Passivity-Preserving Reduction of High-Order Electro-Mechanical Robot Systems
DOI:
https://doi.org/10.18196/jrc.v6i3.26868Keywords:
Balanced Truncation, Electro-Mechanical Robotics, Error Norms, Model Order Reduction, Riccati EquationsAbstract
High-order electro-mechanical robot systems (EMRS) present formidable challenges in real-time simulation and embedded control due to their substantial state-space dimensionality and tightly coupled multi-domain dynamics. Excessive model complexity impedes rapid simulation and controller synthesis exacerbates computational demands in resource-constrained environments. This study systematically investigates passivity-preserving model order reduction (PP-MOR) for electro-mechanical robot systems, prioritizing the retention of essential dynamic fidelity and energy dissipation. In contrast to standard balanced truncation or Krylov subspace approaches, the PP-MOR algorithm maintains physical consistency and achieves an optimal balance between model simplicity and dynamic accuracy. This method that employs positive-real algebraic Riccati equations to compute system Gramians, utilizes congruence transformations for system balancing, and imposes constraints to ensure both stability and strict passivity in the reduced-order models. Reduction experiments on the eight-state EMRS benchmark produced models of orders one, two, and four. The fourth-order model achieved H2 and H∞ errors of 7.2×10-4 and 8.5×10-4, respectively, with time-domain metrics, ISE, IAE, ITAE, and RISE, remaining below 1.1×10-4. Both second-order and third-order reductions yielded errors under 10-1 across all criteria, while first-order truncation resulted in a tenfold increase in worst-case gain mismatch (0.82 vs. 0.07 for fourth order) and significant transient deviations. The fourth-order model also preserved key dynamic features, including resonance peak, bandwidth, phase margin, and step response overshoot, with less than 0.5% deviation from the original system. By enabling simulation and embedded implementation of EMRS models, this approach paves the way for advanced robotic applications in manufacturing and autonomous systems, where computational efficiency and robust performance are paramount.
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