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In a tokamak, magnetic islands need to be suppressed. Suppression is possible with electron cyclotron heating (ECH), which can be positioned using electron cyclotron emission (ECE) temperature measurements. A set-up to detect ECE in the line of sight of ECH has been built for the TEXTOR tokamak and the ASDEX Upgrade tokamak. In TEXTOR, a dielectric filter was used to separate low power ECE from high power ECH and successful aiming of ECH and suppression of a magnetic island could be demonstrated. At ASDEX Upgrade, a fast directional switch (FADIS) was used to separate ECE from ECH. Measurements of magnetic islands at ASDEX Upgrade are presented. The applicability of these measurements for magnetic island detection is discussed.

We present two complementary algorithms suitable for using focal-plane measurements to control a wavefront corrector with an extremely high-spatial resolution. The algorithms use linear approximations to iteratively minimize the aberrations seen by the focal-plane camera. The first algorithm, Fast & Furious (FF), uses a weak-aberration assumption and pupil symmetries to achieve fast wavefront reconstruction. The second algorithm, an extension to FF, can deal with an arbitrary pupil shape; it uses a Gerchberg–Saxton (GS)-style error reduction to determine the pupil amplitudes. Simulations and experimental results are shown for a spatial-light modulator controlling the wavefront with a resolution of 170×170??pixels. The algorithms increase the Strehl ratio from ?0.75 to 0.98–0.99, and the intensity of the scattered light is reduced throughout the whole recorded image of 320×320??pixels. The remaining wavefront rms error is estimated to be ?0.15??rad with FF and ?0.10??rad with FF-GS., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

We investigate methods to calibrate the non-common path aberrations at an adaptive optics system having a wavefront-correcting device working with an extremely high resolution (larger than 150x150 correcting elements). We use focal-plane images collected successively, the corresponding phase-diversity information and numerically efficient algorithms to calculate the required wavefront updates. Different approaches are considered in numerical simulations, and laboratory experiments are shown to confirm the results. We compare the performances of the standard Gerchberg-Saxton algorithm, Fast and Furious (use of small-phase assumption to take advantage of linearisation) and recently proposed phase-retrieval methods based on convex optimisation. The results indicate that the calibration task is easiest with algorithms similar to Fast and Furious, at least in the framework we considered., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

We present two complementary algorithms suitable for using focal-plane measurements to control a wavefront corrector with an extremely high-spatial resolution. The algorithms use linear approximations to iteratively minimize the aberrations seen by the focal-plane camera. The first algorithm, Fast & Furious (FF), uses a weak-aberration assumption and pupil symmetries to achieve fast wavefront reconstruction. The second algorithm, an extension to FF, can deal with an arbitrary pupil shape; it uses a Gerchberg–Saxton (GS)-style error reduction to determine the pupil amplitudes. Simulations and experimental results are shown for a spatial-light modulator controlling the wavefront with a resolution of 170×170??pixels. The algorithms increase the Strehl ratio from ?0.75 to 0.98–0.99, and the intensity of the scattered light is reduced throughout the whole recorded image of 320×320??pixels. The remaining wavefront rms error is estimated to be ?0.15??rad with FF and ?0.10??rad with FF-GS., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

We investigate methods to calibrate the non-common path aberrations at an adaptive optics system having a wavefront-correcting device working with an extremely high resolution (larger than 150x150 correcting elements). We use focal-plane images collected successively, the corresponding phase-diversity information and numerically efficient algorithms to calculate the required wavefront updates. Different approaches are considered in numerical simulations, and laboratory experiments are shown to confirm the results. We compare the performances of the standard Gerchberg-Saxton algorithm, Fast and Furious (use of small-phase assumption to take advantage of linearisation) and recently proposed phase-retrieval methods based on convex optimisation. The results indicate that the calibration task is easiest with algorithms similar to Fast and Furious, at least in the framework we considered., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

