Active Piezoelectric Metamaterials With Model-Free Controller for Large Low-Frequency Vibration Attenuation

In this article, we present a control-oriented model for a piezoelectric (PZT) metamaterial beam based on "amplifier–resonator" (A–R) circuits. This model enables a quantitative investigation of bandgap formation mechanisms. Additionally, our research reveals that resistance plays a crucial role in bandgap formation, and conventional synthetic inductance and synthetic impedance fail to create effective bandgaps at low frequencies due to significant parasitic resistance. To address this issue, we develop a control circuit with minimal parasitic resistance and a model-free digital controller. This controller establishes a quantitative relationship between circuit and bandgap parameters. Through a negative feedback loop, it adjusts the dynamic stiffness and damping of the composite structure, achieving customizable bandgaps. Numerical simulations validated the model and theoretical bandgap derivations. Experimental results demonstrate the superior performance of our controller in reducing low-frequency vibrations compared to analog shunt circuits, achieving over 60 dB attenuation. Our design paves the way for broader applications of active control algorithms in reducing low-frequency vibrations.