Towards the use of H-infinity controller synthesis for seismic active damping

Abstract

In 2015, for the first-time ever, a collision between two black-holes was directly observed. The very new detector allowing to make such an impressive event possible was of a new-kind: a gravitational wave detector. Now, in order to detect more and more events with better resolution, high-technology beasts are being engineered around the world, such as the future Einstein telescope. However, some highly-needed tools still need to mature in order to improve this technology a step further. Indeed the gravitional waves are ridiculously small. It is for exemple, well over 10 orders of magnitude smaller than seismic vibrations. For this reason, it is impossible to observe without mitigating the effects of seismic activity on our detector. Active control is an important part of this process. It allows to counteract the motion created by the vibrations. However, lots of difficulties appear when such a method has to be applied to a complex system, moving and rotating in all directions of space. This is why new approaches, such as the H-infinity method, are studied to be applied on this kind of detector. This method numerically optimizes controllers for a given system, creating what is said to be an "optimal controller". In this work, H-infinity synthesis is applied on different, increasingly complex systems in order to study the effect of different cost functions (also called weighting functions) and criteria to create the best performing controller possible. The caveats of this numerical method, linked to the complexity of the obtained, high-order, controller, its possible instability and the complexity of tuning the frequency related weighting functions are also discussed. A comparison with the performance obtain, through classical control, using some of the systems used for our analysis, is also made in order to ensure that this method is a viable solution to the problem. This work shows that H-infinity can be a practical way of handling, through active damping, coupled motions in order to reduce the effect of ground motion, and that this promising technique might as well be studied for this purpose, in order to achieve better performance in damping applications, and maybe, finally set the bar high enough for detecting more important gravitational event in our galaxy, and in other ones.