Het doel van dit onderzoek was om inzicht te krijgen in de wijze waarop exploratiegedrag leidt tot inzicht bij kinderen, tijdens de uitvoering van puzzels met tandwielen. Uit voorgaand onderzoek blijkt dat de hoeveelheid handelingen invloed heeft op het inzicht dat men ontwikkelt en dat er een bepaald verloop is in de relatie tussen de hoeveelheid handelingen en de opbouw van inzicht tijdens exploratie (Chu & Kita, 2011). Bovendien blijkt dat wanneer kinderen zelf tot de ontdekking van een bepaald principe komen, zij het opgebouwde inzicht sneller inzetten in een andere situatie (Anderson, 2003). Er is nog weinig bekend over non-verbaal exploratiegedrag en de wijze waarop dit leidt tot inzicht. Kinderen rond de 11 jaar werden gevraagd om tandwielbanen te maken, waarbij het eerste en het laatste tandwiel dezelfde richting op moesten draaien. Het onderliggende principe hierbij was een mathematische relatie tussen de draairichting van het eerste en het laatste tandwiel. Vervolgens werd in een computertaak aan het kind gevraagd om de draairichting van tandwielen te voorspellen. Het aantal handelingen tijdens de exploratiefase bleek niet eenduidig te zijn geteld. Daardoor konden geen analyses worden uitgevoerd met deze data. Het getoonde inzicht tijdens de exploratiefase leidde niet tot een hogere prestatie op de computertaak. De verschillen tussen de omgeving tijdens de exploratiefase en de omgeving tijdens de computertaak hebben hier mogelijk een rol in gespeeld. Toekomstig onderzoek zou zich kunnen richten op de invloed van de omgeving op exploratiegedrag.

We propose an efficient approximation to the nonlinear phase diversity (PD) method for wavefront reconstruction and correction from intensity measurements with potential of being used in real-time applications. The new iterative linear phase diversity (ILPD) method assumes that the residual phase aberration is small and makes use of a first-order Taylor expansion of the point spread function (PSF), which allows for arbitrary (large) diversities in order to optimize the phase retrieval. For static disturbances, at each step, the residual phase aberration is estimated based on one defocused image by solving a linear least squares problem, and compensated for with a deformable mirror. Due to the fact that the linear approximation does not have to be updated with each correction step, the computational complexity of the method is reduced to that of a matrix-vector multiplication. The convergence of the ILPD correction steps has been investigated and numerically verified. The comparative study that we make demonstrates the improved performance in computational time with no decrease in accuracy with respect to existing methods that also linearize the PSF., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

Het doel van dit onderzoek was om inzicht te krijgen in de wijze waarop exploratiegedrag leidt tot inzicht bij kinderen, tijdens de uitvoering van puzzels met tandwielen. Uit voorgaand onderzoek blijkt dat de hoeveelheid handelingen invloed heeft op het inzicht dat men ontwikkelt en dat er een bepaald verloop is in de relatie tussen de hoeveelheid handelingen en de opbouw van inzicht tijdens exploratie (Chu & Kita, 2011). Bovendien blijkt dat wanneer kinderen zelf tot de ontdekking van een bepaald principe komen, zij het opgebouwde inzicht sneller inzetten in een andere situatie (Anderson, 2003). Er is nog weinig bekend over non-verbaal exploratiegedrag en de wijze waarop dit leidt tot inzicht. Kinderen rond de 11 jaar werden gevraagd om tandwielbanen te maken, waarbij het eerste en het laatste tandwiel dezelfde richting op moesten draaien. Het onderliggende principe hierbij was een mathematische relatie tussen de draairichting van het eerste en het laatste tandwiel. Vervolgens werd in een computertaak aan het kind gevraagd om de draairichting van tandwielen te voorspellen. Het aantal handelingen tijdens de exploratiefase bleek niet eenduidig te zijn geteld. Daardoor konden geen analyses worden uitgevoerd met deze data. Het getoonde inzicht tijdens de exploratiefase leidde niet tot een hogere prestatie op de computertaak. De verschillen tussen de omgeving tijdens de exploratiefase en de omgeving tijdens de computertaak hebben hier mogelijk een rol in gespeeld. Toekomstig onderzoek zou zich kunnen richten op de invloed van de omgeving op exploratiegedrag.

