Journal of Electrical, Marine and Its Application

Analysis of First-Order and Second-Order Modeling of the FESTO EMMT-AS-80-S-LS-RM DC Servo Motor Using MATLAB/Simulink

Mohammad Dimas Ardiansyah — 2026-04-07

This study focuses on the mathematical modeling and simulation of the FESTO DC servo motor, type EMMT-AS-80-S-LS-RM, using both first-order and second-order approaches. The main objective is to evaluate the accuracy and effectiveness of each model in representing the motor’s dynamics, both in open-loop and closed-loop systems. The modeling process is based on the motor’s technical parameters obtained from its datasheet, utilizing linear differential equations that are simplified into transfer functions. The first-order model is represented as a linear system without considering full inertia, while the second-order model incorporates the complete electromechanical dynamics of the system. Simulations were implemented in the MATLAB/Simulink environment, with a 24 V step input signal. The simulation results indicate that both the first-order and second-order models yield a steady-state angular velocity of 6.957 rad/s. However, theoretical calculations show a value of 314.16 rad/s, resulting in a deviation or error of 44.15%. This discrepancy suggests a unit mismatch and highlights the need for parameter validation and model calibration. Despite this, the second-order model demonstrates more realistic dynamic characteristics compared to the first-order model, especially in transient response. Therefore, the second-order model is recommended for precision control applications, while the first-order model is more suitable for initial design stages and educational purposes. This study also confirms that MATLAB/Simulink is an effective tool for the analysis and development of model-based control systems.

Mathematical Modeling of Mitsumi M36N-4E DC Motor and Fujita ML7122 AC Motor

Dimas Bayu Dwi Saputra — 2026-04-07

Mathematical modeling of electric motors is a critical foundation for developing automatic control systems. This research models the dynamic characteristics of a Mitsumi M36N-4E DC motor and a Fujita ML7122 single-phase AC motor using Laplace transforms and transfer functions. Motor characteristic data were extracted from datasheets to construct differential models and simulate system responses in MATLAB. The DC motor was analyzed in open-loop and closed-loop configurations with PID control, while the AC motor was modeled using the rotating field (dq-axis) approach to address nonlinearities.

Simulation results demonstrate that the DC motor achieved 96.8% accuracy in closed-loop response, whereas the AC motor required coordinate transformation to improve model precision. The contributions of this study include: (1) modeling without feature extraction, (2) an adaptive training scheme for orientation variations, and (3) embedded system implementation with a computational time of <200 ms. These findings can be applied to prosthetics, robotics, and industrial applications, while also serving as a foundation for control system design and electric motor performance optimization.

Thus, this research not only provides accurate mathematical models for both motor types but also offers a framework for developing advanced and efficient control systems.

Comparative Study of Electromechanical Models for Crouzet DC Motor and Mitsubishi Single-Phase AC Motor Using System Identification Methods

Alfareza Dicky Saputra — 2026-04-07

This study presents a comparative analysis of the electromechanical models for the Crouzet DC Motor 82800502 and the Mitsubishi Electric SC-QR 1/2 HP single-phase AC motor using system identification methods. The research focuses on developing mathematical models for both motors, employing Laplace transforms, differential equations, and transfer functions to characterize their dynamic behaviors. The Crouzet DC motor, with its linear and direct current control, is modeled using electrical and mechanical equations, highlighting parameters such as armature resistance (3.9 Ω), inductance (9.35 mH), and torque constant (0.0627 Nm/A). The Mitsubishi AC motor, a capacitor-start induction motor, is analyzed through dq-axis transformations, incorporating stator resistance (4 Ω), inductance (162 mH), and slip-dependent torque characteristics.

System identification techniques, including experimental, analytical, and parameter estimation methods, are applied to derive accurate models for both motors. The DC motor's transient response, with a mechanical time constant of 15 ms, demonstrates faster dynamics compared to the AC motor, which exhibits slower transient behavior due to its starting capacitor and rotational inertia. Steady-state analysis reveals that the AC motor achieves higher efficiency (70%) under nominal conditions, while the DC motor operates at 54% efficiency. Stability assessments, conducted through Laplace domain analysis and MATLAB simulations, confirm the DC motor's superior stability in precision applications, whereas the AC motor requires careful consideration of starting transients.

The study also explores block diagram reduction techniques to simplify the models for controller design, such as PID and adaptive control strategies. Practical implications for microcontroller-based implementations are discussed, emphasizing the trade-offs between dynamic response, efficiency, and control complexity. The findings provide valuable insights for selecting and optimizing motor systems in industrial and household applications, based on performance requirements and operational constraints.

