Computer-Controlled Vibrational set-up for Education and Research

Blekhman, I. I.; Bortsov, Yu. A.; Burmistrov, A. A.; Fradkov, Alexander L.; Gavrilov, S.V.; Kononov, Oleksii; Lavrov, B. P.; Shestakov, Valery; Sokolov, Pavel; Tomchina, Olga P.

doi:10.1016/s1474-6670(17)57087-1

Cited by 19 publications

(26 citation statements)

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“…Consider the two-rotor vibration unit in the startup/spin-up mode [17]. The unit consists of two rotors 4 installed on the vibrating platform 5.…”

Section: Passing Through Resonance Control Algorithm Of Two-rotor Vibmentioning

confidence: 99%

“…At the low levels of constant control action ( ) ≡ (−1) 0 , = 1,2 in the near-resonance zone the rotor angle is "captured, " while increase of the control torque leads to passage through resonance zone towards the desired angular velocity. The simulation results for system (16), (17) (external curves, passage). Simulation of system (17) without elasticity ( = ) and without control ( = = (−1) 0 ) has shown that the lowest constant drive torque 0 providing passing through the resonance is 0.66 N⋅m (Figure 4).…”

Section: Passing Through Resonance Control Algorithm Of Two-rotor Vibmentioning

confidence: 99%

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Controlled Passage through Resonance for Flexible Vibration Units

Tomchin

Tomchina

Fradkov

2015

Mathematical Problems in Engineering

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The problem of controlled passage through resonance zone for mechanical systems with several degrees of freedom is studied. Control algorithm design is based on speed-gradient method and estimate for the frequency of the slow motion near resonance (Blekhman frequency). The simulation results for two-rotor flexible vibration units illustrating efficiency of the proposed algorithms and fractal dependence of the passage time on the initial conditions are presented. The novelty of the results is in demonstration of good behavior of the closed loop system if flexibility is taken into account.

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“…Consider the two-rotor vibration unit in the startup/spin-up mode [17]. The unit consists of two rotors 4 installed on the vibrating platform 5.…”

Section: Passing Through Resonance Control Algorithm Of Two-rotor Vibmentioning

confidence: 99%

Section: Passing Through Resonance Control Algorithm Of Two-rotor Vibmentioning

confidence: 99%

Controlled Passage through Resonance for Flexible Vibration Units

Tomchin

Tomchina

Fradkov

2015

Mathematical Problems in Engineering

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“…In this paper the control algorithms for design and control of inhomogeneous flat oscillation fields for two-rotor VU are proposed and studied using computer simulation. The parameters of the unit model correspond to experimental vibration set-up SV-2M designed in the IPME [Blekhman, Bortsov, Burmistrov, et. al., 1999;Andrievskii, Blekhman, Blekhman, et.al., 2016; Andrievsky and Boikov, 2017; Tomchin, Tomchina, Fradkov, 2015].…”

Section: Introductionmentioning

confidence: 99%

“…The parameter values correspond to the vibration stand SV-2M designed in the IPME [Blekhman, Bortsov, Burmistrov, et. al., 1999;Andrievskii, Blekhman, Blekhman, et.al., 2016].…”

Section: Introductionmentioning

confidence: 99%

Control of vibrational field in a cyber-physical vibration unit

Tomchina

2018

CAP

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“…The numerical results of Fradkov and Andrievsky for this device, [4], show simultaneous and approximate in-phase and anti-phase synchronization, tuned by different initial conditions. In another experimental device made of two rotors controlled by external torques ( [5,6]), Andrievsky et al, [5], reported approximate anti-phase and in-phase synchronization of the two oscillators. In this experiment, the synchronization parameter is the stiffness of a string connecting the two rotors.…”

Section: Introductionmentioning

confidence: 99%

On the Problem of Synchronization of Identical Dynamical Systems: The Huygens’s Clocks

Dilão¹

2009

Variational Analysis and Aerospace Engineering

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In 1665, Christiaan Huygens reported the observation of the synchronization of two pendulum clocks hanged on the wall of his workshop. After synchronization, the clocks swung exactly in the same frequency and 180 o out of phaseanti-phase synchronization. Here, we propose and analyze a new interaction mechanism between oscillators leading to exact anti-phase and in-phase synchronization of pendulum clocks, and we determine a sufficient condition for the existence of an exact anti-phase synchronization state. We show that exact anti-phase and in-phase synchronization states can coexist in phase space, and the periods of the synchronized states are different from the eigen-periods of the individual oscillators. We analyze the robustness of the system when the parameters of the individual pendulum clocks are varied, and we show numerically that exact anti-phase and in-phase synchronization states exist in systems of coupled oscillators with different parameters.

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Computer-Controlled Vibrational set-up for Education and Research

Cited by 19 publications

References 0 publications

Controlled Passage through Resonance for Flexible Vibration Units

Controlled Passage through Resonance for Flexible Vibration Units

Control of vibrational field in a cyber-physical vibration unit

On the Problem of Synchronization of Identical Dynamical Systems: The Huygens’s Clocks

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