### Developing and Implementing a Quantum Algorithm for the Sliding Mode Controller Using Multiple Qubit Operators: Application to DC Motor Speed Drive

#### Abstract

#### Keywords

[1] M. E. A. Boudjoghra, S. A. F. Daimellah, N. Zioui, Y. Mahmoudi, and M. Tadjine, “State-domain equations and their quantum computing solution based HHL algorithm,” *Mathematical Modelling of Engineering Problems*, vol. 9, pp. 879–886, Aug. 2022, doi: 10.18280/mmep.090404.

[2] N. Zioui, A. Mahmoudi, and M. Tadjine, “Design of a new hybrid linearizing-backstepping controller using quantum state equations and quantum spins,” *International Journal of Automation and Control*, vol. 17, pp. 397–417, Apr. 2023, doi: 10.1504/IJAAC.2023.10051373.

[3] U. Maheswararao Ch, Y. S. Kishore Babu, and K. Amaresh, “Sliding mode speed control of a DC motor,” in *2011 International Conference on Communication Systems and Network Technologies*, pp. 387–391 Jun. 2011, doi: 10.1109/CSNT.2011.86.

[4] P. Ghalimath and S. S. Sankeswari, “Speed control of DC motor using sliding mode control approach,” *IOSR Journal of Electrical and Electronics Engineering*, vol. 10, pp. 17–22, Jul. 2015, doi: 10.9790/1676-10411722.

[5] E. H. Dursun and A. Durdu, “Speed control of a DC motor with variable load using sliding mode control,” *International Journal of Computer and Electrical Engineering*, vol. 8, pp. 219–226, Jun. 2016, doi: 10.17706/ijcee.2016.8.3.219-226.

[6] S. Vaez-Zadeh and M. Zamanian, “Permanent magnet DC motor sliding mode control system,” *IJE Transactions A: Basics*, vol. 16, pp. 367–376, Nov. 2003.

[7] B. Ramprasad and K. Venkataratnam, “A novel speed control of DC motor using sliding mode technique,” *International Journal of Current Engineering and Scientific Research*, vol. 6, pp. 40–46, 2019.

[8] N. Bharathi, A. Kavitha, and B. Barathy, “Sliding mode control for speed control of brushless DC motor,” *International Journal of Scientific and Engineering Research*, vol. 5, pp. 22–27, Apr. 2014.

[9] F. D. Chizea, E. Ovie, C. M. Akachukwu, and M. B. Muazu, “Sliding mode control of a miniature brushless DC motor,” *International Journal of Engineering and Technical Research*, vol. 9, pp. 24–27, Aug. 2019.

[10] H. Guldemir, “Sliding mode speed control for DC drive systems,” *Mathematical and Computational Applications*, vol. 8, pp. 377–384, 2003.

[11] B. R. Jo, H. W. Ahn, and M. J. Youn, “Multi-variable sliding mode control of quantum boost SRC,” *IEEE Transactions on Control Systems Technology*, vol. 2, pp. 148–150, Jun. 1994, doi: 10.1109/87.294339.

[12] M. Castilla, L. G. de Vicuña, M. López, O. López, and J. Matas, “On the design of sliding mode control schemes for quantum resonant converters,” *IEEE Transactions on Power Electronics*, vol. 15, pp. 960–973, Nov. 2000, doi: 10.1109/63.892701.

[13] M. Castilla, L. G. de Vicuña, J. M. Guerrero, J. Matas, and J. Miret, “Sliding-mode control of quantum series-parallel resonant converters via input–output linearization,” *IEEE Transactions on Industrial Electronics*, vol. 52, pp. 566–575, Apr. 2005, doi: 10.1109/TIE.2005.844256.

[14] M. Castilla, L. G. de Vicuña, J. Matas, J. Miret, and J. C. Vasquez, “A comparative study of sliding-mode control schemes for quantum series resonant inverters,” *IEEE Transactions on** **Industrial Electronics*, vol. 56, pp. 3487–3495, Sep. 2009, doi: 10.1109/TIE.2009.2022517.