Mathematical modeling of MITSUBISHI ELECTRIC AC motor TYPE SCL-QR 1HP 4P 1PHASE order 1 and order 2

Muhammad Toriq Aghil1 — 2026-04-07

Single-phase AC motors are widely used in industrial and household applications due to their simplicity, but their mathematical modeling is often complex due to nonlinearities and unbalanced magnetic field effects. The main challenge is to simplify the dynamic model of this motor to facilitate system response analysis, controller design, and performance optimization without compromising accuracy. This study aims to develop a mathematical model of the Mitsubishi Electric SCL-QR 1HP 4P single-phase AC motor in first and second-order representations. The model is designed to predict the motor's response to voltage and load variations and serves as a foundation for designing more efficient control systems. The key contributions of this research are: 1. Simplification of the single-phase AC motor dynamic model into first and second-order forms, considering electrical parameters (stator resistance, inductance) and mechanical parameters (moment of inertia, torque).

Comparative analysis of the performance of first and second-order models in predicting transient and steady-state responses. 3. Model validation through MATLAB/Simulink simulations to ensure consistency with the motor's technical data. The research methodology includes: 1. Mathematical modeling based on differential equations and Laplace transforms for transfer functions.
Identification of motor parameters from the datasheet (e.g., stator resistance

, inductance , moment of inertia

Simulation of system responses to step and ramp inputs using MATLAB/Simulink. The results show: 1. The first-order model yields a faster settling time ( seconds) but is less accurate in capturing high-frequency dynamics. 2. The second-order model is more precise, with an overshoot of 8.5% and a settling time of , and can predict resonance at a frequency of 3. The second-order transfer function: , with simulation accuracy reaching 96.8%

The second-order model is more effective for analyzing the dynamics of the SCL-QR 1HP 4P single-phase AC motor, especially in applications requiring high-frequency response. The first-order simplification can be used for quick estimations with certain error tolerances. These findings provide a foundation for developing PID or adaptive controllers to enhance motor performance under various operating conditions.

Analysis of the Transfer Function of a DC Motor HC785LP-012 as a Learning Medium for Fundamentals Basic Control Systems

Muhammad ‘Athaya Akhdan — 2026-04-07

A key obstacle in teaching introductory control systems is the challenge students encounter in connecting abstract mathematical concepts to tangible real-world applications. Transfer function analysis, while foundational, is often viewed as excessively theoretical and detached from practical engineering contexts. Without accessible and relatable examples, students may struggle to understand critical control system behaviors, including stability, damping, and dynamic response. This study seeks to evaluate the transfer function of a DC motor and illustrate its efficacy as a practical and engaging educational tool in foundational control systems courses. The DC motor is selected due to its simplicity, cost-effectiveness, and widespread use in both academic and industrial settings. The primary contribution of this research lies in the development and simulation-based evaluation of a second-order transfer function for a standard DC motor. This model serves as an educational framework, enabling students to explore time-domain and frequency-domain responses while solidifying their understanding of fundamental control principles. The transfer function is derived by applying the Laplace transform to the motor’s electrical and mechanical dynamics. Python-based simulations are employed to analyze the system, including step response evaluation and Bode plot analysis. Key system parameters, such as steady-state gain, damping ratio, natural frequency, rise time, and settling time, are calculated to assess system performance. The analysis reveals a steady-state gain of 0.408, a damping ratio (ζ) of approximately 0.7, and a natural frequency (ωₙ) of 14.7 rad/s. The step response achieves 95% of its steady-state value within 0.25 seconds, exhibiting minimal overshoot and confirming the system’s stable, well-damped characteristics. The findings affirm that the DC motor’s transfer function is an effective pedagogical tool for bridging theoretical concepts and practical applications. This approach fosters enhanced student engagement and a deeper understanding of control systems fundamentals

Mathematical Modeling and Simulation of the Brushless DC Motor DF45M024053-A2 for Control Applications

Edwardana Frans Try Paska Hutajulu — 2026-04-07

This paper presents the mathematical modeling and simulation of the Brushless DC (BLDC) motor DF45M024053-A2, aiming to support the development, analysis, and implementation of reliable and effective control systems. The modeling process begins with the systematic formulation of both the electrical and mechanical subsystems of the motor. For the electrical part, Kirchhoff’s voltage law is applied to represent the circuit dynamics, while for the mechanical subsystem, Newton’s second law of motion is used to describe the rotor’s rotational dynamics under the influence of torque and inertia.

These two subsystems are then integrated into a unified electromechanical model, which is subsequently transformed into the s-domain using the Laplace transform. This process results in a comprehensive transfer function that characterizes the relationship between the input voltage and the motor's angular velocity, providing a foundation for dynamic analysis and control design.

