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

Abstract 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, its strong robustness and effectiveness in chattering suppression are demonstrated. Numerical simulation proved that the FTA-ISMC strategy can quickly and precisely drive the harvester to run on a high-energy orbit within just one second. The rapid attenuation of trajectory error verified the effectiveness and accuracy of the FTA-ISMC strategy. Critically, the FTA-ISMC strategy demonstrates that a brief 1 second 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 seconds 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.