Browsing by Author "Gonzalez Perez, Karen Fernanda"
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Thesis IDENTIFICACIÓN DE MODELOS DE VIBRACIONES PARA CONTROL DE SISTEMAS DE ÓPTICA ADAPTATIVA(2018) Gonzalez Perez, Karen Fernanda; Departamento de Electrónica; Agüero Vásquez, Juan Carlos; Carvajal Guerra, Rodrigo JavierIn all major ground-based astronomical observatories, adaptive optics (AO) has becomean intrinsic technique to bring scienti c observations closer to the diraction limitof the astronomical instruments. This is because AO enables the compensation of theoptical aberrations caused by atmospheric turbulence, as well as the vibrations of thestructure of the telescope induced by elements within the system instrumentation (suchas fans and cooling pumps), wind and movements of the telescope. Since vibrationsstrongly affect the performance of the AO systems and hinder the achievement of goodquality images, it is necessary to obtain a model of these vibrations to later developsimple but effective control techniques that can be implemented in real time. It is forthis reason that in this thesis it is proposed to characterize these vibrations by modelingthem as a linear combination of oscillators each one driven fed by a noise and identifyingthe continuous-time oscillators using regular sampling. The model of the oscillator isrepresented as continuous-time autoregressive model, obtaining its discrete-time equivalentmodel, in terms of the parameters of the model in continuous-time oscillator. Then,the model is identi ed using the method of Maximum Likelihood using local and globaloptimization algorithms.When a local optimization algorithm is used, a good initial estimation is required forthe parameters of the system. Then one performs the corresponding optimization, whichin this case is implemented using the algorithm of quasi Newton. On the other hand,when a global optimization algorithm is used, the equivalent model of sampled data isanalyzed for two cases: i) instantaneous sampling and ii) integrated sampling.Both types of optimization are analyzed in detail, illustrating the behavior of thelog-likelihood function through numerical examples that show that it presents severallocal maxima.
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