Journal of Electrical, Marine and Its Application

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

Ahmad Raafi Fauzi — 2025-10-10

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 However, manufacturers typically do not publish detailed transfer functions for commercial motors, and the Baldor L3510’s dynamics in particular are undocumented.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.

Control of Brushless DC-Servomotors type 1226 012 B using PID-based second-order method

Ananda Ismul Azam — 2025-10-10

DC motors have an important role in various industrial and automation applications due to their ability to provide precise and accurate speed and torque control. Brushless DC-Servomotors type 1226 012 B is one such motor that is often used in systems that require high performance and reliability. To achieve optimal performance, an effective controller is necessary, and a PID (Proportional Integral Derivative) controller is a commonly used method due to its simplicity and effectiveness. This research aims to control the Brushless DC-Servomotors type 1226 012 B using a PID based second order method, which involves modeling the motor as a second order system and applying PID control to regulate the speed and position of the motor. Research methods include mathematical modeling of the motor, PID controller design, and simulation and experimentation to evaluate system performance. The second order model allows for a more accurate representation of the motor dynamics, aiding in the design of more effective controls. The findings from this study show that the second order model based PID control method is able to improve the transient response, stability, and reference following capability compared to the conventional control method. Interpretation of the simulation results shows that each component of the PID control contributes significantly in improving the performance of the DC motor. The benefit of this research is that it provides a more precise approach in the control of Brushless DC-Servomotors Motor type 1226 012 B, which can be applied in various industrial applications to improve system efficiency and reliability.

The Effect of Physical Parameters on the Transient and Steady-State Response of DC Motor Type Moog BN12HS-13AF-01 and Single-Phase AC Motor Type Simtach AC120M-11J30A

Davina Amani Fatihah — 2025-12-10

A core challenge in electromechanical control systems involves grasping how the physical characteristics of electric motors affect their dynamic behavior, especially in transient and steady-state scenarios. Factors like resistance, inductance, moment of inertia, and torque constant are essential in defining motor performance regarding speed, acceleration, and stability. This research intends to examine the impact of essential physical factors on the transient and steady-state behavior of two types of motors: the DC motor Moog BN12HS-13AF-01 and the single-phase AC motor Simtach AC120M-11J30A. This research's main contribution is the mathematical modeling and numerical simulation of electromechanical systems utilizing actual datasheet specifications. It assesses the time-domain reaction of each motor system to step input signals. The research contrasts open-loop and closed-loop scenarios for the DC motor with PID control and creates a simplified first-order model for the AC motor that accurately depicts its physical characteristics. The approach includes using Laplace transform to represent the continuous-time domain and Z-transform for digital discretization, ensuring compatibility with embedded digital control systems. Simulations utilize MATLAB/Simulink, and system performance is assessed through parameters like rise time, overshoot, settling time, and steady-state error. Findings indicate that parameters like the moment of inertia (J) and the damping coefficient (B) greatly influence the system response. The DC motor utilizing PID control in a closed-loop setup demonstrates significantly enhanced performance, featuring quicker response time and minimal steady-state error in comparison to its open-loop version. Conversely, the AC motor reacts more slowly and with less accuracy, yet maintains stability in uncomplicated scenarios. In summary, the physical traits of motors play a vital role in system performance, and choosing suitable parameters and control methods is crucial for attaining efficient, stable electromechanical systems.

Mathematical Modeling and Simulation of Open-Loop and Closed-Loop Second-Order DC Rotary Motor Type S-50-5

Fikri Adrian Putra — 2025-10-10

This study thoroughly discusses the mathematical modeling of DC motors in both open-loop and closed-loop systems, each of which has distinct characteristics and performance. The DC motor itself is one of the most crucial components in various industrial applications, such as production machinery, robotics, and automation systems, due to its ability to provide precise control over the shaft’s speed and position. In an open-loop system, the DC motor is controlled by applying a certain input voltage without any feedback mechanism from the resulting output. This makes the system response less accurate, slower, and more vulnerable to external disturbances or load variations because the system cannot automatically adjust to changes in environmental conditions or workload.

The mathematical model of the open-loop system is based on relatively simple differential equations, which directly describe the relationship between input voltage, current, and motor output speed, without accounting for any correction of output errors. In contrast, the closed-loop system employs a feedback mechanism to continuously monitor the motor output and correct it so that it always matches the desired reference value or setpoint. The mathematical model of the closed-loop system is typically more complex because it involves additional control elements, such as PID (Proportional-Integral-Derivative) controllers, which function to minimize steady-state errors, reduce overshoot, and enhance the system’s stability and response speed to changes.

