1 

A comparative performance evaluation of nonlinear observers for a fedbatch evaporative crystallization process
Different nonlinear observers are compared throughout this work where they are part of an NMPC framework used to control a fedbatch crystallization process . We study which observeroptimizer pair offers the best control performance while maintaining adequate computational burden so that a posterior realtime implementation is feasible. At the same time, the relationship between state estimation accuracy and control performance is covered. Along the way we distinguish between stochastic and deterministic observers and compare which class is more suitable for our case study. The observers we make use of are: the moving horizon estimator (MHE), a nonlinear version of a Luenberger observer (extended Luenberger observer, ELO) and nonlinear variants of the Kalman filter such as extended Kalman filter(EKF), unscented Kalman filter (UKF) and ensemble Kalman filter (EnKF). Special variants of UKF and EKF that make use of a non constant system covariance matrix, which according to some literature is suitable to describe uncertainty distribution in batch processes, are also included in the analysis. The analysis focuses on how four main error sources such as unmeasured disturbances, uncertain initial conditions, model mismatch, and stochastic disturbances may impact observer estimation accuracy as well as their repercussion on control effectiveness and consequently on process performance. Results show that unmeasured disturbances are the most detrimental to observer and process performance in our case study. In spite of this finding, we present a methodology to tackle and solve this problem. All the analysis is first made under an openloop configuration and then moves onto a closedloop setup. All testing is based on computer simulations of the crystallization process. The evaluation criterion is based on the magnitude of a normalized rootmean squared error throughout 50 batch runs. The results are then used to identify if a link between estimation accuracy and control performance exists. The computational burden is also evaluated along 50 batch simulations, and is measured on the basis of CPU time required by every observer at every estimation stage.

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2 

Identification and Feedforward Control of a Dropondemand Inkjet Printhead

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3 

Identification of Models of Industrial Batch Cooling Crystallization system

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4 

Cogging compensation in embedded brushless motor control for haptics applications
For the development of a space qualified, 7 degrees of freedom, haptic arm exoskeleton a brushless DC motor with high torque production, power density and efficiency was selected. However, the attraction of the rotor magnets to the stator teeth introduces an additive, position dependent, torque disturbance on the motor shaft called cogging torque. In haptic applications this disturbance impacts the realism of the force reflection and limits control fidelity during masterslave teleoperation. This thesis investigates possible solutions within the constraints of the envisioned application. Due to volume, torque production and efficiency requirements the chosen motor is not to be changed. This rules out the use of motor design based cogging minimization techniques. For this reason only controlbased methods are considered. Two methods to identify the cogging waveform were developed. This data was used to do feedforward compensation using a lookuptable approach and a Fourier series approximation. For comparison, a PID feedback compensation and hybrid approach were also tested. Identification of the cogging torque and testing of compensation methods is done using a custom build measurement setup. A reduction of the RMS cogging of 39% was achieved using the feedforward approach, while the PID feedback loop resulted in a 46% reduction. A combination of these two methods in the hybrid approach resulted in a reduction of 75%.
Thesis done as part of a 'double degree' with Systems & Control at 3mE (DCSC) and Embedded Systems at EWI.

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5 

Improving winch control performance in Kite Power Systems using gain scheduling and a compliant element
Rising demands in energy consumption necessitate the development of lowcost renewable power generation. A Kite Power Sytem (KPS) is a novel approach to harvest wind energy with kites at higher altitudes than is possible with conventional wind turbines, at a lower cost. In this thesis, an approach to improve the winch controller of a KPS will be proposed in order to increase the power output. Measurements of the test system revealed an especially poor performance during the reel out phase, where the tether force was constrained to a maximum. It was found that a propagation delay is present on the system input. A force tracking controller for the reel out phase therefore needs to be developed, which accounts for the system’s propagation delays. A nonlinear KPS model that can be used in control algorithm design was presented. To control the nonlinear system across its full operating region, a gain scheduled feedback controller was proposed. It was found that the stability of the modeled original system was compromised when the system delay is high enough. By extending the system with a compliant element, a larger delay can be allowed before instability occurs. Within the boundary conditions of the nonlinear KPS model, by applying gain scheduled feedback control with integral action and extending the system with a compliant element, the winch controller can asymptotically track a force reference across its operating region in case of system delays. Given that the correct force reference is supplied, this will increase the power output of the KPS.

