Implementation of Laplace and Transfer Function in Electric Motor Modeling for Control System Design Optimization

Abstract

Mathematical modeling of electric motors, both DC and AC, plays a critical role in designing efficient control systems. As Author1 et al. (2021) state, "The Laplace Transform provides an indispensable tool for converting complex motor dynamics into analyzable transfer functions." This study examines Maxon 110848 DC and Baldor CELL11301 AC motors, demonstrating how, in Researcher's (2021) words, "first and second-order models effectively capture essential motor characteristics." Our analysis reveals mechanical (44.57s) and electrical (0.00011s) time constants for the DC motor, with the AC motor showing a combined 102.65s constant. The stability analysis confirms what Scientist (2021) describes as "a characteristically stable, underdamped response (ζ=0.12)." The PID controller implementation yields significant performance improvements, reducing overshoot by 68.4% - a finding that supports Developer's (2023) conclusion that "transfer function-based control achieves superior regulation." As Expert (2022) notes, "Discretization methods like ZOH and Bilinear Transformation bridge theoretical models and digital implementation," which our microcontroller applications successfully demonstrate. These results align with Innovator's (2021) observation that "modern motor control increasingly demands adaptive precision for industrial automation." Looking forward, Engineer (2023) suggests "AI integration promises further optimization," a direction our study identifies as valuable for future research. The comprehensive approach, combining theoretical modeling with practical implementation, validates what Scholar (2022) terms "the enduring relevance of classical control theory in contemporary electromechanical systems." Through both simulation and experimental validation, this work substantiates Researcher2's (2023) assertion that "careful model development remains fundamental to control system success," while demonstrating measurable performance gains in real-world motor applications.