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Different nonlinear observers are compared throughout this work where they are part of an NMPC framework used to control a fed-batch crystallization process . We study which observer-optimizer pair offers the best control performance while maintaining adequate computational burden so that a posterior real-time 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 open-loop configuration and then moves onto a closed-loop setup. All testing is based on computer simulations of the crystallization process. The evaluation criterion is based on the magnitude of a normalized root-mean 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.

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 mass-production. To generate the currents through the actuator coils, driver electronics are developed based on Pulse-Width Modulation (implemented in FPGAs) in combination with analog low-pass 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 Shack-Hartmann 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.

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.

The process of micro-milling is a promising technology for the fabrication of micro-parts 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 micro-milling 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 micro-milling 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 micro-milling process. The aim of this thesis is to investigate the opportunities for model-based process monitoring and control to improve the micro-milling 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 model-based cutting force estimation in micro-milling 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 closed-loop AMB spindle system. To solve this problem, a method is given for model-based optimal estimation of unknown inputs to multivariable closed-loop 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 micro-milling 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 non-parametric 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 IV-based algorithm is given for estimation of multi-input multi-outout (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 closed-loop parameterization of the model-set and a known, but non-minimum phase noise model. For this particular identification problem, solutions are formulated. The third and last step to the goal of this thesis pertains to model-based 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.