[15] L. G. de Vicuña, M. Castilla, J. Miret, J. Matas, and J. M. Guerrero, “Sliding-mode control for a single-phase AC/AC quantum resonant converter,” *IEEE Transactions on Industrial Electronics*, vol. 56, pp. 3496–3504, Sep. 2009, doi: 10.1109/ TIE.2009.2026766.

[16] D. Dong and I. R. Petersen, “Sliding mode control of quantum systems,” *New Journal of Physics*, vol. 11, pp. 105033–105050, Oct. 2009, doi: 10.1088/1367-2630/11/10/105033.

[17] D. Dong and I. R. Petersen, “Sliding mode control of two-level quantum systems,” *Automatica*, vol. 48, pp. 725–735, Mar. 2012, doi: 10.1016/j. automatica.2012.02.003.

[18] D. Dong and I. R. Petersen, “Sliding mode control of quantum systems,” in *Learning and Robust Control in Quantum Technology *(Communications and Control Engineering). Cham: Springer, 2023, doi: 10.1007/978-3-031-20245-2_6.

[19] M. M. Zirkohi, “Fast terminal sliding mode control design for position control of induction motors using adaptive quantum neural networks,” *Applied Soft Computing*, vol. 115, pp. 108268– 108282, Dec. 2021, doi: 10.1016/j.asoc.2021. 108268.

[20] Z. Tavanaei-Sereshki and M. R. Ramezani-al, “Quantum genetic sliding mode controller design for depth control of an underwater vehicle,” *Measurement and Control*, vol. 51, pp. 336–348, Jun. 2018, doi: 10.1177/0020294018789199.

[21] J. J. Moghaddam and A. Bagheri, “Suppressing vibration in a multilayers composite material plate using quantum-behaved particle swarm optimization and sliding mode control system,” *Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering*, vol. 229, pp. 2095–2105, Nov. 2014, doi: 10.1177/0954410014565678.

[22] F. Chen, R. Jiang, C. Wen, and R. Su, “Self-repairing control of a helicopter with input time delay via adaptive global sliding mode control and quantum logic,” *Information Sciences*, vol. 316, pp. 123–131, Apr. 2015, doi: 10.1016/j.ins. 2015.04.023.

[23] S. Chegini and M. Yarahmadi, “Quantum sliding mode control via error sliding surface,” *Journal of Vibration and Control*, vol. 24, pp. 5345– 5352, Dec. 2017, doi: 10.1177/1077546317752848.

[24] R. B. Griffiths, *Consistent Quantum Theory*. Cambridge: Cambridge University Press, pp. 95–100, 2002.

[25] D. McMahon, *Quantum Computing Explained*. Hoboken, New Jersey: Wiley, pp. 11–37, 2007.

[26] J. Abhijith, A. Adedoyin, J. Ambrosiano, P. Anisimov, W. Casper, G. Chennupati, C. Coffrin, H. Djidjev, D. Gunter, S. Karra, N. Lemons, S. Lin, A. Malyzhenkov, D. Mascarenas, S. Mniszewski, B. Nadiga, D. O'Malley, D. Oyen, S. Pakin, L. Prasad, R. Roberts, P. Romero, N. Santhi, N. Sinitsyn, P. J. Swart, J. G. Wendelberger, B. Yoon, R. Zamora, W. Zhu, S. Eidenbenz, A. Bärtschi, P. J. Coles, M. Vuffray, and A. Y. Lokhov, “Quantum algorithm implementations for beginners,” *ACM Transactions on Quantum Computing*, vol. 24, pp. 1–92, Jul. 2022, doi: 10.1145/3517340.

[27] N. Zioui, A. Mahmoudi, Y. Mahmoudi, and M. Tadjine, “Quantum computing based state domain equations and feedback control,” *Results in Applied Mathematics*, vol. 19, pp. 100385–100393, Aug. 2023, doi: 10.1016/j.rinam.2023.100385.

[28] IBM, “IBM quantum composer,” 2023. [Online]. Available: https://quantum-computing.ibm.com/ composer/files/new

DOI: 10.14416/j.asep.2023.09.005

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