Utilization of Laplace Transform in Mathematical Modeling of Brushless DC-Servomotors type 1226 012 B and Single-phase AC motors type CSR 90S

Abstract

The precise control of electric motors, particularly Brushless DC-Servomotors (BLDC) type 1226 012 B and AC single-phase motors type CSR 90S, is central to improving automation systems and industrial applications. However, the inherent complexity of these motors’ dynamic behaviors poses significant challenges to accurate mathematical modeling and subsequent control design. This study addresses the problem of developing robust and efficient mathematical models for these motor types, which are critical for system analysis, simulation, and controller development. The principal aim of this research is to utilize Laplace Transform techniques to derive and analyze mathematical models of BLDC and AC single-phase motors, focusing on the dynamic and transient responses under different operational conditions. By formulating the governing differential equations and employing the Laplace Transform, this work streamlines the transition from time-domain analysis to the more tractable frequency-domain approach. The main contribution of this research lies in the development of validated transfer function representations for both the Brushless DC-Servomotors 1226 012 B and the AC single phase Motor type CSR 90S, enabling precise prediction of system responses and performance indices such as rise time, settling time, and steady-state error. In addition, the results will show that the Laplace-based model accurately captures realistic motor behavior, as validated through experimental testing under step input and load disturbance scenarios. The developed model offers reliable prediction capabilities and serves as a solid foundation for advanced control and simulation. In conclusion, the application of Laplace Transform significantly improves the modeling and analysis process for both types of motors, paving the way for optimized control strategies in practical applications.