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We have implemented an extended depth of field optical system by wavefront coding with a micromachined membrane deformable mirror. This approach provides a versatile extension to standard wavefront coding based on fixed phase mask. First experimental results validate the feasibility of the use of adaptive optics for variable depth wavefront coding in imaging optical systems. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

Multilevel sequentially semiseparable (MSSS) matrices form a class of structured matrices that have low-rank off-diagonal structure, which allows the matrix-matrix operations to be performed in linear computational complexity. MSSS preconditioners are computed by replacing the Schur complements in the block LU factorization of the global linear system by MSSS matrix approximations with low off-diagonal rank. In this manuscript, we analyze the convergence properties of such preconditioners. We show that the spectrum of the preconditioned system is contained in a circle centered at (1, 0) and give an analytic bound of the radius of this circle. This radius can be made arbitrarily small by properly setting a parameter in the MSSS preconditioner. Our results apply to a wide class of linear systems. The system matrix can be either symmetric or unsymmetric, definite or indefinite. We demonstrate our analysis by numerical experiments., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

In this manuscript, we study preconditioning techniques for optimal in-domain control of the Navier-Stokes equation, where the control only acts on a few parts of the domain. Optimization and linearization of the optimal in-domain control problem results in a generalized linear saddle-point system. The Schur complement for the generalized saddle-point system is very difficult or even impossible to approximate. This prohibits satisfactory performance of the standard block preconditioners. We apply the multilevel sequentially semiseparable (MSSS) preconditioner to the underlying system. Compared with standard block preconditioning techniques, the MSSS preconditioner computes an approximate factorization of the global generalized saddle-point matrix up to a prescribed accuracy in linear computational complexity. This in turn gives parameter independent convergence for MSSS preconditioned Krylov solvers. We use a simple wind farm control example to illustrate the performance of the MSSS preconditioner. We also ompare with the performance of the state-of-the-art preconditioning techniques. Our results show the superiority of the MSSS preconditioning techniques to standard block preconditioning techniques for optimal in-domain control of the Navier-Stokes equation., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

We have implemented an extended depth of field optical system by wavefront coding with a micromachined membrane deformable mirror. This approach provides a versatile extension to standard wavefront coding based on fixed phase mask. First experimental results validate the feasibility of the use of adaptive optics for variable depth wavefront coding in imaging optical systems. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

Multilevel sequentially semiseparable (MSSS) matrices form a class of structured matrices that have low-rank off-diagonal structure, which allows the matrix-matrix operations to be performed in linear computational complexity. MSSS preconditioners are computed by replacing the Schur complements in the block LU factorization of the global linear system by MSSS matrix approximations with low off-diagonal rank. In this manuscript, we analyze the convergence properties of such preconditioners. We show that the spectrum of the preconditioned system is contained in a circle centered at (1, 0) and give an analytic bound of the radius of this circle. This radius can be made arbitrarily small by properly setting a parameter in the MSSS preconditioner. Our results apply to a wide class of linear systems. The system matrix can be either symmetric or unsymmetric, definite or indefinite. We demonstrate our analysis by numerical experiments., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

In this manuscript, we study preconditioning techniques for optimal in-domain control of the Navier-Stokes equation, where the control only acts on a few parts of the domain. Optimization and linearization of the optimal in-domain control problem results in a generalized linear saddle-point system. The Schur complement for the generalized saddle-point system is very difficult or even impossible to approximate. This prohibits satisfactory performance of the standard block preconditioners. We apply the multilevel sequentially semiseparable (MSSS) preconditioner to the underlying system. Compared with standard block preconditioning techniques, the MSSS preconditioner computes an approximate factorization of the global generalized saddle-point matrix up to a prescribed accuracy in linear computational complexity. This in turn gives parameter independent convergence for MSSS preconditioned Krylov solvers. We use a simple wind farm control example to illustrate the performance of the MSSS preconditioner. We also ompare with the performance of the state-of-the-art preconditioning techniques. Our results show the superiority of the MSSS preconditioning techniques to standard block preconditioning techniques for optimal in-domain control of the Navier-Stokes equation., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

