Research Article
Euler Lagrange sistemlerinin uyarlamalı sinir ağları tabanlı çıkış geri beslemeli denetiminde konum sinyalinin sınırlandırılması
Abstract
Bu çalışmada, dinamik belirsizliklere sahip Euler Lagrange (EL) sistemlerinin konum takip problemine odaklanılmıştır. Özellikle, konum bilgisi elde edilirken hız bilgisinin kullanılamadığı ya da kullanılamadığı durum incelenmiştir. İkincil bir amaç olarak, her girişin takip hatasının önceden sınırlandırılması hedeflenmiştir. Konum takip hatasının önceden belirlenen bir bölgede olacak şekilde başlatılıp bu bölgede kalacağı kısıtları altında hedeflenen konumun takip edilmesi motivasyonu ile bir denetleyici tasarlanmıştır. EL sistemlerinin modelindeki belirsizliklerin bir kısmı gürbüz bileşenlerle bastırılarak telafi edilmiş, bir kısmı ise yenilikçi güncelleme kuralları kullanılarak yapay sinir ağları yaklaşımıyla kestirilip denetim yapısında kullanılmıştır. Hız ölçümlerinin mevcut olmaması durumunu telafi etmek için filtre temelli yöntemler kullanılmıştır. Konum sinyalinin sınırlı olması koşulu altında uyarlamalı sinir ağları tabanlı çıkış geri beslemeli yenilikçi bir denetleyici tasarlanmış, kapalı çevrim denetim sisteminin kararlılığı Lyapunov tabanlı metotlarla analiz edilmiştir. Tasarlanan denetleyicinin performansının değerlendirilmesi için iki serbestlik derecesine sahip düzlemsel robot modeli kullanılarak karşılaştırmalı benzetim çalışmaları gerçekleştirilmiştir.
References
- F.L. Lewis, D.M. Dawson and C.T. Abdallah, Robot Manipulator Control: Theory and Practice. CRC Press, Basel, 2003.
- G. Yüksel, T. Yiğit ve H Çelik, DA motor tahrikli dört serbestlik dereceli bir robot kolun 2-DOF PID ile kontrolü. 19. Otomatik Kontrol Türk Millî Komitesi Ulusal Toplantısı, sayfa 410-415, İstanbul, Türkiye, 2018.
- H. Berghuis and H. Nijmeijer, A passivity approach to controller-observer design for robots, IEEE Transactions on Robotics and Automation, 9 (6), 740-754, 1993. https://doi.org/10.1109/70.265918.
- R.O. Astolfi, and A. Venkatraman, A globally exponentially convergent immersion and invariance speed observer for mechanical systems with non-holonomic constraints. Automatica, 46 (5), 182–189, 2010. https://doi.org/10.1016/j.automatica.2009.10.027.
- M. Namvar, A class of globally convergent velocity observers for robotic manipulators. IEEE Transactions Automatic Control. 54 (8), 1956–1961, 2009. https://doi.org/10.1109/tac.2009.2023960.
- C. D. Wit and J. Slotine, Sliding observers for robot manipulators. Automatica, 27 (5), 859–864, 1991. https://doi.org/10.1016/b978-0-08-037022-4.50071-5.
- A. Abdessameud and M. F. Khelfi, A variable structure observer for the control of robot manipulators. International Journal of Applied Mathematics and Computer Science, 16 (2), 189–196, 2006. https://rb.gy/iyfqtb.
- Y. Xiong and M. Saif, Sliding mode observer for nonlinear uncertain systems. IEEE Transactions on Automatic Control, 46 (12), 2012–2017, 2001. https://doi.org/10.1109/9.975511.
- M. Dawson, Z. Qu, and J. C. Carroll, On the state observation and output feedback problems for nonlinear uncertain dynamic systems. Systems and Control Letters. 18, 2, 217–222, 1992. https://doi.org/10.1109/secon.1992.202244.
- A. Teel and L. Praly, Global stabilizability and observability imply semi global stabilizability by output feedback. Systems and Control Letters, 22 (2), 313–325, 1994. https://doi.org/10.1016/0167-6911(94)90029-9.
- N. Atassi and H. K. Khalil, A separation principle for the stabilization of a class of nonlinear systems. IEEE Transactions on Automatic Control, 44 (9), 1672–1687, 1999. https://doi.org/10.23919/ecc.1997.7082714.
- Y. Yuan and Y. Stepanenko, Robust control of robotic manipulators without velocity feedback. International Journal of Robust and Nonlinear Control, 1 (3), 203-213, 1991. https://doi.org/10.1002/rnc.4590010306.
- E. Zergeroglu, W. Dixon, D. Haste ve Dawson D, A composite adaptive output feedback tracking controller for robotic manipulators. Robotica, 17 (6), 591-600, 1999. https://doi.org/10.1109/acc.1999.782314.
