Constrained Gray-Box Identification of Electromechanical Systems Under Unfiltered Step-Response Data

This paper presents a physically constrained grey-box identification framework for electromechanical systems, illustrated through the dynamics of brushed DC motors. The method estimates all electromechanical parameters by minimizing a normalized residual that combines current, velocity, and steady-state algebraic constraints under a current-limit condition. Classical approaches such as least-squares and black-box identification often lack physical interpretability and do not explicitly enforce steady-state consistency, making their estimates susceptible to nonphysical parameter drift. The proposed formulation incorporates these physical constraints within a Levenberg–Marquardt scheme with signal normalization, enabling the joint minimization of current and velocity errors. Validation was performed using step-response data from two DC motors under both synthetic and experimental conditions. When applied to unfiltered measurements, the method maintained steady-state relative errors below 1% and achieved low trajectory discrepancies, with NRMSE in velocity between 2.6 and 3.2% and NRMSE in current between 0.9 and 1.2% across both motors. Embedding physical and steady-state constraints directly into the cost function improves robustness and ensures physically consistent parameter estimates, even under high measurement noise and without filtering. The approach provides a general strategy for dynamic system identification under physical consistency requirements and is suitable for rapid calibration, diagnostic monitoring, and controller tuning in robotic and mechatronic applications.