Research Article
BibTex RIS Cite

Fırçasız DA motorları ile sürülen ve dinamik model belirsizlikleri içeren robot kollarının uyarlamalı denetimi

Year 2025, Volume: 31 Issue: 2, 225 - 234, 29.04.2025

Şükrü Ünver Erman Selim , Enver Tatlıcıoğlu , Erkan Zergeroğlu , Musa Alcı

Abstract

Bu çalışmada, eklemleri fırçasız doğru akım (DA) motorları kullanılarak sürülen ve dinamik modelinde parametrik belirsizlikler olan robot kolları için eyleyici dinamikleri de ele alınarak uyarlamalı görev uzayı takip denetleyicisi tasarımı gerçekleştirilmiştir. Denetleyici tasarımının doğrudan görev uzayında gerçekleştirilmesi sayesinde önerilen denetleyici yapısı pozisyon seviyesinde ters kinematik hesaplamalarına ihtiyaç duymamaktadır. Geliştirilen tam durum geri beslemeli ve ivme ölçümlerine ihtiyaç duymayan denetleyici yapısının robot dinamik modelindeki parametrik belirsizliklere rağmen küresel asimptotik kararlılığı Lyapunov tarzı sentez ve kararlılık analizi yöntemi kullanılarak garanti edilmiştir. Önerilen yöntemin performansını ve uygulanabilirliğini göstermek amacıyla düzlemde çalışan, iki serbestlik dereceli, eklemleri fırçasız DA motorları kullanılarak sürülen robot kolu modeli kullanılarak benzetim çalışması gerçekleştirilmiştir.

Keywords

Uyarlamalı denetim Robot kolları Görev uzayı Doğrusal olmayan kontrol Fırçasız DA motorları

