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Fuzzy-Based Intelligent Controller Design for Robust Speed Control of PMDC Motor in Unstable Conditions

Year 2020, Volume: 8 Issue: 2, 237 - 248, 26.05.2020
https://doi.org/10.21541/apjes.657914

Abstract

In this study, the Fuzzy Logic based smart and durable speed controller design of PMDC motor at non-linear reference speeds under constant and variable loads are realized. Intelligent control methods aim to develop systems capable of imitating human's intuitive and conscious behavior. The designed control methods are: Fuzzy Logic controller (FLC), proportional-integral (PI) type FLC (FLCPI) and Self-Tuning Fuzzy PI (STFPI) controllers. The purpose of the control algorithm is to force the speed of the motor to always follow the desired reference speed. The designed controller must meet this request for different speed / time changes, regardless of load failure and parameter changes. The performances of the controllers on durable speed control under unstable operating conditions have compared and the results obtained have discussed. According to the comparison and simulation results obtained, the STFPI control method showed better results than others in meeting the desired control criteria.

References

  • [1] C. Rossi and A. Tonielli, “Robust control of permanent magnet motors: VSS techniques lead to simple hardware implementations,” IEEE Trans. Ind. Electron., vol. 41, no. 4, pp. 451–460, 1994.
  • [2] V. Sankardoss and P. Geethanjali, “PMDC Motor Parameter Estimation Using Bio-Inspired Optimization Algorithms,” IEEE Access, vol. 5, pp. 11244–11254, 2017.
  • [3] A. Terki, A. Moussi, A. Betka, and N. Terki, “An improved efficiency of fuzzy logic control of PMBLDC for PV pumping system,” Appl. Math. Model., vol. 36, no. 3, pp. 934–944, Mar. 2012.
  • [4] V. Sankardoss and P. Geethanjali, “Parameter estimation and speed control of a PMDC motor used in wheelchair,” Energy Procedia, vol. 117, pp. 345–352, Jun. 2017.
  • [5] Hong-xing Wu, Shu-kang Cheng, and Shu-mei Cui, “A controller of brushless DC motor for electric vehicle,” IEEE Trans. Magn., vol. 41, no. 1, pp. 509–513, Jan. 2005.
  • [6] X. Wu, J. Liu, Y. Zhou, Q. Lv, and C. Hu, “Movement Control and Attitude Adjustment of Climbing Robot on Flexible Surfaces,” IEEE Trans. Ind. Electron., vol. 65, no. 3, pp. 2618–2628, Mar. 2018.
  • [7] D. Petković, M. Issa, N. D. Pavlović, L. Zentner, and Ž. Ćojbašić, “Adaptive neuro fuzzy controller for adaptive compliant robotic gripper,” Expert Syst. Appl., vol. 39, no. 18, pp. 13295–13304, Dec. 2012.
  • [8] S. A. K. Mozaffari Niapour, S. Danyali, M. B. B. Sharifian, and M. R. Feyzi, “Brushless DC motor drives supplied by PV power system based on Z-source inverter and FL-IC MPPT controller,” Energy Convers. Manag., vol. 52, no. 8–9, pp. 3043–3059, Aug. 2011.
  • [9] S. S. Patil and P. Bhaskar, “Design and Real Time Implementation of Integrated Fuzzy Logic Controller for a High Speed PMDC Motor,” Int. J. Electron. Eng. Res., vol. 1, no. 1, pp. 13–25, 2009.
  • [10] T. Özer, S. Kivrak, Y. Oğuz, and S. Kıvrak, “H Bridge DC Motor Driver Design and Implementation with Using dsPIC30f4011,” Int. J. Innov. Res. Sci. Eng. Technol., vol. 6, no. 10, pp. 75–83, 2017.
