First and Second Order Mathematical Modeling of the Baldor L3510 AC Motor Based on Step Response

Abstract

Accurate dynamic models of AC induction motors are essential for control design and simulation. However, manufacturers typically do not publish detailed transfer functions for commercial motors, and the Baldor L3510’s dynamics in particular are undocumented. This work addresses that gap by identifying low order transfer-function models of a Baldor L3510 motor using experimental step-response data. The aim is to derive both a first-order and a second-order speed-response model that capture the motor’s behavior. As a main contribution, we propose two simplified linear models (first-order and standard second-order form) fitted to measured data, and we validate them against the motor’s actual response. In the method, a step voltage was applied to the L3510 motor and the rotor speed was recorded over time. The first-order model is assumed as   where the static gain  and time constant  are extracted from the step curve (for example,  is taken at the 63%-rise point with natural frequency  and damping ratio  chosen to match the observed rise time and any overshoot). These model structures follow standard system-identification practice. Notably, the motor’s stator circuit is essentially an RL network, whose dynamics are intrinsically first-order, justifying a one-pole model. The results show that both models closely reproduce the measured step response. For our data, the first-order fit yielded  (rad/s per volt) and s, giving . The second-order fit gave  and rad/s, i.e. . Under these models the predicted 5% settling time was s (close to the measured s) and the steady-state gain matched within 2%. These accuracies are consistent with prior findings (e.g. a similar DC motor first-order model predicted settling time within ~3.5% of actual). In simulation the identified transfer functions yielded speed responses virtually identical to the experimental data, confirming model validity. In conclusion, the Baldor L3510’s step-response dynamics can be well-approximated by simple low-order models. The first-order model suffices to capture the dominant behavior (gain and time constant), while the second-order form provides a slightly better fit to the transient shape. The identified transfer functions and parameters are based on sound measurement and established theory, making them reliable for subsequent control design and analysis of this motor.