References

  • [1] Yılmaz BM, Tatlıcıoğlu E, Savran A, Alcı M. “Self-adjusting fuzzy logic based control of robot manipulators in task space”. IEEE Transactions on Industrial Electronics, 69(2), 1620-1629, 2022.
  • [2] Uzuner S, Akkus N, Toz M. “5-DOF serial robot manipulator design, application and inverse kinematic solution through analytical method and simple search technique”. Pamukkale University Journal of Engineering Sciences, 26(2), 392-401, 2020.
  • [3] Uzuner S, Akkus N, Toz M. “5-DOF serial robot manipulator design, application and inverse kinematic solution through analytical method and simple search technique”. Pamukkale University Journal of Engineering Sciences, 26(2), 392-401, 2020.
  • [4] Cetin K. Control of Redundant Robot Manipulators with Telerobotic Applications. PhD Thesis, Izmir Institute of Technology, Izmir, Türkiye, 2016.
  • [5] Nakanishi J, Cory R, Mistry M, Peters J, Schaal S. “Operational space control: A theoretical and empirical comparison”. The International Journal of Robotics Research, 27(6), 737-757, 2008.
  • [6] Siciliano B, Khatib O, Kröger T. Springer Handbook of Robotics. 2nd ed. Berlin, Germany, Springer, 2008.
  • [7] Tarn TJ, Bejczy AK, Yun X, Li Z. “Effect of motor dynamics on nonlinear feedback robot arm control”. IEEE Transactions on Robotics and Automation, 7(1), 114-122, 1991.
  • [8] Wai RJ, Muthusamy R. “Design of fuzzy-neural-networkinherited backstepping control for robot manipulator including actuator dynamics”. IEEE Transactions on Fuzzy Systems, 22(4), 709-722, 2014.
  • [9] Good MC, Sweet LM, Strobel KL. “Dynamic models for control system design of integrated robot and drive systems”. Journal of Dynamic Systems, Measurement, and Control, 107(1), 53-59, 1985.
  • [10] Chwa D, Kwon H. “Nonlinear robust control of unknown robot manipulator systems with actuators and disturbances using system identification and integral sliding mode disturbance observer”. IEEE Access, 10, 35410-35421, 2022.
  • [11] Javad K, Xu B, Alfi A, Arabkoohsar A, Nazmara G. “Compound FAT-based prespecified performance learning control of robotic manipulators with actuator dynamics”. ISA Transactions, 131, 246-263, 2022.
  • [12] Saleki A, Fateh MM. “Model-free control of electrically driven robot manipulators using an extended state observer”. Computers and Electrical Engineering, 87, 106768, 2020.
  • [13] Shojaei K, Kazemy A, Chatraei A. “An observer-based neural adaptive PID2 controller for robot manipulators including motor dynamics with a prescribed performance”. IEEE/ASME Transactions on Mechatronics, 26(3), 1689-1699, 2021.
  • [14] Chen Z, Yang X, Liu X. “RBFNN-based nonsingular fast terminal sliding mode control for robotic manipulators including actuator dynamics”. Neurocomputing, 362, 72-82, 2019.
  • [15] Keighobadi J, Fateh MM, Xu B. “Adaptive fuzzy voltagebased backstepping tracking control for uncertain robotic manipulators subject to partial state constraints and input delay”. Nonlinear Dynamics, 100 (3), 2609–2634, 2020.
  • [16] Sedaghati A, Pariz N, Siahi M, Barzamini R. “A new fuzzy control system based on the adaptive immersion and invariance control for brushless DC motors”. International Journal of Dynamics and Control, 9(2), 807-817, 2021.
  • [17] Cheah CC. “Task-space regulation of robots with approximate actuator model”. Robotica, 21(1), 95–104, 2003.
  • [18] Liu C, Cheah CC. “Task-space adaptive setpoint control for robots with uncertain kinematics and actuator model”. IEEE Transactions on Automatic Control, 50(11), 1854-1860, 2005.
  • [19] Liu C, Cheah CC, Slotine JJ. “Adaptive jacobian PID regulation for robots with uncertain kinematics and actuator model”. IEEE/RSJ International Conference on Intelligent Robots and Systems, 3044-3049, 2006.
  • [20] Carrillo-Serrano RV, Hernández-Guzmán VM, Santibáñez V. “PD control with feedforward compensation for rigid robots actuated by brushless DC motors”. Robotica, 29(4), 507-514, 2011.
  • [21] Si W, Zhao L, Wei J, Guan Z. “Task-space regulation of rigidlink electrically-driven robots with uncertain kinematics using neural networks”. Measurement and Control, 54(1-2), 102-115, 2021.
  • [22] Kelek MM, Oğuz Y, Fidan U, Özer T. “Real-time control of load cell based two-wheel balancing robot using PID controller”. Pamukkale University Journal of Engineering Sciences, 27(5), 597-603, 2021.