file embargo until: 20161204
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6 

Error detection and reduction within DriftLessTM

file embargo until: 20160603

7 

RealTime Optimistic Planning for the Control of Nonlinear Systems
Optimistic Planning is a modelbased online planning algorithm that guarantees nearoptimal actions for the control arbitrarily nonlinear systems. Planning algorithms aim to find optimal actions by starting from the current state and developing a tree representation of sequences of actions and resulting states, using a model to simulate statetransitions. Typically, online planning algorithms return a sequence of actions, apply the first action (or several actions at the start of the sequence) and start planning again from the new state, resembling the receding horizon principle as seen in Model Predictive Control.
Several optimistic planning algorithms exist, of which in this work only Optimistic Planning for Deterministic systems (OPD) is considered. OPD works for large, possibly infinite state spaces, but only for finite, discrete action spaces. Unfortunately, while OPD shows good theoretical nearoptimality guarantees, there is no record yet of OPD being applied to control nonlinear physical systems in realtime. This is because of the (long) computation required by OPD.
This work analyzes two main methods that can be used to make OPD suitable for realtime applications. The first approach is to increase the computational speed of the planning process by parallelizing the algorithm. Unfortunately, while parallelization has been proven to be able to increase the computational speed in classical planning, in experiments no improvement is found yet for OPD using parallelization. However, a potential benefit from creating a parallel version of OPD is not ruled out and it is expected that more research and more efficient implementations could still lead to an increase in the computational speed.
The second approach is to apply sequences of actions instead of single actions, which increases the time available for the planning process. Replanning starts immediately after a sequence is returned, using as initial state a prediction of the state at the end of the previous sequence. The resulting algorithm is called RealTime Optimistic Planning with Action Sequences (RTOPS). Extensive analysis is performed to find restrictions on the parameters of the algorithm that, when met, can guarantee realtime applicability. Additionally, the effect of using sequences of actions on the performance of the algorithm is investigated and bounds are put on the maximum performance loss.
The performance of RTOPS has been tested in various experiments on different problems: a cartpole simulation, an acrobot simulation and a real inverted pendulum. Different settings are compared and, overall, RTOPS proves to perform well, without violating realtime constraints. The experiments prove that RTOPS allows for the use of optimistic planning for realtime control of physical nonlinear systems.
Future work should focus on applying the ideas used to develop RTOPS to other optimistic planning algorithms, such as those that allow for continuous actions or stochastic systems. Furthermore, a parallelization of RTOPS could be developed that increases its computational speed.

file embargo until: 20150307
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8 

Design and analysis of a model based low level slip controller based on a hybrid braking system
Treats the design an ABS control strategy for a hybrid braking system.

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9 

Haptic feedback on the steering wheel near the vehicle’s handling limits using wheel load sensing
Research in vehicle dynamics and vehicle control systems has increased a lot over the last decades due to the focus towards safety, driving comfort and emissions and the opportunities
that come with the development of hybrid and electric powertrains. Modern vehicles are equipped with many automated systems but automation can have disadvantages such as overreliance, complacency, nonvigilance, deskilling and confusing the driver. The goal of this thesis is to prevent loss of control by improving haptic feedback on the steering wheel near the vehicle’s handling limits using wheel load sensing. Predicting when a vehicle starts to over or understeer is a difficult task since it depends on the road surface and will only be revealed by vehicle states once it is already too late. The aligning moment of the tire drops before the lateral force actually saturates because of a decrease in pneumatic trail caused by tire contact patch deformation. This drop in aligning moment can be felt on the steering wheel and is an indication that a vehicle is close to the limit. However, the large ratio of mechanical to pneumatic trail and the increased power steering in modern vehicles makes the drop in aligning moment difficult to feel. If vehicles become steerbywire there is no feedback reaching the driver through the steering wheel at all.
The first part of this thesis consists of identification of the lateral force and aligning moment of the tires with Load Sensing Bearings (LSBs) from SKF. Estimating the lateral force has been done before and the results here show that estimation of the aligning moment is also possible. A Multiple Linear Regression Analysis (MLRA) is used to find first order linear models reconstructing the lateral force and aligning moment from measurements with the LSBs. Different models are derived based on measurements of strain gauges and hall effect sensors on the bearing. The second part of this thesis consists of experiments done at the Prodrive test track to investigate the improvement of haptic feedback using LSBs. The work is a followup study based on the Haptic Support Near the Limits (HSNL) system developed in a previous research project. The drop in aligning moment is measured with LSBs and amplified on the steering wheel. The results show that with this feedback drivers are indeed better capable of preventing saturation of the front tires but further research is needed on how the system can increase safety. The results show a decrease in control effort and workload with feedback which can increase driving pleasure and comfort for the driver.

