Results 1  10
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13
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...
Computational Methods for Identification and Feedback Control in Structures with Piezoceramic Actuators and Sensors
 in Recent Advances in Adaptive and Sensor Materials and their Applications
, 1992
"... In this note we give fundamental existence, uniqueness, and continuous dependence results (wellposedness) for a variational formulation of a class of damped second order partial differential equations with unbounded input or control coefficients. Included as special cases in this class are structur ..."
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Cited by 5 (3 self)
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In this note we give fundamental existence, uniqueness, and continuous dependence results (wellposedness) for a variational formulation of a class of damped second order partial differential equations with unbounded input or control coefficients. Included as special cases in this class are structures with piezoceramic actuators. We then consider approximation techniques leading to computational methods in the context of both parameter estimation and feedback control problems for these systems. Rigorous convergence results for parameter estimates and feedback gains are presented. 1. INTRODUCTION One of the important issues in design and understanding of smart structures and materials is the development of high fidelity dynamic models for use in identification and control methodologies. Along with these models, which are inherently distributed in nature, one requires computational techniques which must in turn be based on approximation ideas. Our recent efforts with piezoceramic actuat...
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
LQR Control Of Thin Shell Dynamics: Formulation And Numerical Implementation
 ICASE Report 9759, 1997; Journal of Intelligent Material Systems and Structures, submitted
, 1997
"... . A PDEbased feedback control method for thin cylindrical shells with surfacemounted piezoceramic actuators is presented. DonnellMushtari equations modified to incorporate both passive and active piezoceramic patch contributions are used to model the system dynamics. The wellposedness of this mo ..."
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Cited by 3 (3 self)
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. A PDEbased feedback control method for thin cylindrical shells with surfacemounted piezoceramic actuators is presented. DonnellMushtari equations modified to incorporate both passive and active piezoceramic patch contributions are used to model the system dynamics. The wellposedness of this model and the associated LQR problem with an unbounded input operator are established through analytic semigroup theory. The model is discretized using a Galerkin expansion with basis functions constructed from Fourier polynomials tensored with cubic splines, and convergence criteria for the associated approximate LQR problem are established. The e#ectiveness of the method for attenuating the coupled longitudinal, circumferential and transverse shell displacements is illustrated through a set of numerical examples. Key words. LQR method, PDE thin shell model, Galerkin approximation, piezoceramic actuators Subject classification. Applied and Numerical Mathematics 1. Introduction. Thin shell mod...
2009b Control, estimation and optimization of energy efficient buildings
 In Proceedings of IEEE American Control Conference. St
"... Abstract — Commercial buildings are responsible for a significant fraction of the energy consumption and greenhouse gas emissions in the U.S. and worldwide. Consequently, the design, optimization and control of energy efficient buildings can have a tremendous impact on energy cost and greenhouse gas ..."
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Cited by 2 (1 self)
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Abstract — Commercial buildings are responsible for a significant fraction of the energy consumption and greenhouse gas emissions in the U.S. and worldwide. Consequently, the design, optimization and control of energy efficient buildings can have a tremendous impact on energy cost and greenhouse gas emission. Buildings are complex, multiscale in time and space, multiphysics and highly uncertain dynamic systems with wide varieties of disturbances. Recent results have shown that by considering the whole building as an integrated system and applying modern estimation and control techniques to this system, one can achieve greater efficiencies than obtained by optimizing individual building components such as lighting and HVAC. We consider estimation and control for a distributed parameter model of a multiroom building. In particular, we show that distributed parameter control theory, coupled with high performance computing, can provide insight and computational algorithms for the optimal placement of sensors and actuators to maximize observability and controllability. Numerical examples are provided to illustrate the approach. We also discuss the problems of design and optimization (for energy and CO2 reduction) and control (both local and supervisory) of whole buildings and demonstrate how sensitivities can be used to address these problems. I.
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 approximation (ref ..."
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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...
Convergence of Approximations in Feedback Control of Structures
 North Carolina State University
, 1998
"... Convergence of linear quadratic regulator (LQR) problems in structures is discussed. The abstract formulation of the system using a variational framework based on sesquilinear forms is considered. Since convergence theorems require uniform stabilizability of the finite dimensional approximating syst ..."
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Cited by 1 (1 self)
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Convergence of linear quadratic regulator (LQR) problems in structures is discussed. The abstract formulation of the system using a variational framework based on sesquilinear forms is considered. Since convergence theorems require uniform stabilizability of the finite dimensional approximating system, we present a detailed proof of a fundamental lemma due to Banks and Ito which can be used to easily verify this condition for many applications. Existing results for the well posedness of the infinite dimensional system and convergence of Galerkin approximations are summarized. Keywords feedback control, approximation, LQR, control convergence 1 Introduction In this paper we discuss in detail the proof of Lemma 6.2 in the electronic and CRSC technical report versions of [1] (stated as Lemma 7.13 in [2]) which allows verification of uniform stabilizability of a family of finite dimensional approximating systems arising in feedback control formulations. This uniform stabilizability condi...
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. Modified DonnellMushtari shell equations incorporating strong or KelvinVoigt damping are used to ..."
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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. Modified 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 effectiveness of the method are presented. 1 This research was supported in part by the National Aeronautics and Space Administration under NASA Contract Number NAS119480 while RCS was a visiting scientist at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681. Additional support was also provided in par...
Modeling and Control of a Multiple Component Structure
 JOURNAL OF MATHEMATICAL SYSTEMS, ESTIMATION, AND CONTROL
, 1994
"... In this paper, a mathematical model is presented for a multiple component structure (MCS) composed of two EulerBernoulli beams, two distributed masses, and a rotating hub through which a torque control is applied. Imposition of a control of this type results in a bounded control operator. Since the ..."
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Cited by 1 (0 self)
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In this paper, a mathematical model is presented for a multiple component structure (MCS) composed of two EulerBernoulli beams, two distributed masses, and a rotating hub through which a torque control is applied. Imposition of a control of this type results in a bounded control operator. Since the control is bounded, damping in the beam model is required to stabilize the system. The KelvinVoigt damping model is assumed. The weak formulation is used to show the model is wellposed. A convergent Galerkin finite element approximation scheme is constructed for the model and is used to compute a sequence of controls which approximate an optimal control for the structure. This control is the solution to the linear quadratic regulator (LQR) problem for the MCS.
EExperimental Confirmation of a PDEBased Approach to Design of Feedback Controls
 SIAM Journal on Control and Optimization
, 1995
"... Issues regarding the experimental implementation of PDEbased controllers are discussed in this work. While the motivating application involves the reduction of vibration levels for a circular plate through excitation of surfacemounted piezoceramic patches, the general techniques described here wil ..."
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Issues regarding the experimental implementation of PDEbased controllers are discussed in this work. While the motivating application involves the reduction of vibration levels for a circular plate through excitation of surfacemounted piezoceramic patches, the general techniques described here will extend to a variety of applications. The initial step is the development of a PDE model which accurately captures the physics of the underlying process. This model is then discretized to yield a vectorvalued initial value problem. Optimal control theory is used to determine continuoustime voltages to the patches, and the approximations needed to facilitate discrete time implementation are addressed. Finally, experimental results demonstrating the control of both transient and steady state vibrations through these techniques are presented.