  • [23] Bridges MM, Dawson DM. “Adaptive control of rigid-link electrically-driven robots actuated with brushless DC motors”. IEEE Conference on Decision and Control, Lake Buena Vista FL, USA, 14-16 December 1994.
  • [24] Ümütlü RC, Öztürk H, Bıdıklı B. “An adaptive controller design for ATMD system used in structures under the effect of unknown nonlinear effects”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi, 24(71), 571-579, 2022.
  • [25] Krstic M, Kanellakopoulos I, Kokotovic P. Nonlinear and Adaptive Control Design. 1st ed. New York, USA, John Wiley & Sons, Inc, 1995.
  • [26] Bıdıklı B. “A backstepping nonlinear control design for variable speed wind turbines”. Pamukkale University Journal of Engineering Sciences, 25(5), 560-570, 2019.
  • [27] Soltanpour MR, Khalilpour J, Soltani M. “Robust nonlinear control of robot manipulator with uncertainties in kinematics, dynamics and actuator models”. International Journal of Innovative Computing, Information and Control, 8(8), 5487-5498, 2012.
  • [28] Liu H, Zhang T. “Neural network-based robust finite-time control for robotic manipulators considering actuator dynamics”. Robotics and Computer-Integrated Manufacturing, 29(2), 301-308, 2013.
  • [29] Moreno-Valenzuela J, Campa R, Santibáñez V. “Modelbased control of a class of voltage-driven robot manipulators with non-passive dynamics”. Computers & Electrical Engineering, 39(7), 2086-2099, 2013.
  • [30] Zhou B, Yang L, Wang C, Chen Y, Chen K. “Inverse Jacobian adaptive tracking control of robot manipulators with kinematic, dynamic, and actuator uncertainties”. Complexity, 2020, 1-12, 2020.
  • [31] Seçil GE, Obuz S, Parlaktuna O. “Robust position/force control of nonholonomic mobile manipulator for constrained motion on surface in task space”. Turkish Journal of Electrical Engineering and Computer Sciences, 30(3), 785-804, 2022.
  • [32] Yılmaz BM, Tatlicioglu E. “Robot kolları için doğrusal süzgeç tabanlı çıkış geri beslemeli kontrolör tasarımında uyarlamalı yöntem yaklaşımı”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 30(6), 756-762, 2024.
  • [33] Dawson DM, Bridges MM, Qu Z. Nonlinear Control of Robotic Systems for Environmental waste and Restoration. 1st ed. New Jersey, USA, Prentice-Hall Inc, 1995.
  • [34] Lewis F, Dawson DM, Abdallah CT. Robot Manipulator Control: Theory and Practice. 2nd ed, Boca Raton, USA, CRC Press, 2003.
  • [35] Braganza DD, Dixon WE, Dawson DM, Xian B. “Tracking control for robot manipulators with kinematic and dynamic uncertainty”. International Journal of Robotics and Automation, 23(2), 5293-5297, 2008.
  • [36] Şahan G. “Exponential stability and boundedness of nonlinear perturbed systems by unbounded perturbation terms”. Journal of the Franklin Institute, 360(13), 10275-10296, 2023.
  • [37] Şahan G, Özdemir D. “Uniform asymptotic and input to state stability by indefinite Lyapunov functions”. European Journal of Control, 76, 100945, 2024.
  • [38] Bridges MM, Dawson DM, Gao X. “Adaptive control of rigid-link electrically-driven robots”. IEEE Conference on Decision and Control, Lake Buena Vista FL, USA, 14-16 December 1994.
  • [39] Kokotovic PV. “The joy of feedback: nonlinear and adaptive”. IEEE Control Systems Magazine, 12(3), 7-17, 1992.
  • [40] Şahan G. “Relaxation of conditions of Lyapunov functions”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 25(2), 238-244, 2021.
  • [41] Marquez HJ. Nonlinear Control Systems: Analysis and Design. 1st. ed. Edmonton Alberta, Canada. John Wiley & Sons, Inc, 2003.
  • [42] Şahan G. “Stability analysis by a nonlinear upper bound on the derivative of Lyapunov function”. European Journal of Control, 56, 118-123, 2020.
  • [43] Khalil HK. Nonlinear Systems. 2nd ed. New Jersey, USA, Prentice-Hall, Inc., 1996.
  • [44] Zergeroğlu E, Tatlıcıoğlu E. “Observer based output feedback tracking control of robot manipulators”. IEEE International Conference on Control Applications, Yokohama, Japan, 8-10 September 2010.
  • [45] Beyhan S. “An adaptive extended fuzzy function stateobserver based control with unknown control direction”. Pamukkale University Journal of Engineering Sciences, 23(5), 519-526, 2017.