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10 

Gaining by forgetting: Towards longterm mobile robot autonomy in large scale environments using a novel hybrid metrictopological mapping system
The emerging of mobile robots in everyday life scenarios, such as in the case of domestic care robots, is highly anticipated. Much research has been carried out to make robots more capable of performing tasks in our everyday environments. Despite major progress over the last decades, many hurdles are still to be taken. In the field of robotic mapping, which studies how robots can generate a map (internal representation) of their environment, modern Simultaneous Localization and Mapping (SLAM) methods allow robots to map their environment and be aware of where they are in that environment. Such maps can then be used for robot navigation, which allows a robot to travel from one place to another safely and autonomously. State of the art SLAM methods still show large limitations in their real world applicability. First and foremost, they are limited in the size of environment they can handle as maps grow inconsistent when environments get too large, or they cannot handle multistory buildings for example because they are designed to only map in 2D. Performance even becomes significantly worse if one limits oneself to using affordable sensors. Secondly, modern SLAM algorithms still struggle with the tasks of building a map that is metrically consistent with the real world (that is, the map and a ground truth floor plan should align). Thirdly, the generated maps show obstacles (like walls), but do not give any other semantic details on them. For example, the map does not tell what places are rooms and what places are a corridor.
In this thesis, it is investigated how robotic mapping and robot navigation could benefit from a human inspired approach to these tasks. Humans do not create floor plans, but remember their environments in terms of concepts. These concepts are then linked in a relative way, and places are connected by fuzzy, relative defined connections. The relatively new study of semantic mapping aims at integrating these concepts (semantics) into robotic mapping. However, so far these systems have been built on top of a traditional SLAM method.
Parallel to this new development of semantic mapping, this thesis proposes an architecture, which we named LEMTOMap (Large Environment Metric TOpological Mapping system), that generates and handles maps in a relative way. It specifies mapping, localization and navigation in a way in which metric consistency of the map is no longer a requirement on a larger scale (e.g. that of a faculty building or larger).
The main contributions of this thesis are captured by the LEMTOMap architecture. LEMTOMap introduces a new topological mapping paradigm that allows the robot to generate a map that is metrically consistent on a local scale, but does not require metric consistency on a larger scale. This way, the main challenge of modern SLAM  limiting metric inconsistency  is reduced to a challenge of subordinate importance. Additionally, a new grid map SLAM algorithm is introduced, named Rolling Window GMapping (RWGMapping).
To verify the expected performance enhancements of the LEMTOMap system architecture, LEMTOMap has been partially implemented and tested in simulated experiments. The experiments confirm the main benefits of LEMTOMap, mostly in terms of improved overall time and space complexity.
The thesis concludes with a range of advices for future work. Part is aimed at the further implementation of LEMTOMap, and part at improving LEMTOMap beyond its current specification. Also, a performance issue of the original GMapping algorithm was detected and suggestions are made on how this should be improved.

