Numerical estimation of the lock-in domain of a DC/AC inverter
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917237493858304 |
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| author | Ponomarev, Anton Gröll, Lutz Hagenmeyer, Veit |
| author_facet | Ponomarev, Anton Gröll, Lutz Hagenmeyer, Veit |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20374 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical estimation of the lock-in domain of a DC/AC inverter Ponomarev, Anton Gröll, Lutz Hagenmeyer, Veit Optimization and Control Systems and Control 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. |
| title | Numerical estimation of the lock-in domain of a DC/AC inverter |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2505.20374 |