has been successfully validated through a series of experiments.

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Low-order continuous-time robust repetitive control: Application in nanopositioning

Cited by 22 publications

References 48 publications

Improving Robustness Filter Bandwidth in Repetitive Control by Considering Model Mismatch

Improving Robustness Filter Bandwidth in Repetitive Control by Considering Model Mismatch

Two-degrees-of-freedom PI2D controller for precise nanopositioning in the presence of hardware-induced constant time delay

Force control of piezoelectric walker

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