For a horizontal-axis wind turbine (HAWT), a dynamic nonlinear model with four degrees of freedom is derived and transformed into a Takagi-Sugeno (TS) model structure using the sector nonlinearity approach. Thereby, an exact transformation of the nonlinear model is obtained as a weighted combination of linear models. This structure allows for a convenient design of controller and observer structures. The maps of the rotor thrust and torque coefficients can be implemented in the model as look-up tables or, alternatively, as analytical nonlinear functions. Open-loop simulation results of the derived TS model for a reference model turbine are compared to those obtained with the aero-elastic code FAST. The small deviations obtained demonstrate the high model quality of the control-oriented TS model. In future work, the derived TS model shall be used as a basis for the design of fault detection and isolation (FDI) concepts.

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The electron transfer kinetics of redox proteins adsorbed on metal electrodes coated with self-assembled monolayers (SAMs) of mercaptanes shows an unusual distance-dependence. For thick SAMs, the experimentally measured electron transfer rate constant k{exp} obeys the behavior predicted by Marcus theory [R. A. Marcus and N. Sutin, Biochim. Biophys. Acta 811, 265 (1985)], whereas for thin SAMs, k{exp} remains virtually constant [Z. Q. Feng, J. Chem. Soc., Faraday Trans. 93, 1367 (1997)]. In this work, we present a simple theoretical model system for the redox protein cytochrome c electrostatically bound to a SAM-coated electrode. A statistical average of the electron tunneling rate is calculated by accounting for all possible orientations of the model protein. This approach, which takes into account the electric field dependent orientational distribution, allows for a satisfactory description of the "saturation" regime in the high electric field limit. It further predicts a nonexponential behavior of the average electron transfer processes that may be experimentally checked by extending kinetic experiments to shorter sampling times, i.e., 1/k{exp}. For a comprehensive description of the overall kinetics in the saturation regime at sampling times of the order of <<1/k{exp}, it is essential to consider the dynamics of protein reorientation, which is not implemented in the present model.