  • [11] A. M. Ali, A. Prof, A. H. Mohammed, A. Dr, and H. M. Alwan, “Tuning PID Controllers for DC Motor by Using Microcomputer,” Int. J. Appl. Eng. Res., vol. 14, no. 1, pp. 202–206, 2019.
  • [12] A. M. Zaki, M. El-Bardini, F. A. S. Soliman, and M. M. Sharaf, “Embedded two level direct adaptive fuzzy controller for DC motor speed control,” Ain Shams Eng. J., vol. 9, no. 1, pp. 65–75, Mar. 2018.
  • [13] R. Kandiban and R. Arulmozhiyal, “Speed Control of BLDC Motor Using Adaptive Fuzzy PID Controller,” Procedia Eng., vol. 38, pp. 306–313, Jan. 2012.
  • [14] M. Tuna, B. Fidan, S. Kocabey, and S. Görgülü, “Effective and Reliable Speed Control of Permanent Magnet DC (PMDC) Motor under Variable Loads,” J Electr Eng Technol, vol. 10, pp. 1921–718, 2015.
  • [15] A. A. El-samahy and M. A. Shamseldin, “Brushless DC motor tracking control using self-tuning fuzzy PID control and model reference adaptive control,” Ain Shams Eng. J., vol. 9, no. 3, pp. 341–352, Sep. 2018.
  • [16] Y. Oğuz, “Fuzzy PI Control with Parallel Fuzzy PD Control for Automatic Generation Control of a Two-Area Power Systems,” Gazi Univ. J. Sci. GU J Sci, vol. 24, no. 4, pp. 805–816, 2011.
  • [17] J. Sharma, N. Gupta, P. Nain, M. Tech Scholar, and A. Professor, “Speed Control of Separately Excited DC Motor Using Fuzzy Logic Controller,” Int. J. Tech. Res., vol. 2, no. 4, pp. 27–39, 2012.
  • [18] E. Natsheh, K. A. Buragga, and S. Arabia, “Comparison between Conventional and Fuzzy Logic PID Controllers for Controlling DC Motors,” IJCSI Int. J. Comput. Sci. Issues, vol. 7, no. 5, pp. 128–134, 2010.
  • [19] S. R. Khuntia, S. P. Mohanty, and C. Ardil, “A Comparative Study of P-I, I-P, Fuzzy and Neuro-Fuzzy Controllers for Speed Control of DC Motor Drive,” World Acad. Sci. Eng. Technol. Int. J. Electr. Comput. Eng., vol. 5, no. 5, pp. 714–718, 2011.
  • [20] U. Kumar Bansal and R. Narvey, “Speed Control of DC Motor Using Fuzzy PID Controller,” Adv. Electron. Electr. Eng., vol. 3, no. 9, pp. 1209–1220, 2013.
  • [21] M. E. Fisher, A. Ghosh, and A. M. Sharaf, “Intelligent control strategies for permanent magnet DC motor drives,” Proc. Int. Conf. Power Electron. Drives Energy Syst. Ind. Growth, pp. 360–366, 1996.
  • [22] M. G. Simoes, B. K. Bose, and R. J. Spiegel, “Fuzzy logic based intelligent control of a variable speed cage machine wind generation system,” IEEE Trans. Power Electron., vol. 12, no. 1, pp. 87–95, 1997.
  • [23] M. Venkata, G. Babu, and R. S. Naik, “Comparitive Analysis of P-I, I-P, PID and Fuzzy Controllers for Speed Control of DC Motor,” Int. Res. J. Eng. Technol., vol. 4, no. 10, pp. 500–504, 2017.
  • [24] S. R. Khuntia, K. B. Mohanty, S. Panda, and C. Ardil, “A Comparative Study of PI , IP , Fuzzy and Neuro-Fuzzy Controllers for Speed Control of DC Motor Drive,” Int. J. Electr. Syst. Sci. Eng., vol. 1, no. 1, pp. 1–5, 2010.
  • [25] A. Varshney, D. Gupta, and B. Dwivedi, “Speed response of brushless DC motor using fuzzy PID controller under varying load condition,” J. Electr. Syst. Inf. Technol., vol. 4, no. 2, pp. 310–321, Sep. 2017.
