Control of oscillations in two-rotor cyberphysical vibration units with time-varying observer

Abstract

In this paper the control of oscillations in the two-rotor vibration unit is studied. It is assumed that the velocity of the oscillation of the platform cannot be accurately measured. The time-varying observer is proposed to restore it. In order to guarantee stability of the frequency and amplitude of oscillations of the vibrating parts of a two-rotor vibration unit special control algorithms based on speed-gradient methodology. Simulation results confirm stability of the synchronous rotation modes of the unbalanced rotors of the vibration unit.

Bidirectional Controlled Multiple Synchronization of Unbalanced Rotors and Its Experimental Evaluation

“…4 Linear Analysis of Simplified Model The overall system, including the mechanical part, induction motors and the controller is a highly nonlinear complex system of the high order (cf. (Galitskaya and Tomchina, 2012;Fradkov et al, 2013;Tomchina, 2018;Tomchina, 2020;Fradkov et al, 2021)). However, as stated in (Fradkov et al, 2021), in medium and high frequency ranges, the so-called the averaging property, which is widely exploited in the vibrational mechanics is valid.…”

“…To this end the normalization gain κ > 0 is introduced, so that the desired rotation frequencies of the left ω * l and right ω * r rotors are related as ω * r = ω * l /κ and, consequently, the normalized phase shift ψ between the rotors is calculated as ψ = κϕ r − ϕ l , cf. (Tomchina et al, 2009;Galitskaya and Tomchina, 2012;Tomchina, 2020). Summarizing, the adopted bidirectional control law for multiple synchronization of debalance rotors is as follows:…”

“…In (Tomchina et al, 2009;Galitskaya and Tomchina, 2012;Tomchina, 2020), a multiple synchronization algorithm for a two-rotor vibration machine is proposed, based on the integro-differentiating Speed-gradient algorithms (Fradkov, 1979;Andrievsky et al, 1989;Fradkov and Pogromsky, 1998;Fradkov et al, 1999). It is shown that the proposed solution to the problem of controlling the multiple synchronization of rotors of two-rotor vibration machines affects the value of the steady-state normalized phase shift, making it possible to regulate the performance of the system.…”

Control of vibrational field in an elastic vibration unit with DC motors and time-varying observer

“…However, the technical implementation of such algorithms requires information on the full state vector of the mechanical subsystem, which is not always feasible. This problem can be solved by using a non-stationary (time-varying) observer [Tomchina, 2020].…”

“…3 Speed-Gradient Control Algorithms with timevarying observers for synchronization of tworotor vibration unit The problem of maintaining a stable synchronous mode of rotation of unbalanced rotors of a two-rotor VU for a model that takes into account the dynamics of electric drives, using observer estimates in the control algorithm, was considered in [Tomchina, 2020]. Algorithm [Tomchina, 2020] can also be applied when solving the problem of controlling the vibration field of a two-rotor VU.…”