Deep imaging in turbid media such as biological tissue is challenging due to scattering and optical aberrations. Adaptive optics has the potential to compensate the tissue aberrations. We present a wavefront sensing scheme for multi-photon scanning microscopes using the pulsed, near-infrared light reflected back from the sample utilising coherence gating and a confocal pinhole to isolate the light from a layer of interest. By interfering the back-reflected light with a tilted reference beam, we create a fringe pattern with a known spatial carrier frequency in an image of the back-aperture plane of the microscope objective. The wavefront aberrations distort this fringe pattern and thereby imprint themselves at the carrier frequency, which allows us to separate the aberrations in the Fourier domain from low spatial frequency noise. A Fourier analysis of the modulated fringes combined with a virtual Shack-Hartmann sensor for smoothing yields a modal representation of the wavefront suitable for correction. We show results with this method correcting both DM-induced and sample-induced aberrations in rat tail collagen fibres as well as a Hoechst-stained MCF-7 spheroid of cancer cells., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

Optical aberrations have detrimental effects in multiphoton microscopy. These effects can be curtailed by implementing model-based wavefront sensorless adaptive optics, which only requires the addition of a wavefront shaping device, such as a deformable mirror (DM) to an existing microscope. The aberration correction is achieved by maximizing a suitable image quality metric. We implement a model-based aberration correction algorithm in a second-harmonic microscope. The tip, tilt, and defocus aberrations are removed from the basis functions used for the control of the DM, as these aberrations induce distortions in the acquired images. We compute the parameters of a quadratic polynomial that is used to model the image quality metric directly from experimental input–output measurements. Finally, we apply the aberration correction by maximizing the image quality metric using the least-squares estimate of the unknown aberration., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

In this paper, we consider preconditioning for PDE-constrained optimization problems. The underlying problems yield a linear saddle-point system. We study a class of preconditioners based on multilevel sequentially semiseparable (MSSS) matrix computations. The novel global preconditioner is to make use of the global structure of the saddle-point system, while the block preconditioner makes use of the block structure of the saddle-point system. For the novel global preconditioner, it is independent of the regularization parameter, while for the block preconditioner, this property does not hold. For this MSSS matrix computation approach, model order reduction algorithms are essential to obtain a low computational complexity. We study two different model order reduction approaches, one is the new approximate balanced truncation algorithm with low-rank approximated Gramians and the other is the standard Hankel blocks approximation algorithm. We test the global preconditioner and the block preconditioner for the problem of optimal control of the Poisson equation and optimal control of the convection-diffusion equation. Numerical experiments illustrate that both preconditioners give linear computational complexity and the global preconditioner yields the fewest number of iterations and computing time. Moreover, the approximate balanced truncation algorithm consumes less floating-point operations (flops) than the Hankel blocks approximation algorithm., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

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

Optical aberrations have detrimental effects in multiphoton microscopy. These effects can be curtailed by implementing model-based wavefront sensorless adaptive optics, which only requires the addition of a wavefront shaping device, such as a deformable mirror (DM) to an existing microscope. The aberration correction is achieved by maximizing a suitable image quality metric. We implement a model-based aberration correction algorithm in a second-harmonic microscope. The tip, tilt, and defocus aberrations are removed from the basis functions used for the control of the DM, as these aberrations induce distortions in the acquired images. We compute the parameters of a quadratic polynomial that is used to model the image quality metric directly from experimental input–output measurements. Finally, we apply the aberration correction by maximizing the image quality metric using the least-squares estimate of the unknown aberration., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