- Y. H. Kim, F. Lewis and D.M. Dawson, Intelligent optimal control of robotic manipulators using neural networks. Automatica, 36 (9), 1355-1364, 2000. https://doi.org/10.1016/s0005-1098(00)00045-5.
- N. Cobanoglu, B.M. Yilmaz, E. Tatlicioglu ve E. Zergeroglu, Repetitive control of robotic manipulators in operational space: A neural network-based approach. International Journal of Robotics and Automation, 37 (3), 2022. https://doi.org/10.2316/j.2021.206-0654.
- K. B. Ngo, R. Mahony, and Z. P. Jiang, Integrator backstepping using barrier functions for systems with multiple state constraints, Proceedings of the 44th Conferance Decision and Control, pp. 8306–8312, Seville, Spain, 2005.
- K. P. Tee, S.S. Ge, ve E. H. Tay, Barrier Lyapunov functions for the control of output-constrained nonlinear systems, Automatica, 45 (4), 918–927, 2009. https://doi.org/10.1016/j.sysconle.2013.07.003.
- Y. Karayiannidis and Z. Doulgeri, Model-free robot joint position regulation and tracking with prescribed performance guarantees. Robotics and Autonomous Systems, 60 (2), 214–226, 2012. https://doi.org/10.1016/j.robot.2011.10.007.
- Y. Karayiannidis, D. Papageorgiou, and Z. Doulgeri, A model–free controller for guaranteed prescribed performance tracking of both robot joint positions and velocities. IEEE Robotics and Automation Letters, 1 (1), 267–273, 2016. https://doi.org/10.1109/lra.2016.2516245.
- S. Gul, E. Zergeroglu, and E. Tatlicioglu, Position Constrained, Adaptive Control of Robotic Manipulators without Velocity Measurements. arXiv preprint arXiv:2107.03056, 2021.
- S. Gul, E. Zergeroglu, E. Tatlicioglu, and M.V. Kilinc, Desired model compensation-based position constrained control of robotic manipulators. Robotica, 40 (2), 279-293, 2022. https://doi.org/10.1017/s0263574721000527.
- H. K. Khalil, Nonlinear Systems, Prentice Hall, Upper Saddle River, NJ, 2002.
- F. Lewis, S. Jagannathan and A. Yesildirek, Neural Network Control of Robot Manipulators and Nonlinear Systems. Taylor-Francis, London, 2020.
- P. Tomei, Adaptive PD controller for robot manipulators, IEEE Trans. Robotic and Automation, 7, 4, 565–570, 1991. https://doi.org/10.1109/70.86088.
Limitation of position signal in output feedback control based on adaptive neural networks of Euler Lagrange systems
Abstract
In this study, the position tracking problem of Euler-Lagrange (EL) systems with dynamic uncertainties is addressed. Specifically, the case where velocity information is not utilized while obtaining position information is investigated. As a secondary objective, the aim is to pre-bound the tracking error of each input. A controller has been designed with the motivation of tracking the desired position within a predetermined region, initiated with the position tracking error being confined to this region. In the model of EL systems, some of the uncertainties have been suppressed and compensated using robust components, while the remaining uncertainties have been estimated using an artificial neural network approach with innovative update rules and incorporated into the control structure. An innovative controller with output feedback based on adaptive neural networks was designed under the condition of limited position signal, and the stability of the closed-loop control system was analyzed by Lyapunov-based methods. Comparative simulation studies have been conducted to evaluate the performance of the designed controller using a two-degree-of-freedom planar robot model.
References
- F.L. Lewis, D.M. Dawson and C.T. Abdallah, Robot Manipulator Control: Theory and Practice. CRC Press, Basel, 2003.
- G. Yüksel, T. Yiğit ve H Çelik, DA motor tahrikli dört serbestlik dereceli bir robot kolun 2-DOF PID ile kontrolü. 19. Otomatik Kontrol Türk Millî Komitesi Ulusal Toplantısı, sayfa 410-415, İstanbul, Türkiye, 2018.
- H. Berghuis and H. Nijmeijer, A passivity approach to controller-observer design for robots, IEEE Transactions on Robotics and Automation, 9 (6), 740-754, 1993. https://doi.org/10.1109/70.265918.
- R.O. Astolfi, and A. Venkatraman, A globally exponentially convergent immersion and invariance speed observer for mechanical systems with non-holonomic constraints. Automatica, 46 (5), 182–189, 2010. https://doi.org/10.1016/j.automatica.2009.10.027.
- M. Namvar, A class of globally convergent velocity observers for robotic manipulators. IEEE Transactions Automatic Control. 54 (8), 1956–1961, 2009. https://doi.org/10.1109/tac.2009.2023960.
