@article{banks_rosario_tran_2002, title={Proper orthogonal decomposition-based control of transverse beam vibrations: Experimental implementation}, volume={10}, ISSN={["1063-6536"]}, DOI={10.1109/TCST.2002.801793}, abstractNote={Linear quadratic Gaussian (LQG) compensator control of transverse vibrations was implemented on an aluminum cantilevered beam in a "smart structure" paradigm. The beam was mounted with two self-sensing self-actuating piezoceramic patches. The Euler-Bernoulli 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.}, number={5}, journal={IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY}, author={Banks, HT and Rosario, RCH and Tran, HT}, year={2002}, month={Sep}, pages={717–726} }
 @article{banks_rosario_2001, title={Convergence of approximations in feedback control of structures}, volume={33}, ISSN={["0895-7177"]}, DOI={10.1016/S0895-7177(00)00229-6}, abstractNote={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 [1] 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.}, number={1-3}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Banks, HT and Rosario, RCH}, year={2001}, pages={65–78} }
 @article{banks_rosario_smith_2000, title={Reduced-order model feedback control design: Numerical implementation in a thin shell model}, volume={45}, ISSN={["0018-9286"]}, DOI={10.1109/9.867024}, abstractNote={Reduced-order models employing the Lagrange and popular proper orthogonal decomposition (POD) reduced-basis methods in numerical approximation and feedback control of systems are presented and numerically tested. The system under consideration is a thin cylindrical shell with surface-mounted piezoceramic actuators. Donnell-Mushtari equations, modified to include Kelvin-Voigt 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. As a first step toward investigating the behavior of the methods when implemented in physical systems, the use of reduced-order model feedback control gains in the full order model is considered and numerical examples are presented.}, number={7}, journal={IEEE TRANSACTIONS ON AUTOMATIC CONTROL}, author={Banks, HT and Rosario, RCH and Smith, RC}, year={2000}, month={Jul}, pages={1312–1324} }
 @article{del rosario_smith_1998, title={LQR control of thin shell dynamics: Formulation and numerical implementation}, volume={9}, ISSN={["1045-389X"]}, DOI={10.1177/1045389X9800900408}, abstractNote={ A PDE-based feedback control method for thin cylindrical shells with surface-mounted piezoceramic actuators is presented. Donnell-Mushtari equations modified to incorporate both passive and active piezoceramic patch contributions are used to model the system dynamics. The well-posedness 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 and basis functions constructed from Fourier polynomials tensored with cubic splines, and convergence criteria for the associated approximate LQR problem are established. The effectiveness of the method for attenuating the coupled longitudinal, circumferential and transverse shell displacements is illustrated through a set of numerical examples. }, number={4}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Del Rosario, RCH and Smith, RC}, year={1998}, month={Apr}, pages={301–320} }
 @article{rosario_smith_1997, title={Spline approximation of thin shell dynamics}, volume={40}, DOI={10.1002/(sici)1097-0207(19970815)40:15<2807::aid-nme192>3.0.co;2-h}, abstractNote={Abstract : A spline-based method for approximating thin shell dynamics is presented here. While the method is developed in the context of the Donnell-Mushtari thin shell equations, it can be easily extended to the Byrne-Flugge-Lur'ye equations or other models for shells of revolution as warranted by applications. The primary requirements for the method include accuracy, flexibility and efficiency in smart material applications. To accomplish this, the method was designed to be flexible with regard to boundary conditions, material nonhomogeneities due to sensors and actuators, and inputs from smart material actuators such as piezoceramic patches. The accuracy of the method was also of primary concern, both to guarantee full resolution of structural dynamics and to facilitate the development of PDE-based controllers which ultimately require real-time implementation. Several numerical examples provide initial evidence demonstrating the efficacy of the method.}, number={15}, journal={International Journal for Numerical Methods in Engineering}, author={Rosario, R. C. Del and Smith, Ralph}, year={1997}, pages={2807–2840} }