In this paper, we consider preconditioning for PDE-constrained optimization problems. The underlying problems yield a linear saddle-point system. We study a class of preconditioners based on multilevel sequentially semiseparable (MSSS) matrix computations. The novel global preconditioner is to make use of the global structure of the saddle-point system, while the block preconditioner makes use of the block structure of the saddle-point system. For the novel global preconditioner, it is independent of the regularization parameter, while for the block preconditioner, this property does not hold. For this MSSS matrix computation approach, model order reduction algorithms are essential to obtain a low computational complexity. We study two different model order reduction approaches, one is the new approximate balanced truncation algorithm with low-rank approximated Gramians and the other is the standard Hankel blocks approximation algorithm. We test the global preconditioner and the block preconditioner for the problem of optimal control of the Poisson equation and optimal control of the convection-diffusion equation. Numerical experiments illustrate that both preconditioners give linear computational complexity and the global preconditioner yields the fewest number of iterations and computing time. Moreover, the approximate balanced truncation algorithm consumes less floating-point operations (flops) than the Hankel blocks approximation algorithm., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

Deep imaging in turbid media such as biological tissue is challenging due to scattering and optical aberrations. Adaptive optics has the potential to compensate the tissue aberrations. We present a wavefront sensing scheme for multi-photon scanning microscopes using the pulsed, near-infrared light reflected back from the sample utilising coherence gating and a confocal pinhole to isolate the light from a layer of interest. By interfering the back-reflected light with a tilted reference beam, we create a fringe pattern with a known spatial carrier frequency in an image of the back-aperture plane of the microscope objective. The wavefront aberrations distort this fringe pattern and thereby imprint themselves at the carrier frequency, which allows us to separate the aberrations in the Fourier domain from low spatial frequency noise. A Fourier analysis of the modulated fringes combined with a virtual Shack-Hartmann sensor for smoothing yields a modal representation of the wavefront suitable for correction. We show results with this method correcting both DM-induced and sample-induced aberrations in rat tail collagen fibres as well as a Hoechst-stained MCF-7 spheroid of cancer cells., 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

This paper studies a new preconditioning technique for sparse systems arising from discretized partial differential equations (PDEs) in computational fluid dynamics (CFD), which exploit the multilevel sequentially semiseparable (MSSS) structure of the system matrix. MSSS matrix computations give a data-sparse way to approximate the LU factorization of a sparse matrix from discretized PDEs in linear computational complexity with respect to the problem size. In contrast to the standard block preconditioners, we exploit the global MSSS structure of the 2 by 2 block system from the discretized Stokes equation and linearized Navier-Stokes equation. This avoids the approximation of the Schur complement, which is a big advantage over standard block preconditioners. Numerical experiments on standard CFD benchmark problems in IFISS were carried out to evaluate the performance of the MSSS preconditioners. It was illustrated that the MSSS preconditioner yields mesh size independence convergence. Moreover, the convergence is almost insensitive to the viscosity parameter. Comparison with the algebraic multigrid (AMG) method and the geometric multigrid (GMG) method, the MSSS preconditioning technique is more robust than both the AMG method and the GMG method, and considerably faster than the AMG method., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

A new method for adaptive prediction and correction of wavefront errors in adaptive optics (AO) is introduced. The new method is based on receding-horizon control design and an adaptive lattice filter. Experimental results presented illustrate the capability of the new adaptive controller to predict and correct aero-optical wavefronts derived from recent flight-test data. The experimental results compare the performance of the new adaptive controller the performance of a minimum-variance adaptive controller previously used in AO. These results demonstrate the reduced sensitivity of the receding-horizon adaptive controller to high-frequency sensor noise, Delft Center for Systems and Control, Electrical Engineering, Mathematics and Computer Science

We propose an efficient approximation to the nonlinear phase diversity method for wavefront reconstruction from intensity measurements. The new method, iterative linear phase diversity (ILPD), assumes that the residual phase aberration is small and makes use of a first order Taylor expansion of the point spread function (PSF) performed for an arbitrary (large) diversity in order to optimize the phase retrieval. For static aberrations, ILPD makes use of two images collected at each iteration of the algorithm. In each step, the residual phase aberrations are estimated by solving a linear least squares problem, followed by the use of a deformable mirror to correct for the aberrations. A further contribution of the paper is the extension of the static ILPD to the case of dynamic wavefront reconstruction for which a computationally efficient H2 controller is presented., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

