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Browsing by Author "Paruchuri, Sai Tej"

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    Modeling and Estimation of Linear and Nonlinear Piezoelectric Systems
    Paruchuri, Sai Tej (Virginia Tech, 2020-10-13)
    A bulk of the research on piezoelectric systems in recent years can be classified into two categories, 1) studies of linear piezoelectric oscillator arrays, 2) studies of nonlinear piezoelectric oscillators. This dissertation derives novel linear and nonlinear modeling and estimation methods for such piezoelectric systems. In the first part, this work develops modeling and design methods for Piezoelectric Subordinate Oscillator Arrays (PSOAs) for the wideband vibration attenuation problem. PSOAs offer a straightforward and low mass ratio solution to cancel out the resonant peaks in a host structure's frequency domain. Further, they provide adaptability through shunt tuning, which gives them the ability to recover performance losses because of structural parameter errors. This dissertation studies the derivation of governing equations that result in a closed-form expression for the frequency response function. It also analyzes systematic approaches to assign distributions to the nondimensional parameters in the frequency response function to achieve the desired flat-band frequency response. Finally, the effectiveness of PSOAs under ideal and nonideal conditions are demonstrated in this dissertation through extensive numerical and experimental studies. The concept of performance recovery, introduced in empirical studies, gives a measure of the PSOA's effectiveness in the presence of disorder before and after capacitive tuning. The second part of this dissertation introduces novel modeling and estimation methods for nonlinear piezoelectric oscillators. Traditional modeling techniques require knowledge of the structure as well as the source of nonlinearity. Data-driven modeling techniques used extensively in recent times build approximations. An adaptive estimation method, that uses reproducing kernel Hilbert space (RKHS) embedding methods, can estimate the underlying nonlinear function that governs the system's dynamics. A model built by such a method can overcome some of the limitations of the modeling approaches mentioned above. This dissertation discusses (i) how to construct the RKHS based estimator for the piezoelectric oscillator problem, (ii) how to choose kernel centers for approximating the RKHS, and (iii) derives sufficient conditions for convergence of the function estimate to the actual function. In each of these discussions, numerical studies are used to show the RKHS based adaptive estimator's effectiveness for identifying linearities in piezoelectric oscillators.
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    Output Regulation of Systems Governed by Delay Differential Equations: Approximations and Robustness
    Paruchuri, Sai Tej (Virginia Tech, 2020-04-08)
    This thesis considers the problem of robust geometric regulation for tracking and disturbance rejection of systems governed by delay differential equations. It is well known that geometric regulation can be highly sensitive to system parameters and hence such designs are not always robust. In particular, when employing numerical approximations to delay systems, the resulting finite dimensional models inherit natural approximation errors that can impact robustness. This demonstrates this lack of robustness and then addresses robustness by employing versions of robust regulation that have been developed for infinite dimensional systems. Numerical examples are given to illustrate the ideas and to test the robustness of the regulator.