Control of oscillations in vibration machines: Start up and passage through resonance

Abstract

Control of oscillations in mechanical systems in the start-up and passage through resonance modes is studied. In both cases, the control algorithm is based on the speed-gradient method with energy-based goal functions. It is shown that for Hamiltonian 1-degree of freedom (DOF) systems, it is generically possible to move the system from any initial state to any final state by means of a controlling force of arbitrarily small intensity. Controlled passage through resonance is studied for a 5-DOF vibration machine taking friction into account. It is shown by simulation that applying feedback control makes passage through lower resonance feasible with smaller control intensity compared with passage through resonance under constant control torque. The specific feature of this paper is consideration of the case when constant control torques do not allow the rotors even to start rotation. Applying feedback control allows rotors to overcome gravity and to start rotation. Another key novelty of this paper is comparison of the results obtained from the simulation with the experimental results obtained from the two-rotor laboratory mechatronic stand. It appears that most results are qualitatively the same, which confirms the adequacy of the model.

On average values of nonlinear functions of oscillating quantities and their applications

“…At the same time, the vibration-transformed function depends on the phase difference β 1 − β 2 . This is essential for the possibility of control; in particular, for vibrational process machines [Fradkov, 2007;Blekhman, 2012;Andrievskii et al, 2016;Fradkov et al, 2016;Tomchina et al, 2018;Tomchina et al, 2021;Tomchina, 2022] , when the function F represents a characteristic of the process (see Sec. 4).…”

Bidirectional Controlled Multiple Synchronization of Unbalanced Rotors and Its Experimental Evaluation

“…The Multiresonance Mechatronic Laboratory Setup (MMLS) SV-2M of the IPME RAS, described in (Boikov et al, 2016;Fradkov et al, 2016;Andrievsky and Boikov, 2017;Andrievsky et al, 2019;Fradkov et al, 2021), is used for experimental investigations. For the sake of clearness, the SV-2M is briefly described below.…”

Bifurcation Dodge: Avoidance of a Thermoacoustic Instability under Transient Operation

“…The latter problem has been the subject of many studies in literature, and it is well known that the ramp rate of the harmonic forcing frequency has a substantial influence on the maximum amplitude reached during the transient [49,50]. This is for example highly relevant for rotating machines at the startup [51,52] or for hoist systems [53]. In the present work, the nonlinear system exhibits self-sustained oscillations at fixed frequency ≈ ω 0 /2π for the middle range of the bifurcation parameter, and damped oscillations at about the 2)), which was identified from the experiments (see fig.…”