Using time delay in the nonlinear oscillations of magnetic levitation for simultaneous energy harvesting and vibration suppression. (November 2019) - Firoozy, Peyman; Friswell, Michael I; Gao, Qingbin
Highlights: Theoretical model is developed to study nonlinear oscillations of magnetic levitation in the presence of time delay for vibration suppression and energy harvesting. The effects of the main parameters of the system, such as time delay parameters, distance between magnets, and external resistance load, is studied. In order to summarize the electrical and mechanical behaviors of the system, the perfection rate (PR) is used. The presence of the time delay and choosing a point from the region of multiple periodic solutions enhances the output power and suppresses higher levels of vibration. Abstract: In this paper, the nonlinear oscillations of magnetic levitation in the presence of a time delay is investigated, with the purpose of simultaneous energy harvesting and vibration suppression. To harvest energy, a coil with seven layers of 36 gage wire wound around the outer casing is utilized. Although the proposed control feedback consumes some power, the results show the harvestable power can be much larger than the consumed power, which makes the proposed concept feasible. The first-order perturbation method is utilized to examine the possibility of energy harvesting and vibration suppression for different selections of the delay parameters, the distances between the magnets and the external load resistances. In addition, the stability map of the time-delayed control is analytically determined. The influence of the time delay parameters chosen from Single Periodic Solutions (SPS) and Multiple Periodic Solutions (MPS) on the vibration and power amplitudes is studied. It is shown that a point chosen from the MPS region enables the system to harvest power over a broad range of excitation frequencies. Also, the effect of the distance between the magnets on the frequency response of the system is examined. In addition, to select the optimum value for the distance between the magnets for different values of the time delay parameters, a parameter called the Perfection Rate (PR), which reflects both the electrical and mechanical behavior of the system, is used. Finally, it is shown that the presence of the time delay and a point chosen from the MPS region enables the system to harvest more power over a broad range of excitation frequency and to suppress higher levels of vibration, than for a point chosen from the SPS region and without time delay. Graphical abstract: Image, graphical abstract