We propose an efficient approximation to the nonlinear phase diversity (PD) method for wavefront reconstruction and correction from intensity measurements with potential of being used in real-time applications. The new iterative linear phase diversity (ILPD) method assumes that the residual phase aberration is small and makes use of a first-order Taylor expansion of the point spread function (PSF), which allows for arbitrary (large) diversities in order to optimize the phase retrieval. For static disturbances, at each step, the residual phase aberration is estimated based on one defocused image by solving a linear least squares problem, and compensated for with a deformable mirror. Due to the fact that the linear approximation does not have to be updated with each correction step, the computational complexity of the method is reduced to that of a matrix-vector multiplication. The convergence of the ILPD correction steps has been investigated and numerically verified. The comparative study that we make demonstrates the improved performance in computational time with no decrease in accuracy with respect to existing methods that also linearize the PSF., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

Het doel van dit onderzoek was om de relatie tussen perspectief name, emotieregulatie, geslacht en twee conflictresolutiestijlen bij adolescenten in kaart te brengen. Door middel van vragenlijstonderzoek werden adolescenten bevraagd over hun omgang met emoties en conflicten en over het zich kunnen verplaatsen in anderen. Respondenten waren 15 en 16-jarige scholieren op een middelbare school. Er werd gedeeltelijke ondersteuning gevonden voor het effect van perspectief name op emotie regulatie. Geslacht bleek een significant effect te hebben op perspectief name. Er werd gedeeltelijke ondersteuning gevonden voor het verschil in geslacht voor emotie regulatie. Voor het effect van emotie regulatie op de conflictresolutiestijlen probleemoplossing en terugtrekking werd eveneens gedeeltelijke ondersteuning gevonden. Drie subschalen die emotie regulatie maten gaven een significant effect weer op probleemoplossing en terugtrekking. Perspectief name is positief gerelateerd aan emotioneel bewustzijn van de adolescenten. Een hoge mate van perspectief name is gerelateerd aan minder problemen in doelgericht gedragen, een grotere acceptatie van emotionele responsen en meer toegang tot emotie regulatie strategieën. Geslacht bleek invloed te hebben op zowel perspectief name als op emotieregulatie. Hoe emotioneler bewust de adolescent was, des te meer werd probleemoplossing gehanteerd. Terugtrekking werd meer gehanteerd door adolescenten die moeite hebben met het accepteren van emotionele responsen en een beperkte toegang hebben tot emotie regulatie strategieën.

A CW capable inline electron cyclotron emission (ECE) separation system for feedback control, featuring oversized corrugated waveguides, is commissioned on ASDEX upgrade (AUG). The system is based on a combination of a polarization independent, non-resonant, Mach-Zehnder diplexer equipped with dielectric plate beam splitters [2, 3] employed as corrugated oversized waveguide filter, and a resonant Fast Directional Switch, FADIS [4, 5, 6, 7] as ECE/ECCD separation system. This paper presents an overview of the system, the low power characterisation tests and first high power commissioning on AUG.

Het doel van dit onderzoek was om de relatie tussen perspectief name, emotieregulatie, geslacht en twee conflictresolutiestijlen bij adolescenten in kaart te brengen. Door middel van vragenlijstonderzoek werden adolescenten bevraagd over hun omgang met emoties en conflicten en over het zich kunnen verplaatsen in anderen. Respondenten waren 15 en 16-jarige scholieren op een middelbare school. Er werd gedeeltelijke ondersteuning gevonden voor het effect van perspectief name op emotie regulatie. Geslacht bleek een significant effect te hebben op perspectief name. Er werd gedeeltelijke ondersteuning gevonden voor het verschil in geslacht voor emotie regulatie. Voor het effect van emotie regulatie op de conflictresolutiestijlen probleemoplossing en terugtrekking werd eveneens gedeeltelijke ondersteuning gevonden. Drie subschalen die emotie regulatie maten gaven een significant effect weer op probleemoplossing en terugtrekking. Perspectief name is positief gerelateerd aan emotioneel bewustzijn van de adolescenten. Een hoge mate van perspectief name is gerelateerd aan minder problemen in doelgericht gedragen, een grotere acceptatie van emotionele responsen en meer toegang tot emotie regulatie strategieën. Geslacht bleek invloed te hebben op zowel perspectief name als op emotieregulatie. Hoe emotioneler bewust de adolescent was, des te meer werd probleemoplossing gehanteerd. Terugtrekking werd meer gehanteerd door adolescenten die moeite hebben met het accepteren van emotionele responsen en een beperkte toegang hebben tot emotie regulatie strategieën.

