Physics-Informed Hybrid ANN-P&O Optimal-Flux Control for Energy-Efficient Induction Motor Drives

Abstract

This paper proposes a physics-informed hybrid artificial neural network (ANN) and perturb-and-observe (P&O) optimal-flux controller for reducing losses in a field-oriented induction motor drive. The ANN rapidly estimates the optimal rotor-flux reference from measured operating variables, and a bounded P&O search locally refines this estimate using averaged input power. Paired MATLAB/Simulink simulations under a common 20 s operating profile show that the proposed controller reduces average loss power and input energy relative to constant-flux field-oriented control while maintaining low steady-state flux-command ripple. A coefficient-sensitivity study indicates positive calculated energy savings across the evaluated core-loss range. The results are limited to simulation; experimental parameter identification and hardware validation remain necessary.

Introduction

The text presents a physics-informed hybrid ANN–P&O loss-minimization controller for induction motors. Induction motors are reliable and inexpensive, but conventional field-oriented control (FOC) keeps rotor flux near its rated value, which causes unnecessary copper and iron losses, particularly at light loads.

Existing loss-minimization methods have limitations. Model-based methods depend on accurate motor and loss parameters, which can vary with temperature and magnetic saturation. Perturb-and-observe (P&O) methods require less modeling but can converge slowly and produce steady-state oscillations. Artificial neural networks (ANNs) offer fast flux estimation but may perform poorly outside their training conditions.

To combine the advantages of both approaches, the proposed method uses an ANN to rapidly predict the optimal rotor flux and a bounded adaptive P&O algorithm to make a small online correction. The ANN is trained using optimal flux targets generated from a physics-based loss model that accounts for stator copper, rotor copper, and iron losses.

The main features of the proposed controller are:

• A four-input ANN using motor speed, electromagnetic torque, d-axis current, and q-axis current.

• One hidden layer containing 64 neurons with tanh activation.

• Offline generation of optimal rotor-flux targets by minimizing the modeled motor losses over a bounded flux range.

• Online P&O refinement based on 50 ms averaged total input power. μs simulation step. Five controllers—constant-flux FOC, Loss Model Control, conventional P&O, ANN-only, and the proposed Hybrid ANN–P&O—were evaluated under identical

• Adaptive P&O step sizes of 0.003, 0.0015, and 0.0005 Wb, depending on the magnitude of power variation.

• P&O operation restricted to ±0.015 Wb around the ANN estimate.

• Filtering of ANN inputs and output, together with a 1 Wb/s flux-rate limiter, to reduce ripple and abrupt changes.

• Torque-dependent minimum flux limits to maintain safe motor operation.

The induction-motor model is developed in the abc, αβ, and dq reference frames. Under rotor-field orientation, rotor flux is aligned with the d-axis. The analysis shows that total motor loss can be represented approximately as

Ploss(ψr)=K1ψr2+K2ψr2,

which has a unique minimum. As the load torque decreases, the optimal rotor flux also decreases, allowing both iron and copper losses to be reduced.

The ANN was trained using 99,894 samples and achieved a test RMSE of 0.01918 Wb, MAE of 0.01107 Wb, and correlation coefficient R=0.99205. The complete controller was implemented in MATLAB/Simulink R2024b with a 2 μs simulation step. Five controllers—constant-flux FOC, Loss Model Control, conventional P&O, ANN-only, and the proposed Hybrid ANN–P&O—were evaluated under identical operating conditions.

Conclusion

This paper presented a physics-informed Hybrid ANN-P&O optimal-flux strategy for loss-minimizing field-oriented control of an induction motor drive. The method combines constrained loss-model target generation, rapid ANN-based flux prediction, bounded P&O refinement, input and output filtering, torque-dependent flux constraints, and flux-command rate limiting. Under the paired MATLAB/Simulink R2024b simulations, the proposed controller reduced average loss power from 3943.80 W to 3744.53 W and increased average efficiency from 64.657% to 65.777% relative to constant-flux FOC. Input energy over the 20 s profile decreased by 1.9442%, and average d-axis current decreased from 27.666 A to 21.725 A. The filtered flux command exhibited 0.00063 Wb steady-state ripple and a 0.12230 s settling time. The deployed ANN achieved test RMSE = 0.01918 Wb, MAE = 0.01107 Wb, MAPE = 1.5116%, R2 = 0.98416, and R = 0.99205. The controller\'s nominal energy saving was comparable to ANN-only and slightly lower than Loss Model Control; therefore, no claim of universal superiority is made. Future work should identify the loss coefficients experimentally, test parameter and measurement mismatch explicitly, compare computational burden, and validate the controller on a DSP- or FPGA-based drive platform.

