Tip–tilt disturbance model identification for Kalman-based control scheme: application to XAO and ELT systems

Meimon, Serge; Petit, Cyril; Fusco, Thierry; Kulcsár, Caroline

doi:10.1364/josaa.27.00a122

Cited by 69 publications

(62 citation statements)

References 18 publications

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“…Here we follow the Meimon et al (2010) statement that the evolution of both the atmospheric and the vibration components can be described by an autoregressive model of order two in the form:…”

Section: State-space Formalismmentioning

confidence: 99%

“…where δ v n is the vth component of the disturbance at time step n, the coefficients a v 1 and a v 2 are computed from the component characteristics (natural frequency and damping coefficient, the later being lower than 1 for vibrations and greater than 1 for the atmospheric turbulence), and v n a white noise of standard deviation σ v triggering the excitation of the component (see Meimon et al 2010, for the derivation of the coefficients a v 1 and a v 2 ). In our simulated case, given N comp the total number of disturbance components, all baselines included, this evolution model can be generalized to the following matrix form:…”

Section: State-space Formalismmentioning

confidence: 99%

“…To do so, we used a similar approach than those described in Menu et al (2012) and Meimon et al (2010), with a few adaptations to our case.…”

Section: Model Identificationmentioning

confidence: 99%

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Comparison of fringe-tracking algorithms for single-mode near-infrared long-baseline interferometers

Choquet

Perrin

et al. 2014

A&A

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To enable optical long baseline interferometry toward faint objects, long integrations are necessary despite atmospheric turbulence. Fringe trackers are needed to stabilize the fringes and thus increase the fringe visibility and phase signal-to-noise ratio (S/N), with efficient controllers robust to instrumental vibrations and to subsequent path fluctuations and flux drop-outs. We report on simulations, analysis, and comparison of the performances of a classical integrator controller and of a Kalman controller, both optimized to track fringes under realistic observing conditions for different source magnitudes, disturbance conditions, and sampling frequencies. The key parameters of our simulations (instrument photometric performance, detection noise, turbulence, and vibrations statistics) are based on typical observing conditions at the Very Large Telescope observatory and on the design of the GRAVITY instrument, a 4-telescope single-mode long-baseline interferometer in the near-infrared, next in line to be installed at VLT Interferometer. We find that both controller performances follow a two-regime law with the star magnitude, a constant disturbance limited regime, and a diverging regime limited by both the detector and photon-noise. Moreover, we find that the Kalman controller is optimal in the high and medium S/N regime owing to its predictive commands based on an accurate disturbance model. In the low S/N regime, the model is not accurate enough to be more robust than an integrator controller. Identifying the disturbances from high S/N measurements improves the Kalman performances in the case of strong optical path difference disturbances.

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Section: State-space Formalismmentioning

confidence: 99%

Section: State-space Formalismmentioning

confidence: 99%

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Comparison of fringe-tracking algorithms for single-mode near-infrared long-baseline interferometers

Choquet

Perrin

et al. 2014

A&A

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“…For a more complete introduction to this model, we refer to Le Roux et al (2004) and Petit (2006), which are the papers on which the current section is based. The notation we use is (mainly) that of Meimon et al (2010).…”

Section: Basic Case: Two-telescope Kalman-filter Controlmentioning

confidence: 99%

“…This property led Meimon et al (2010) to use an AR(2) model for the turbulence description. We follow their argumentation and write …”