Adaptive control of robot manipulators driven by brushless DC motors with uncertainties in dynamic model

Year 2025, Volume: 31 Issue: 2, 225 - 234, 29.04.2025

Şükrü Ünver Erman Selim , Enver Tatlıcıoğlu , Erkan Zergeroğlu , Musa Alcı

Abstract

In this study, an adaptive controller design is carried out for robot manipulators whose joints are driven using brushless direct current (BLDC) motors and which have parametric uncertainties in the dynamic model, by considering the actuator dynamics. Thanks to the realization of controller design directly in the task space, the proposed controller structure does not need inverse kinematics calculations at the position level. Despite the parametric uncertainties in the robot dynamic model, the global asymptotic stability of the developed controller structure with full state feedback, which does not need acceleration measurements, is guaranteed by using Lyapunov type synthesis and stability analysis method. To demonstrate the performance and feasibility of the proposed method, a simulation study was carried out using a two degree of freedom, planar robot manipulator model, whose joints are driven using BLDC motors.

Keywords

Adaptive control Robotic manipulators Task space Nonlinear control BLDC motors

References

  • [1] Yılmaz BM, Tatlıcıoğlu E, Savran A, Alcı M. “Self-adjusting fuzzy logic based control of robot manipulators in task space”. IEEE Transactions on Industrial Electronics, 69(2), 1620-1629, 2022.
  • [2] Uzuner S, Akkus N, Toz M. “5-DOF serial robot manipulator design, application and inverse kinematic solution through analytical method and simple search technique”. Pamukkale University Journal of Engineering Sciences, 26(2), 392-401, 2020.
  • [3] Uzuner S, Akkus N, Toz M. “5-DOF serial robot manipulator design, application and inverse kinematic solution through analytical method and simple search technique”. Pamukkale University Journal of Engineering Sciences, 26(2), 392-401, 2020.
  • [4] Cetin K. Control of Redundant Robot Manipulators with Telerobotic Applications. PhD Thesis, Izmir Institute of Technology, Izmir, Türkiye, 2016.
  • [5] Nakanishi J, Cory R, Mistry M, Peters J, Schaal S. “Operational space control: A theoretical and empirical comparison”. The International Journal of Robotics Research, 27(6), 737-757, 2008.
  • [6] Siciliano B, Khatib O, Kröger T. Springer Handbook of Robotics. 2nd ed. Berlin, Germany, Springer, 2008.
  • [7] Tarn TJ, Bejczy AK, Yun X, Li Z. “Effect of motor dynamics on nonlinear feedback robot arm control”. IEEE Transactions on Robotics and Automation, 7(1), 114-122, 1991.
  • [8] Wai RJ, Muthusamy R. “Design of fuzzy-neural-networkinherited backstepping control for robot manipulator including actuator dynamics”. IEEE Transactions on Fuzzy Systems, 22(4), 709-722, 2014.
  • [9] Good MC, Sweet LM, Strobel KL. “Dynamic models for control system design of integrated robot and drive systems”. Journal of Dynamic Systems, Measurement, and Control, 107(1), 53-59, 1985.
  • [10] Chwa D, Kwon H. “Nonlinear robust control of unknown robot manipulator systems with actuators and disturbances using system identification and integral sliding mode disturbance observer”. IEEE Access, 10, 35410-35421, 2022.
  • [11] Javad K, Xu B, Alfi A, Arabkoohsar A, Nazmara G. “Compound FAT-based prespecified performance learning control of robotic manipulators with actuator dynamics”. ISA Transactions, 131, 246-263, 2022.
  • [12] Saleki A, Fateh MM. “Model-free control of electrically driven robot manipulators using an extended state observer”. Computers and Electrical Engineering, 87, 106768, 2020.
  • [13] Shojaei K, Kazemy A, Chatraei A. “An observer-based neural adaptive PID2 controller for robot manipulators including motor dynamics with a prescribed performance”. IEEE/ASME Transactions on Mechatronics, 26(3), 1689-1699, 2021.
  • [14] Chen Z, Yang X, Liu X. “RBFNN-based nonsingular fast terminal sliding mode control for robotic manipulators including actuator dynamics”. Neurocomputing, 362, 72-82, 2019.
  • [15] Keighobadi J, Fateh MM, Xu B. “Adaptive fuzzy voltagebased backstepping tracking control for uncertain robotic manipulators subject to partial state constraints and input delay”. Nonlinear Dynamics, 100 (3), 2609–2634, 2020.
  • [16] Sedaghati A, Pariz N, Siahi M, Barzamini R. “A new fuzzy control system based on the adaptive immersion and invariance control for brushless DC motors”. International Journal of Dynamics and Control, 9(2), 807-817, 2021.
  • [17] Cheah CC. “Task-space regulation of robots with approximate actuator model”. Robotica, 21(1), 95–104, 2003.
  • [18] Liu C, Cheah CC. “Task-space adaptive setpoint control for robots with uncertain kinematics and actuator model”. IEEE Transactions on Automatic Control, 50(11), 1854-1860, 2005.
