Designing active vibration control with minimum order for flexible structure

Abstract

This paper concerned with the designing active control for flexible structure. The structure has 4 stories and each story is modeled such that it has a single degree of freedom in the transverse direction and one more degree of freedom in the angle of torsion around the centroid of the story. The model of structure, absorber and stroke are combined such that the number of state is 30. The order of state is reduced up to 7 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> order by using the balanced truncation. The active control is designed by using the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -control theory.