Alexander Keck

Accelerometer-based online reconstruction of vibrations in extremely large telescopes

Abstract Recent efforts to improve imaging quality of extremely large telescopes are based on compensating for structural vibrations with a compensation mirror canceling out the optical pathway deviations caused by vibrations of the telescope structure. To drive this mirror, the displacement of optical elements has to be reconstructed online from accelerometer measurements. The goal is to obtain high reconstruction accuracy and good disturbance rejection in spite of low-frequency drift and high-frequency noise highly deteriorating the measurements. A reconstructor based on double integration and filtering, a disturbance observer and a novel reconstruction approach based on adaptive resonators are implemented on a laboratory test setup simulating typical telescope vibrations. The true displacement is measured with a strain gauge and serves as a reference for reconstruction accuracy.

Parametric Model Order Reduction via Balanced Truncation with Taylor Series Representation

This paper presents a new method for parametric model order reduction based on balanced truncation. Parametric model order reduction seeks to generate low-order models from larger models without losing the dependence on a parameter. Using a Taylor expansion of the original system, a Taylor expansion of the balanced system can be obtained. In contrast to interpolation-based approaches for the solution of the parametric model order reduction problem, the proposed approach permits calculation of the reduced system as well as the corresponding projection matrix for different parameter values with reduced computation power. This bypasses the problem of incompatible subspaces from different snapshot points potentially occurring in interpolation based approaches that can lead to unexpected behavior up to instability. The presented method can handle multidimensional parameter spaces. Sufficient conditions for the convergence of the Taylor series of the balanced system based on holomorphic functions are derived. The truncation step as well as error bounds are discussed. A Bernoulli beam model is used as an example to demonstrate the performance of the technique.

Improving the performance of interferometric imaging through the use of disturbance feedforward

In this paper, we present a disturbance compensation technique to improve the performance of interferometric imaging for extremely large ground-based telescopes, e.g., the Large Binocular Telescope (LBT), which serves as the application example in this contribution. The most significant disturbance sources at ground-based telescopes are wind-induced mechanical vibrations in the range of 8-60 Hz. Traditionally, their optical effect is eliminated by feedback systems, such as the adaptive optics control loop combined with a fringe tracking system within the interferometric instrument. In this paper, accelerometers are used to measure the vibrations. These measurements are used to estimate the motion of the mirrors, i.e., tip, tilt and piston, with a dynamic estimator. Additional delay compensation methods are presented to cancel sensor network delays and actuator input delays, improving the estimation result even more, particularly at higher frequencies. Because various instruments benefit from the implementation of telescope vibration mitigation, the estimator is implemented as a separate, independent software on the telescope, publishing the estimated values via multicast on the telescopes ethernet. Every client capable of using and correcting the estimated disturbances can subscribe and use these values in a feedforward for its compensation device, e.g., the deformable mirror, the piston mirror of LINC-NIRVANA, or the fast path length corrector of the Large Binocular Telescope Interferometer. This easy-to-use approach eventually leveraged the presented technology for interferometric use at the LBT and now significantly improves the sky coverage, performance, and operational robustness of interferometric imaging on a regular basis.

SAMMY - an algorithm for efficient computation of a smooth path for reference trajectory generation

An efficient algorithm to generate smooth paths from polygonal lines is presented. The smooth path is used in combination with a trajectory generator to create reference values for the 2DOF control of a multi-sensor measuring system. The algorithm handles large amounts of target points without an increase in computation time and is able to construct a path based on noisy measurement data.

Automation and control of a multi-sensor measuring system for quality inspection of technical surfaces

The automation and motion control aspects of a developed multi-sensor measuring system are described in this contribution. The measuring system is designed to automatically detect and survey surface defects of microscopic size on macroscopic mechanical components. It is based on the hierarchical combination of optical sensors with different working ranges and resolutions. This measurement approach requires a high level of automation to perform the inspection and measurement tasks. From a control engineering point of view, the path planning and trajectory generation as well as the high-accuracy motion control and friction compensation system are particularly challenging and compose the focus of this contribution.