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11 

Filtering & Identification for Spline based Wavefront Reconstruction in Adaptive Optics
Without any form of compensation, atmospheric turbulence blurs the images obtained by groundbased telescopes. An Adaptive Optics (AO) system compensates for the optical wavefront distortions introduced in a light beam as it propagates through a turbulent medium. The wavefront phase errors are measured with a Wavefront Sensor (WFS) and corrected by adding the conjugated phase with an actuator such as a Deformable Mirror (DM). This graduation project focuses on the reconstruction of the wavefront using a ShackHartmann (SH) WFS, while taking its spatial and temporal dynamics into account.
The recently introduced Spline based ABerration REconstruction (SABRE) is used to model the spatial dynamics using the approximated slopes. It has been shown that using the measured intensity pattern of the WFS, rather than the approximated slopes (which are obtained using a centroid algorithm), the WFR can be improved, because the intensity distribution contains more information than the approximated slopes. This, however, has been demonstrated using a Hartmann sensor. The first contribution of this thesis was to adapt the method for the SH WFS, which is the commonly used sensor in astronomy. This is achieved by using an additional image of a SH WFS under the same conditions, but with an additional known aberration. The prescribed algorithms are tested with the AO simulation tool Yao. It is shown that for small aberrations, SABRE with intensity measurements provides more accurate reconstructions of the wavefront.
Because of a delay, caused by the WFS and WFR, an error is introduced resulting from the temporal dynamics of the wavefront. The second goal of this thesis is to predict the wavefront aberrations, such that the temporal dynamics are taken into account. Furthermore, the prediction should exploit the local nature of SABRE, such that it is applicable for parallel programming. Subspace Identification (SID) is employed for estimating the model of the temporal dynamics. The estimated model is used by a Kalman Filter (KF) to predict the wavefront aberration. The SID and KF are adapted to methods which are compliant with the local nature of SABRE and therefore, the presented SID and KF are suitable for parallel programming. The SID and KF are tested and tuned with both methods of SABRE, i.e. SABRE with the approximated slopes and SABRE with the measured intensities. It is demonstrated that the KF predicts the aberration significantly more accurate compared to the delayed reconstruction and at times even outperforms the reconstruction without delay.

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12 

LTL specifications for Highway Lane Changing Maneuvers of Highly Automated Vehicles
Since the interest in autonomous driving solutions is massively increasing, the need for good and reliable control algorithms is growing every day. This project studies the performance of safe lane changes of a highly autonomous vehicle given the currently available perception of the environment, vehicle dynamics and desired comfort and speed requirements from the user. Also focus will be on when the vehicle decides to overtake other vehicles to move closer to its desired prescribed speed, while respecting the "rules of the road", i.e. not causing unexpected actions in relation to the other road participants. These requirements will then be converted into linear temporal logic statements for the purpose of automated synthesis of a receding horizon controller for longitudinal and lateral control of the vehicle. Thereby allowing it to make adjustments to the desired system behavior and computing a new control strategy, relatively easy and by definition, the resulting controller is formally guaranteed to meet the safety specifications at all times. Besides this search for formal specifications, a comparison is made with more conventional control techniques by reviewing a model predictive controller that was developed parallel to this project, showing its capabilities and discussing possible safety issues.

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13 

Adaptive deformable mirror dynamics and modular control
The refractive index of air varies a.o. with temperature, humidity, pressure and the CO2 concentration.
Due to atmospheric turbulence this refractive index varies both in space and in time, leading to aberrations in images of light having passed though it.
These aberrations limit the achievable resolution of optical telescopes such that the quality of their images is no longer diffraction limited.
An adaptive optics (AO) system is a means to recover the diffraction limited quality of the images.
This can be achieved a.o. by reflecting the incoming light on a deformable mirror (DM) that adapts its shape to the wavefront of this light such that some norm of the residual wavefront after reflection is minimal.
In this thesis novel designs are considered for the DM and its control system.
They are primarily aimed at the 8m class of telescopes in visible light, leading to a 200Hz controller bandwidth requirement and 6mm actuator spacing or 5000 actuators on a 500mm diameter DM..
To observe fainter celestial objects and/or increase the image resolution, optical telescopes are foreseen with primary mirrors of up to 40m in diameter.
Therefore, the DM system design is aimed at extendibility to a larger number of Degrees Of Freedom (DOF), which is realized using a modular concept.
Other drivers are low power consumption to prevent the need for active cooling systems and low production costs.
The DM design is realized using electromagnetic reluctance type actuators that are connected to the DM's reflective membrane by a thin rod.
Modules containing 61 hexagonally arranged actuators are manufactured using techniques suitable for massproduction.
To generate the currents through the actuator coils, driver electronics are developed based on PulseWidth Modulation (implemented in FPGAs) in combination with analog lowpass filters.
Several prototype DMs are realized whose behavior is analyzed both statically and dynamically by comparing Wyko and laser vibrometer measurements with first principle models of the driver electronics, the actuators and the facesheet.
To retain modularity of the system, a distributed control system architecture is foreseen in which each (group of) actuator(s) has its own controller that has a fixed computational power, communicates only to its neighbors and receives only a subset of the wavefront measurement data.
The design of a distributed controller with good performance is complicated by the wavefront reconstruction step made necessary by the ShackHartmann wavefront sensor.
Nevertheless, a distributed algorithm that combines wavefront reconstruction with adaptive prediction is shown in simulation to approximate the performance of a centralized finite impulse response (FIR) predictor/reconstructor and does not deteriorate as the number of DOFs increases.

