Affiliations: Department of Computational Mechanics, DMC, Faculty of
Mechanical Engineering, FEM, State University of Campinas, UNICAMP, 13083-970,
Campinas, SP, Brazil
Note: [] Corresponding author: Alberto Luiz Serpa, Department of
Computational Mechanics, DMC, Faculty of Mechanical Engineering, FEM, State
University of Campinas, UNICAMP, 13083-970, Campinas, SP, Brazil. Tel.: +55 19
37883387; Fax: +55 19 32893722; E-mail: serpa@fem.unicamp.br
Abstract: Many practical problems in structural dynamics are modeled with a
high number of degrees of freedom in order to properly describe the structure.
A formulation to design robust controllers is the
H_{&infty;} technique where the controller has the same
order of the mathematical model and this becomes unpractical and infeasible for
most practical problems where the number of degrees of freedom is not small.
One way to overcome this difficulty is to employ a model reduction technique,
and design a reduced order controller based on this reduced model. In this
case, it is required that the reduced controller ensures a good performance
also for the nominal model (reduced) and for the real model (non-reduced) of
the structure. Since the reduced controller is designed based on a truncated
dynamic model, the non-modeled vibration modes can be excited causing the
spillover phenomena, which is a severe undesirable effect. This work
investigates the behavior of a reduced order controller obtained based on a
reduced model through the Guyan reduction. The
H_{&infty;} robust control and Linear Matrix Inequalities
(LMI) formulations are employed to the problem of controlling a flexible
structure subjected to an external disturbance. Some simulations are performed
using a cantilever beam modeled by the finite element method. The results show
that the Guyan reduced order model can be used to design a controller to the
non-reduced model with success.
