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24
Identification of Hysteretic Control Influence Operators Representing Smart Actuators: Convergent Approximations
 Mathematical Problems in Engineering, submitted
, 1997
"... In a previous paper, the authors investigated the lowersemicontinuity properties of two generalizations of the classical Preisach operator; the smoothed Preisach operator and the Krasnoselskii / Pokrovskii (KP) integral hysteresis operators. In particular, it was demonstrated that the output least s ..."
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Cited by 26 (6 self)
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In a previous paper, the authors investigated the lowersemicontinuity properties of two generalizations of the classical Preisach operator; the smoothed Preisach operator and the Krasnoselskii / Pokrovskii (KP) integral hysteresis operators. In particular, it was demonstrated that the output least squares identification problem for the KP operator is wellposed over compact subsets of the Preisach plane. The identification of the hysteretic control influence operator was shown to be equivalent to the identification of a measure in the space of probability measures taken with the weak topology. In this paper, a consistent and convergent approximation scheme is introduced for this class of integral hysteresis operator. The Galerkin approximation scheme is shown to be function space parameter convergent. A numerical example is presented that illustrates aspects of the theory derived in this paper. 1 Introduction and Motivation While there has been unprecedented interest in utilizin...
Approximation in LQR Problems for Infinite Dimensional Systems With Unbounded Input Operators
, 1990
"... We present a variational framework based on sesquilinear forms for Galerkin approximation techniques for state feedback control in problems governed by infinite dimensional dynamical systems. Both parabolic and second order in time, hyperbolic partial differential equations with unbounded input and ..."
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Cited by 13 (6 self)
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We present a variational framework based on sesquilinear forms for Galerkin approximation techniques for state feedback control in problems governed by infinite dimensional dynamical systems. Both parabolic and second order in time, hyperbolic partial differential equations with unbounded input and unbounded observation operators are included as special cases of our treatment. 1 Introduction In this paper we discuss the linear quadratic regulator (LQR) problem for a class of (essentially parabolic) unbounded input or boundary control problems. A variational framework using sesquilinear forms is developed to treat Dirichlet and Neuman boundary control problems for parabolic equations and strongly damped elastic systems. Using such a framework, convergence of Galerkin approximations to solutions of Riccati equations is also established. The boundary control problem for parabolic systems has been studied extensively over the last two decades, inspired by the monograph of J.L. Lions [21] ...
Modeling And Parameter Estimation For An Imperfectly Clamped Plate
 Computation and Control IV
, 1995
"... In this paper, the modeling of boundary conditions for an imperfectly clamped circular plate is discussed. This model is derived under the assumption that there is some variation in both the boundary displacement and slope when the plate oscillates. To account for this oscillation, boundary moment t ..."
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Cited by 9 (9 self)
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In this paper, the modeling of boundary conditions for an imperfectly clamped circular plate is discussed. This model is derived under the assumption that there is some variation in both the boundary displacement and slope when the plate oscillates. To account for this oscillation, boundary moment terms, involving parameters to be estimated through fittodata techniques, are included in the model. The wellposedness of the model is demonstrated and appropriate approximation techniques are outlined. Finally, under natural assumptions for this model and approximation scheme, results leading to parameter convergence are given. 1 Introduction An important consideration in the modeling of structural and structural acoustic systems involves the determination of appropriate boundary conditions for the vibrating structure. In many applications, the clamped nature of the structure leads to the use of clamped or fixed boundary conditions, in which case, it is assumed that zero displacements an...
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 8 (8 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
Computational Methods for Estimation in the Modeling of Nonlinear Elastomers
 CRSCTR9540, Kybernetika
, 1995
"... We report on our efforts to model nonlinear dynamics in elastomers. Our efforts include the development of computational techniques for simulation studies and for use in inverse or system identification problems. As a first step towards the full dynamic case, we present the static inverse problem, w ..."
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Cited by 8 (8 self)
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We report on our efforts to model nonlinear dynamics in elastomers. Our efforts include the development of computational techniques for simulation studies and for use in inverse or system identification problems. As a first step towards the full dynamic case, we present the static inverse problem, with experimental results. We also present results from the simulation of dynamic experiments. 1 Introduction A problem of fundamental interest and great importance in modern material sciences is the development of new materials for use as both passive and active vibration suppression devices. Materials such as elastomers, rubberlike composites typically filled with inactive particles such as carbon black and silica, are frequently used in parts such as engine mounts and springs. One could imagine using active fillers, such as piezoelectric, magnetic, or conductive particles, to create a "smart" material which could be used as an active vibration suppression device. In the quest to develop...
Hysteresis modeling in magnetostrictive materials via Preisach operators
 ICASE Report 9723; J. Math. Systems, Estimation and Control
"... A phenomenological characterization of hysteresis in magnetostrictive materials is presented. Such hysteresis is due to both the driving magnetic elds and stress relations within the material and is signi cant throughout most of the drive range of magnetostrictive transducers. An accurate characteri ..."
