Reduced-Order Dynamic Modeling for a DC Motor Coupled with Flywheel and Torsion Shaft Using the Eigenmode Truncation Method
DOI:
https://doi.org/10.18196/jrc.v6i3.26459Keywords:
Computational Efficiency, DC Motor Coupled, Flywheel and Torsion Shaft, Eigenmode-Based Reduction, Model ReductionAbstract
This study assesses the effectiveness of model order reduction for the DC Motor Coupled with Flywheel and Torsion Shaft Mechanism (DCM‑FTSM) by minimizing the number of state variables from nine to three while preserving essential dynamic behavior. Unlike balanced truncation, the Eigenmode Truncation (ET) algorithm prioritizes modal dominance rather than energy‑based approximations, selecting modes that most significantly influencing the system’s response. By transforming the system into modal coordinates and extracting the critical submatrix of eigenvectors, the original ninth‑order model is reduced to third order without compromising stability or performance in either the time or frequency domains. MATLAB simulations demonstrate that the reduced‑order model achieves an H∞ norm error of 11.9456, a mean step response error of 0, and average phase and magnitude errors of 14.8858 deg and 0.0055 dB, respectively. Key time‑domain metrics (rise time, overshoot, peak value, peak time) and frequency‑domain parameters (gain margin, phase margin, phase crossover frequency) align closely with those of the full‑order model within the typical operating range. Moreover, by reducing the state dimension by 67%, ET yields significant computational savings, facilitating faster simulation and real‑time controller computation. The ET method thus enables real‑time control of complex electromechanical systems by balancing accuracy and computational efficiency.
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