[Paper Review] Model-Free Based Digital Control for Magnetic Measurements

Loïc Michel, Olivier Ghibaudo+5 more|arXiv (Cornell University)|Mar 15, 2017

Magnetic Properties and Applications11 references3 citations

TL;DR

This paper presents a model-free digital control strategy for Epstein frame-based magnetic material characterization, enabling precise waveform shaping of magnetic induction B despite material nonlinearity and hysteresis. By using a derivative-free variant of the model-free controller, the method achieves sub-1% form factor (FF) across sinusoidal and square wave references at 10–50 Hz, significantly reducing harmonic distortion even near saturation.

ABSTRACT

This paper presents a novel digital control strategy successfully implemented for a soft magnetic material characterization bench (Epstein frame type). The main objective is to control the magnetic induction waveform whatever the applied excitation and the material under study. Given the nonlinear nature of the magnetization curves of magnetic materials, an original model-free based control technique is considered. Special mention should be made of the interesting dynamic properties in closed-loop against the changes of the operating point related basically to the hysteresis form. The operation and the performances of the digital control method are illustrated in different working conditions through both simulation and experimental measurements.

Motivation & Objective

• To address the challenge of maintaining precise magnetic induction waveforms (e.g., sinusoidal, triangular) in soft magnetic material characterization under nonlinear and hysteretic material behavior.
• To overcome limitations of conventional analog feedback and model-based control in high-induction regimes where nonlinearities and power supply distortions degrade waveform fidelity.
• To develop a robust, real-time digital control method that does not require an explicit model of the magnetic material or Epstein frame dynamics.
• To ensure compliance with IEC standards (FF < 1%) across varying excitation frequencies and material states, including near-saturation conditions.
• To enable symmetrical excitation current to prevent DC bias and unwanted magnetization in the core, improving measurement accuracy.

Proposed method

• Adopts a model-free control framework derived from Fliess and Join’s approach, avoiding reliance on system models or derivative estimation of the output signal.
• Uses a recursive control algorithm that adjusts the input voltage waveform in real time based on feedback from the secondary coil voltage $v_B$, which is integrated to estimate $B(t)$.
• Implements a derivative-free variant of the model-free controller to improve robustness and reduce noise sensitivity in the feedback loop.
• Applies a symmetrization technique to the control signal to ensure balanced excitation current $i_H$, eliminating DC components that could bias the core.
• Employs digital signal processing to compute the form factor $FF(\%)$ in real time using RMS and rectified average values of $v_B$, enabling dynamic performance monitoring.
• Validates the control strategy through both simulation and experimental measurements on non-oriented SiFe steel at 10 Hz and 50 Hz with sinusoidal and square wave references.

Experimental results

Research questions

• RQ1 Can a model-free digital control strategy effectively maintain low harmonic distortion in magnetic induction waveforms across varying excitation frequencies and material nonlinearities?
• RQ2 How does the proposed derivative-free model-free controller compare to traditional analog or model-based feedback in terms of dynamic performance and stability near saturation?
• RQ3 To what extent can the control method suppress voltage drops and waveform distortions caused by core nonlinearities and power supply limitations?
• RQ4 Can the controller maintain waveform symmetry and eliminate DC bias in the excitation current, ensuring accurate hysteresis loop measurements?
• RQ5 What is the achievable form factor (FF) improvement when using the proposed digital control compared to open-loop operation?

Key findings

• The proposed digital control reduces the form factor (FF) of the magnetic induction waveform from 6.1% (open-loop) to 0.53% at 10 Hz, achieving compliance with IEC standards.
• At 50 Hz, the form factor is reduced to 0.7% with symmetrization, demonstrating effective harmonic suppression even under high-frequency excitation.
• The controller successfully compensates for voltage drops in the secondary coil, maintaining a stable and accurate $v_B$ waveform despite nonlinear core behavior.
• The controller maintains quasi-sinusoidal and quasi-triangular $B$ waveforms across both sinusoidal and square reference inputs, even near saturation.
• The symmetrization technique successfully eliminates DC components in the excitation current, preventing core biasing and ensuring accurate hysteresis loop measurements.
• The method demonstrates robust dynamic performance across different operating points, including high induction levels, without requiring prior knowledge of the material’s magnetic model.