  • [26] K. Premkumar and B. V. Manikandan, “Bat algorithm optimized fuzzy PD based speed controller for brushless direct current motor,” Eng. Sci. Technol. an Int. J., vol. 19, no. 2, pp. 818–840, Jun. 2016.
  • [27] R. Arulmozhiyal, “Design and Implementation of Fuzzy PID controller for BLDC motor using FPGA,” 2012 IEEE Int. Conf. Power Electron. Drives Energy Syst., pp. 1–6, Dec. 2012.
  • [28] E. Hasan Dursun and A. Durdu, “Speed Control of a DC Motor with Variable Load Using Sliding Mode Control,” Int. J. Comput. Electr. Eng., vol. 8, no. 3, pp. 219–226, 2016.
  • [29] I. Eminolu and .H. Alts, “A method to form fuzzy logic control rules for a PMDC motor drive system,” Electr. Power Syst. Res., vol. 39, no. 2, pp. 81–87, Nov. 1996.
  • [30]I. Guney, Y. Oguz, and F. Serteller, “Dynamic behaviour model of permanent magnet synchronous motor fed by PWM inverter and fuzzy logic controller for stator phase current, flux and torque control of PMSM,” in IEMDC 2001. IEEE International Electric Machines and Drives Conference (Cat. No.01EX485), pp. 479–485.
  • [31] İ. Eker and Y. Torun, “Fuzzy logic control to be conventional method,” Energy Convers. Manag., vol. 47, no. 4, pp. 377–394, Mar. 2006.
  • [32] İ. Eminoğlu and İ. H. Altaş, “The effects of the number of rules on the output of a fuzzy logic controller employed to a PM d.c. motor,” Comput. Electr. Eng., vol. 24, no. 3–4, pp. 245–261, May 1998.
  • [33] M. Namazov and O. Basturk, “DC motor position control using fuzzy proportional-derivative controllers with different defuzzification methods,” J. Turkish Fuzzy Syst. Assoc., vol. 1, no. 1, pp. 36–54, 2010.
  • [34]E. A. E.-H. M. Ramadan, M. El-Bardini, N. M. El-Rabaie, and M. A. Fkirin, “Embedded system based on a real time fuzzy motor speed controller,” Ain Shams Eng. J., vol. 5, no. 2, pp. 399–409, Jun. 2014.
  • [35]M. Nour, O. Bouketir, and C. Eng Yong, “Self-Tuning of PI Speed Controller Gains Using Fuzzy Logic Controller,” Mod. Appl. Sci., vol. 2, no. 6, p. p55, Nov. 2008.
  • [36]H. B. Kazemian, “Comparative study of a learning fuzzy PID controller and a self-tuning controller,” ISA Trans., vol. 40, no. 3, pp. 245–253, Jul. 2001.
  • [37] E. Y eşil, M. Güzelkaya, and İ. Eksin, “Self tuning fuzzy PID type load and frequency controller,” Energy Convers. Manag., vol. 45, no. 3, pp. 377–390, Feb. 2004.
  • [38]M. Paksoy, R. Guclu, and S. Cetin, “Semiactive Self-Tuning Fuzzy Logic Control of Full Vehicle Model with MR Damper,” Adv. Mech. Eng., vol. 6, p. 816813, Jan. 2014.
  • [39]A. Karakaya and E. Karakas, “Performance Analysis of PM Synchronous Motors Using Fuzzy Logic And Self Tuning Fuzzy PI Speed Controls,” Arab. J. Sci. Eng., vol. 33, no. 1B, pp. 153–177, 2008.
  • [40]Y. Guo and H. Long, “Self organizing fuzzy sliding mode controller for the position control of a permanent magnet synchronous motor drive,” Ain Shams Eng. J., vol. 2, no. 2, pp. 109–118, Jun. 2011.
  • [41] S. Sezer, S. Cetin, and A. E. Atalay, “Application of Self Tuning Fuzzy Logic Control to Full Railway Vehicle Model,” Procedia Comput. Sci., vol. 6, no. 2011, pp. 487–492, 2011.
  • [42] A. K. Pal and I. Naskar, “Design of Self-Tuning Fuzzy PI controller in LABVIEW for Control of a Real Time Process,” Int. J. Electron. Comput. Sci. Eng., vol. 2, no. 2, pp. 538–545, 2013.

