H∞ controller with output feedback using linear matrix

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Proceedings of COBEM 2007
Copyright © 2007 by ABCM

19th International Congress of Mechanical Engineering
November 5-9, 2007, Brasília, DF

H∞ CONTROLLER WITH OUTPUT FEEDBACK USING LINEAR MATRIX
INEQUALITIES FOR APPLICATION IN BUILDING MODEL
Rodrigo Borges Santos, rborges@dem.feis.unesp.br
Douglas Domingues Bueno, ddbueno@dem.feis.unesp.br
Clayton Rodrigo Marqui,clayton_rm@dem.feis.unesp.br
Vicente Lopes Junior, vicente@dem.feis.unesp.br
GMSINT – Grupo de Materiais e Sistemas Inteligentes, Mechanical Engineering Department, Faculdade de Engenharia de Ilha
Solteira – UNESP, Av. Brasil 56, Ilha Solteira, SP, Brazil, ZIP CODE 15385000, www.dem.feis.unesp.br/gmsint

Abstract. Experimental verification of structural vibrations control strategies is essential for eventualfull-scale
implementations. However, few researchers have facilities readily available to them that are capable of even smallscale structural control experiments. Appropriately constructed bench-scale models can be used to study important
aspects of full-scale structural vibrations control implementations, including: control-structure interaction, actuator
and sensor dynamics, states feedback design,control spillover, etc. In this sense, the purpose of this article is the
project of H∞ controller with output feedback using linear matrix inequalities (LMIs) for vibration attenuation in a
flexible building like structure. The considered structure is manufactured by Quanser Consulting Inc., and it is
controlled by an active mass driver (AMD). The structure consists of a steel frame with acontrollable mass located at
the top, which can be configured to have either 1 or 2 floors. In this paper, a 2-floor configuration is employed. The
actual experiment considered herein is an effective way to deal with challenges associated with active control of
flexible structures.
Keywords: Active Vibration Control, H∞ controller, Linear Matrix Inequalities (LMIs) and Active Mass Driver (AMD)1. INTRODUCTION
Experimental investigations are essential to obtain a fundamental understanding of many phenomena. However,
when physical systems are scaled down to a size appropriate for laboratory study, salient features of their behavior may
be lost. This is particularly true for large civil engineering structures (Battaini, et al., 1998). In the area of control of
civil structures, it iswell-recognized that experimental verification of control strategies is necessary to focus research
efforts in the most promising directions (Housner, et al. 1994a,b). However, few researchers have experimental
facilities readily available to them that are capable of even small-scale structural control experiments. Consequently, the
majority of control studies to date have been analytical innature, a substantial number may have employed models that
lacked important features of the physical problem. One such phenomena that has been neglected for many years is the
control-structure interaction (CSI). Through a series of analytical and experimental studies, Dyke, et al. (1995)
recognized that understanding CSI was key to developing acceleration feedback control strategies and showedthat
accounting for CSI is fundamental to achieving high performance controllers.
A variety of techniques have been intensively studied to reduce the structural vibration in order to achieve highspeed and high-precision motions (Singer and Seering, 1989). Recent development in microelectronics and smart
structure techniques have provided new solutions for vibration control (Clark et al.,1998).“Smart structures” adopt
microprocessors and distributed transducers to modify structural dynamics to actively suppress vibration in timevarying working environments. Use of smart structure techniques can lead to lightweight structures, leading to higher
performance.
There are many robust techniques well know in the structural control literature to outline these problems. In this
research work,...
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