Open-loop shape control for continuous microelectromechanical system deformable mirror

Diouf, Alioune; Legendre, Andrew P.; Stewart, Jason B.; Bifano, Thomas G.; Lu, Yang

doi:10.1364/ao.49.00g148

Cited by 14 publications

(2 citation statements)

References 13 publications

(34 reference statements)

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“…The DM stroke is 3.5 [µm] and the pitch is 400 [µm]. The behavior of this DM type has been analyzed in many papers, see for example [53], [54] and follow-up works. Consequently, due to paper brevity, we do not further summarize other mirror properties.…”

Section: Resultsmentioning

confidence: 99%

Dual-Update Data-Driven Control of Deformable Mirrors Using Walsh Basis Functions

Haber,

Bifano

2021

Preprint

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In this paper, we develop a novel data-driven method for Deformable Mirror (DM) control. The developed method updates both the DM model and DM control actions that produce desired mirror surface shapes. The novel method explicitly takes into account actuator constraints and couples a feedback control algorithm with an algorithm for recursive estimation of DM influence function models.In addition to this, we explore the possibility of using Walsh basis functions for DM control. By expressing the desired and observed mirror surface shapes as sums of Walsh pattern matrices, we formulate the control problem in the 2D Walsh basis domain. We thoroughly experimentally verify the developed approach on a 140-actuator MEMS DM, developed by Boston Micromachines. Our resultsshow that the novel method produces the root-mean-square surface error in the 14 − 40 nanometer range. These results can additionally be improved by tuning the control and estimation parameters. The developed approach is also applicable to other DM types, such as for example, segmented DMs. I. INTRODUCTION Deformable Mirrors (DMs) are one of the main components of Adaptive Optics (AO) systems [1], [2]. A typical DM consist of a reflective optical surface that is deformed by a set of actuators. By precisely shaping the surface of a DM, we can compensate for wave-front aberrations in AO systems [3]-[16].In this paper, we consider the problem of developing control algorithms for DMs. There are a large number of approaches for DM control. A complete survey of all the methods goes well beyond the length limits of this manuscript. Consequently, we briefly mention only the most

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Section: Resultsmentioning

confidence: 99%

Dual-Update Data-Driven Control of Deformable Mirrors Using Walsh Basis Functions

Haber,

Bifano

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…As an exception, Chen and Ou [30] discussed the control of continuous mechanical systems, wherein the dynamic behavior was simulated using the finite element method. However, at a preliminary design stage; an analytical-numerical model could be beneficial to the designers as it offers flexibility in carrying out a detailed parametric study with relatively less computational effort (see, as an example; the open loop control of a deformable mirror shape which has been modeled as a deformable thin plate [40][41][42]). For simulating the dynamic electromechanical response of continuous mechanical systems (beams, plates, membranes), a variety of macro-models have been proposed in the literature, including those based on simplified approaches, such as the energy-based techniques and modal superposition method [43,44], to computationally extensive approaches including the finite element/boundary element methods and a family of meshless techniques [45][46][47][48].…”

Section: Journal Of Micromechanics and Microengineeringmentioning

confidence: 99%

Mitigation of residual oscillations in electrostatically actuated microbeams using a command-shaping approach

Godara

Joglekar

2015

J. Micromech. Microeng.

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When electrostatically actuated microbeams are driven by an input-waveform comprising multiple voltage steps, the resulting response inherently contains residual oscillations, which may prove detrimental to the device performance and accuracy. In this article, we report the systematic development of a command shaping technique for mitigating such residual oscillations in electrostatically actuated microbeams and achieving fast switching between the successive equilibrium states. Invoking the force balance at a critical point in an oscillation cycle, the proposed technique relies on bringing the actuator to a stagnation state by applying an additional voltage signal of specific amplitude at a predetermined time. The underlying principle of the technique is enunciated for the lumped parallel-plates model of the microactuator, and further extended to the cases of microbeams. The electromechanical model of the microbeam incorporates the effects of full-order electrostatic nonlinearity, moderately large deflections, viscous energy dissipation, and fringing fields. The modal superposition method is employed to obtain the dynamic response of microbeams. Based on a single-mode assumption, the proposed technique lends itself to a simple multistep waveform, which is attractive from the implementation point of view. The applicability of the proposed technique is demonstrated by considering a wide range of parameters involving variations in the extent of geometric nonlinearity, damping, and equilibrium sequences. The impact of higher modes on the stabilized response is exposited, and a command shaping approach based on the multi-mode response of the actuator is suggested. In particular, such an approach is shown to be effective in controlling the motion of the beam in the vicinity of the static pull-in displacement, which is associated with strong electrostatic nonlinearity. The present investigation can find its potential use in the development of an open-loop controller for electrostatically actuated microbeams.

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Alleviation of residual oscillations in electrostatically actuated variable-width microbeams using a feedforward control strategy

Godara

Joglekar

2016

Microsyst Technol

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Open-loop shape control for continuous microelectromechanical system deformable mirror

Cited by 14 publications

References 13 publications

Dual-Update Data-Driven Control of Deformable Mirrors Using Walsh Basis Functions

Dual-Update Data-Driven Control of Deformable Mirrors Using Walsh Basis Functions

Mitigation of residual oscillations in electrostatically actuated microbeams using a command-shaping approach

Alleviation of residual oscillations in electrostatically actuated variable-width microbeams using a feedforward control strategy

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