Decoupled Measurement of Conductivity and Permeability in Eddy Current Testing Based on Multi-Frequency Closed-Loop Control

Accurate decoupling measurement of electrical conductivity and magnetic permeability in ferromagnetic materials remains a significant challenge in eddy current testing (ECT) due to strong parameter coupling and lift-off interference. To address this issue, this article proposes a multivariable coupled control framework that enables high-accuracy multiparameter characterization through frequency-domain decoupling. Theoretical analysis based on the Dodd–Deeds model reveals that the mutual inductance at low frequencies is predominantly governed by magnetic permeability, which provides a basis for separating permeability and conductivity measurements. A dual closed-loop control strategy is developed in the low-to-medium frequency range, where the permeability estimated at low frequency is fed back to compensate for the medium-frequency conductivity inversion process. This iterative scheme progressively reduces parameter deviation and achieves simultaneous inversion of both parameters. Furthermore, a high-frequency feedforward controller is introduced to suppress lift-off-induced disturbances. Experimental validation demonstrates that the relative errors of the measured conductivity and permeability are within ±3.21% and ±3.65%, respectively. The proposed framework provides a systematic solution for multiparameter decoupling measurement in ferromagnetic materials.