Cuccato, Davide
Modeling, estimation and control of ring laser gyroscopes for the accurate estimation of the earth rotation [Tesi di dottorato]

He ? Ne ring lasers gyroscopes are, at present, the most precise devices for absolute angular velocity measurements. Limitations to their performances come from the non-linear dynamics of the laser. Accordingly to the Lamb semi-classical theory of gas lasers, a model can be applied to a He–Ne ring laser gyroscope to estimate and remove the laser dynamics contribution from the rotation measurements. We find a set of critical parameters affecting the long term stability of the system. We propose a method for estimating the long term drift of the laser parameters, and for filtering out the laser dynamics effects, e.g. the light backscattering. The intensities of the counterpropagating laser beams exiting one cavity mirror are continuously measured, together with the monitor of the laser population inversion. These quantities, once properly calibrated with a dedicated procedure, allow us to estimate cold cavity and active medium parameters of the Lamb theory. Our identification procedure, based on the perturbative solutions of the laser dynamics, allow us for the application of the Kalman Filter theory for the estimation of the angular velocity. The parameter identification and backscattering subtraction procedure has been verified by means of a Monte Carlo studies of the system, and then applied to the experimental data of the ring lasers G-PISA and G-WETTZELL. After the subtraction of laser dynamics effects by Kalman filter, the relative systematic error of G-PISA reduces from 50 to 5 parts in 103, and it can be attributed to the residual uncertainties on geometrical scale factor and orientation of the ring. We also report that after the backscattering subtraction, the relative systematic errors of G-WETTZELL are reduced too. Conversely, in the last decade an increasing attention was drawn to high precision optical experiments, e.g. ring laser experiments, which combine high sensitivity, accuracy and long term stability. Due to the experimental requirements, position and orientation of optical elements and laser beams formation must be controlled in the field of nano-positioning and ultra-precision instruments. Existing methods for beam direction computing in resonators, e.g. iterative ray tracing or generalized ray transfer matrices, are either computationally expensive or rely on overparametrized models of optical elements. By exploiting the Fermat’s principle, we develop a novel method to compute the beam directions in resonant optical cavities formed by spherical mirrors, as a function of mirror positions and curvature radii. The proposed procedure is based on the geometric Newton method on matrix manifold, a tool with second order convergence rate that relies on a second order model of the cavity optical length. As we avoid coordinates to parametrize the beam position on mirror surfaces, the computation of the second order model does not involve the second derivatives of the parametrization. With the help of numerical tests, we show that the convergence properties of our procedure hold for non-planar polygonal cavities, and we assess the effectiveness of the geometric Newton method in determining their configurations with an high degree of accuracy and negligible computational effort. We also presents a method to account for the (ring laser) cavity deformations due to mirrors displacement, seen as the residual motions of the mirrors centers after the removal of rigid body motions. Having the cavity configuration and the model to account for mirrors movements, the calibration and active control of the optical cavity can be addressed as a control problem. In fact, our results are of some importance not only for the design and simulation of ring laser gyroscopes, but also for the active control of the optical cavities. In the final part of this work we detail a complete model including the simulation of the physical processes of interest in the operation of a ring laser gyroscope. Simulation results for the application of the model to the ring laser GP2 are presented and discussed

In relazione con
ING-INF/04 - Automatica

Tesi di dottorato. | Lingua: | Paese: | BID: TD16054961