  • [19] Liu C, Cheah CC, Slotine JJ. “Adaptive jacobian PID regulation for robots with uncertain kinematics and actuator model”. IEEE/RSJ International Conference on Intelligent Robots and Systems, 3044-3049, 2006.
  • [20] Carrillo-Serrano RV, Hernández-Guzmán VM, Santibáñez V. “PD control with feedforward compensation for rigid robots actuated by brushless DC motors”. Robotica, 29(4), 507-514, 2011.
  • [21] Si W, Zhao L, Wei J, Guan Z. “Task-space regulation of rigidlink electrically-driven robots with uncertain kinematics using neural networks”. Measurement and Control, 54(1-2), 102-115, 2021.
  • [22] Kelek MM, Oğuz Y, Fidan U, Özer T. “Real-time control of load cell based two-wheel balancing robot using PID controller”. Pamukkale University Journal of Engineering Sciences, 27(5), 597-603, 2021.
  • [23] Bridges MM, Dawson DM. “Adaptive control of rigid-link electrically-driven robots actuated with brushless DC motors”. IEEE Conference on Decision and Control, Lake Buena Vista FL, USA, 14-16 December 1994.
  • [24] Ümütlü RC, Öztürk H, Bıdıklı B. “An adaptive controller design for ATMD system used in structures under the effect of unknown nonlinear effects”. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi, 24(71), 571-579, 2022.
  • [25] Krstic M, Kanellakopoulos I, Kokotovic P. Nonlinear and Adaptive Control Design. 1st ed. New York, USA, John Wiley & Sons, Inc, 1995.
  • [26] Bıdıklı B. “A backstepping nonlinear control design for variable speed wind turbines”. Pamukkale University Journal of Engineering Sciences, 25(5), 560-570, 2019.
  • [27] Soltanpour MR, Khalilpour J, Soltani M. “Robust nonlinear control of robot manipulator with uncertainties in kinematics, dynamics and actuator models”. International Journal of Innovative Computing, Information and Control, 8(8), 5487-5498, 2012.
  • [28] Liu H, Zhang T. “Neural network-based robust finite-time control for robotic manipulators considering actuator dynamics”. Robotics and Computer-Integrated Manufacturing, 29(2), 301-308, 2013.
  • [29] Moreno-Valenzuela J, Campa R, Santibáñez V. “Modelbased control of a class of voltage-driven robot manipulators with non-passive dynamics”. Computers & Electrical Engineering, 39(7), 2086-2099, 2013.
  • [30] Zhou B, Yang L, Wang C, Chen Y, Chen K. “Inverse Jacobian adaptive tracking control of robot manipulators with kinematic, dynamic, and actuator uncertainties”. Complexity, 2020, 1-12, 2020.
  • [31] Seçil GE, Obuz S, Parlaktuna O. “Robust position/force control of nonholonomic mobile manipulator for constrained motion on surface in task space”. Turkish Journal of Electrical Engineering and Computer Sciences, 30(3), 785-804, 2022.
  • [32] Yılmaz BM, Tatlicioglu E. “Robot kolları için doğrusal süzgeç tabanlı çıkış geri beslemeli kontrolör tasarımında uyarlamalı yöntem yaklaşımı”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 30(6), 756-762, 2024.
  • [33] Dawson DM, Bridges MM, Qu Z. Nonlinear Control of Robotic Systems for Environmental waste and Restoration. 1st ed. New Jersey, USA, Prentice-Hall Inc, 1995.
  • [34] Lewis F, Dawson DM, Abdallah CT. Robot Manipulator Control: Theory and Practice. 2nd ed, Boca Raton, USA, CRC Press, 2003.
  • [35] Braganza DD, Dixon WE, Dawson DM, Xian B. “Tracking control for robot manipulators with kinematic and dynamic uncertainty”. International Journal of Robotics and Automation, 23(2), 5293-5297, 2008.
  • [36] Şahan G. “Exponential stability and boundedness of nonlinear perturbed systems by unbounded perturbation terms”. Journal of the Franklin Institute, 360(13), 10275-10296, 2023.
  • [37] Şahan G, Özdemir D. “Uniform asymptotic and input to state stability by indefinite Lyapunov functions”. European Journal of Control, 76, 100945, 2024.
  • [38] Bridges MM, Dawson DM, Gao X. “Adaptive control of rigid-link electrically-driven robots”. IEEE Conference on Decision and Control, Lake Buena Vista FL, USA, 14-16 December 1994.
  • [39] Kokotovic PV. “The joy of feedback: nonlinear and adaptive”. IEEE Control Systems Magazine, 12(3), 7-17, 1992.
  • [40] Şahan G. “Relaxation of conditions of Lyapunov functions”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 25(2), 238-244, 2021.
  • [41] Marquez HJ. Nonlinear Control Systems: Analysis and Design. 1st. ed. Edmonton Alberta, Canada. John Wiley & Sons, Inc, 2003.
  • [42] Şahan G. “Stability analysis by a nonlinear upper bound on the derivative of Lyapunov function”. European Journal of Control, 56, 118-123, 2020.
  • [43] Khalil HK. Nonlinear Systems. 2nd ed. New Jersey, USA, Prentice-Hall, Inc., 1996.
  • [44] Zergeroğlu E, Tatlıcıoğlu E. “Observer based output feedback tracking control of robot manipulators”. IEEE International Conference on Control Applications, Yokohama, Japan, 8-10 September 2010.
  • [45] Beyhan S. “An adaptive extended fuzzy function stateobserver based control with unknown control direction”. Pamukkale University Journal of Engineering Sciences, 23(5), 519-526, 2017.
There are 45 citations in total.

