Performance of energy harvesters with parameter mismatch

TL;DR

The paper addresses how parameter mismatch affects the stability of cross-well motion in multistable energy harvesters. It uses basin stability with parameter mismatch and Monte Carlo sampling over a 2D excitation space defined by $P$ (amplitude) and $\Omega$ (frequency) to compare four harvester designs (S1–S4). The results show piezoelectric harvesters (S3,S4) are more robust to parameter variations than electromagnetic ones (S1,S2), preserving cross-well dynamics across larger regions and with smaller changes in basin stability. These findings provide practical safe operating ranges and design guidance for robust energy harvesters under real-world parameter uncertainties.

Abstract

This study explores the impact of parameter mismatch on the stability of cross-well motion in energy harvesters, using a basin stability metric. Energy harvesters, essential for converting ambient energy into electricity, increasingly incorporate multi-well systems to enhance efficiency. However, these systems are sensitive to initial conditions and parameter variations, which can affect their ability to sustain optimal cross-well motion -- a state associated with maximum power output. Our analysis compared four harvester types under varying levels of parameter mismatch, assessing resilience of the devices to parameter variations. By identifying safe operating ranges within the excitation parameter space, this study provides practical guidance for designing robust, stable harvesters capable of maintaining cross-well motion despite parameter uncertainties. These insights contribute to advancing the reliability of energy harvesting devices in real-world applications where parameter mismatches are inevitable.

Figures (7)

• Figure 1: Schematic diagrams of four investigated systems. a) Classical electromagnetic bistable energy harvester (S1). b) Electromagnetic bistable energy harvester with non-linear boundary (S2), introduced by Li2023. c) Asymmetric piezoelectric energy harvester (S3), introduced by Wang2024. d,e) Two degrees of freedom piezoelectric energy harvester (S4), introduced by Costa2024.
• Figure 2: a) Elastic potential energy of S1 for different values of $h$ parameter. Red dots represents unstable equilibrium positions, black dots stable equilibrium positions. Blue solid line is for $h_{1S1}=h_{2S1}=0.6l_{0}$ , orange dashed for $h_{1S1}=h_{2S1}=0.7l_{0}$, green dotted for $h_{1S1}=h_{2S1}=0.8l_{0}$ b) Restoring force (in $X$ direction) generated by spring along $X$ axis.
• Figure 3: Probability of reaching stable cross-well motion for S1. Parameters that are mismatched: $\gamma_{2S1}$, $\theta_{S1}$, $\varepsilon_{S1}$, $\varphi_{S1}$ represent respectively: potential well shape, electromechanical coupling, and mechanical damping. Range of initial conditions: $\overline{x}_{S1}$, $\dot{\overline{x}}_{S1}\epsilon<-1,1>$ Degree of parameter mismatch: a) No mismatch b) $\pm2.5\%$ c) $\pm5\%$ d) $\pm10\%$.
• Figure 4: Probability of reaching stable cross-well motion for S2. Parameters that are mismatched:$\eta_{1S2}$, $\eta_{2S2}$, $\rho_{S2}$, $\varepsilon_{S2}$, $\varphi_{1S2}$, $\varphi_{1S2}$ represent respectively: potential well shape, electromechanical coupling, and mechanical damping. Range of initial conditions: $\mathrm{X}$, $\dot{\mathrm{X}}\epsilon<-1,1>$ Degree of parameters mismatch: a) No mismatch b) $\pm2.5\%$ c) $\pm5\%$ d) $\pm10\%$.
• Figure 5: Probability of reaching stable cross-well motion for S3. Parameters that are mismatched:$K_{S3}$, $\kappa_{S3}$, $\zeta_{1S3}$, $\zeta_{2S3}$ represent respectively: stiffness of the unilateral stop, electromechanical coupling, and mechanical damping. Range of initial conditions: $\mathrm{y}\epsilon<-0.55,2>$, $\dot{\mathrm{y}}\epsilon<-2,2>$ Degree of parameter mismatch: a) No mismatch b) $\pm2.5\%$ c) $\pm5\%$ d) $\pm10\%$.