Vibration attenuation control designs are proposed for reduced plant models consisting of n-degree-of-freedom base seismically-isolated structures (i.e., a specific type of earthquake-resistant design), modeled by uncertain nonlinear systems and subjected to one-dimensional horizontal ground acceleration (i.e. the earthquake signal), treated as unknown disturbance but assumed to be bounded.In control systems literature, this is a perturbation attenuation problem.The main result of this PhD is the development of a modified version of Leitmann and co-authors' classical result on the stabilization of uncertain nonlinear systems. The proposed theorem consists of a bounded nonlinear feedback control law that is capable of ensuring uniform boundedness and uniform ultimate boundedness in closed-loop. In particular, it can be applied to solving semi-active control design problems, which are currently dealt with in earthquake engineering.The control objective is to improve the behavior (i.e. response) of mixed base-isolated structures to external disturbance, namely earthquakes. What differentiates our problem from the majority to be found in the literature is that: (i) attention is being paid to the protection of equipment placed inside the structure an not only to the structure itself; (ii) instead of using regular performance indicators expressed in terms of relative base displacement versus floors accelerations, we use solely the pseudo-acceleration floor response spectra, as it was proposed in previous recent works by Politopoulos and Pham.Actually, this work is an attempt to explicitly use floor response spectra as performance criterion.Concerning the application procedure, some of the topics that were detailed are:(i) modeling of earthquake signals;(ii) tuning of control law parameters based on vibration theory;(iii) validation and testing of the closed-loop behavior using numerical simulations: for simplicity reasons, we take n=2.This procedure can be used on structures of both nuclear industry as well as civil engineering.Other topics include an attempt to using time-frequency concepts and in particular the Wigner-Ville distribution to the control law design procedure, in order to better control transitory components of both perturbation (the input) and state variables signals (the output).
