IDENTIFICACIÓN DE MODELOS DE VIBRACIONES PARA CONTROL DE SISTEMAS DE ÓPTICA ADAPTATIVA

Abstract

En todos los principales observatorios astronomicos terrestres, la optica adaptativa(AO) se ha convertido en una tecnica intrínseca para acercar las observaciones cient íficasal límite de difraccion de los instrumentos astronomicos. Esto se debe a que AO permitela compensacion de las aberraciones ópticas causadas por la turbulencia atmosferica,as como las vibraciones de la estructura del telescopio inducidas por elementos dentrode la instrumentacion del sistema (como ventiladores y bombas de enfriamiento), elviento y los movimientos del telescopio. Ya que las vibraciones afectan fuertemente elrendimiento de los sistemas AO y di cultan el logro de imagenes de buena calidad,es necesario obtener un modelo de estas vibraciones para posteriormente desarrollartecnicas de control simples, pero efectivas, que se puedan implementar en tiempo real.Es por ello que en esta tesis se propone caracterizar estas vibraciones modelandolascomo una combinacion lineal de osciladores alimentados cada uno de ellos por un ruidoe identi cando dichos osciladores de tiempo continuo utilizando un muestreo regular. Serepresenta el modelo del oscilador como un modelo autoregresivo en tiempo continuo paraluego obtener su modelo equivalente en tiempo discreto, en funcion de los parametros del

In 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.