IMAACA'2004 Vibration Reduction of magnet quadrupole for beam positioning within a CLIC system J. Lottin*, M. Corduneanu** *LISTIC-ESIA, Université de Savoie, Annecy, F74016 France Phone: +33 450 096 551, Fax: +33 450 096 559, E-mail: jacques.lottin@univ-savoie.fr **Universitatea Polytehnica, Bucuresti, Romania Abstract - A new procedure to compensate vibrations in a mechanical system is introduced in this paper. It is based on the decomposition of the periodic measures in sine and cosine components in order to apply appropriate control input. It is assumed that the system behavior is linear, which is realistic in the case of very small disturbances like in CLIC system. Furthermore, this procedure does not need good models to perform well, as long as disturbances can be supposed stationary with respect to the period of the signals. In this paper, after a brief description of some features of the CLIC system, the compensation procedure is presented. Then performances are illustrated by means of simulations that are carried out using a particular mechanical system. Robustness is analysed with respect to model mismatch and it is shown that good performances are still obtained. Keywords: active vibration isolation, vibration control I. INTRODUCTION Much work has been done in the field of vibration attenuation, usually based on model of mechanical system. The aim of this study is to analyze active compensation of vibrations of magnet quadrupole used for beam positioning in a Compact Linear Collider (CLIC) system. Exact compensation relies on appropriate excitation by means of reduced actuators, such as PZT, which move small masses, on the basis of information provided by sensors, either acceleration or velocity. For each frequency within the bandwidth, it is necessary to determine amplitude and phase of the excitation signal. In this study, these are replaced by sine and cosine components. Since it is not possible to build an accurate dynamical model of the system on the one hand, and since main characteristics of disturbance signals evolve very slowly on the second hand, a closed loop control scheme is built in order to make the component amplitude to converge to the best value. The first section gives general information about CLIC system. The second section introduces the compensation procedure, especially the criterion and the way to correct the component amplitude. An example is presented in the third section, where a particular mechanical model is built in order to illustrate the behavior of the system using Matlab Simulink Software. Tuning of parameters as well as sensitivity with respect to model mismatch are analyzed in section four. Finally extension to multi-dimensional case as well as other robustness analysis are discussed in the conclusion. II. SYSTEM DESCRIPTION The nanometer beam size at the Interaction point in the Compact Linear Collider (CLIC) imposes magnet vibration tolerances that range from 0.2 nm to a few nm. It is necessary to introduce active vibration damping in order to compensate disturbances that come from floor vibration, due to roads, operating accelerators, or simply cooling water. Fig 1 below shows the effect of this disturbance for several values of the flow of cooling water. Fig. 1. Example of spectral analysis. Because of the complexity of the mechanical system that is involved to focus the beam, it is difficult to derive a precise model of the system behavior. It is why a new procedure is studied, in order to make the compensation force to converge to the right form so that the vibration is minimized, at least at the sensor location. It is supposed that locations of sensors and actuators are well chosen with respect to the mechanical structure. .....