Computational Methods for Feedback Control in Structural Systems

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Title: Computational Methods for Feedback Control in Structural Systems
Author: Rosario, Ricardo C.H.
Advisors: H.T. Banks, Chair
R.C. Smith, Member
K. Ito, Member
H.T. Tran, Member
Abstract: Numerical methods, LQR control, an abstract formulation andreduced basis techniques for a system consisting of a thin cylindrical shellwith surface-mounted piezoceramic actuators are investigated.Donnell-Mushtari equations,modified to include Kelvin-Voigt damping and passive patch contributions,are used to model the system dynamics. The voltage-induced piezoceramicpatch contributions, used as input inthe control regime, enter the equations as externalforces and moments. Existence and uniqueness of solutions are demonstratedthrough variational and semigroup formulations of the system equations.The semigroup formulation is also used to establish theoretical controlresults and illustrate convergence of the finite dimensional controlsand Riccati operators.The spatial components of the state arediscretized using a Galerkin expansion resulting in an ordinarydifferential equation that can be readily marched in time by existingordinary differential equationsolvers.Full order approximation methods which employ standard basiselements such as cubic or linear splines result in large matrixdimensions rendering the system computationally expensive for real-timesimulations. To lessen on-line computational requirements, reducedbasis methods employing snapshots of the full order model as basisfunctions are investigated. As a first step in validating the model, a shell with obtainable analyticnatural frequencies and modes was considered. The derived frequenciesand modeswere then compared with numerical approximations using full order basisfunctions. Further testing on the static and dynamic performance of the fullorder model was carried out through the following steps:(i) choose true state solutions, (ii) solve for the forces in theequations that would lead to these known solutions, and (iii) comparenumerical results excited by the derived forces with the true solutions.Reduced order methods employing the Lagrange and theKarhunen-Loève proper orthogonal decomposition (POD)basis functions are implemented on the model. Finally, a statefeedback method was developed and investigated computationally for both the full order and reduced ordermodels.
Date: 1998-11-05
Degree: PhD
Discipline: Applied Mathematics

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