Kararsız Koşullarda SMDA Motorun Dayanıklı Hız Kontrolü İçin Bulanık-Tabanlı Akıllı Denetleyici Tasarımı

Year 2020, Volume: 8 Issue: 2, 237 - 248, 26.05.2020
https://doi.org/10.21541/apjes.657914

Abstract

Bu çalışmada, sabit ve değişken yükler altında doğrusal olmayan referans hızlarda çalışan SMDA motorun bulanık mantık tabanlı akıllı ve dayanıklı hız kontrolör tasarımı gerçekleştirilmiştir. Akıllı kontrol, insanın bulucu ve uyarlayıcı davranışlarını taklit edebilecek niteliğe sahip sistemler geliştirmeyi hedeflemektedir. Tasarlanan akıllı kontrol teknikleri; Bulanık Mantık denetleyici (BMD), oransal-integral (PI) tipli BMD ve Kendini Ayarlayan (Öz uyarlamalı) Bulanık PI (KABPI) denetleyicidir. Kontrol algoritmasının amacı, rotor hızının istenen referans hızını her zaman güçlükle takip etmeye zorlamaktır. Bu amaca, yükte bozulma ve parametre değişikliklerinden bağımsız olarak farklı hız/zaman değişimleri içinde ulaşılmalıdır. Tasarlanan denetleyicilerin kararsız çalışma koşulları altında dayanıklı hız denetimi üzerindeki performansları karşılaştırılmış ve alınan sonuçlar tartışılmıştır. Elde edilen karşılaştırma ve benzetim sonuçlarına göre, KABPI kontrol yöntemi istenen kontrol kriterlerini karşılamada diğerlerine nazaran daha iyi sonuçlar göstermiştir.

