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Hybrid Type-2 Fuzzy Logic–Extended Kalman Filter Approach for ITSC Fault Detection in PMSM Drives for Electric Vehicles Cover

Hybrid Type-2 Fuzzy Logic–Extended Kalman Filter Approach for ITSC Fault Detection in PMSM Drives for Electric Vehicles

Open Access
|Mar 2026

Figures & Tables

Figure 1.

Faulty phase equivalent circuit.

Figure 2.

T2-FL–EKF conceptual model. PMSM, permanent magnet synchronous motor; T2-FL–EKF, type-2 fuzzy logic–extended Kalman filter.

Figure 3.

EKF flow diagram. EKF, extended Kalman filter.

Figure 4.

T2-FL estimator configuration. T2-FL, type-2 fuzzy logic.

Figure 5.

T2-FL estimator structure. T2-FL, type-2 fuzzy logic.

Figure 6.

T2-FL membership functions configuration. T2-FL, type-2 fuzzy logic. (a) Input variables and (b) Output variable.

Figure 7.

Dynamic speed regression.

Figure 8.

Rotor angular velocity.

Figure 9.

Angular position.

Figure 10.

Iabc stator currents.

Figure 11.

Vector control currents.

Figure 12.

Stator resistance measurements. (a) μ = 25% and (b) μ = 50%.

Figure 13.

Fault current measurements. (a) μ = 25% and (b) μ = 50%.

Figure 14.

Rs estimation precision: (a) EKF approach, (b) FL–EKF approach and (c) T2-FL–EKF approach. T2-FL–EKF, type-2 fuzzy logic and extended Kalman filter; FL–EKF, fuzzy logic–extended Kalman filter.

ITSC fault current values_

For Rf = 1 ΩEstimated If moyMeasured If moyRMSE
μ = 25%0.01820.02160.2303
μ = 50%0.03210.04160.5513

Indication of ITSC severity_

µ (%)TfaultSeverityIndication
Rf = 1 Ωµ = 2540 turnsHighPoor visibility
µ = 5080 turnsExtremely highHigher visibility

T2-FL rule set for Rs determination_

E/ENMNSZPSPM
NMNMNMNSZPS
NSNMNSZPSPM
ZNSZZZPS
PSZPSPSPMPM
PMPSPMPMPMPM

Summary of comparative techniques under the same simulation conditions_

Control strategyRMSE of Rs estimationMAPE of Rs estimation (%)Estimation of RsPrecision
EKF0.0103781.8435MediumMedium
FL–EKF0.00669251.6348HighHigh
Proposed optimised method0.00664161.6101HighVery high
DOI: https://doi.org/10.2478/pead-2026-0004 | Journal eISSN: 2543-4292 | Journal ISSN: 2451-0262
Language: English
Page range: 61 - 78
Submitted on: Dec 9, 2025
Accepted on: Feb 8, 2026
Published on: Mar 16, 2026
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2026 Mabrouka Romdhane, Mohamed Naoui, Abdelmalek Gacem, Ali Mansouri, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution 4.0 License.