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arXiv · 2505.20374

Numerical estimation of the lock-in domain of a DC/AC inverter

Anton Ponomarev·Lutz Gröll·Veit Hagenmeyer
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Abstract

We estimate the lock-in domain of the origin of a current control system which is used in common DC/AC inverter designs. The system is a cascade connection of a 4-dimensional linear system (current controller, CC) followed by a two-dimensional nonlinear system (phase-locked loop, PLL). For the PLL, we construct a Lyapunov function via numerical approximation of its level curves. In combination with the quadratic Lyapunov function of the CC, it forms a vector Lyapunov function (VLF) for the overall system. A forward-invariant set of the VLF is found via numerical application of the comparison principle. By LaSalle's invariance principle, convergence to the origin is established.

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Anton Ponomarev, Lutz Gröll, Veit Hagenmeyer. 2025-05-26. Numerical estimation of the lock-in domain of a DC/AC inverter. https://doi.org/10.1016/j.ifacol.2025.11.053

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