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Abstract
A robust algorithm in the form of a 3-D dynamic system is introduced to identify the frequency, the in-phase component, the orthogonal component, and the amplitude of a sinusoidal signal with unknown frequency. The condition for asymptotically convergent property of the dynamic system is analyzed sequentially by time scale change, variable transformation, slow integral manifold, averaging method, Lyapunov stability theorem, and stability theory of Mathieu equation. The robustness is embodied in two aspects: 1) the actual values of both frequency and amplitude slightly influence the convergent property and 2) two design parameters have independent effects on performance of both frequency identification and amplitude identification, respectively. Simulation results verify the validity.
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