Through simulations and performance analysis, this study demonstrates that the closed-loop system significantly outperforms the open-loop system, particularly in terms of transient response, disturbance tolerance, and overall system stability. These findings further underscore the importance of implementing feedback in DC motors to improve the effectiveness, efficiency, and reliability of the system in practical applications within the modern industrial world.

Mathematical Representation of the Dynamic System of the EUMA JY-1B-2 AC Motor

Alvian Dwi Prasetya — 2025-10-10

Single-phase induction motors are one of the most widely used AC motors in various light industrial and household applications. Although their construction is simpler than three-phase motors, the dynamic analysis of single-phase motors is more complex because they only produce an alternating magnetic field (not a rotating field) during starting, thus requiring auxiliary capacitors or additional windings. This study aims to represent the dynamic characteristics of single-phase induction motors in the form of a mathematical model and simulate it in MATLAB/Simulink environment to evaluate system performance. The mathematical representation is built based on a per-phase equivalent model in the form of a T-equivalent circuit, which includes stator, rotor, and magnetization impedances. Parameter data are obtained from the technical specifications of the EUMA JY-1B-2 motor. Simulations are performed with sinusoidal voltage input and the analysis focuses on changes in current and torque with respect to load. The simulation results show that the mathematical model is able to represent the motor's behavior dynamically and provides a valid basis for the development of control systems and energy efficiency in single-phase AC motors. This study also opens opportunities for the application of digital controllers in motor systems based on mathematical models.

Control of JY-09B-2 AC Motor Using Open Loop and Closed Loop Systems

Edwardo Pratenta Ginting — 2025-10-10

In this era of rapid technological development, innovation in engineering is increasingly dominating various industrial sectors. One crucial approach to improving system performance is through optimization, which aims to achieve optimal system conditions in terms of both efficiency and stability. System optimization is not limited to improving energy efficiency but also involves precise dynamic control, such as in the AC motor system of the JY-09B-2 type, which is widely used in industrial and robotic applications due to its fast dynamic response and stable torque. This study analyzes the performance comparison between open-loop and closed-loop control systems in the JY-09B-2 AC motor. The open-loop system was tested with a constant voltage supply without feedback, while the closed-loop system utilized an encoder sensor as speed feedback combined with a PID (Proportional-Integral-Derivative) controller to correct errors. The experimental results show that the closed-loop system can reduce steady-state error by up to 90% compared to the open-loop system, as well as improve resistance to load disturbances (load disturbance rejection). However, the open-loop system remains superior in terms of implementation simplicity for applications that do not require high precision. This study provides guidance on selecting the optimal control strategy based on application requirements.

Perancangan Sistem Kontrol Kecepatan Motor DC Moog C23-L23 Winding 50 Berbasis PID

Ary Pratama Paluga — 2025-10-10

The DC motor is widely applied in industrial systems due to its precise speed control characteristics. However, controlling the speed of the Moog C23-L23 Winding 50 DC motor under various loads remains a challenge due to its nonlinear behavior and external disturbances. This study aims to design a Proportional-Integral-Derivative (PID) controller to optimize the speed control of the Moog C23-L23 motor by minimizing steady-state error and improving response time.

The contribution of this research is the development and evaluation of a PID controller tuned using the Ziegler-Nichols method and tested through simulation and real-time implementation. The designed controller ensures improved stability and performance under varying load conditions.

The methodology consists of deriving the transfer function of the motor system using system identification techniques, implementing a PID control algorithm, and conducting performance evaluation through simulation in MATLAB/Simulink. The motor's speed response is analyzed based on standard time-domain performance criteria, including rise time, settling time, overshoot, and steady-state error.

The results indicate that the PID controller successfully regulates motor speed with minimal overshoot and fast settling time. The achieved accuracy demonstrates a significant improvement compared to the uncontrolled system. In conclusion, the designed PID-based control system is effective for dynamic speed regulation of the Moog C23-L23 motor and is suitable for industrial applications requiring precise motor control. Future work will include adaptive and robust control strategies to further enhance performance.

