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We contribute to the refined understanding of language-logic-algebra interplay in a recent algebraic framework over countable words. Algebraic characterizations of the one variable fragment of FO as well as the boolean closure of the existential fragment of FO are established. We develop a seamless integration of the block product operation in the countable setting, and generalize well-known decompositional characterizations of FO and its two variable fragment. We propose an extension of FO admitting infinitary quantifiers to reason about inherent infinitary properties of countable words, and obtain a natural hierarchical block-product based characterization of this extension. Properties expressible in this extension can be simultaneously expressed in the classical logical systems such as WMSO and FO[cut]. We also rule out the possibility of a finite-basis for a block-product based characterization of these logical systems. Finally, we report algebraic characterizations of one variable fragments of the hierarchies of the new extension. [ABSTRACT FROM AUTHOR]

Vibration control is an essential component of safe and sustained operation of modern large wind turbine towers. As the blade-tower assembly offers time-dependent system matrices that periodically evolves with the rotational speed of the turbine, control theories (e.g. linear quadratic Gaussian) can not be directly adopted in this case. With this in view, the present study aims to develop a semi-active strategy using multiple magneto-rheological tuned liquid column dampers (MR-TLCDs) to mitigate excessive vibration of the horizontal axis wind turbine towers. The design of the controller is achieved by the multi-blade coordinate transformation that converts the system matrices into a non-rotating framework followed by time averaging to enable the application of linear control law. Parameters of the non-linear MR-TLCDs are optimally tuned to dissipate maximum energy. Aerodynamic loads are evaluated using modified blade element momentum theory. The performance of the proposed control strategy is assessed against different wind speeds. Clipping laws are employed to keep the semi-active control force in the feasible range. Two different clipping laws are compared in this paper. Finally, sensitivity analysis is carried out to demonstrate the performance envelope and robustness of the proposed controller. • Semi-active control of wind turbine tower using multiple MR-TLCDs. • Response characterization using blade-tower interaction. • Aerodynamic load estimation using BEM theory and rotationally sampled spectra. • Optimal control force estimation in LQG/LTR framework using MBC transformation. • Sensitivity analysis using actual large scale wind turbine parameters is carried out. [ABSTRACT FROM AUTHOR]

This paper proposes a wavelet multi-resolution based individual pitch control strategy for spar-type floating offshore wind turbines (FOWTs) and investigates its performance under joint wind-wave-current loads considering the effects of wave-current interactions. A multi-resolution analysis (MRA) based wavelet controller that modifies an optimal control problem cast in linear quadratic regulator (LQR) form constrained to a band of frequency has been used in this paper. The weighting matrices of the LQ regulator are varied in different frequency bands depending on the emphasis to be placed on the response energy and control effort to minimize the cost functional of that frequency band. This formulation results in frequency band dependent controller gains that lead to a time-varying controller. Daubechies wavelet is used in the MRA based filter that ensures perfect decomposition of the time signal over a finite interval and fast numerical implementation for control application. The multi-resolution wavelet-LQR individual blade pitch controller is used to control blade out-of-plane vibrations with additional emphasis on 1P frequency of the wind turbine. The emphasis on 1P frequency along with the blade's out-of-plane natural frequency is shown to reduce aerodynamic loads corresponding to 1st rotational frequency of the wind turbine which in turn reduces vibrations in other modes of the wind turbine. The proposed controller is simulated using a 5-MW baseline offshore wind turbine with realistic operational conditions including wave-current interactions. The controller has been proved to be effective in every analyzed met-ocean condition. [ABSTRACT FROM AUTHOR]