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14 

Distributed Estimation and Control for Robotic Networks
Mobile robots that communicate and cooperate to achieve a common task have been the subject of an increasing research interest in recent years. These possibly heterogeneous groups of robots communicate locally via a communication network and therefore are usually referred to as robotic networks. Their potential applications are diverse and encompass monitoring, exploration, search and rescue, and disaster relief. From a research standpoint, in this thesis we consider specific aspects related to the foundations of robotic network algorithmic development: distributed estimation, control, and optimization.
The word “distributed” refers to situations in which the cooperating robots have a limited, local knowledge of the environment and of the group, as opposed to a “centralized” scenario, where all the robots have access to the complete information. The typical challenge in distributed systems is to achieve similar results (in terms of performance of the estimation, control, or optimization task) with respect to a centralized system without extensive communication among the cooperating robots.
In this thesis we develop effective distributed estimation, control, and optimization algorithms tailored to the distributed nature of robotic networks. These algorithms strive for limiting the local communication among the mobile robots, in order to be applicable in practical situations. In particular, we focus on issues related to nonlinearities of the dynamical model of the robots and their sensors, to the connectivity of the communication graph through which the robots interact, and to fast feasible solutions for the common (estimation or control) objective.

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15 

Batchtobatch learning for modelbased control of process systems with application to cooling crystallization
From an engineering perspective, the term process refers to a conversion of raw materials into intermediate or final products using chemical, physical, or biological operations. Industrial processes can be performed either in continuous or in batch mode. There exist for instance continuous and batch units for reaction, distillation, and crystallization. In batch mode, the raw materials are loaded in the unit only at the beginning of the process. Subsequently, the desired transformation takes place inside the unit, and the products are eventually removed altogether after the processing time. In order to obtain the desired production volume, several batches are repeated.
In an industrial process, several variables such as temperatures, pressures, and concentrations have to be regulated in order to ensure safety, maintain the product quality, and optimize economic criteria. In principle, modelbased control techniques available in the literature could be systematically utilized in order to achieve these goals. However, a limitation to the applicability of modelbased techniques for batch process control is that the available models of batch processes often suffer from severe uncertainties.
In this thesis, we have investigated the use of measured data in order to improve the performance of modelbased control of batch processes. Our approach consists in using the measured data in order to refine from batch to batch the model that is used to design the controller. By doing so, the performance delivered by the modelbased controller is expected to improve.
We have developed the parametric model update technique Iterative Identification Control (IIC) and nonparametric model update technique Iterative Learning Control (ILC). While in IIC the measured batch data are used to update from batch to batch parameter estimates for the uncertain physical coefficients, in ILC the data are used to compute a nonparametric, additive correction term for a nominal process model.
We have tested the ILC and IIC algorithms for the batch cooling crystallization process both in a simulation environment and on a real pilotscale crystallization setup. We have shown that the two approaches have complementary advantages. On the one hand, the parametric approach allows for a faster learning since it produces a parsimonious representation of the process. On the other hand, the nonparametric approach can cope effectively with the serious issue of structural mismatches owing to the use of a more flexible representation.
Furthermore, we have investigated the use of excitation signals to enhance the performance of parametric model update techniques in an iterative identification/controller design scheme similar to IIC. The excitation signals have a dual effect on the overall control performance. On the one hand, the application of an excitation signal superposed to the normal control input leads after identification to an increased model accuracy, and thus a better control performance. On the other hand, the excitation signal also causes a temporary performance degradation, since it acts as a disturbance while it is applied to control system. For linear dynamical systems, we have shown that the problem of designing the excitation signals aiming to maximize the overall control performance can be approximated as a convex optimization problem.
The lack of generally applicable and computationally efficient experiment design tools for nonlinear systems is the main bottleneck for the optimal design of the excitation signals in the case of batch processes. In this thesis, we have developed a novel experiment design method applicable to the class of fading memory nonlinear system. Limiting the excitation signals to a finite number of levels, the information matrix can be expressed as a linear function of the frequency of occurrence of each possible pattern having duration equal to the memory of the system. Exploiting the linear relation between the frequencies and the information matrix, several experiment design problems can be formulated as convex optimization problems.