We present an iterative learning control (ILC) algorithm for controlling the shape of a membrane deformable mirror (DM). We furthermore give a physical interpretation of the design parameters of the ILC algorithm. On the basis of this insight, we derive a simple tuning procedure for the ILC algorithm that, in practice, guarantees stable and fast convergence of the membrane to the desired shape. In order to demonstrate the performance of the algorithm, we have built an experimental setup that consists of a commercial membrane DM, a wavefront sensor, and a real-time controller. The experimental results show that, by using the ILC algorithm, we are able to achieve a relatively small error between the real and desired shape of the DM while at the same time we are able to control the saturation of the actuators. Moreover, we show that the ILC algorithm outperforms other control algorithms available in the literature., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

This paper studies a new preconditioning technique for sparse systems arising from discretized partial differential equations (PDEs) in computational fluid dynamics (CFD), which exploit the multilevel sequentially semiseparable (MSSS) structure of the system matrix. MSSS matrix computations give a data-sparse way to approximate the LU factorization of a sparse matrix from discretized PDEs in linear computational complexity with respect to the problem size. In contrast to the standard block preconditioners, we exploit the global MSSS structure of the 2 by 2 block system from the discretized Stokes equation and linearized Navier-Stokes equation. This avoids the approximation of the Schur complement, which is a big advantage over standard block preconditioners. Numerical experiments on standard CFD benchmark problems in IFISS were carried out to evaluate the performance of the MSSS preconditioners. It was illustrated that the MSSS preconditioner yields mesh size independence convergence. Moreover, the convergence is almost insensitive to the viscosity parameter. Comparison with the algebraic multigrid (AMG) method and the geometric multigrid (GMG) method, the MSSS preconditioning technique is more robust than both the AMG method and the GMG method, and considerably faster than the AMG method., Delft Institute of Applied Mathematics, Electrical Engineering, Mathematics and Computer Science

We propose an efficient approximation to the nonlinear phase diversity method for wavefront reconstruction from intensity measurements. The new method, iterative linear phase diversity (ILPD), assumes that the residual phase aberration is small and makes use of a first order Taylor expansion of the point spread function (PSF) performed for an arbitrary (large) diversity in order to optimize the phase retrieval. For static aberrations, ILPD makes use of two images collected at each iteration of the algorithm. In each step, the residual phase aberrations are estimated by solving a linear least squares problem, followed by the use of a deformable mirror to correct for the aberrations. A further contribution of the paper is the extension of the static ILPD to the case of dynamic wavefront reconstruction for which a computationally efficient H2 controller is presented., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

A new method for adaptive prediction and correction of wavefront errors in adaptive optics (AO) is introduced. The new method is based on receding-horizon control design and an adaptive lattice filter. Experimental results presented illustrate the capability of the new adaptive controller to predict and correct aero-optical wavefronts derived from recent flight-test data. The experimental results compare the performance of the new adaptive controller the performance of a minimum-variance adaptive controller previously used in AO. These results demonstrate the reduced sensitivity of the receding-horizon adaptive controller to high-frequency sensor noise, Delft Center for Systems and Control, Electrical Engineering, Mathematics and Computer Science

We present an iterative learning control (ILC) algorithm for controlling the shape of a membrane deformable mirror (DM). We furthermore give a physical interpretation of the design parameters of the ILC algorithm. On the basis of this insight, we derive a simple tuning procedure for the ILC algorithm that, in practice, guarantees stable and fast convergence of the membrane to the desired shape. In order to demonstrate the performance of the algorithm, we have built an experimental setup that consists of a commercial membrane DM, a wavefront sensor, and a real-time controller. The experimental results show that, by using the ILC algorithm, we are able to achieve a relatively small error between the real and desired shape of the DM while at the same time we are able to control the saturation of the actuators. Moreover, we show that the ILC algorithm outperforms other control algorithms available in the literature., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

