Abdul Hadi, Rindilla Antika, M. Farhan, Akmal Arif Ridhi Putra, Diva Ramadhan

Least Square-Based Modelling of 0.5 HP Single-Phase Induction Motor

Introduction

Least square-based modelling of 0.5 hp single-phase induction motor. Precise Least Squares modeling of 0.5 HP single-phase induction motors. Validates control system performance with Simulink, showing low error and consistent responses.

Abstract

A single-phase induction motor is a cost-effective device for converting electrical energy into mechanical energy, making it widely used by small and medium-sized enterprises (SMEs). Understanding motor characteristics and analyzing control system performance requires precise mathematical modelling. Nevertheless, it is difficult to derive models from physical laws, and frequently overlooks fundamental elements like usage duration and environmental conditions. This study proposes using the Least Squares method to model a 0.5 HP single-phase induction motor. With an MSE of 0.0307 and an RMSE of 0.1753, the results demonstrate that the estimated model closely resembles the real system, with only minor errors. Simulink simulations demonstrate consistent delay time and settling time values across different input variations in both open and closed-loop tests. In closed-loop conditions, rise time was nonlinear, with the slowest response occurring at 220 V and the fastest at 190 V. In open-loop conditions, rise time increased linearly with input reference. These results demonstrate that, without requiring in-depth knowledge of the physical system, the Least Squares method offers a productive and useful way to create precise mathematical models of single-phase induction motors.

Review

This paper addresses the pertinent challenge of accurately modeling single-phase induction motors (SPIMs), which are ubiquitous in small and medium-sized enterprises. Recognizing the difficulties associated with deriving models from fundamental physical laws—particularly in accounting for real-world factors like usage duration and environmental conditions—the authors propose an elegant solution: applying the Least Squares method. This data-driven approach aims to create a precise mathematical model for a 0.5 HP SPIM, promising a pragmatic alternative to conventional methods that often demand extensive physical system knowledge. The choice of methodology is well-justified given the stated limitations of traditional modeling paradigms. The core findings presented are compelling and indicative of a robust model. The estimated model achieved a low Mean Squared Error (MSE) of 0.0307 and a Root Mean Squared Error (RMSE) of 0.1753, quantitatively demonstrating a close resemblance to the real system with minimal deviation. Further insights were gleaned from Simulink simulations across both open and closed-loop conditions. Notably, delay time and settling time exhibited consistent values regardless of input variations. The rise time, however, presented intriguing dynamics: it increased linearly with input reference in open-loop, but showed a nonlinear response in closed-loop, surprisingly being slowest at 220 V and fastest at 190 V, suggesting complex underlying system interactions that warrant further investigation. Overall, this study successfully showcases the utility and effectiveness of the Least Squares method as a productive tool for developing precise mathematical models of single-phase induction motors. Its primary strength lies in enabling accurate modeling without requiring an in-depth understanding of the intricate physical system, which significantly lowers the barrier to entry for engineers and researchers. The results provide valuable insights into the dynamic characteristics of SPIMs under various operating conditions and hold considerable practical implications for control system design and performance analysis, particularly for SMEs. This work represents a valuable contribution to the field, offering a straightforward yet powerful modeling technique.

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