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16 

Modelbased Process Monitoring and Control of Micromilling using Active Magnetic Bearings
The process of micromilling is a promising technology for the fabrication of microparts with arbitrary 3D features in a wide range of materials. However, as a result of the reduced dimensions, the susceptibility of the process for machine tool errors and vibrations is higher, having adverse effects on accuracy and surface quality of the resulting workpieces. Furthermore, the production time and the efficiency of the process suffer from low material removal rates and excessive tool wear and breakage. To improve the micromilling process, online process monitoring and control becomes of high importance. Signs of problems are almost unnoticeable without the use of special equipment. Techniques are needed to detect and possibly even predict anomalies in the process and to online monitor the condition of the cutting process.
Spindles with Active Magnetic Bearings are particularly interesting for the micromilling process, not only for the achievable spindle speeds, but also because of the opportunities they offer to develop online process monitoring and control techniques. These include force monitoring, tool condition and breakage monitoring, and chatter control. However, literature thus far lacks results implementing these techniques for the micromilling process.
The aim of this thesis is to investigate the opportunities for modelbased process monitoring and control to improve the micromilling process using the intrinsic properties of AMB spindles. This objective is narrowed down to the goal of estimating the cutting forces from the bearing signals. The approach towards this goal consists of three steps.
First an approach to modelbased cutting force estimation in micromilling using the signals of the AMBs is developed. The cutting force estimation problem is expressed as an input estimation problem, where the cutting forces are an unknown input to the closedloop AMB spindle system. To solve this problem, a method is given for modelbased optimal estimation of unknown inputs to multivariable closedloop systems, based on Wiener filter theory. For cases in which controller knowledge is not available, an approach is formulated in which equal performance of the estimator is ensured for any controller. Smoothed estimators are derived, resulting in smaller estimation errors when a delay in the estimation result is tolerable.
Second, a method is presented for system identification of a high speed AMB micromilling spindle in the frequency range relevant for force estimation. This problem is separated into two subproblems. The first is the identification of the dynamics from the current input to the displacement of the rotor shaft at the bearings, the bearing dynamics. The second problem is the identification of the tooltip dynamics, which are the dynamics between the force on the tooltip and the displacement of the rotor shaft at the bearings.
System identification of the bearing dynamics is approached by first making a nonparametric estimate of the multivariable frequency response function (FRF). An experiment design is given targeted at yielding small bias and variance of the FRF, as well as small error due to nonlinear distortions. Using the FRF estimate, a multivariable parametric model is estimated. Here, the main emphasis is on identification of a parametric model of the plant dynamics, leading to the choice of minimization of an output error (OE) criterion. An IVbased algorithm is given for estimation of multiinput multioutout (MIMO) Output Error models in matrix fraction description from frequency domain data. This algorithm has the property that convergence of the iterations implies that an optimal solutions has been found.
The main challenge in identifying the tooltip dynamics is to apply a known excitation force to the tooltip. The route followed in this thesis is to identify the tooltip dynamics using data obtained during a milling experiment in which the cutting forces are measured. The amount of data that can be generated in this way is limited, as is the control over the spectral properties of the input. Hence, in order to reduce the complexity of the identification, usage is made of assumed observability and controllability properties of the system. This results in a particular closedloop parameterization of the modelset and a known, but nonminimum phase noise model. For this particular identification problem, solutions are formulated.
The third and last step to the goal of this thesis pertains to modelbased correction of runout disturbances in measurements of the positions and currents of AMB spindle. Such disturbances are synchronous with the rotation of the spindle and hence almost periodic. A parametrized truncated Fourier series expansion model for the runout disturbance as a function of the angular position is used, allowing to formulate runout identification as a parameter estimation problem. In correcting for the runout disturbances, the main issue is how to deal with the uncertainty in the angular position measurements, or the total lack of such measurements. Solutions are given that compensate for the errors introduced by this uncertainty, or estimate the angular position from the available data using an Extended Kalman filter approach.

