New Classes of Volterra Integral Equations of the First Kind Related to the Modeling of the Wind Turbine Dynamics

An approach based on Volterra polynomials with vector input signals has been developed for numerical modeling of the process of controlling the dynamics of an "input-output" type object. The nonparametric identification problem is considered as a conjugate one with respect to the deconvolution problem. The paper focuses on a new algorithm of identifying Volterra polynomials of the second degree that is based on the active experiment by the test sets of inputs. New classes of Volterra integral equations of the first kind are defined. They appear when the duration of the rise front is taken into account in test signals. The test signals are chosen considering specific features of the inputs arising in practice as applied to dynamics of wind turbines with horizontal rotation axis. The inversion formulas for indicated classes of one-and two-dimensional Volterra integral equations of the first kind are obtained.