- C. D. Wit and J. Slotine, Sliding observers for robot manipulators. Automatica, 27 (5), 859–864, 1991. https://doi.org/10.1016/b978-0-08-037022-4.50071-5.
- A. Abdessameud and M. F. Khelfi, A variable structure observer for the control of robot manipulators. International Journal of Applied Mathematics and Computer Science, 16 (2), 189–196, 2006. https://rb.gy/iyfqtb.
- Y. Xiong and M. Saif, Sliding mode observer for nonlinear uncertain systems. IEEE Transactions on Automatic Control, 46 (12), 2012–2017, 2001. https://doi.org/10.1109/9.975511.
- M. Dawson, Z. Qu, and J. C. Carroll, On the state observation and output feedback problems for nonlinear uncertain dynamic systems. Systems and Control Letters. 18, 2, 217–222, 1992. https://doi.org/10.1109/secon.1992.202244.
- A. Teel and L. Praly, Global stabilizability and observability imply semi global stabilizability by output feedback. Systems and Control Letters, 22 (2), 313–325, 1994. https://doi.org/10.1016/0167-6911(94)90029-9.
- N. Atassi and H. K. Khalil, A separation principle for the stabilization of a class of nonlinear systems. IEEE Transactions on Automatic Control, 44 (9), 1672–1687, 1999. https://doi.org/10.23919/ecc.1997.7082714.
- Y. Yuan and Y. Stepanenko, Robust control of robotic manipulators without velocity feedback. International Journal of Robust and Nonlinear Control, 1 (3), 203-213, 1991. https://doi.org/10.1002/rnc.4590010306.
- E. Zergeroglu, W. Dixon, D. Haste ve Dawson D, A composite adaptive output feedback tracking controller for robotic manipulators. Robotica, 17 (6), 591-600, 1999. https://doi.org/10.1109/acc.1999.782314.
- Y. H. Kim, F. Lewis and D.M. Dawson, Intelligent optimal control of robotic manipulators using neural networks. Automatica, 36 (9), 1355-1364, 2000. https://doi.org/10.1016/s0005-1098(00)00045-5.
- N. Cobanoglu, B.M. Yilmaz, E. Tatlicioglu ve E. Zergeroglu, Repetitive control of robotic manipulators in operational space: A neural network-based approach. International Journal of Robotics and Automation, 37 (3), 2022. https://doi.org/10.2316/j.2021.206-0654.
- K. B. Ngo, R. Mahony, and Z. P. Jiang, Integrator backstepping using barrier functions for systems with multiple state constraints, Proceedings of the 44th Conferance Decision and Control, pp. 8306–8312, Seville, Spain, 2005.
- K. P. Tee, S.S. Ge, ve E. H. Tay, Barrier Lyapunov functions for the control of output-constrained nonlinear systems, Automatica, 45 (4), 918–927, 2009. https://doi.org/10.1016/j.sysconle.2013.07.003.
- Y. Karayiannidis and Z. Doulgeri, Model-free robot joint position regulation and tracking with prescribed performance guarantees. Robotics and Autonomous Systems, 60 (2), 214–226, 2012. https://doi.org/10.1016/j.robot.2011.10.007.
- Y. Karayiannidis, D. Papageorgiou, and Z. Doulgeri, A model–free controller for guaranteed prescribed performance tracking of both robot joint positions and velocities. IEEE Robotics and Automation Letters, 1 (1), 267–273, 2016. https://doi.org/10.1109/lra.2016.2516245.
- S. Gul, E. Zergeroglu, and E. Tatlicioglu, Position Constrained, Adaptive Control of Robotic Manipulators without Velocity Measurements. arXiv preprint arXiv:2107.03056, 2021.
- S. Gul, E. Zergeroglu, E. Tatlicioglu, and M.V. Kilinc, Desired model compensation-based position constrained control of robotic manipulators. Robotica, 40 (2), 279-293, 2022. https://doi.org/10.1017/s0263574721000527.
- H. K. Khalil, Nonlinear Systems, Prentice Hall, Upper Saddle River, NJ, 2002.
- F. Lewis, S. Jagannathan and A. Yesildirek, Neural Network Control of Robot Manipulators and Nonlinear Systems. Taylor-Francis, London, 2020.
- P. Tomei, Adaptive PD controller for robot manipulators, IEEE Trans. Robotic and Automation, 7, 4, 565–570, 1991. https://doi.org/10.1109/70.86088.
There are 24 citations in total.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Control Engineering |
| Journal Section | Research Articles |
| Authors | |
| Early Pub Date | December 20, 2023 |
| Publication Date | January 15, 2024 |
| Submission Date | July 12, 2023 |
| Acceptance Date | November 1, 2023 |
| Published in Issue | Year 2024 Volume: 13 Issue: 1 |