A CW capable inline electron cyclotron emission (ECE) separation system for feedback control, featuring oversized corrugated waveguides, is commissioned on ASDEX upgrade (AUG). The system is based on a combination of a polarization independent, non-resonant, Mach-Zehnder diplexer equipped with dielectric plate beam splitters [2, 3] employed as corrugated oversized waveguide filter, and a resonant Fast Directional Switch, FADIS [4, 5, 6, 7] as ECE/ECCD separation system. This paper presents an overview of the system, the low power characterisation tests and first high power commissioning on AUG.

A CW capable inline electron cyclotron emission (ECE) separation system for feedback control, featuring oversized corrugated waveguides, is commissioned on ASDEX upgrade (AUG). The system is based on a combination of a polarization independent, non-resonant, Mach-Zehnder diplexer equipped with dielectric plate beam splitters [2, 3] employed as corrugated oversized waveguide filter, and a resonant Fast Directional Switch, FADIS [4, 5, 6, 7] as ECE/ECCD separation system. This paper presents an overview of the system, the low power characterisation tests and first high power commissioning on AUG.

A CW capable inline electron cyclotron emission (ECE) separation system for feedback control, featuring oversized corrugated waveguides, is commissioned on ASDEX upgrade (AUG). The system is based on a combination of a polarization independent, non-resonant, Mach-Zehnder diplexer equipped with dielectric plate beam splitters [2, 3] employed as corrugated oversized waveguide filter, and a resonant Fast Directional Switch, FADIS [4, 5, 6, 7] as ECE/ECCD separation system. This paper presents an overview of the system, the low power characterisation tests and first high power commissioning on AUG.

We study different possibilities to use adaptive optics (AO) and phase diversity (PD) together in a jointly optimized system. The potential of the joint system is demonstrated through numerical simulations. We find that the most significant benefits are obtained from the improved deconvolution of AO-corrected wavefronts and the additional wavefront sensor (WFS) information that reduces the computational demands of PD algorithms. When applied together, it is seen that the image error can be reduced by 20% compared to traditional PD, working with one focused and one defocused camera image, and the computational load is reduced by a factor of 20 compared to a more reliable PD algorithm requiring more camera images. In addition, we find that the system performance can be optimized by adjusting the magnitude of the applied diversity wavefronts., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

We study different possibilities to use adaptive optics (AO) and phase diversity (PD) together in a jointly optimized system. The potential of the joint system is demonstrated through numerical simulations. We find that the most significant benefits are obtained from the improved deconvolution of AO-corrected wavefronts and the additional wavefront sensor (WFS) information that reduces the computational demands of PD algorithms. When applied together, it is seen that the image error can be reduced by 20% compared to traditional PD, working with one focused and one defocused camera image, and the computational load is reduced by a factor of 20 compared to a more reliable PD algorithm requiring more camera images. In addition, we find that the system performance can be optimized by adjusting the magnitude of the applied diversity wavefronts., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

In recent years various researchers have proposed an optimal control approach for the rejection of turbulence-induced wavefront distortions in an AO system. The essential element in the design of an optimal controller is the choice for the turbulence model, which predicts the turbulence to compensate for the inherent delay in the AO control loop. In this paper various models as proposed in literature are considered; ranging from first order temporal models to high-order full spatialtemporal models. The various models are analyzed and the resulting 1-step ahead predictors are derived. The performance of the predictors are compared for a von Karman type of turbulence with frozen flow propagation in and time-varying propagation directions., Delft Centre for Systems and Control, Mechanical, Maritime and Materials Engineering

