Operator-based Phase Control of Dual-Layer Triboelectric Nanogenerators Using Right Coprime Factorization

This paper presents a control-oriented study of a mechanically coupled, dual-layer contact-separation triboelectric nanogenerator (CS-TENG) for phase-coordinated voltage generation. A dynamic model is established to capture the spring-mass-damper coupling between layers under external sinusoidal excitation, in which each layer’s voltage output is modeled as a nonlinear function of displacement, naturally resulting in a phase difference between the two outputs. To achieve active phase control, a tunable RC phase-shift circuit is designed, where the variable capacitance is mechanically adjusted to modulate the output signal phase. A proportional–integral (PI) controller is synthesized within an operator-based framework using right coprime factorization (RCF), providing robust phase tracking and tolerance to parameter uncertainties. Simulation results demonstrate that the proposed approach achieves precise dual-output phase control and flexible voltage shaping with fast convergence and strong robustness, offering a promising solution for synchronized energy harvesting, distributed sensing, and coordinated power delivery in multi-layer TENG systems.