Control of Periodic Modes of a System with the Parametric Disturbance in Basic Parametric Resonance Conditions

摘要

A single-mass mechanical system containing nonlinearity and exposed to a parametric harmonic disturbance at the frequency, the half value of which is close to the eigenfrequency of the system, is considered. The force control action, on the intensity of which the integral quadratic restriction is imposed, is introduced into the system. Depending on the particular application of the system, the purpose of its introduction is to increase or decrease the intensity of the steady-state oscillation of the system. Based on the harmonic approximation of the solution of the system and variational methods, the structure and parameters of quasioptimal control action are determined. It is shown by the example of nonlinearity of the quadratic friction type that, when the oscillations are suppressed, the strong suppression effect can occur at small control intensities.