Efficient and optimal prediction of frozen flow turbulence using the complete observation history of the wavefront sensor is an important issue in adaptive optics for large ground-based telescopes. At least for the sake of error budgeting and algorithm performance, the evaluation of an accurate estimate of the optimal performance of a particular adaptive optics configuration is important. However, due to the large number of grid points, high sampling rates, and the non-rationality of the turbulence power spectral density, the computational complexity of the optimal predictor is huge. This paper shows how a structure in the frozen flow propagation can be exploited to obtain a state-space innovation model with a particular sparsity structure. This sparsity structure enables one to efficiently compute a structured Kalman filter. By simulation it is shown that the performance can be improved and the computational complexity can be reduced in comparison with auto-regressive predictors of low order., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

In recent years various researchers have proposed an optimal control approach for the rejection of turbulence-induced wavefront distortions in an AO system. The essential element in the design of an optimal controller is the choice for the turbulence model, which predicts the turbulence to compensate for the inherent delay in the AO control loop. In this paper various models as proposed in literature are considered; ranging from first order temporal models to high-order full spatialtemporal models. The various models are analyzed and the resulting 1-step ahead predictors are derived. The performance of the predictors are compared for a von Karman type of turbulence with frozen flow propagation in and time-varying propagation directions., Delft Centre for Systems and Control, Mechanical, Maritime and Materials Engineering

Efficient and optimal prediction of frozen flow turbulence using the complete observation history of the wavefront sensor is an important issue in adaptive optics for large ground-based telescopes. At least for the sake of error budgeting and algorithm performance, the evaluation of an accurate estimate of the optimal performance of a particular adaptive optics configuration is important. However, due to the large number of grid points, high sampling rates, and the non-rationality of the turbulence power spectral density, the computational complexity of the optimal predictor is huge. This paper shows how a structure in the frozen flow propagation can be exploited to obtain a state-space innovation model with a particular sparsity structure. This sparsity structure enables one to efficiently compute a structured Kalman filter. By simulation it is shown that the performance can be improved and the computational complexity can be reduced in comparison with auto-regressive predictors of low order., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

Using a matching pursuit (MP) approach to solve least squares problems with a sparsity constraint sparse controllers are computed to compensate for atmospheric turbulence. The method has been validated by simulation of von K´arm´an turbulence with frozen flow for the case of prediction, reconstruction and control., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

Using a matching pursuit (MP) approach to solve least squares problems with a sparsity constraint sparse controllers are computed to compensate for atmospheric turbulence. The method has been validated by simulation of von K´arm´an turbulence with frozen flow for the case of prediction, reconstruction and control., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

Adaptive optics (AO) is used in ground-based astronomical telescopes to improve the resolution by counteracting the effects of atmospheric turbulence. Most AO systems are based on a simple control law that neglects the temporal evolution of the distortions introduced by the atmosphere. This paper presents a datadriven control design approach that is able to exploit the spatiotemporal correlation in the wavefront, without assuming any form of decoupling. The approach consists of a dedicated subspace-identification algorithm to identify an atmospheric disturbance model from open-loop wavefront sensor data, followed by 2-optimal control design. It is shown that in the case that the deformable mirror and wavefront sensor dynamics can be represented by a delay and a two taps impulse response, it is possible to derive an analytical expression for the 2-optimal controller. Numerical simulations onAOtest bench data demonstrate a performance improvement with respect to the common AO control approach., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

A new prototype adaptive deformable mirror for future AO-systems is presented that consists of a thin continuous membrane on which push-pull actuators impose out-of-plane displacements. Each actuator has ±10?m stroke, nanometer resolution and only mW’s heat dissipation. The mirror’s modular design makes the mechanics, electronics and control system extendable towards large numbers of actuators. Models of the mirror are derived that are validated using influence and transfer function measurements. First results of a prototype with 427 actuators are also presented., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

