In this paper, we develop an identification technique based on continuous-time Kautz basis functions and Maximum Likelihood estimation from discrete-time data to obtain a continuous-time model of a laboratory adaptive optics system. We illustrate the proposed identification method using synthetic data and experimental data of a laboratory adaptive optics setup. Finally we utilize the estimated model to develop a Model Predictive Control strategy that considers the deformable mirror actuation constraints. We illustrate the benefits of the model predictive control strategy via simulations and compare it against the classical Proportional-Integral controller.
Vibration effects acting in the science light path reduce the performance of the adaptive optics systems (AO). In order to mitigate the vibration effects and to improve the performance of the AO systems, an adequate model for the vibration in necessary. Traditionally, those vibrations are modelled as oscillators (with or without damping) driven by white noise. In this work, we address the identification of a continuous-time oscillator from discrete-time samples of the position. To this end, we use Maximum Likelihood estimation method to estimate the vibrations frequency.
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