Semi-active damping and energy harvesting using an electromagnetic transducer

This article studies a semi-active control strategy applied to a vibration damping and to an energy harvesting problem. In particular, a single-degree-of freedom oscillating device is considered, comprising a mass connected to the ground by means of a spring, a dashpot and an electromagnetic transducer. The latter component yields a damping contribution which can be easily modulated between a minimum and a maximum value. By applying the Pontryagin maximum principle to the vibration damping problem, it is shown that the time optimal control law consists of a switching of the electromechanical damping contribution between the maximum and the minimum values. The same Principle is then applied to the optimization of the energy harvestable by the same structure under periodic excitation. Differently from the case of vibration damping, the solution of the latter problem can contain both regular phases (during which the optimal choice of the modulated damping is either at its maximum or at its minimum value) and singular phases (during which the optimal damping has smooth variations). Interestingly, it is also shown that when the objective is to dissipate rather than to harvest energy from the device, optimal strategies only consist of regular phases. Both the proposed semi-active strategies are shown to outperform corresponding optimized passive classic solutions, used as a benchmark for comparison.