In many scientific and medical applications, such as laser systems and microscopes, wavefront-sensor-less (WFSless) adaptive optics (AO) systems are used to improve the laser beam quality or the image resolution by correcting the wavefront aberration in the optical path. The lack of direct wavefront measurement in WFSless AO systems imposes a challenge to achieve efficient aberration correction. This paper presents an aberration correction approach for WFSlss AO systems based on the model of the WFSless AO system and a small number of intensity measurements, where the model is identified from the input-output data of the WFSless AO system by black-box identification. This approach is validated in an experimental setup with 20 static aberrations having Kolmogorov spatial distributions. By correcting N = 9 Zernike modes (N is the number of aberration modes), an intensity improvement from 49% of the maximum value to 89% has been achieved in average based on N +5 = 14 intensity measurements. With the worst initial intensity, an improvement from 17% of the maximum value to 86% has been achieved based on N + 4 = 13 intensity measurements., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

This paper studies the load reduction potential of a prototyped “smart” rotor. This is, a rotor where the blades are equipped with a number of control devices that locally change the lift profile on the blade, combined with appropriate sensors and controllers. Experimental models, using dedicated system identification techniques, are developed of a scaled rotating two-bladed “smart” rotor of which each blade is equipped with trailing-edge flaps and strain sensors. A feedback controller based on -loop shaping combined with a fixed-structure feedforward control are designed that minimizes the root bending moment in the flapping direction of the two blades. We evaluated the performance using a number of different realistic load scenarios. We show that with appropriate control techniques the variance of the load signals can be reduced up to 90%., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

In this paper, we consider the problem of designing a distributed controller for a formation of spacecraft following a periodic orbit. Each satellite is controlled locally on the basis of information from only a subset of the others (the nearest ones). We describe the dynamics of each spacecraft by means of a linear time-periodic (LTP) approximation, and we cast the satellite formation into a state-space formulation that facilitates control synthesis. Our technique exploits a novel modal decomposition of the state-space model and uses linear matrix inequalities (LMIs) for suboptimal control design of distributed controllers with guaranteed performance for formations of any size. The application of the method is shown in two case studies. The first example is inspired by a mission in a low, sun-synchronous Earth orbit, namely the new Dutch-Chinese Formation for Atmospheric Science and Technology demonstration mission (FAST), which is now in the preliminary design phase. The second example deals with a formation of spacecraft in a halo orbit., Delft Center 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 many scientific and medical applications, such as laser systems and microscopes, wavefront-sensor-less (WFSless) adaptive optics (AO) systems are used to improve the laser beam quality or the image resolution by correcting the wavefront aberration in the optical path. The lack of direct wavefront measurement in WFSless AO systems imposes a challenge to achieve efficient aberration correction. This paper presents an aberration correction approach for WFSlss AO systems based on the model of the WFSless AO system and a small number of intensity measurements, where the model is identified from the input-output data of the WFSless AO system by black-box identification. This approach is validated in an experimental setup with 20 static aberrations having Kolmogorov spatial distributions. By correcting N = 9 Zernike modes (N is the number of aberration modes), an intensity improvement from 49% of the maximum value to 89% has been achieved in average based on N +5 = 14 intensity measurements. With the worst initial intensity, an improvement from 17% of the maximum value to 86% has been achieved based on N + 4 = 13 intensity measurements., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

This paper studies the load reduction potential of a prototyped “smart” rotor. This is, a rotor where the blades are equipped with a number of control devices that locally change the lift profile on the blade, combined with appropriate sensors and controllers. Experimental models, using dedicated system identification techniques, are developed of a scaled rotating two-bladed “smart” rotor of which each blade is equipped with trailing-edge flaps and strain sensors. A feedback controller based on -loop shaping combined with a fixed-structure feedforward control are designed that minimizes the root bending moment in the flapping direction of the two blades. We evaluated the performance using a number of different realistic load scenarios. We show that with appropriate control techniques the variance of the load signals can be reduced up to 90%., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

In this paper, we consider the problem of designing a distributed controller for a formation of spacecraft following a periodic orbit. Each satellite is controlled locally on the basis of information from only a subset of the others (the nearest ones). We describe the dynamics of each spacecraft by means of a linear time-periodic (LTP) approximation, and we cast the satellite formation into a state-space formulation that facilitates control synthesis. Our technique exploits a novel modal decomposition of the state-space model and uses linear matrix inequalities (LMIs) for suboptimal control design of distributed controllers with guaranteed performance for formations of any size. The application of the method is shown in two case studies. The first example is inspired by a mission in a low, sun-synchronous Earth orbit, namely the new Dutch-Chinese Formation for Atmospheric Science and Technology demonstration mission (FAST), which is now in the preliminary design phase. The second example deals with a formation of spacecraft in a halo orbit., Delft Center 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

