Discrete optimal couple tracking: A control scheme for electrical-tuning of strong coupling piezoelectric energy harvesters

In order to track the maximum power point of piezoelectric energy harvesters, an effective approach consists in designing interfaces able to electrically tune the harvester dynamics. Such interface should exhibit—at least—two tunable parameters in order to independently optimize the harvester damping and resonant frequency, that is, an electromechanical impedance matching of the real and imaginary parts of the electrical load. In order to optimize and control these two parameters, it is necessary to implement two control loops that simultaneously impact the harvester dynamics. Furthermore, these loops should combine quick convergence time with low-power consumption in order to react sufficiently fast to compensate for any shift in the vibration frequency and to consume only a small portion of the harvested power. In this paper, we propose a control-law based on the successive evaluation of couples of parameters in order to select the optimal one. First, we determine analytically the expression of a set of optimal couples valid for any two-parameters electrical interfaces. Thereafter, we prove that only a few well-chosen couples of parameters are sufficient to maximize the power on a large frequency band. The proposed methodology has been experimentally verified on a tunable interface, the short-circuit synchronous electric charge extraction. Combined with a strongly coupled piezoelectric energy harvester, we have been able to maintain the harvested power close to the maximal achievable power (i.e. >70% of the maximal achievable power) on a 20 Hz frequency band, with only five couples of parameters. Such approach allows to substitute a multi-parameters convergence algorithm by a single-couple of parameters convergence algorithm, greatly simplifying the algorithm and reducing its convergence time.