Adaptive optics (AO) is used in ground-based astronomical telescopes to improve the resolution by counteracting the effects of atmospheric turbulence. Most AO systems are based on a simple control law that neglects the temporal evolution of the distortions introduced by the atmosphere. This paper presents a datadriven control design approach that is able to exploit the spatiotemporal correlation in the wavefront, without assuming any form of decoupling. The approach consists of a dedicated subspace-identification algorithm to identify an atmospheric disturbance model from open-loop wavefront sensor data, followed by 2-optimal control design. It is shown that in the case that the deformable mirror and wavefront sensor dynamics can be represented by a delay and a two taps impulse response, it is possible to derive an analytical expression for the 2-optimal controller. Numerical simulations onAOtest bench data demonstrate a performance improvement with respect to the common AO control approach., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

A new prototype adaptive deformable mirror for future AO-systems is presented that consists of a thin continuous membrane on which push-pull actuators impose out-of-plane displacements. Each actuator has ±10?m stroke, nanometer resolution and only mW’s heat dissipation. The mirror’s modular design makes the mechanics, electronics and control system extendable towards large numbers of actuators. Models of the mirror are derived that are validated using influence and transfer function measurements. First results of a prototype with 427 actuators are also presented., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

A recently proposed data-driven H2-optimal control approach is demonstrated on a laboratory setup. Most adaptive optics (AO) systems are based on a control law that neglects the temporal evolution of the wavefront. The proposed control approach is able to exploit the spatiotemporal correlation in the wavefront without assuming any form of decoupling. By analyzing the dynamic behavior of the wavefront sensor (WFS), it is shown that if the wavefront correction device can be considered static, the transfer function from control input to WFS output reduces to a two-tap impulse response and an integer number of samples delay. Considering this model structure, a data-driven identification procedure is developed to estimate the relevant parameters from measurement data. The specific structure allows for an analytical expression of the optimal controller in terms of the system matrices of the minimum-phase spectral factor of the atmospheric disturbance model. The performance of the optimal controller is compared with that of the standard AO control law. An analysis of the dominant error sources shows that optimal control may reduce the temporal error., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

A recently proposed data-driven H2-optimal control approach is demonstrated on a laboratory setup. Most adaptive optics (AO) systems are based on a control law that neglects the temporal evolution of the wavefront. The proposed control approach is able to exploit the spatiotemporal correlation in the wavefront without assuming any form of decoupling. By analyzing the dynamic behavior of the wavefront sensor (WFS), it is shown that if the wavefront correction device can be considered static, the transfer function from control input to WFS output reduces to a two-tap impulse response and an integer number of samples delay. Considering this model structure, a data-driven identification procedure is developed to estimate the relevant parameters from measurement data. The specific structure allows for an analytical expression of the optimal controller in terms of the system matrices of the minimum-phase spectral factor of the atmospheric disturbance model. The performance of the optimal controller is compared with that of the standard AO control law. An analysis of the dominant error sources shows that optimal control may reduce the temporal error., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

Most adaptive optics systems (AO) are based on a simple control law that is unable to account for the temporal evolution of the wavefront. In this paper, a recently proposed data-driven H2-optimal control approach is demonstrated on an AO laboratory setup. The proposed control approach does not assume any form of decoupling and can therefore exploit the spatio-temporal correlation in the wavefront. The performance of the optimal control approach is compared with a conventional method. An analysis of the dominant error sources shows that the optimal control approach leads to a significant reduction in the temporal error. Since the temporal error grows with the Greenwood to sampling frequency ratio, the performance gain is especially large at large ratios., Delft Centre for Systems and Control, Mechanical, Maritime and Materials Engineering

In the design of a large adaptive deformable membrane mirror, variable reluctance actuators are used. These consist of a closed magnetic circuit in which a strong permanent magnet provides a static magnetic force on a ferromagnetic core which is suspended in a membrane. By applying a current through the coil which is situated around the magnet, this force is influenced, providing movement of the ferromagnetic core. This movement is transferred via a rod imposing the out-ofplane displacements in the reflective deformable membrane. In the actuator design a match is made between the negative stiffness of the magnet and the positive stiffness of the membrane suspension. If the locality of the influence functions, mirror modes as well as force and power dissipation are taken into account, a resonance frequency of 1500 Hz and an overall stiffness of 1000 N/m for the actuators is needed. The actuators are fabricated and the dynamic response tested in a dedicated setup. The Bode diagram shows a first eigenfrequency of 950 Hz. This is due to a lower magnetic force than expected. A Helmholtz coil setup was designed to measure the differences in a large set of permanent magnets. With the same setup the 2nd quadrant of the B-H curve is reconstructed by stacking of the magnets and using the demagnetization factor. It is shown that the values for Hc and Br of the magnets are indeed lower than the values used for the initial design. New actuators, with increased magnet thickness, are designed and currently fabricated., Center for Systems and Control, Mechanical, Maritime and Materials Engineering

