Disturbance rejection and performance enhancement of perturbed tri-stable energy harvesters by adaptive finite-time disturbance observer

Tristable energy harvesters (TEHs) have been proposed to achieve broad frequency bandwidth and superior low-frequency energy harvesting performance. However, due to the coexistence of three potential wells and the sensitivity to system conditions and external disturbances, the desired high-amplitude inter-well oscillation in the TEHs may be replaced by the chaotic or intra-well oscillations with inferior energy output. Specifically, the chaos has an unpredictable trajectory and may cause system damages, lessen the structural durability as well as require a more complicated circuit for power management. Therefore, in this paper, we firstly propose an adaptive finite-time disturbance observer (AFTDO) for performance enhancement of TEHs by detecting the external disturbances that induce the chaos, and reject them for the recovery of the desired inter-well motion. The proposed AFTDO eliminates the need to know in advance the upper bounds of imposed perturbations in conventional observers by means of the proposed adaptive protocols, leading to the higher efficacy of estimation. The mathematical model of the piezoelectric TEH system and the AFTDO is provided. To demonstrate the effectiveness of the AFTDO, a series of numerical simulations have been performed. Results show that for both cases with sinusoidal and impulsive disturbances, the AFTDO can successfully track the trajectories of the disturbance signals with the adaptive gain, and reject the disturbance to enable the TEH to sustain the periodic inter-well oscillation with effective energy harvesting performance. [Figure not available: see fulltext.]