References

[1] R. Abdelati and M. F. Mimouni, \"Optimal control strategy of an induction motor for loss minimization using Pontryaguin principle,\" European Journal of Control, vol. 49, pp. 94-106, 2019, doi: 10.1016/j.ejcon.2019.02.004. [2] A. El Fadili, F. Giri, A. El Magri, R. Lajouad, and F. Z. Chaoui, \"Towards a global control strategy for induction motor: Speed regulation, flux optimization and power factor correction,\" International Journal of Electrical Power & Energy Systems, vol. 43, no. 1, pp. 1082-1096, 2012, doi: 10.1016/j.ijepes.2012.05.022. [3] A. El Fadili, F. Giri, A. El Magri, R. Lajouad, and F. Z. Chaoui, \"Adaptive control strategy with flux reference optimization for sensorless induction motors,\" Control Engineering Practice, vol. 26, pp. 91-106, 2014, doi: 10.1016/j.conengprac.2013.12.005. [4] D. H. Kim and K. Hirota, \"Vector control for loss minimization of induction motor using GA-PSO,\" Applied Soft Computing, vol. 8, no. 4, pp. 1692-1702, 2008, doi: 10.1016/j.asoc.2006.09.001. [5] S. Sujitjorn and K.-L. Areerak, \"Numerical approach to loss minimization in an induction motor,\" Applied Energy, vol. 79, no. 1, pp. 87-96, 2004, doi: 10.1016/j.apenergy.2003.11.001. [6] A. Arias, L. Romeral, E. Aldabas, and M. Jayne, \"Stator flux optimised Direct Torque Control system for induction motors,\" Electric Power Systems Research, vol. 73, no. 3, pp. 257-265, 2005, doi: 10.1016/j.epsr.2004.06.014. [7] K. Rai, S. B. L. Seksena, and A. Thakur, \"A Golden Section Search Algorithm Based Loss Minimization for Induction Motor Drive,\" International Journal on Electrical Engineering and Informatics, vol. 11, no. 1, pp. 159-177, 2019, doi: 10.15676/ijeei.2019.11.1.9. [8] C. Chen, H. Yu, F. Gong, and H. Wu, \"Induction Motor Adaptive Backstepping Control and Efficiency Optimization Based on Load Observer,\" Energies, vol. 13, no. 14, Art. no. 3712, 2020, doi: 10.3390/en13143712. [9] F. Tazerart, Z. Mokrani, D. Rekioua, and T. Rekioua, \"Direct torque control implementation with losses minimization of induction motor for electric vehicle applications with high operating life of the battery,\" International Journal of Hydrogen Energy, vol. 40, no. 39, pp. 13827-13838, 2015, doi: 10.1016/j.ijhydene.2015.04.052. [10] S. Karpe, S. A. Deokar, and A. M. Dixit, \"Switching losses minimization by using direct torque control of induction motor,\" Journal of Electrical Systems and Information Technology, vol. 4, no. 2, pp. 225-242, 2017, doi: 10.1016/j.jesit.2016.08.007. [11] L. M. Phuong, L. D. Dung, N. V. Thuyen, and N. H. Phong, \"Real-time loss minimization control in induction machines based on DSP TMS320LF2812,\" Science & Technology Development Journal, vol. 16, no. K4, pp. 5-15, 2013. [12] B. Hima Deepthi, P. Srinivasa Varma, M. Kiran Kumar, and K. V. Govardhan Rao, \"An Enhanced Loss Model Based Online Flux Optimization Technique for Vector-Controlled Induction Motor Drives Including Leakage Inductance,\" International Journal of Electrical and Electronics Research, vol. 14, no. 1, pp. 110-122, 2026, doi: 10.37391/ijeer.140112. [13] S. S. Sivaraju, T. Senthilkumar, R. Sankar, T. Anuradha, S. Usha, and I. B. Musirin, \"Improving the efficiency of induction motor drive by flux and torque control: A hybrid LSE-RERNN approach,\" ISA Transactions, vol. 147, pp. 215-226, 2024, doi: 10.1016/j.isatra.2024.01.034. [14] R. C. B. Rego, C. A. Diniz, J. J. Eckert, and L. C. A. Silva, \"An adaptive unscented Kalman Filter with nonlinear model predictive control based on reinforcement learning for the induction motor control in electric vehicles,\" Engineering Applications of Artificial Intelligence, 2026, doi: 10.1016/j.engappai.2026.115363. [15] U. K. Potnuru, S. K. Teegala, L. R. Kalabarige, V. Ippili, and M. R. Holla, \"Dataset for optimized design parameters of three-phase induction motors with validation through machine learning,\" Data in Brief, vol. 63, Art. no. 112274, 2025, doi: 10.1016/j.dib.2025.112274. [16] A. D Amico, S. Longo, M. Cellura, M. Caruso, and R. Miceli, \"Environmental benefits and impacts forecasting for three-phase induction motors operations in marine applications: A multiple linear regression approach,\" Energy Reports, 2026, doi: 10.1016/j.egyr.2025.12.025. [17] A. Kalinov, V. Melnykov, M. Z. Qawaqzeh, M. Zagirnyak, A. Szczesny, and E. Korzeniewska, \"The methods and systems of Fault-Tolerant frequency vector control of induction motors in case of the stator circuit damage,\" International Journal of Electrical Power & Energy Systems, 2025, doi: 10.1016/j.ijepes.2025.110974. [18] A. Kasri, K. Ouari, Y. Belkhier, D. Ziane, M. F. Benkhoris, and M. Benbouzid, \"Optimized voltage vector selection for dual-star induction motor: Robust predictive direct torque control-based hysteresis-free approach,\" ISA Transactions, 2025, doi: 10.1016/j.isatra.2025.09.015.

Copyright

Copyright © 2026 Tan Minh Le. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.