Details

Primary Language Turkish
Subjects Computer System Software, Electrical Engineering (Other)
Journal Section Research Article
Authors

Şükrü Ünver

Erman Selim

Enver Tatlıcıoğlu

Erkan Zergeroğlu

Musa Alcı

Publication Date April 29, 2025
Published in Issue Year 2025 Volume: 31 Issue: 2

Cite

APA Ünver, Ş., Selim, E., Tatlıcıoğlu, E., Zergeroğlu, E., et al. (2025). Fırçasız DA motorları ile sürülen ve dinamik model belirsizlikleri içeren robot kollarının uyarlamalı denetimi. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, 31(2), 225-234.
AMA Ünver Ş, Selim E, Tatlıcıoğlu E, Zergeroğlu E, Alcı M. Fırçasız DA motorları ile sürülen ve dinamik model belirsizlikleri içeren robot kollarının uyarlamalı denetimi. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi. April 2025;31(2):225-234.
Chicago Ünver, Şükrü, Erman Selim, Enver Tatlıcıoğlu, Erkan Zergeroğlu, and Musa Alcı. “Fırçasız DA Motorları Ile sürülen Ve Dinamik Model Belirsizlikleri içeren Robot kollarının Uyarlamalı Denetimi”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi 31, no. 2 (April 2025): 225-34.
EndNote Ünver Ş, Selim E, Tatlıcıoğlu E, Zergeroğlu E, Alcı M (April 1, 2025) Fırçasız DA motorları ile sürülen ve dinamik model belirsizlikleri içeren robot kollarının uyarlamalı denetimi. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi 31 2 225–234.
IEEE Ş. Ünver, E. Selim, E. Tatlıcıoğlu, E. Zergeroğlu, and M. Alcı, “Fırçasız DA motorları ile sürülen ve dinamik model belirsizlikleri içeren robot kollarının uyarlamalı denetimi”, Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, vol. 31, no. 2, pp. 225–234, 2025.
ISNAD Ünver, Şükrü et al. “Fırçasız DA Motorları Ile sürülen Ve Dinamik Model Belirsizlikleri içeren Robot kollarının Uyarlamalı Denetimi”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi 31/2 (April 2025), 225-234.
JAMA Ünver Ş, Selim E, Tatlıcıoğlu E, Zergeroğlu E, Alcı M. Fırçasız DA motorları ile sürülen ve dinamik model belirsizlikleri içeren robot kollarının uyarlamalı denetimi. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi. 2025;31:225–234.
MLA Ünver, Şükrü et al. “Fırçasız DA Motorları Ile sürülen Ve Dinamik Model Belirsizlikleri içeren Robot kollarının Uyarlamalı Denetimi”. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi, vol. 31, no. 2, 2025, pp. 225-34.
Vancouver Ünver Ş, Selim E, Tatlıcıoğlu E, Zergeroğlu E, Alcı M. Fırçasız DA motorları ile sürülen ve dinamik model belirsizlikleri içeren robot kollarının uyarlamalı denetimi. Pamukkale Üniversitesi Mühendislik Bilimleri Dergisi. 2025;31(2):225-34.





Creative Commons Lisansı
Bu dergi Creative Commons Al 4.0 Uluslararası Lisansı ile lisanslanmıştır.