Section: Description Of the Opd Evolutionmentioning

confidence: 99%

Kalman-filter control schemes for fringe tracking

Perrin

Choquet

et al. 2012

A&A

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Context. The implementation of fringe tracking for optical interferometers is inevitable when optimal exploitation of the instrumental capacities is desired. Fringe tracking allows continuous fringe observation, considerably increasing the sensitivity of the interferometric system. In addition to the correction of atmospheric path-length differences, a decent control algorithm should correct for disturbances introduced by instrumental vibrations, and deal with other errors propagating in the optical trains. Aims. In an effort to improve upon existing fringe-tracking control, especially with respect to vibrations, we attempt to construct control schemes based on Kalman filters. Kalman filtering is an optimal data processing algorithm for tracking and correcting a system on which observations are performed. As a direct application, control schemes are designed for GRAVITY, a future four-telescope near-infrared beam combiner for the Very Large Telescope Interferometer (VLTI). Methods. We base our study on recent work in adaptive-optics control. The technique is to describe perturbations of fringe phases in terms of an a priori model. The model allows us to optimize the tracking of fringes, in that it is adapted to the prevailing perturbations. Since the model is of a parametric nature, a parameter identification needs to be included. Different possibilities exist to generalize to the four-telescope fringe tracking that is useful for GRAVITY. Results. On the basis of a two-telescope Kalman-filtering control algorithm, a set of two properly working control algorithms for four-telescope fringe tracking is constructed. The control schemes are designed to take into account flux problems and low-signal baselines. First simulations of the fringe-tracking process indicate that the defined schemes meet the requirements for GRAVITY and allow us to distinguish in performance. In a future paper, we will compare the performances of classical fringe tracking to our Kalman-filter control. Conclusions. Kalman-filter based control schemes will likely become the next standard for fringe tracking, providing the possibility to maximize the tracking performance. The results of the present study are currently being incorporated into the final design of GRAVITY.

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Bounded‐error state and parameter estimation of tip‐tilt disturbances in adaptive optics systems

Khemane

Abbas-Turki

Durieu

et al. 2013

Adaptive Control & Signal

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The main objective of this paper was to estimate tip-tilt disturbances in adaptive optics systems. In a bounded-error context, set inversion methods based on interval analysis are used to guarantee both state and parameter estimation of tip-tilt disturbances. Consequently, two methods are performed. The first method is based on contraction-bisection, and the second one is based only on contraction. Both methods are thus compared, and results are discussed according to computational time and pessimism introduced on each estimated parameter. Deformable mirror (DM): This component features a reflective surface that can be deformed in real time using an array of piezo-stack or voice-coil actuators. The control input is the vector of actuation signals (usually voltages). Wavefront sensor (WFS): This component measures the distorted wavefront. Several kinds of WFS exist. However, one of the most used in AO systems is the Shack-Hartmann sensor, because of its simple and robust technology [1]. Real-time computer: It estimates disturbance parameters, and accordingly, the DM is then deformed to correct the disturbance effect on the wavefront.Deformed wavefront High resolution camera Corrected wavefront Beam splitter Figure 1. Scheme of adaptive optics system.Hence, the WFS measures the residual wavefront or (in the case of so-called open-loop AO systems) directly the disturbance wavefront. WFS measurements are fed into the real-time computer, which computes the DM controls in order to minimize the residual distortion seen by the imaging camera.Tip-tilt disturbances, according to the Zernike representation [5], are the first two terms of the atmospheric disturbance modal expansion. As their name suggests, they are generated by simply tilting a flat wavefront along the x or y axis. Thus, tip tilt is induced not only by atmospheric turbulence but also by displacements of the optical beam relatively to the optical system. This includes displacements of the optical system itself generated by various sources, such as wind shake (wind-induced telescope movements) and mechanical vibrations of the telescope's structure and/or instruments. One can refer to [6-10] and the references therein for more details.Another particularity of the tip and tilt modes is that they can be compensated in a decoupled manner, using two dedicated SISO controllers. In order to decouple these specialized loops from the rest of the AO system, on the actuation side, the separation can be effected by constraining the control vector into the appropriate 2D subspace, by adding to the AO system a specialized flat tiptilt mirror, or by mounting the DM itself on a tip-tilt platform. On the sensing side, adequate tip-tilt measurements are provided by computing the so-called x and y mean slopes, that is, the averages of WFS's slopes in the x and y directions. In an ideal case (Shack-Hartmann perfectly linear), and by neglecting both noise and the effect of higher-order modes, the mean slopes correspond respectively to tip and tilt modes with nearly multiplicative ...

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Tip–tilt disturbance model identification for Kalman-based control scheme: application to XAO and ELT systems

Cited by 69 publications

References 18 publications

Comparison of fringe-tracking algorithms for single-mode near-infrared long-baseline interferometers

Comparison of fringe-tracking algorithms for single-mode near-infrared long-baseline interferometers

Kalman-filter control schemes for fringe tracking

Bounded‐error state and parameter estimation of tip‐tilt disturbances in adaptive optics systems

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