Validation of DC and AC 1 Phase Mathematical Model of Motors with System Identification Method and MATLAB/Simulink Simulation

Abstract

Mathematical modeling of DC and single-phase AC motors is an important step in the analysis and design of control systems, but the complexity of nonlinearities and parameter variations often leads to inaccuracies in physics-based models. The main problem in this research is the lack of validation of the mathematical models of the BCI-52.XX DC motor and the SCL-QR 1HP 4P single-phase AC motor against experimental data, as well as the need to optimize control system performance by considering complex electromechanical dynamics. The objective of this research is to validate the mathematical models of both motors using system identification methods and Matlab/Simulink simulations, as well as to analyze their dynamic responses under various operating conditions. The main contributions of this research include: Development of accurate mathematical models for DC and single-phase AC motors by combining Laplace transform and transfer function approaches, Implementation of system identification methods such as least squares and prediction error method (PEM) to extract empirical parameters and A comparative analysis between simulation results and technical data from motor datasheets. The methods used involve dynamic modeling of the DC motor with electromechanical equations (armature resistance , inductance , torque constant  and the single-phase AC motor using a rotating field model (slip , nominal torque . Simulations were conducted using Matlab/Simulink to evaluate transient and steady-state responses, including a DC motor rise time of 0.12 seconds and 8.5% overshoot. The research results show that the validated mathematical models have high accuracy, with errors of less than 5% compared to experimental data, as well as consistent performance under various loads (DC motor speed stabilized at 377 rad/s). Additionally, system parameter identification demonstrates that analytical and experimental methods yield consistent parameter values, such as the DC motor rotor inertia ( ) and the back-EMF constant (  in the AC motor. The conclusion of this research confirms that the validated mathematical models can serve as a reliable basis for designing PID or adaptive controllers, while emphasizing the importance of integrating theoretical modeling and empirical validation in motor system optimization. Practical implications include cost savings in physical testing and improved reliability of control systems in industrial applications.

Abstract   Mathematical modeling of DC and single-phase AC motors is an important step in the analysis and design of control systems, but the complexity of nonlinearities and parameter variations often leads to inaccuracies in physics-based models. The main problem in this research is the lack of validation of the mathematical models of the BCI-52.XX DC motor and the SCL-QR 1HP 4P single-phase AC motor against experimental data, as well as the need to optimize control system performance by considering complex electromechanical dynamics. The objective of this research is to validate the mathematical models of both motors using system identification methods and Matlab/Simulink simulations, as well as to analyze their dynamic responses under various operating conditions. The main contributions of this research include: Development of accurate mathematical models for DC and single-phase AC motors by combining Laplace transform and transfer function approaches, Implementation of system identification methods such as least squares and prediction error method (PEM) to extract empirical parameters and A comparative analysis between simulation results and technical data from motor datasheets. The methods used involve dynamic modeling of the DC motor with electromechanical equations (armature resistance , inductance , torque constant  and the single-phase AC motor using a rotating field model (slip , nominal torque . Simulations were conducted using Matlab/Simulink to evaluate transient and steady-state responses, including a DC motor rise time of 0.12 seconds and 8.5% overshoot. The research results show that the validated mathematical models have high accuracy, with errors of less than 5% compared to experimental data, as well as consistent performance under various loads (DC motor speed stabilized at 377 rad/s). Additionally, system parameter identification demonstrates that analytical and experimental methods yield consistent parameter values, such as the DC motor rotor inertia ( ) and the back-EMF constant (  in the AC motor. The conclusion of this research confirms that the validated mathematical models can serve as a reliable basis for designing PID or adaptive controllers, while emphasizing the importance of integrating theoretical modeling and empirical validation in motor system optimization. Practical implications include cost savings in physical testing and improved reliability of control systems in industrial applications.