Modelling of a piezoelectric beam with a full-bridge rectifier under arbitrary excitation: experimental validation

Abstract

This paper presents a set of nonlinear differential equations to model a piezoelectric energy harvesting (PEH) system with a full-bridge waveform rectifier (FWR) under arbitrary base excitations. The PEH comprises a piezoelectric element modeled as a current source with a capacitor in parallel, which are connected with an inductor and a resistor. The inductor is proposed to smooth the current generated by the piezoelectric element under rapid mechanical variations and improve the convergence of the set of differential equations. The equations are obtained using piecewise linear modelling for the diodes. The main advantage of this piecewise linear modelling is considering different bias points to represent the nonlinear characteristics of real diodes. Numerical simulations are employed to obtain the optimum inductor value through a comparison with an analytical result, validated with experimental tests. A real case of random acceleration in a bike is applied to the PEH-FWR to evaluate the performance of the proposed equations. They are validated with experiments, a LTspice formulation and a numerical previous one. The proposed formulation can estimate the output DC voltage and energy for a large range of excitation frequencies, including resonant and nonresonant conditions and arbitrary or harmonically externally excited PEHs with FWR.