Synchronization control of parametric pendulums for wave energy extraction

Abstract

Abstract.In this work the dynamics of a parametric pendulums system has been studied with a view to its application for sea wave's energy extraction. The idea is based on the conversion of the oscillatory motion of the waves into rotation of the pendulums. The system approximating a floating structure with two pendulums mounted on it has been modelled and analyzed. In the first stage of the study the general dynamics of the parametric pendulums has been investigated numerically and experimentally. The focus lies on synchronized rotational solutions, representing a most energetically favourable state of motion. The target state is to achieve a synchronized counter rotation of both pendulums. The controlling strategy, with the aim of initiating and maintaining the desired response, has been developed and verified numerically and experimentally. Different methods based on the delayed-feedback control have been suggested. The numerical and experimental results showing the difference in the system dynamics with and without control have been presented. Finally the energy extraction from the system has been simulated numerically and energy extraction control has been discussed.

Initiation and directional control of period-1 rotation for a parametric pendulum

“…However, our study with the control law given in the conference paper[13] does not lead to the basin of attraction reported therein. We find that the form of the control law given in the PhD thesis of Najdecka[14] leads to a similar basin of attraction as reported in[13].…”

“…This external torque, F c , should vanish for period-1 rotation(s), so that there could be a net energy harvesting. The previous time-delayed control laws proposed in [13][14][15] satisfy this criterion. In this paper, we use another time-delayed control law that not only vanishes for the period-1 rotation(s), but also vanishes for all period-1 solutions.…”

“…There have been limited studies on the control aspect of period-1 rotation [13][14][15][16][17][18] and all of them are based on time-delayed feedback. In a conference paper, Najdecka et al [13] proposed an extended time-delayed feedback control and showed that all initial disturbances led to either anticlockwise or clockwise period-1 rotation. 1 A similar control law has been reported in the PhD thesis of Najdecka [14].…”

“…In a related study, de Paula et al [17] used another extended time-delayed feedback control to prevent period-doubling bifurcation of the period-1 rotation, but they have not discussed the various attractors and their basins. Vaziri et al [18] experimentally showed the initiation and maintenance of period-1 rotation using the control proposed by Najdecka [13] for some initial disturbances. In this paper, we propose an alternate time-delayed feedback control law that can be reliably used to obtain period-1 rotation for all initial conditions as well as choose a preferential direction of rotation for all sets of forcing parameters.…”

“…Rotating solution of a parametric pendulum has gained a lot of attention from researchers in recent times [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] especially with a view to exploiting it for harvesting energy from waves [19]. Period-1 rotation is the simplest such solution and can exist for the smallest magnitude of the parametric forcing.…”