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Reduced Order Model Feedback Control Design: Computational Studies for Thin Cylindrical Shells
 IEEE Trans. Auto. Contr
, 1998
"... Reduced order models employing the Lagrange and POD reduced basis methods in numerical approximation and feedback control of systems are presented and numerically tested. The system considered is a thin cylindrical shell with surfacemounted piezoceramic actuators. DonnellMushtari equations, modifi ..."
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Cited by 22 (11 self)
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Reduced order models employing the Lagrange and POD reduced basis methods in numerical approximation and feedback control of systems are presented and numerically tested. The system considered is a thin cylindrical shell with surfacemounted piezoceramic actuators. DonnellMushtari equations, modified to include KelvinVoigt damping, are used to model the system dynamics. Basis functions constructed from Fourier polynomials tensored with cubic splines are employed in the Galerkin expansion of the full order model. Reduced basis elements are then formed from full order approximations of the exogenously excited shell taken at different time instances. Numerical examples illustrating the features of the reduced basis methods are presented. To investigate the behavior of the methods when executed on physical systems, the numerical implementation of reduced order control gains in the full order model is developed and numerical examples are presented. 1 Research supported in part by the U.S...
Model Development for Atomic Force Microscope Stage Mechanisms
"... In this paper, we develop nonlinear constitutive equations and resulting system models quantifying the nonlinear and hysteretic fielddisplacement relations inherent to lead zirconate titanate (PZT) devices employed in atomic force microscope stage mechanisms. We focus specifically on PZT rods utili ..."
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Cited by 9 (9 self)
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In this paper, we develop nonlinear constitutive equations and resulting system models quantifying the nonlinear and hysteretic fielddisplacement relations inherent to lead zirconate titanate (PZT) devices employed in atomic force microscope stage mechanisms. We focus specifically on PZT rods utilizing d33 motion and PZT shells driven in d31 regimes, but the modeling framework is sufficiently general to accommodate a variety of drive geometries. In the first step of the model development, latticelevel energy relations are combined with stochastic homogenization techniques to construct nonlinear constitutive relations which accommodate the hysteresis inherent to ferroelectric compounds. Secondly, these constitutive relations are employed in classical rod and shell relations to construct system models appropriate for presently employed nanopositioner designs. The capability of the models to quantify the frequencydependent hysteresis inherent to the PZT stages is illustrated through comparison with experimental data. i 1
LQR CONTROL OF THIN SHELL DYNAMICS: FORMULATION AND NUMERICAL IMPLEMENTATION
, 1997
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Proper Orthogonal Decomposition Based Control of Transverse Beam Vibrations: Experimental Implementation
, 1999
"... LQG compensator control of transverse vibrations was implemented on an aluminum cantilevered beam in a "smart structure" paradigm. The beam was mounted with two selfsensing, selfactuating piezoceramic patches. The EulerBernoulli beam equation was discretized via a Galerkin type approxim ..."
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Cited by 2 (1 self)
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LQG compensator control of transverse vibrations was implemented on an aluminum cantilevered beam in a "smart structure" paradigm. The beam was mounted with two selfsensing, selfactuating piezoceramic patches. The EulerBernoulli beam equation was discretized via a Galerkin type approximation (referred to as the full order model). To reduce the size of the resulting finite dimensional approximating system, the Proper Orthogonal Decomposition (POD) was employed as a reduced basis method. A reduction of dimension from 34 to 2 was obtained through the model reduction technique. Feedback control based on the reduced order system was implemented in real time using a dSpace DS1103 control system. Experimental results indicate that POD based control achieves comparable control attenuation with full order model based control. 1 Introduction Realtime control of smart material structures requires numerical integration of the linear system at each discrete time step at which the realtime pro...
Model Development for Piezoceramic Nanopositioners
 Proc. 42nd IEEE Conf. Dec. and Control, Maui, HA
, 2003
"... In this paper, we develop nonlinear constitutive equations and resulting system models quantifying the nonlinear and hysteretic fielddisplacement relations inherent to piezoceramic elements employed in present nanopositioner designs. We focus specifically on piezoceramic rods utilizing d33 motion a ..."
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Cited by 2 (1 self)
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In this paper, we develop nonlinear constitutive equations and resulting system models quantifying the nonlinear and hysteretic fielddisplacement relations inherent to piezoceramic elements employed in present nanopositioner designs. We focus specifically on piezoceramic rods utilizing d33 motion and piezoceramic shells driven in d31 regimes, but the modeling framework is sufficiently general to accommodate a variety of drive geometries. In the first step of the model development, latticelevel energy relations are combined with stochastic homogenization techniques to construct nonlinear constitutive relations which accommodate the hysteresis inherent to piezoceramic compounds. Secondly, these constitutive relations are employed in classical rod and shell relations to construct system models appropriate for presently employed nanopositioner designs. 1.
LQR control of shell vibrations via piezoceramic actuators
 International Series in Numerical Mathematics
, 1998
"... A modelbased LQR method for controlling vibrations in cylindrical shells is presented. Surfacemounted piezoceramic patches are employed as actuators which leads to unbounded control input operators. Modi ed DonnellMushtari shell equations incorporating strong or KelvinVoigt damping are used to m ..."
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Cited by 1 (1 self)
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A modelbased LQR method for controlling vibrations in cylindrical shells is presented. Surfacemounted piezoceramic patches are employed as actuators which leads to unbounded control input operators. Modi ed DonnellMushtari shell equations incorporating strong or KelvinVoigt damping are used to model the system. The model is then abstractly formulated in terms of sesquilinear forms. This provides a framework amenable for proving model wellposedness and convergence of LQR gains using analytic semigroup results combined with LQR theory for unbounded input operators. Finally, numerical examples demonstrating the e ectiveness of the method are presented. 1