Future large optical telescopes require adaptive optics (AO) systems whose deformable mirrors (DM) have ever more degrees of freedom. This paper describes advances that are made in a project aimed to design a new AO system that is extendible to meet tomorrow’s specifications. Advances on the mechanical design are reported in a companion paper [6272-75], whereas this paper discusses the controller design aspects. The numerical complexity of controller designs often used for AO scales with the fourth power in the diameter of the telescope’s primary mirror. For future large telescopes this will undoubtedly become a critical aspect. This paper demonstrates the feasibility of solving this issue with a distributed controller design. A distributed framework will be introduced in which each actuator has a separate processor that can communicate with a few direct neighbors. First, the DM will be modeled and shown to be compatible with the framework. Then, adaptive turbulence models that fit the framework will be shown to adequately capture the spatio-temporal behavior of the atmospheric disturbance, constituting a first step towards a distributed optimal control. Finally, the wavefront reconstruction step is fitted into the distributed framework such that the computational complexity for each processor increases only linearly with the telescope diameter., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

Most adaptive optics systems (AO) are based on a simple control law that is unable to account for the temporal evolution of the wavefront. In this paper, a recently proposed data-driven H2-optimal control approach is demonstrated on an AO laboratory setup. The proposed control approach does not assume any form of decoupling and can therefore exploit the spatio-temporal correlation in the wavefront. The performance of the optimal control approach is compared with a conventional method. An analysis of the dominant error sources shows that the optimal control approach leads to a significant reduction in the temporal error. Since the temporal error grows with the Greenwood to sampling frequency ratio, the performance gain is especially large at large ratios., Delft Centre for Systems and Control, Mechanical, Maritime and Materials Engineering

In the design of a large adaptive deformable membrane mirror, variable reluctance actuators are used. These consist of a closed magnetic circuit in which a strong permanent magnet provides a static magnetic force on a ferromagnetic core which is suspended in a membrane. By applying a current through the coil which is situated around the magnet, this force is influenced, providing movement of the ferromagnetic core. This movement is transferred via a rod imposing the out-ofplane displacements in the reflective deformable membrane. In the actuator design a match is made between the negative stiffness of the magnet and the positive stiffness of the membrane suspension. If the locality of the influence functions, mirror modes as well as force and power dissipation are taken into account, a resonance frequency of 1500 Hz and an overall stiffness of 1000 N/m for the actuators is needed. The actuators are fabricated and the dynamic response tested in a dedicated setup. The Bode diagram shows a first eigenfrequency of 950 Hz. This is due to a lower magnetic force than expected. A Helmholtz coil setup was designed to measure the differences in a large set of permanent magnets. With the same setup the 2nd quadrant of the B-H curve is reconstructed by stacking of the magnets and using the demagnetization factor. It is shown that the values for Hc and Br of the magnets are indeed lower than the values used for the initial design. New actuators, with increased magnet thickness, are designed and currently fabricated., Center for Systems and Control, Mechanical, Maritime and Materials Engineering

