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Energy flow control in a system of coupled pendulums using magnetic field
(Wydawnictwo Politechniki Łódzkiej, 2021) Pilipchuk, Valery; Polczyński, Krystian; Bednarek, Maksymilian; Awrejcewicz, Jan
In the presented work, we proposed a methodology of controlling the resonance energy exchange in mechanical systems by creating appropriate electromagnetic fields around the system’s structural subcomponents. It has been shown theoretically and confirmed experimentally that properly guided magnetic fields can effectively change mechanical potentials in such a way that the energy flow between the oscillators takes the desired direction. In particular, a model of two weakly coupled pendulums subjected to an electromagnetic load using a specific set of descriptive functions was considered. The developed control strategies are based on the observation that, in the case of antiphase oscillation, the energy is moving from the pendulum, which is in the repelling magnetic field, to the oscillator not subjected to magnetic field. The advantage of the suggested control strategy is that the temporal rate of inputs is dictated by the speed of beating, which is relatively slow compared to the carrying oscillations.
Guidance of the resonance energy flow in the mechanism of coupled magnetic pendulums
(Elsevier, 2022) Pilipchuk, Valery N.; Polczyński, Krystian; Bednarek, Maksymilian; Awrejcewicz, Jan
This paper presents a methodology of controlling the resonance energy exchange in mechanical system consisting of two weakly coupled magnetic pendulums interacting with the magnetic field generated by coils placed underneath. It is shown that properly guided magnetic fields can effectively change mechanical potentials in a way that the energy flow between the oscillators takes the desired direction. Studies were considered by using a specific set of descriptive functions characterizing the total excitation level, its distribution between the pendulums, and the phase shift. The developed control strategies are based on the observation that, in the case of antiphase oscillation, the energy is moving from the pendulum subjected to the repelling magnetic field, to the oscillator under the attracting field. In contrast, during the inphase oscillations, the energy flow is reversed. Therefore, closed-loop controller requires only the information about phase shift, which is easily estimated from dynamic state signals through the coherency index. Advantage of suggested control strategy is that the temporal rate of inputs is dictated by the speed of beating, which is relatively slow compared to the carrying oscillations.
Magnetic oscillator under excitation with controlled initial phase
(Wydawnictwo Politechniki Łódzkiej, 2021) Polczyński, Krystian; Bednarek, Maksymilian; Awrejcewicz, Jan
The work contains the results of numerical simulations of the dynamics of a magnetic pendulum system subjected to excitation with a varying initial phase. A magnetic pendulum consists of a magnet fixed to the end of its arm and an electric coil below it. The initial phase of the excitation is presented as a linear function of the dynamic variable of the system, which is the angular position of the pendulum. The obtained basins of attraction indicate the occurrence of multi-periodic solutions in the system depending on the changes in the parameters of this system. The periodicities of the observed solutions are quantified mostly by odd numbers.