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Cited by 6 (5 self)
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A phenomenological characterization of hysteresis in magnetostrictive materials is presented. Such hysteresis is due to both the driving magnetic elds and stress relations within the material and is signi cant throughout most of the drive range of magnetostrictive transducers. An accurate characterization of the hysteresis and material nonlinearities is necessary to fully utilize the actuator/sensor capabilities of the magnetostrictive materials. Such a characterization is made here in the context of generalized Preisach operators. This yields a framework amenable to proving the wellposedness of structural models that incorporate the magnetostrictive transducers. It also provides a natural setting in which to develop practical approximation techniques. An example illustrating this framework in the context of a Timoshenko beam model is presented.
Vibration Suppression with Approximate Finite Dimensional Compensators for Distributed Systems: Computational Methods and Experimental Results
 Proc. of the Second International Conference on Intelligent Materials
, 1994
"... Based on a distributed parameter model for vibrations, an approximate nite dimensional dynamic compensator is designed to suppress vibrations (multiple modes with a broad band of frequencies) of a circular plate with KelvinVoigt damping and clamped boundary conditions. The control is realized via p ..."
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Cited by 4 (3 self)
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Based on a distributed parameter model for vibrations, an approximate nite dimensional dynamic compensator is designed to suppress vibrations (multiple modes with a broad band of frequencies) of a circular plate with KelvinVoigt damping and clamped boundary conditions. The control is realized via piezoceramic patches bonded to the plate and is calculated from information available from several pointwise observed state variables. Examples from computational studies as well as use in laboratory experiments are presented to demonstrate the e ectiveness of this design. 1
Nonlinear Elastomers: Modeling and Estimation
 in Proceedings of the 3rd IEEE Mediterranean Symposium on New Directions in Control and Automation
, 1995
"... We report on our efforts to model nonlinear dynamics in elastomers. Our efforts include the development of computational techniques for simulation studies and for use in inverse or system identification problems. 1 Introduction A problem of fundamental interest and great importance in modern materi ..."
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Cited by 4 (4 self)
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We report on our efforts to model nonlinear dynamics in elastomers. Our efforts include the development of computational techniques for simulation studies and for use in inverse or system identification problems. 1 Introduction A problem of fundamental interest and great importance in modern material sciences is the development of both passive and active ("smart") vibration devices constructed from polymer (long molecular chains of covalently bonded atoms often having crosslinking chains) composites such as elastomers filled with carbon black and/or silica or with active elements (i.e., piezoelectric, magnetic or conductive particles). These rubber based products (even without active elements) involve very complex viscoelastic materials that are not at all like metals (where large deformations lead to permanent material changes) and do not satisfy the usual, welldeveloped linear theory of (infinitesimal) elasticity for deformable bodies. They typically exhibit mechanical properties ...
Approximation Results for Parameter Estimation in Nonlinear Elastomers
 CRSCTR9634, NCSU; CONTROL AND ESTIMATION OF DISTRIBUTED PARAMETER SYSTEMS
, 1997
"... In this paper we present an approximation framework and theoretical convergence results for a class of parameter estimation problems for general abstract nonlinear hyperbolic systems. These systems include as a special case those modeling a large class of nonlinear elastomers. ..."
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Cited by 3 (3 self)
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In this paper we present an approximation framework and theoretical convergence results for a class of parameter estimation problems for general abstract nonlinear hyperbolic systems. These systems include as a special case those modeling a large class of nonlinear elastomers.
Parameter Estimation in a Structural Acoustic System with Fully Nonlinear Coupling
 Conditions, Mathematical and Computer Modeling
, 1996
"... A methodology for estimating physical parameters in a class of structural acoustic systems is presented. The general model under consideration consists of an interior cavity which is separated from an exterior noise source by an enclosing elastic structure. Piezoceramic patches are bonded to or embe ..."
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Cited by 2 (2 self)
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A methodology for estimating physical parameters in a class of structural acoustic systems is presented. The general model under consideration consists of an interior cavity which is separated from an exterior noise source by an enclosing elastic structure. Piezoceramic patches are bonded to or embedded in the structure; these can be used both as actuators and sensors in applications ranging from the control of interior noise levels to the determination of structural aws through nondestructive evaluation techniques. The presence and excitation of the patches, however, changes the geometry and material properties of the structure as well as involves unknown patch parameters, thus necessitating the development of parameter estimation techniques which are applicable in this coupled setting. In developing a framework for approximation, parameter estimation and implementation, strong consideration is given to the fact that the input operator is unbonded due to the discrete nature of the patches. Moreover, the model is weakly nonlinear as a result of the coupling mechanism between the structural vibrations and the interior acoustic dynamics. Within this context, an illustrating model is given, wellposedness and approximation results are discussed and an applicable parameter estimation methodology is presented. The scheme is then illustrated through several numerical examples with simulations modeling a variety of commonly used structural acoustic techniques for system excitation and data collection.