Future large optical telescopes require adaptive optics (AO) systems whose deformable mirrors (DM) have ever more degrees of freedom. This paper describes advances that are made in a project aimed to design a new AO system that is extendible to meet tomorrow’s specifications. Advances on the mechanical design are reported in a companion paper [6272-75], whereas this paper discusses the controller design aspects. The numerical complexity of controller designs often used for AO scales with the fourth power in the diameter of the telescope’s primary mirror. For future large telescopes this will undoubtedly become a critical aspect. This paper demonstrates the feasibility of solving this issue with a distributed controller design. A distributed framework will be introduced in which each actuator has a separate processor that can communicate with a few direct neighbors. First, the DM will be modeled and shown to be compatible with the framework. Then, adaptive turbulence models that fit the framework will be shown to adequately capture the spatio-temporal behavior of the atmospheric disturbance, constituting a first step towards a distributed optimal control. Finally, the wavefront reconstruction step is fitted into the distributed framework such that the computational complexity for each processor increases only linearly with the telescope diameter., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

Even though the wavefront distortion introduced by atmospheric turbulence is a dynamic process, its temporal evolution is usually neglected in the adaptive optics (AO) control design. Most AO control systems consider only the spatial correlation in a separate wavefront reconstruction step. By accounting for the temporal evolution of the wavefront it should be possible to further reduce the residual phase error and enable the use of fainter guide stars. Designing a controller that takes full advantage of the spatio-temporal correlation in the wavefront requires a detailed model of the wavefront distortion. In this paper we present a dedicated subspace identification algorithm that is able to provide the required prior knowledge. On the basis of open-loop wavefront slope data it estimates a multi-variable state-space model of the wavefront disturbance. The model provides a full description of the spatio-temporal statistics in a form that is suitable for control. The algorithm is demonstrated on open-loop wavefront data., Delft Centre for Systems and Control, Mechanical, Maritime and Materials Engineering

The problem of finding the closed-loop optimal controller is formulated in an H2-optimal control framework. This provides a natural way to account for the fact that in many AO systems the wavefront phase cannot be measured directly. Given a multi-variable disturbance model of both wavefront slopes and wavefront phases,3 this provides a general procedure to compute the closed-loop controller. If the wavefront sensor and deformable mirror are static and the only dynamics in the system is a unit-sample delay between measurement and correction, an analytical expression for the optimal controller can be derived. This results in a control approach, in which both identification and computation of the optimal controller are exclusively based on standard matrix operations. No Riccati equation needs to be solved to compute the optimal controller. The proposed H2-control approach is numerically validated on open-loop wavefront sensor data and its performance is compared with the common approach. Also the sensitivity to measurement noise is considered., Delft Centre for Systems and Control, Mechanical, Maritime and Materials Engineering

Even though the wavefront distortion introduced by atmospheric turbulence is a dynamic process, its temporal evolution is usually neglected in the adaptive optics (AO) control design. Most AO control systems consider only the spatial correlation in a separate wavefront reconstruction step. By accounting for the temporal evolution of the wavefront it should be possible to further reduce the residual phase error and enable the use of fainter guide stars. Designing a controller that takes full advantage of the spatio-temporal correlation in the wavefront requires a detailed model of the wavefront distortion. In this paper we present a dedicated subspace identification algorithm that is able to provide the required prior knowledge. On the basis of open-loop wavefront slope data it estimates a multi-variable state-space model of the wavefront disturbance. The model provides a full description of the spatio-temporal statistics in a form that is suitable for control. The algorithm is demonstrated on open-loop wavefront data., Delft Centre for Systems and Control, Mechanical, Maritime and Materials Engineering

The problem of finding the closed-loop optimal controller is formulated in an H2-optimal control framework. This provides a natural way to account for the fact that in many AO systems the wavefront phase cannot be measured directly. Given a multi-variable disturbance model of both wavefront slopes and wavefront phases,3 this provides a general procedure to compute the closed-loop controller. If the wavefront sensor and deformable mirror are static and the only dynamics in the system is a unit-sample delay between measurement and correction, an analytical expression for the optimal controller can be derived. This results in a control approach, in which both identification and computation of the optimal controller are exclusively based on standard matrix operations. No Riccati equation needs to be solved to compute the optimal controller. The proposed H2-control approach is numerically validated on open-loop wavefront sensor data and its performance is compared with the common approach. Also the sensitivity to measurement noise is considered., Delft Centre for Systems and Control, Mechanical, Maritime and Materials Engineering

Mechanical, Maritime and Materials Engineering

Mechanical, Maritime and Materials Engineering