Comparison of Dynamic Response Between Maxon DCX 35 L DC Motor and WEG W22 Single Phase AC Motor Using Second Order Transfer Function Based on MATLAB Simulation.

Mohamad Sufyan Tegar Pratama — 2025-10-10

Accurate modeling of electric motors is essential in control system design to ensure reliable and efficient performance, especially for systems requiring precision and responsiveness. This study compares the dynamic response characteristics of two commonly used electric motors: the Maxon DCX 35 L direct current (DC) motor and the WEG W22 single phase alternating current (AC) motor. Both motors are modeled using a second order transfer function approach derived from their respective datasheets. The modeling process involves identifying electrical and mechanical parameters such as resistance, inductance, moment of inertia, torque constant, and friction coefficient. These parameters are incorporated into mathematical formulations based on Kirchhoff’s and Newton’s laws and converted into Laplace domain transfer functions. The simulation was performed in MATLAB/Simulink using a unit step input under closed loop conditions. The system response was evaluated based on key performance metrics such as rise time, settling time, peak value, and steady state error. Compared to the AC motor, the DC motor model exhibited a significantly faster response, with a rise time and settling time approximately 30–35% shorter. Both systems showed zero overshoot and high stability. The DC motor’s dynamic behavior is more suitable for applications requiring rapid control response, while the AC motor provided smoother convergence albeit with slower system dynamics. This comparative modeling study provides insight into how different motor types respond to control inputs under similar second order system assumptions. The results serve as a practical reference for selecting appropriate motor types in control applications that demand specific time domain behaviors.

Mathematical Representation and Simulation of DC054B-5 Motor Dynamic System for Control System Applications

Muhammad Ihsan P. — 2025-09-10

This paper presents the mathematical representation and simulation of the DC054B-5 motor dynamic system, aimed at facilitating the development and implementation of effective control systems. The modeling process begins with the formulation of the electrical, mechanical, and electromechanical components of the motor using fundamental physical laws, including Kirchhoff’s voltage law for the electrical circuit and Newton’s second law for the rotational system. These models are then integrated and transformed into the s-domain using Laplace transformation to derive the motor’s transfer function, representing the relationship between input voltage and angular velocity.

Key parameters such as armature resistance, inductance, torque constant, and moment of inertia are determined through datasheet analysis and supporting calculations. The derived transfer function is used to simulate the system’s behavior under various conditions. Both first-order and second-order models are analyzed to capture the motor’s transient and steady-state characteristics. The simulation is carried out using MATLAB/Simulink in open-loop and closed-loop configurations to evaluate system response, stability, and performance under feedback control.

The results demonstrate that the mathematical model accurately reflects the real behavior of the motor and provides a reliable basis for control design. The analysis also highlights the importance of parameter estimation and model reduction in simplifying system dynamics without significant loss of fidelity. This work contributes to the design of control strategies for DC motors in industrial and academic applications, offering a robust framework for further development in motor control and system identification.

Mathematical Modeling and System Response Analysis of FABL3640-12-V1 DC Motor Using First and Second Order Approaches

Fahrur Rozi — 2025-10-10

Mathematical modeling of DC motors plays a crucial role in designing accurate and efficient control systems. This study aims to analyze and compare first-order and second-order mathematical models of a DC motor, specifically the FABL3640-12-V1 type, to evaluate their performance and suitability for control system applications. The modeling process involves identifying motor parameters, including input voltage, nominal current, torque constant, armature resistance, inductance, and moment of inertia. These parameters are then used to derive the transfer functions in the Laplace domain.

Simulation and validation are conducted using MATLAB/Simulink to observe each model's response to a unit step input. The first-order model, due to its simplicity, produces a faster response with a rise time of approximately 0.0015 seconds and a settling time of 0.0042 seconds. However, it lacks the ability to reflect the physical dynamics of the motor, especially inertia and damping effects, resulting in an idealized but less realistic performance profile. In contrast, the second-order model includes mechanical dynamics, such as inertia and viscous friction, leading to a slightly slower response (rise time of 0.0022 seconds and settling time of 0.0056 seconds), but a significantly more accurate and stable representation of the motor’s behavior.

The findings confirm that while the first-order model is beneficial for basic or embedded control applications requiring fast computation, the second-order model is more appropriate for precision control systems where dynamic accuracy and stability are essential. The study highlights the importance of selecting the appropriate model order to balance computational efficiency and physical realism in control system design.