References

  • [1] C. Rossi and A. Tonielli, “Robust control of permanent magnet motors: VSS techniques lead to simple hardware implementations,” IEEE Trans. Ind. Electron., vol. 41, no. 4, pp. 451–460, 1994.
  • [2] V. Sankardoss and P. Geethanjali, “PMDC Motor Parameter Estimation Using Bio-Inspired Optimization Algorithms,” IEEE Access, vol. 5, pp. 11244–11254, 2017.
  • [3] A. Terki, A. Moussi, A. Betka, and N. Terki, “An improved efficiency of fuzzy logic control of PMBLDC for PV pumping system,” Appl. Math. Model., vol. 36, no. 3, pp. 934–944, Mar. 2012.
  • [4] V. Sankardoss and P. Geethanjali, “Parameter estimation and speed control of a PMDC motor used in wheelchair,” Energy Procedia, vol. 117, pp. 345–352, Jun. 2017.
  • [5] Hong-xing Wu, Shu-kang Cheng, and Shu-mei Cui, “A controller of brushless DC motor for electric vehicle,” IEEE Trans. Magn., vol. 41, no. 1, pp. 509–513, Jan. 2005.
  • [6] X. Wu, J. Liu, Y. Zhou, Q. Lv, and C. Hu, “Movement Control and Attitude Adjustment of Climbing Robot on Flexible Surfaces,” IEEE Trans. Ind. Electron., vol. 65, no. 3, pp. 2618–2628, Mar. 2018.
  • [7] D. Petković, M. Issa, N. D. Pavlović, L. Zentner, and Ž. Ćojbašić, “Adaptive neuro fuzzy controller for adaptive compliant robotic gripper,” Expert Syst. Appl., vol. 39, no. 18, pp. 13295–13304, Dec. 2012.
  • [8] S. A. K. Mozaffari Niapour, S. Danyali, M. B. B. Sharifian, and M. R. Feyzi, “Brushless DC motor drives supplied by PV power system based on Z-source inverter and FL-IC MPPT controller,” Energy Convers. Manag., vol. 52, no. 8–9, pp. 3043–3059, Aug. 2011.
  • [9] S. S. Patil and P. Bhaskar, “Design and Real Time Implementation of Integrated Fuzzy Logic Controller for a High Speed PMDC Motor,” Int. J. Electron. Eng. Res., vol. 1, no. 1, pp. 13–25, 2009.
  • [10] T. Özer, S. Kivrak, Y. Oğuz, and S. Kıvrak, “H Bridge DC Motor Driver Design and Implementation with Using dsPIC30f4011,” Int. J. Innov. Res. Sci. Eng. Technol., vol. 6, no. 10, pp. 75–83, 2017.
  • [11] A. M. Ali, A. Prof, A. H. Mohammed, A. Dr, and H. M. Alwan, “Tuning PID Controllers for DC Motor by Using Microcomputer,” Int. J. Appl. Eng. Res., vol. 14, no. 1, pp. 202–206, 2019.
  • [12] A. M. Zaki, M. El-Bardini, F. A. S. Soliman, and M. M. Sharaf, “Embedded two level direct adaptive fuzzy controller for DC motor speed control,” Ain Shams Eng. J., vol. 9, no. 1, pp. 65–75, Mar. 2018.
  • [13] R. Kandiban and R. Arulmozhiyal, “Speed Control of BLDC Motor Using Adaptive Fuzzy PID Controller,” Procedia Eng., vol. 38, pp. 306–313, Jan. 2012.
  • [14] M. Tuna, B. Fidan, S. Kocabey, and S. Görgülü, “Effective and Reliable Speed Control of Permanent Magnet DC (PMDC) Motor under Variable Loads,” J Electr Eng Technol, vol. 10, pp. 1921–718, 2015.
  • [15] A. A. El-samahy and M. A. Shamseldin, “Brushless DC motor tracking control using self-tuning fuzzy PID control and model reference adaptive control,” Ain Shams Eng. J., vol. 9, no. 3, pp. 341–352, Sep. 2018.
  • [16] Y. Oğuz, “Fuzzy PI Control with Parallel Fuzzy PD Control for Automatic Generation Control of a Two-Area Power Systems,” Gazi Univ. J. Sci. GU J Sci, vol. 24, no. 4, pp. 805–816, 2011.
  • [17] J. Sharma, N. Gupta, P. Nain, M. Tech Scholar, and A. Professor, “Speed Control of Separately Excited DC Motor Using Fuzzy Logic Controller,” Int. J. Tech. Res., vol. 2, no. 4, pp. 27–39, 2012.
  • [18] E. Natsheh, K. A. Buragga, and S. Arabia, “Comparison between Conventional and Fuzzy Logic PID Controllers for Controlling DC Motors,” IJCSI Int. J. Comput. Sci. Issues, vol. 7, no. 5, pp. 128–134, 2010.
  • [19] S. R. Khuntia, S. P. Mohanty, and C. Ardil, “A Comparative Study of P-I, I-P, Fuzzy and Neuro-Fuzzy Controllers for Speed Control of DC Motor Drive,” World Acad. Sci. Eng. Technol. Int. J. Electr. Comput. Eng., vol. 5, no. 5, pp. 714–718, 2011.
  • [20] U. Kumar Bansal and R. Narvey, “Speed Control of DC Motor Using Fuzzy PID Controller,” Adv. Electron. Electr. Eng., vol. 3, no. 9, pp. 1209–1220, 2013.
  • [21] M. E. Fisher, A. Ghosh, and A. M. Sharaf, “Intelligent control strategies for permanent magnet DC motor drives,” Proc. Int. Conf. Power Electron. Drives Energy Syst. Ind. Growth, pp. 360–366, 1996.
  • [22] M. G. Simoes, B. K. Bose, and R. J. Spiegel, “Fuzzy logic based intelligent control of a variable speed cage machine wind generation system,” IEEE Trans. Power Electron., vol. 12, no. 1, pp. 87–95, 1997.
