Model-Based Feedforward Control of Large Deformable Mirrors

Ruppel, Thomas; Sawodny, Oliver

doi:10.3166/ejc.17.261-272

Cited by 18 publications

(9 citation statements)

References 20 publications

(39 reference statements)

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“…The approach presented here could also be extended to two-stage controller structures combining a discrete-time turbulence reconstructor and a faster-rate or even continuoustime DM surface deformation controller, e.g. a feedforward surface deformation controller [17]. For such control architectures, the approach outlined in this paper would enable to manage and optimize the interactions between the outer, slower WFS-based disturbance estimation stage (in practice, a Kalman filter) and the inner, faster DM control loop.…”

Section: Conclusion and Perpectivesmentioning

confidence: 97%

Mirrors' dynamics: A plague for adaptive optics systems performance?

Nechak¹,

Raynaud²,

Kulcsár³

et al. 2014

2014 European Control Conference (ECC)

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This paper proposes a constructive controller design technique to optimize the closed-loop performance of adaptive optics systems in presence of deformable mirror's dynamics, based on LTI continuous-time models of the disturbance and mirror. This sampled-data stochastic minimum-variance control problem has an equivalent discrete-time and tractable LQG control formulation. We show that the optimal solution can be obtained in a simpler way than what was proposed previously in the literature, with all control calculations being performed using off-the-shelf state-space control software. The proposed formulation provides an easy tool for performance evaluation of sub-optimal controllers.As an illustrative example, control of the tip-tilt wavefront distortion modes for an Extremely Large Telescope (ELT)-class AO system in presence of poorly damped second order DM's dynamics well within the disturbance rejection bandwidth is presented. Variance calculations and time-domain simulations show that in this case, infinite actuator bandwidth is not mandatory, on the condition DM's dynamics be adequately accounted for.

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Section: Conclusion and Perpectivesmentioning

confidence: 97%

Mirrors' dynamics: A plague for adaptive optics systems performance?

Nechak¹,

Raynaud²,

Kulcsár³

et al. 2014

2014 European Control Conference (ECC)

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“…It is assumed that the DM satisfies the Kirchhoff–Love plate theory assumptions. The governing equation of the DM is given as (Ruppel et al, 2011; Vdovin et al, 2011; Vogel et al, 2010)…”

Section: Modelling Of the Deformable Mirrormentioning

confidence: 99%

H∞ Suboptimal controller design for adaptive optic systems

Erol

Altıner

Adali

et al. 2018

Transactions of the Institute of Measurement and Control

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In this paper, an alternative approach to conventional H ∞ control is proposed for adaptive optic (AO) systems. In order to account for the dynamics of the deformable mirror (DM), the Kirchhoff plate equation is considered. Phase wavefront aberrations, which are the effect of atmospheric turbulence, are modelled using the orthogonal set of Zernike polynomials. The first part of this study concerns the derivation of mathematical models for the DM and the atmospheric turbulence. The AO systems used for disturbance rejection concentrate on a specific frequency band, as the disturbance occurs in that region. However, the conventional weighted H ∞ controller is not applicable due to its order. The proposed controller handles this problem by using frequency weighted balanced model reduction. The efficiency of the proposed approach is examined on Zernike’s tip and tilt, focus, astigmatism, coma, trefoil, spherical, secondary astigmatism and quadrafoil modes.

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“…The most difficult task for control of deformable mirrors clearly is not the stabilization of the shell in a static shape, but changing the mirrors deflection in a predefined time and maintaining system stability. Instead of using a pure feedback controller for this task, model-based feedforward control concepts are proposed as in [20,21]. In the past, the concept of model-based feedforward control has successfully been applied to various classes of dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

“…Since typical deformable mirrors do not significantly change their dynamical behavior over time, model-based time-invariant feedforward control can efficiently reduce load on implemented feedback controllers. Studies on model-based feedforward control of large deformable mirrors show that either with poorly tuned feedback control or even without feedback control, high speed and high precision deformations of deformable mirrors can be achieved [20,21]. 1 The required dynamical model of the DM can be identified based on internal position measurements of excited DM actuators.…”

Section: Introductionmentioning

confidence: 99%