We consider the problem of designing controllers for spatially-varying interconnected systems distributed in one spatial dimension. The matrix structure of such systems can be exploited to allow fast analysis and design of centralized controllers with simple distributed implementations. Iterative algorithms are provided for stability analysis, H infin analysis and sub-optimal controller synthesis. For practical implementation of the algorithms, approximations can be used, and the computational efficiency and accuracy are demonstrated on an example., 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

We consider the problem of designing controllers for spatially-varying interconnected systems distributed in one spatial dimension. The matrix structure of such systems can be exploited to allow fast analysis and design of centralized controllers with simple distributed implementations. Iterative algorithms are provided for stability analysis, H infin analysis and sub-optimal controller synthesis. For practical implementation of the algorithms, approximations can be used, and the computational efficiency and accuracy are demonstrated on an example., Delft Center for Systems and Control, Mechanical, Maritime and Materials Engineering

We consider the problem of designing distributed controllers for a class of systems which can be obtained from the interconnection of a number of identical subsystems. If the state space matrices of these systems satisfy a certain structural property, then it is possible to derive a procedure for designing a distributed controller which has the same interconnection pattern as the plant. This procedure is basically a multiobjective optimization under linear matrix inequality constraints, with system norms as performance indices. The explicit expressions for computing these controllers are given for both H infin or H 2 performance, and both for static state feedback and dynamic output feedback (in discrete time). At the end of the paper, two application examples illustrate the effectiveness of the approach., 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

In many scientific and medical applications wavefront-sensorless adaptive optics (AO) systems are used to correct the wavefront aberration by optimizing a certain target parameter, which is nonlinear with respect to the control signal to the deformable mirror (DM). Hysteresis is the most common nonlinearity of DMs, which can be corrected if the information about the hysteresis behavior is present. We report a general approach to extract hysteresis from the nonlinear behavior of the adaptive optical system, with the illustration of a Foucault knife test, where the voltage–intensity relationship consists of both hysteresis and some memoryless nonlinearity. The hysteresis extracted here can be used for modeling and linearization of the AO system., 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

In many scientific and medical applications wavefront-sensorless adaptive optics (AO) systems are used to correct the wavefront aberration by optimizing a certain target parameter, which is nonlinear with respect to the control signal to the deformable mirror (DM). Hysteresis is the most common nonlinearity of DMs, which can be corrected if the information about the hysteresis behavior is present. We report a general approach to extract hysteresis from the nonlinear behavior of the adaptive optical system, with the illustration of a Foucault knife test, where the voltage–intensity relationship consists of both hysteresis and some memoryless nonlinearity. The hysteresis extracted here can be used for modeling and linearization of the AO system., 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

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

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

This paper considers the problem of estimating an unknown input (bias) by means of the augmented-state Kalman (AKF) filter. To reduce the computational complexity of the AKF, [12] recently developed an optimal two-stage Kalman filter (TS-AKF) that separates the bias estimation from the state estimation, and shows that his new two-stage estimator is equivalent to the standard AKF, but requires less computations per iteration. This paper focuses on the derivation of the optimal two-stage estimator for the square-root covariance implementation of the Kalman filter (TS-SRCKF), which is known to be numerically more robust than the standard covariance implementation. The new TS-SRCKF also estimates the state and the bias separately while at the same time it remains equivalent to the standard augmented-state SRCKF. It is experimentally shown in the paper that the new TS-SRCKF may require less flops per iteration for some problems than the Hsieh's TS-AKF [12]. Furthermore a second, even faster (single-stage) algorithm has been derived in the paper by exploiting the structure of the least-squares problem and the square-root covariance formulation of the AKF. The computational complexities of the two proposed methods have been analyzed and compared the those of other existing implementations of the AKF., 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