Key parameters including armature resistance, phase inductance, back EMF constant, torque constant, friction coefficient, and rotor inertia are obtained from the motor datasheet and validated through supporting calculations where necessary. Using this mathematical model, the motor’s behavior is simulated under both open-loop and closed-loop conditions in MATLAB/Simulink, allowing observation of its transient and steady-state performance.

Both first-order and second-order models are developed to compare dynamic responses and highlight the trade-offs between model simplicity and accuracy. The results demonstrate that the derived model accurately reflects the real-world dynamics of the motor and is suitable for control system development. This study also emphasizes the significance of parameter identification and model order reduction in optimizing system performance without compromising essential dynamic characteristics

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

Maulana Latif — 2026-04-07

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.

First and Second Order Mathematical Modeling of the JY-3A-4 AC Motor Based on Step Response

Mario Saputra — 2026-04-07

Accurate mathematical modeling plays a vital role in the analysis and design of control systems, especially for applications that demand precision, such as industrial automation and robotics. This study focuses on developing and comparing first-order and second-order mathematical models of the JY-3A-4 single-phase AC motor, based on its step response behavior. A step input voltage was applied to the motor, and the resulting rotational speed was recorded using an optical sensor connected to a microcontroller-based data acquisition system.

The first-order model provides a basic approximation of the motor’s response and is commonly used for simplified analysis. Meanwhile, the second-order model offers a more detailed representation, capturing dynamic behaviors such as oscillations, overshoot, and settling characteristics. Both models were derived from experimental data using time-domain analysis methods.

The results show that the second-order model more accurately reflects the real behavior of the motor, particularly in its transient response. It demonstrates faster rise time, shorter settling time, and a closer fit to the experimental data, with significantly lower error compared to the first-order model. The presence of overshoot and damped oscillation observed in the actual motor response is better captured using the second-order approach.

This study emphasizes the importance of choosing the appropriate model order for motor control applications. While a first-order model may suffice for systems that do not require high precision, a second-order model is more suitable for designing advanced control systems where accuracy and stability are critical. The findings contribute to the improvement of modeling practices for AC motors and support the development of more efficient and reliable control systems in practical applications.

Dynamic Modeling of Single-Phase EMMS-AS-100-L-HS-RR DC Motor for Control System Design

Nanda Rachmad Hidayahtullah1 — 2026-04-07

The mathematical modeling of DC motors is essential for the development of effective control systems in industrial and robotic applications. This study presents the transfer function modeling and simulation of the DC motor EMMS-AS-100-L-HS-RR using fundamental principles of electrical and mechanical system analysis. The motor’s dynamic behavior was described using first-order differential equations derived from its electrical armature circuit and mechanical rotational dynamics. Key parameters such as armature resistance, inductance, back-EMF constant, torque constant, moment of inertia, and damping coefficient were extracted and converted appropriately to SI units to suit the modeling framework. The system's transfer function was obtained in the Laplace domain and analyzed to observe the relationship between input voltage and angular velocity. MATLAB/Simulink was utilized to simulate the system’s time-domain response, allowing validation against expected dynamic characteristics. The modeling results demonstrated that the DC motor system exhibits a typical first-order lag behavior with a dominant time constant and steady-state gain that can be used as a reference in control system design, especially for speed regulation. Furthermore, this study highlights the importance of accurate parameter estimation from datasheets and provides a systematic approach for converting non-standard units commonly found in manufacturer specifications. The developed model can serve as a foundation for further implementation of closed-loop controllers such as PID or state-feedback control. The results of this research can be applied in real-time embedded system development for automation processes involving precision DC motors.

Modeling of the DC Motor Maxon RE 15

Gerard Christofel Abimanyu Bramantyo — 2026-04-07

The increasing demand for lightweight, efficient, and accurate actuators in automation and educational platforms highlights the need for validated mathematical models of DC motors. The Maxon RE 15 a brushed DC motor offers high efficiency and compactness, making it widely applicable in mechatronics, robotics, and marine instrumentation systems. Despite its popularity, comprehensive dynamic models incorporating both electrical and mechanical dynamics for this motor are not widely documented in literature. This study presents a structured approach to modeling and simulating the Maxon RE 15 DC motor using transfer function and state-space representations based on Kirchhoff’s and Newton’s laws. Parameters such as resistance, inductance, back-EMF constant, and rotor inertia were derived from datasheet analysis and validated through experimental testing. MATLAB/Simulink was used for model implementation, and both open loop and PID controlled closed-loop simulations were conducted. Results indicate that the closed-loop model achieved a rise time of 0.18 seconds and reduced overshoot to 3.1%, with model accuracy validated against hardware measurements showing less than 5% deviation. This model supports control algorithm development and serves as a reference for embedded system design and electrical engineering education.