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Energies
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20 December 2025

Robust Control of an Electrical Drive with a Flexible Joint Using PI Controllers Based on Torsional Torque Derivative Feedback

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1
Faculty of Electrical Engineering, Wrocław University of Science and Technology, PL50370 Wroclaw, Poland
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Department of System Design Engineering, Keio University, Yokohama 223-8522, Japan
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Author to whom correspondence should be addressed.
Energies2026, 19(1), 32;https://doi.org/10.3390/en19010032 
(registering DOI)
This article belongs to the Special Issue Drive System and Control Strategy of Electric Vehicle

Abstract

Electric drives are responsible for torque generation in most industrial processes and devices, including electromobility. The operational performance of industrial drives is often limited by torsional vibrations and time-varying load inertia. To address these challenges, this paper proposes and compares three robust control structures based on PI controllers augmented with additional feedback from the first and second derivatives of torsional torque. A higher-order integral disturbance observer (IDO) is employed to estimate the unmeasurable derivatives of torsional torque, enabling accurate compensation. Furthermore, a bio-inspired optimization algorithm (Britch-inspired Optimization Algorithm, BiOA) is utilized to determine the optimal gain coefficients for the PI controller and the additional feedback loops. The proposed methodologies are validated through simulations and experimental testing on a physical setup, demonstrating improved reference-trajectory tracking and enhanced torsional vibration suppression under varying load conditions.

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