Development of new concepts to minimize the impact of fast telescope vibrations seen by the E-ELT/MICADO wavefront sensors

We present our recently started eort to realize feedforward vibration control loops with a full adaptive optics (AO) testbed in the laboratory. A piezo-driven tip-tilt mirror unit introduces an arbitrary, but controllable, vibration power-spectrum to simulate telescope mirror vibrations of any kind on the wavefront sensor. Our ultimate goal is to demonstrate in realistic laboratory tests, how telescope vibrations faster than atmospheric tip-tilt can be measured by accelerometers, and controlled in real-time feedforward to allow for longer and more sensitive wavefront sensor (WFS) integrations.

Accelerometer-based online reconstruction of fast telescope vibrations from delayed measurements

A feedforward vibration cancellation system can be used to compensate for fast wind-induced telescope vibrations. Crucial is the position reconstructors ability to provide the compensation mirror with an accurate online estimate of the vibrational displacement. The authors have developed and presented a position reconstructor based on adaptive resonators. However, network data transmission of the acceleration signals introduces a time delay into the measurement chain. Any feedforward compensation setup can only function well if a delay-free estimate of the disturbance signal is provided. Three delay-compensating extensions of the developed position reconstructor are presented and analyzed.

Accelerometer-based online reconstruction of vibrations from delayed measurements

Online position reconstruction from acceleration measurements is an important control engineering task in many applications such as feedforward vibration compensation in telescopes. A sophisticated position reconstruction algorithm based on adaptive resonators solving this task has been developed and presented by the authors. An additional challenge arises when the acceleration signal is subjected to a time delay in the measurement chain. Any effective feedforward compensation setup can only function well if a delay-free estimate of the disturbance signal is provided. The consequences of a measurement time delay for vibrational feedforward compensation are discussed and three delay-compensating extensions of the developed position reconstructor are presented.

Multisensorisches Messsystem zur dreidimensionalen Inspektion technischer Oberflächen

Zusammenfassung Um die Fertigungsqualität mechanischer Bauteile aus Kleinserienproduktionen sicherzustellen werden flexible Inspektionssysteme benötigt. Zur Erfüllung dieser Anforderungen wird in diesem Beitrag eine multiskalige Inspektionsstrategie und deren Implementierung an einem Demonstrator vorgestellt. Dieser besteht aus mehreren optischen Sensoren sowie einem Aktoriksystem, das mithilfe einer angepassten Messablaufsteuerung und Regelung zur Inspektion von Unvollkommenheiten an kleinen Bauteilen wie Zahnrädern eingesetzt werden kann.

Accelerometer-based position reconstruction for the feedforward compensation of fast telescope vibrations in the E-ELT/MICADO

The amount of image motion caused by vibrations of the telescope structure increases with the size of the telescope. Compensating the effects of structural vibrations in the optical path will be a major design question for adaptive optics (AO) systems in future extremely large telescopes like the E-ELT. A promising control system architecture is the recently developed Dual-Loop-Approach, with a feedforward loop based on accelerometer measurements, compensating for the vibrations in addition to the classical AO feedback loop compensating for atmospheric turbulences. We present our efforts to develop sophisticated estimation and control algorithms for this feedforward loop. The major task from a control engineering point of view is reconstructing the position of the vibrating elements from accelerometer measurements highly deteriorated by low-frequency drift and highfrequency noise. The algorithms are evaluated and compared using a realistic Tip-Tilt-Vibration laboratory test setup. Position reconstruction for a realistic 8 Hz structural resonance with an error of only 4% is achieved. Our ultimate goal is to achieve longer and more sensitive wavefront sensor (WFS) integrations by permitting a smaller bandwidth of the AO feedback loop in the E-ELT/MICADO.