Infinite-time optimal feedback control of a 3-phase asynchronous motor exploiting a nonlinear finite element model

Authors

  • Cezary Jedryczka Institute of Electrical Engineering and Electronics Poznan University of Technology, Piotrowo 3a, 60-965 Poznan, Poland https://orcid.org/0000-0001-5427-059X
  • Sławomir Stepien Institute of Automatic Control and Robotics, Poznan University of Technology Piotrowo 3a, 60-965 Poznan, Poland https://orcid.org/0000-0001-7777-7684
  • Andrzej Demenko Institute of Electrical Engineering and Electronics Poznan University of Technology, Piotrowo 3a, 60-965 Poznan, Poland https://orcid.org/0000-0002-0833-4561
  • Mirosław Nowakowski Air Force Institute of Technology, Ksiecia Boleslawa St. 6, 01-494 Warsaw, Poland

DOI:

https://doi.org/10.24425/aee.2024.152103

Abstract

This paper presents modelling of a squirrel-cage induction motor and an optimal control method based on suboptimal control for nonlinear systems to minimise consumed energy and power losses in an induction motor drive. A coupled motor model with optimal control as a closed-loop integrated system is proposed. For modelling of the squirrel-cage asynchronous machine, a field-circuit-mechanical finite-element (FE) model is employed, in which mechanical motion is realised by a moving-mesh method and fixed mesh approach. For the control problem purpose, a surrogate induction motor model, described in a stationary rotor reference d–q frame, is applied. The optimal control is realised by a nonlinear feedback compensator method based on the state-dependent Riccati equation (SDRE) with an infinite time horizon with the surrogate model state-dependent parametrisation (SDP). To perform the control strategy, a SDRE technique with Moore–Penrose pseudoinverse is adopted. To improve the accuracy of the optimisation procedure, a finite element model was used to calculate the motor performance.

References

[1] Aghili F., Adaptive reshaping of excitation currents for accurate torque control of brushless motors, in IEEE Transactions on Control Systems Technology, vol. 16, no. 2, pp. 356–364 (2008), DOI: 10.1109/TCST.2007.908213.

[2] Brock S., Sliding mode control of a permanent magnet direct drive under non-linear friction, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 30, no. 3, pp. 853–863 (2011), DOI: 10.1108/03321641111110825.

[3] Allihalli H., Bayindir M.I., Time-energy optimal control of vector controlled induction motor, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 21, no. 2, pp. 235–251 (2002), DOI: 10.1108/03321640210416331.

[4] Bernat J., Stępień S., Minimum energy control analysis of the switched reluctance stepper motor considering a nonlinear finite element model, Simulation Modelling Practice and Theory, vol. 28, pp. 1–11 (2012), DOI: 10.1016/j.simpat.2012.05.005.

[5] Bernat J., Stępień S., Modeling and optimal control of variable reluctance stepper motor, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 30, no. 2, pp. 726–740 (2011), DOI: 10.1108/03321641111101177.

[6] Ignaciuk P., Bartoszewicz A., Linear-quadratic optimal control of periodic-review perishable inventory systems, in IEEE Transactions on Control Systems Technology, vol. 20, no. 5, pp. 1400–1407 (2012), DOI: 10.1109/TCST.2011.2161086.

[7] Banks H.T., Lewis B.M., Tran H.T., Nonlinear feedback controllers and compensators: a state-dependent Riccati equation approach, Computational Optimization and Applications, vol. 37, no. 2, pp. 177–218 (2007), DOI: 10.1007/s10589-007-9015-2.

[8] Çimen T., Systematic and effective design of nonlinear feedback controllers via the state-dependent Riccati equation (SDRE) method, Annual Reviews in Control, vol. 34, no. 1, pp. 32–51 (2010), DOI: 10.1016/j.arcontrol.2010.03.001.

[9] Mir S., Islam M.S., Sebastian T., Husain I., Fault-tolerant switched reluctance motor drive using adaptive fuzzy logic controller, in IEEE Transactions on Power Electronics, vol. 19, no. 2, pp. 289–295 (2004), DOI: 10.1109/TPEL.2003.823244.

[10] Cheng Z., Takahashi N., Forghani B., Gilbert G., Du Y., Fan Y., Liu L., Zhai Z., Wu W., Zhang J., Effect of Excitation Patterns on Both Iron Loss and Flux in Solid and Laminated Steel Configurations, in IEEE Transactions on Magnetics, vol. 46, no. 8, pp. 3185–3188 (2010), DOI: 10.1109/TMAG.2010.2044765.

[11] Jang G.H., Lee C.J., Design and control of the phase current of a brushless dc motor to eliminate cogging torque, Journal of Applied Physics, vol. 99, no. 8, 08R305 (2006), DOI: 10.1063/1.2165603.

[12] Bernat J., Kolota J., Stępień S., Sykulski J., A steady state solver for modelling rotating electromechanical devices exploiting the transformation from time to position domain, International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, vol. 27, no. 2, pp. 213–228 (2014), DOI: 10.1002/jnm.1916.

[13] Mao S.H., Tsai M.C., An analysis of the optimum operating point for a switched reluctance motor, Journal of Magnetism and Magnetic Materials, vol. 282, pp. 53–56 (2004), DOI: 10.1016/j.jmmm.2004.04.012.

[14] Stepień S., Jędryczka C., Demenko A., Optimal control of 3-phase induction machine exploiting a FEM model, Tenth International Conference on Computational Electromagnetics (CEM 2019), Edinburgh, UK, pp. 1–2 (2019), DOI: 10.1049/cp.2019.0111.

[15] Jędryczka C., Wojciechowski R.M., Demenko A., Finite element analysis of the asynchronous torque in LSPMSM with non-symmetrical squirrel cage winding, International Journal of Applied Electromagnetics and Mechanics, vol. 46, no. 2, pp. 367–373 (2014), DOI: 10.3233/JAE-141947.

[16] Wojciechowski R.M., Demenko A., Sykulski J.K., Comparative analysis of A-V and A-T-T0 calculations of induced currents in multiply connected regions, IET Science Measurement & Technology, vol. 6, no. 5, pp. 312–318 (2012), DOI: 10.1049/iet-smt.2011.0114.

[17] Wojciechowski R.M., Jędryczka C., A description of the sources of magnetic field using edge values of the current vector potential, Archives of Electrical Engineering, vol. 67, no. 1 (2018), DOI: 10.24425/118988.

[18] Demenko A., Nowak L., Finite element analysis of saturation effects in a squirrel cage electrical machine, COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 15, no. 4, pp. 88–95 (1996), DOI: 10.1108/03321649610154249.

[19] Barata J.C.A., Hussein M.S., The Moore–Penrose Pseudoinverse. A Tutorial Review of the Theory, Brazilian Journal of Physics, vol. 42, no. 1, pp. 146–165 (2012), DOI: 10.1007/s13538-011-0052-z.

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Published

2024-12-30

How to Cite

Jedryczka, Cezary, et al. “Infinite-Time Optimal Feedback Control of a 3-Phase Asynchronous Motor Exploiting a Nonlinear Finite Element Model”. Archives of Electrical Engineering , vol. 73, no. 4, Dec. 2024, pp. 927-39, doi:10.24425/aee.2024.152103.

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