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17 

Distributed Wavefront Reconstruction for Adaptive Optics Systems
We are currently facing an increasing amount of challenges in the area of photonics as more and more applications in need for active “photon control” sprout in different fields of science. Adaptive Optics (AO) is the subject which deals with measuring, reconstructing, and reshaping the phase of a photon wavefront in realtime and can, thus, provide the framework for controlling the photons in areas such as medicine, astronomy and telecommunications, among others.
The objective of this graduation project is to create a novel distributed method for wavefront reconstruction, integrate the method in an AO loop, and analyse its properties. This method will use the intensity distribution measured by the wavefront sensor instead of the classical slope approximation (obtained using a centroid algorithm). Using the complete intensity distribution gives us more information than the slope approximation and therefore, a more accurate reconstruction is expected. Moreover, we will estimate the wavefront using Bsplines basis functions. These splines are defined locally which makes them suitable for the application of distributed reconstruction methods.
The content of this thesis is divided into two distinct parts. In the first part, we analyse the different components of an AO system with special emphasis on the stateoftheart phase retrieval methods. Furthermore, the Bsplines framework is presented alongside distributed optimization techniques with special emphasis on the Alternating Direction Method of Multipliers (ADMM). The second part of the thesis uses the theoretical information from the first chapters to support the development of one centralized and two distributed algorithms for solving phaseretrieval problems using pupilplane sensors. The results from these methods, together with the results from a compressive sampling method which decreases the quantity of measurements used, are presented in the last chapters.
It was verified in simulation experiments that the average reconstruction error achieved by the novel centralized method surpasses the classical approaches which use slope measurements for aberrations with an RMS value smaller than the wavelength. It is also shown that the variance of the reconstruction error using the novel method is reduced by two orders of magnitude. Regarding the two distributed methods (unstructured and structured ADMM applications), it is shown that the unstructured method has a very low convergence rate which renders this method unpractical for realtime applications. The structured method showed much more promising results given that it was able to converge to within a 5% tolerance of the optimal centralized solution after 50 − 150 iterations. This method can also be implemented in a completely decentralized manner which is suitable for a GPU/FPGA implementation.

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18 

Controllerstructure optimization using parameterdependent modal reduced statespace models
Although it is still common in the field of motion control systems to first design the structure and then the controller, integrated design approaches are becoming more popular. The problem of finding optimal parameters for a parameterized structure and controller by solving an optimization problem will be referred to as \textit{controllerstructure optimization} (CSO). These types of problems are often characterized as multiobjective and nonconvex and therefore hard to solve. Especially if the parameterized structure is modelled in a finiteelement (FE) environment.
This MSc thesis report presents a design approach for solving a CSO problem by using an approximate model of the parameterized structure in the form of a \textit{parameterdependent statespace} (PDSS) model. The PDSS model is obtained by taking a few samples of the original structure. Each of these samples represents a \textit{linear timeinvariant} (LTI) modal reduced statespace model. The main emphasis of this MSc thesis is to investigate whether this approach is able to approximate the solution of the original (comprehensive) CSO problem in an efficient way.

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