Modeling and control of a gravitational wave detector

Large-scale gravitational-wave detectors like VIRGO or LIGO are currently under construction. These Michelson interferometers use multiple optical cavities with kilometer-scale arms lengths. In order for the detector to be operational the lengths of the cavity should be controlled. Hence a knowledge of the dynamic response of the interferometer is needed in order to operate it. In this paper a linear control model relating the lengths to control and the measured signals is derived. Finally, this model is used after inversion to recover the error signals. An H∞ controller is then used to control the interferometer. A nonlinear simulation of the interferometer shows a well behaviour of both the extraction method and the closed loop system