Control with delay of combined motion of the structure with the free surfaced liquid

Abstract

The problem of delay control on a combined motion of the structure with a free surfaced liquid in the nonlinear range of perturbations of surface is considered. It is assumed that the reservoir is of cylindrical shape and it is filled with an ideal homogeneous incompressible liquid. The mathematical model of the system is constructed based on the aggregate use of the Hamilton–Ostrogradsky variational principle with preliminarily elimination of all kinematical restrictions of the problem, approaches of nonlinear mechanics and the Kantorovich method. In the end this enables to get the nonlinear dynamical model of the system in the form of ordinary differential equations with respect to amplitudes of perturbations of normal modes of liquid oscillations and parameter of the reservoir translational motion. The system control is done based on the principle of compensation of the force response of the liquid on reservoir walls. We consider the case of the delayed control, when the control starts immediately, during an active loading and after completion of the active loading. Specific characters of the delayed control were ascertained.