Multiple-Frequency Force Estimation of Controlled Vibrating Systems with Generalized Nonlinear Stiffness

An on-line estimation technique of multiple-frequency oscillatory forces combined with the Hilbert–Huang transform for an important class actively controlled, forced vibrating mechanical systems nonlinear stiffness is proposed. Polynomial parametric nonlinearities are incorporated in significantly perturbed system dynamics. This can exhibit harmful large-amplitude vibrations, which inadmissible many engineering applications. Disturbing oscillations be also provoked due to interactions primary protected against dangerous vibrations other uncertain multidegree-of-freedom systems. Taylor’s series expansion dynamically model into a small time window real-time purposes employed. Intrinsic mode functions then obtained by Hilbert-Huang transform. Uncertain instantaneous frequencies and amplitudes disturbing directly computed temporal space. active vibration control scheme efficient robust tracking prescribed motion reference profiles based on multiple frequency force introduced as well. The presented closed-loop extended classes Analytical, experimental numerical results prove effectiveness presented. Numerical show reasonable errors less than 2%.