Structured Eigenvalue Equalization for Balanced Multi-Harmonic Disturbance Rejection in Adaptive Feedforward Control

Adaptive feedforward control of multi-harmonic disturbances in rotating machinery faces a fundamental challenge when harmonic amplitudes exhibit high dynamic range (HDR >50dB): standard adaptive controllers suffer from severe mode-wise convergence imbalance, where weak harmonics remain unregulated while dominant modes saturate. This control performance disparity stems from ill-conditioning (condition number κ∼105) in the filtered reference correlation matrix, causing convergence time constants to differ by four orders of magnitude across modes.Within the PNANC block-diagonal structure, per-channel normalization and steady-state sinusoidal mapping can be integrated into a unified framework that simultaneously achieves balanced mode regulation and computational efficiency. The resulting low-complexity eigenvalue-equalized (LC-EE) algorithm exploits the block-diagonal eigenstructure for structured per-channel normalization and the sinusoidal reference structure for steady-state replacement of FIR convolution by O(K) matrix operations. This restores uniform controllability by compressing the condition number from κ≈9×104 toward unity through diagonal preconditioning, while reducing arithmetic complexity by 98.4% compared to conventional implementations.Performance is validated through controlled simulation and semi-synthetic experiments using authentic industrial broadband noise from the MIMII dataset. The integrated framework achieves 23.4× convergence acceleration and 9.3 dB improvement in average steady-state disturbance attenuation relative to standard PNANC. Per-harmonic convergence analysis confirms that all K=8 controlled harmonics converge uniformly under eigenvalue equalization, whereas only the fundamental mode adapts under standard PNANC. Statistical analysis across 12 recordings from 4 distinct machines confirms significance (p<0.001). Robust stability is maintained under severe broadband turbulence (SNR to −5dB), secondary-path magnitude modeling errors up to 30%, and frequency jitter up to 0.5 Hz RMS. Extended mismatch testing across seven scenarios establishes practical limits: combined magnitude, phase, and delay errors should remain within approximately ±10%, ±15°, and ±5 samples, respectively, for guaranteed stability. These results suggest that the observed performance improvements stem primarily from structural properties of the PNANC framework rather than parameter retuning, and indicate the potential of the proposed realization for low-cost embedded implementation in HDR disturbance control applications.