Decoupling of the 10 m GranTeCan telescope´s primary mirror dynamics and design of a controller for noise rejection

The goal of the paper is to present a method for the decoupling of a multivariable system and to show how this procedure allows the problem of vibrations rejection to be faced. The system we have worked with represents the dynamic behaviour of the GTC´s (Gran Telescopio Canarias) 10 m diameter primary mirror. This telescope will be built in the island of La Palma (Spain). The big size of this mirror has caused its segmentation into 36 hexagonal pieces called segments. The system has 108 inputs and the same number of outputs coupled among them. With the decoupling method we present in this work, the problem of designing a controller for a MIMO system has been converted into the calculus of 108 SISO controllers. One of these controllers is presented as an example of how the decoupling process facilitates the noise rejection