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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Sensorless Control of SPM Motor for e-Bike Applications Using Second-Order Integrator Flux Observer

by
Abdin Abdin
† and
Nicola Bianchi
*,†
Department of Electrical Engineering, University of Padova, 35131 Padova, Italy
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Designs 2026, 10(1), 2; https://doi.org/10.3390/designs10010002
Submission received: 12 October 2025 / Revised: 10 December 2025 / Accepted: 11 December 2025 / Published: 22 December 2025
(This article belongs to the Topic Advanced Electrical Machines and Drives Technologies, 3rd Edition)
Versions Notes

Abstract

The aim of this research is to present both a sensorless control and a torque derating algorithm in the overload region of a permanent magnet motor for e-bikes. First, the theoretical backgrounds and the field-oriented control are presented. Then, a sensorless control is designed based on the back-emf estimation with a second-order generalized integral flux observer for the permanent magnet motor. The second-order generalized integral flux observer is an adaptive filter which can eliminate the DC offset and strongly attenuate the harmonics of the estimated rotor flux. The algorithms have been simulated and then validated by means of tests on a permanent magnet motor for e-bikes.
Keywords: field oriented control; second order generalized integral flux observer; Park transformation; Clarke transformation; sensorless algorithm; phase locked loop; quadrature signal generator field oriented control; second order generalized integral flux observer; Park transformation; Clarke transformation; sensorless algorithm; phase locked loop; quadrature signal generator

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MDPI and ACS Style

Abdin, A.; Bianchi, N. Sensorless Control of SPM Motor for e-Bike Applications Using Second-Order Integrator Flux Observer. Designs 2026, 10, 2. https://doi.org/10.3390/designs10010002

AMA Style

Abdin A, Bianchi N. Sensorless Control of SPM Motor for e-Bike Applications Using Second-Order Integrator Flux Observer. Designs. 2026; 10(1):2. https://doi.org/10.3390/designs10010002

Chicago/Turabian Style

Abdin, Abdin, and Nicola Bianchi. 2026. "Sensorless Control of SPM Motor for e-Bike Applications Using Second-Order Integrator Flux Observer" Designs 10, no. 1: 2. https://doi.org/10.3390/designs10010002

APA Style

Abdin, A., & Bianchi, N. (2026). Sensorless Control of SPM Motor for e-Bike Applications Using Second-Order Integrator Flux Observer. Designs, 10(1), 2. https://doi.org/10.3390/designs10010002

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