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Introduction: This paper proposes a sigmoid-based adaptive inertia control strategy for grid-forming (GFM) inverter to enhance frequency stability.Methods: Firstly, the frequency response characteristics under different disturbances are analyzed theoretically. Then, to solve the problem that fixed inertia leads to a contradiction between the maximum frequency deviation and the setting time, a non-linear inertia regulator is investigated. This non-linear inertia regulator, which is based on an improved sigmoid function, is applied to achieve real-time inertia by the frequency deviation. Moreover, the full-order small-signal model of the system containing the nonlinear inertia regulator is established and thus the stability of the proposed strategy is analyzed.Result and Discussion: The proposed control strategy is implemented without derivative action, which may suffer from high-frequency noises. Finally, the hardware-inthe-loop (HIL) results verify the remarkable performance of the proposed control strategy.