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10
Well Posedness For Damped Second Order Systems With Unbounded Input Operators
 DIFFERENTIAL AND INTEGRAL EQUATIONS
, 1995
"... We consider damped second order in time systems such as those arising in structures with piezoceramic actuators and sensors. These systems are naturally formulated as abstract second order systems with unbounded nonhomogeneous term. Existence, uniqueness and continuous dependence of solutions in a ..."
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Cited by 24 (17 self)
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We consider damped second order in time systems such as those arising in structures with piezoceramic actuators and sensors. These systems are naturally formulated as abstract second order systems with unbounded nonhomogeneous term. Existence, uniqueness and continuous dependence of solutions in a weak or variational setting are given. A semigroup formulation is presented and conditions under which the variational solutions and semigroup solutions are the same are discussed.
Computational issues in parameter estimation and feedback control problems for partial differential equation systems
 PHYSICA D
, 1992
"... We consider computational aspects of two problems governed by partial differential equations systems: (i) the computation of approximate Riccati feedback gains for LQR control problems, (ii) the estimation of parameters using methods based on approximate gradients computed via a costate algorithm. S ..."
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Cited by 10 (2 self)
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We consider computational aspects of two problems governed by partial differential equations systems: (i) the computation of approximate Riccati feedback gains for LQR control problems, (ii) the estimation of parameters using methods based on approximate gradients computed via a costate algorithm. Sufficient conditions for convergence of algorithms for these problems are discussed; in both cases, some type of adjoint or costate system convergence is required in addition to the expected system convergence. Examples are discussed that illustrate computational di#culties which may arise if only convergence of the approximate system holds (i.e., in the event costate convergence does not hold).
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...
Estimation of Material Parameters for Grid Structures
 J. MATH. SYSTEMS, ESTIM. CONTROL
, 1991
"... A numerical approximation scheme is developed for the identification of spatially varying stiffness parameters along with KelvinVoigt and viscous damping parameters in LoveKirchhoff models for the transverse vibrations of thin, flexible grids. The inverse problem is formulated as a least squares f ..."
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Cited by 5 (3 self)
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A numerical approximation scheme is developed for the identification of spatially varying stiffness parameters along with KelvinVoigt and viscous damping parameters in LoveKirchhoff models for the transverse vibrations of thin, flexible grids. The inverse problem is formulated as a least squares fit to data. Splinebased finite element approximations are used to solve the partial differential equation which describes the dynamics of the grid. Theoretical convergence results concerning the parameter estimates are obtained. Several numerical examples are discussed.
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
The Estimation of Material and Patch Parameters in a PDEBased Circular Plate Model
 Journal of Sound and Vibration
, 1997
"... The estimation of material and patch parameters for a system involving a circular plate, to which piezoceramic patches are bonded, is considered. A partial di erential equation (PDE) model for the thin circular plate is used with the passive and active contributions from the patches included in the ..."
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Cited by 4 (3 self)
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The estimation of material and patch parameters for a system involving a circular plate, to which piezoceramic patches are bonded, is considered. A partial di erential equation (PDE) model for the thin circular plate is used with the passive and active contributions from the patches included in the internal and external bending moments. This model contains piecewise constant parameters describing the density, exural rigidity, Poisson ratio and KelvinVoigt damping for the system as well as patch constants and a coe cient for viscous air damping. Examples demonstrating the estimation of these parameters with experimental acceleration data and a variety of inputs to the experimental plate are presented. By using a physicallyderived PDE model to describe the system, parameter sets consistent across experiments are obtained, even when phenomena such as damping due to electric circuits a ect the system dynamics. 1
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.
Approximation Issues For Applications In Optimal Control And Parameter Estimation
, 1997
"... We consider computational aspects of using semidiscrete approximation schemes to solve problems with infinitedimensional dynamics. We survey theory and convergence results for the simulation or forward problem, the feedback control problem, and the parameter estimation problem, all for the case in ..."
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Cited by 1 (0 self)
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We consider computational aspects of using semidiscrete approximation schemes to solve problems with infinitedimensional dynamics. We survey theory and convergence results for the simulation or forward problem, the feedback control problem, and the parameter estimation problem, all for the case in which the underlying system dynamics is governed by a partial differential equation. In particular we investigate the critical sufficient conditions required for convergence of semidiscrete approximations of these problems. These sufficient conditions require that the approximation scheme demonstrate system convergence, adjoint system convergence, and uniform preservation of system stability. By considering in detail several specific examples, we illustrate the difficulties which may arise when these sufficient conditions are not satisfied.
Center for Applied Mathematical Sciences
 in Differential Equations with Applications
, 1991
"... We present new convergence and stability results for least squares inverse problems involving systems described by analytic semigroups. The practical importance of these results is demonstrated by application to several examples from problems of estimation of material parameters in flexible structur ..."
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We present new convergence and stability results for least squares inverse problems involving systems described by analytic semigroups. The practical importance of these results is demonstrated by application to several examples from problems of estimation of material parameters in flexible structures using accelerometer data. 1 This research was supported in part by the Air Force Office of Scientific Research under Contract F4962086C0111, by the National Aeronautics and Space Administration under NASA Grant NAG1517, and by the National Science Foundation under NSF Grant DMS8818530. Part of this research was carried out while the first author was a visiting scientist at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA, which is operated under NASA contract NAS118605. 2 Invited Lecture, International Conference on Differential Equations and Applications, Retzhof, Austria, June 1824, 1989. 1. Introduction ...