  • [23] M. Venkata, G. Babu, and R. S. Naik, “Comparitive Analysis of P-I, I-P, PID and Fuzzy Controllers for Speed Control of DC Motor,” Int. Res. J. Eng. Technol., vol. 4, no. 10, pp. 500–504, 2017.
  • [24] S. R. Khuntia, K. B. Mohanty, S. Panda, and C. Ardil, “A Comparative Study of PI , IP , Fuzzy and Neuro-Fuzzy Controllers for Speed Control of DC Motor Drive,” Int. J. Electr. Syst. Sci. Eng., vol. 1, no. 1, pp. 1–5, 2010.
  • [25] A. Varshney, D. Gupta, and B. Dwivedi, “Speed response of brushless DC motor using fuzzy PID controller under varying load condition,” J. Electr. Syst. Inf. Technol., vol. 4, no. 2, pp. 310–321, Sep. 2017.
  • [26] K. Premkumar and B. V. Manikandan, “Bat algorithm optimized fuzzy PD based speed controller for brushless direct current motor,” Eng. Sci. Technol. an Int. J., vol. 19, no. 2, pp. 818–840, Jun. 2016.
  • [27] R. Arulmozhiyal, “Design and Implementation of Fuzzy PID controller for BLDC motor using FPGA,” 2012 IEEE Int. Conf. Power Electron. Drives Energy Syst., pp. 1–6, Dec. 2012.
  • [28] E. Hasan Dursun and A. Durdu, “Speed Control of a DC Motor with Variable Load Using Sliding Mode Control,” Int. J. Comput. Electr. Eng., vol. 8, no. 3, pp. 219–226, 2016.
  • [29] I. Eminolu and .H. Alts, “A method to form fuzzy logic control rules for a PMDC motor drive system,” Electr. Power Syst. Res., vol. 39, no. 2, pp. 81–87, Nov. 1996.
  • [30]I. Guney, Y. Oguz, and F. Serteller, “Dynamic behaviour model of permanent magnet synchronous motor fed by PWM inverter and fuzzy logic controller for stator phase current, flux and torque control of PMSM,” in IEMDC 2001. IEEE International Electric Machines and Drives Conference (Cat. No.01EX485), pp. 479–485.
  • [31] İ. Eker and Y. Torun, “Fuzzy logic control to be conventional method,” Energy Convers. Manag., vol. 47, no. 4, pp. 377–394, Mar. 2006.
  • [32] İ. Eminoğlu and İ. H. Altaş, “The effects of the number of rules on the output of a fuzzy logic controller employed to a PM d.c. motor,” Comput. Electr. Eng., vol. 24, no. 3–4, pp. 245–261, May 1998.
  • [33] M. Namazov and O. Basturk, “DC motor position control using fuzzy proportional-derivative controllers with different defuzzification methods,” J. Turkish Fuzzy Syst. Assoc., vol. 1, no. 1, pp. 36–54, 2010.
  • [34]E. A. E.-H. M. Ramadan, M. El-Bardini, N. M. El-Rabaie, and M. A. Fkirin, “Embedded system based on a real time fuzzy motor speed controller,” Ain Shams Eng. J., vol. 5, no. 2, pp. 399–409, Jun. 2014.
  • [35]M. Nour, O. Bouketir, and C. Eng Yong, “Self-Tuning of PI Speed Controller Gains Using Fuzzy Logic Controller,” Mod. Appl. Sci., vol. 2, no. 6, p. p55, Nov. 2008.
  • [36]H. B. Kazemian, “Comparative study of a learning fuzzy PID controller and a self-tuning controller,” ISA Trans., vol. 40, no. 3, pp. 245–253, Jul. 2001.
  • [37] E. Y eşil, M. Güzelkaya, and İ. Eksin, “Self tuning fuzzy PID type load and frequency controller,” Energy Convers. Manag., vol. 45, no. 3, pp. 377–390, Feb. 2004.
  • [38]M. Paksoy, R. Guclu, and S. Cetin, “Semiactive Self-Tuning Fuzzy Logic Control of Full Vehicle Model with MR Damper,” Adv. Mech. Eng., vol. 6, p. 816813, Jan. 2014.
  • [39]A. Karakaya and E. Karakas, “Performance Analysis of PM Synchronous Motors Using Fuzzy Logic And Self Tuning Fuzzy PI Speed Controls,” Arab. J. Sci. Eng., vol. 33, no. 1B, pp. 153–177, 2008.
  • [40]Y. Guo and H. Long, “Self organizing fuzzy sliding mode controller for the position control of a permanent magnet synchronous motor drive,” Ain Shams Eng. J., vol. 2, no. 2, pp. 109–118, Jun. 2011.
  • [41] S. Sezer, S. Cetin, and A. E. Atalay, “Application of Self Tuning Fuzzy Logic Control to Full Railway Vehicle Model,” Procedia Comput. Sci., vol. 6, no. 2011, pp. 487–492, 2011.
  • [42] A. K. Pal and I. Naskar, “Design of Self-Tuning Fuzzy PI controller in LABVIEW for Control of a Real Time Process,” Int. J. Electron. Comput. Sci. Eng., vol. 2, no. 2, pp. 538–545, 2013.
There are 42 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Murat Tuna 0000-0003-3511-1336

Publication Date May 26, 2020
Submission Date December 11, 2019
Published in Issue Year 2020 Volume: 8 Issue: 2

Cite

IEEE M. Tuna, “Kararsız Koşullarda SMDA Motorun Dayanıklı Hız Kontrolü İçin Bulanık-Tabanlı Akıllı Denetleyici Tasarımı”, APJES, vol. 8, no. 2, pp. 237–248, 2020, doi: 10.21541/apjes.657914.