Modeling, complexity and finite-time modified adaptive control of a novel electromagnetic energy harvester

This paper details the modeling, complexity analysis and finite-time modified adaptive control (FTA-ISMC) of a novel stacked electromagnetic energy harvester that exhibits a negative stiffness characteristic. A cubic nonlinear dynamic model is first established based on precise magnetic field modeling and equivalent stiffness analysis. Bifurcation and complexity analyses reveal dynamic behaviors, including the coexistence of low-energy, high-energy periodic orbits, multiple periods and chaotic states. Then, an FTA-ISMC strategy is designed to drive the harvester to a high energy state, proving its strong robustness and effectiveness in chattering suppression. Comparative simulations demonstrate that the proposed strategy outperforms standard sliding mode and PID controllers by minimizing control effort and eliminating both chattering and overshoot. It precisely drives the harvester to a high energy orbit within just one second. Critically, the FTA-ISMC strategy demonstrated that a brief 1 s control pulse, requiring a mere 0.14 J of energy, is sufficient to permanently unlock a high-energy orbit. This initial energy cost is fully recovered within just 57.6 s of operation, after which the system yields a net energy gain. This work provides an integrated design and control framework, facilitating the practical use of high-performance energy harvesters.