Using the eXtended Finite Element Method (XFEM) to Simulate Own Frequency under External Influences of a Closed System based on Dynamic Compensation Method

Many mechanical systems with elastic and damping properties are prone to resonant phenomena at natural frequencies under the action of external forces. Resonance phenomena can also be preserved in control systems of such objects closed by negative feedback, which reduces the quality of the functioning of these systems. The paper under review deals with the practically important problem of suppressing oscillations at natural frequencies in control systems for a linear oscillator, which is traditionally considered a dynamic object described by a second-order differential equation with complex roots of the characteristic equation. The focus of the work is the question of the roughness of the system in relation to inaccurate knowledge of the resonant frequency of the controlled object (which is typical for many technical applications).