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Giriş Kısıtlı Ters Sarkaç Mekanizmasının Optimal Kontrolü

Year 2021, Issue: 25, 247 - 255, 31.08.2021
https://doi.org/10.31590/ejosat.898753

Abstract

Günümüz eyleyici ve algılayıcı teknolojilerindeki hızlı gelişmeler, çok farklı eyleyici ve algılayıcı kombinasyonları içeren platformlarının geliştirilmesine öncülük etmiştir. Bahsi geçen platformların potansiyellerini en iyi şekilde değerlendirebilmek amacıyla kontrol sistemlerinde yeni metotların geliştirilmesi bir gereklilik haline gelmiş ve yeni kontrol metotları modern kontrol adı altında toplanmaya başlamıştır. Modern kontrolün alt başlıklarından biri olan optimal kontrol, bilgisayarların işlem güçlerinin artmasıyla birlikte günümüzde çok yaygın olarak kullanılmaya başlanmıştır. Bu çalışmada klasik kontrol metotlarına kıyasla çeşitli avantajları olan optimal kontrolün alt başlıklarından dört tanesi olan sonlu ufuklu LQR, sonsuz ufuklu LQR, sonlu ufuklu MPC ve ikili mod MPC kontrolcülerinin uygulamaları incelenmiştir. Bu inceleme dijital bilgisayarların doğasına uygun olarak süreksiz zaman uzayında gerçekleştirilmiştir. Bahsi geçen dört kontrolcünün kontrol performanslarının gözlenebilmesi amacıyla bir ters sarkaç sistem modeli kullanılmıştır. Ters sarkaç mekanizması doğrusal olmayan, stabil olmayan ve eklem sayısından daha az sayıda eyleyiciye sahip olan yapısı sebebiyle kapsayıcı bir dinamik modeldir. Bu çalışmayı incelemesinin ardından okuyucu bu dört kontrol sistemleri arasından hangisinin hangi durumlarda nasıl uygulanması gerektiği hakkında fikir sahibi olacaktır.

References

  • Akgul, E., Mutlu, M., Saranli, A., & Yazicioglu, Y. (2012). A comparative evaluation of adaptive and non-adaptive Sliding Mode, LQR & PID control for platform stabilization. 2012 IEEE International Conference on Control Applications. doi:10.1109/cca.2012.6402701
  • Arifianto, O., & Farhood, M. (2015). Optimal control of a small fixed-wing UAV about concatenated trajectories. Control Engineering Practice, 40, 113-132. doi:10.1016/j.conengprac.2015.03.007
  • Batkovic, I., Zanon, M., Ali, M., & Falcone, P. (2019). Real-time constrained trajectory planning and vehicle control for proactive autonomous driving with road users. 2019 18th European Control Conference (ECC). doi:10.23919/ecc.2019.8796099
  • Çeven, S , Albayrak, A . (2020). Çift Ters Sarkaç Sisteminin Kontrolü için PID ve LQR Kontrolcü Tasarımlarının Modellenmesi . Avrupa Bilim ve Teknoloji Dergisi , Ejosat Özel Sayı 2020 (HORA) , 323-330 . DOI: 10.31590/ejosat.780070
  • Ding, Y., Pandala, A., & Park, H. (2019). Real-time Model Predictive Control for Versatile Dynamic Motions in Quadrupedal Robots. 2019 International Conference on Robotics and Automation (ICRA). doi:10.1109/icra.2019.8793669
  • Frasch, J. V., Gray, A., Zanon, M., Ferreau, H. J., Sager, S., Borrelli, F., & Diehl, M. (2013). An auto-generated nonlinear mpc algorithm for real-time obstacle avoidance of ground vehicles. 2013 European Control Conference (ECC). doi:10.23919/ecc.2013.6669836
  • Greer, W. B., & Sultan, C. (2020). Shrinking horizon model predictive control method for helicopter–ship touchdown. Journal of Guidance, Control, and Dynamics, 43(5), 884-900. doi:10.2514/1.g004374
  • Kamel, M., Burri, M., & Siegwart, R. (2017). Linear vs Nonlinear MPC for Trajectory Tracking Applied to Rotary Wing Micro Aerial Vehicles. IFAC-PapersOnLine, 50(1), 3463-3469. doi:10.1016/j.ifacol.2017.08.849
  • Kirk, D. E. (2004). Optimal control theory: An introduction. Mineola, NY: Dover Publications.
  • Villarreal, O., Barasuol, V., Wensing, P. M., Caldwell, D. G., & Semini, C. (2020). MPC-based controller with terrain insight for DYNAMIC legged locomotion. 2020 IEEE International Conference on Robotics and Automation (ICRA). doi:10.1109/icra40945.2020.9197312
  • Zhang, H., Cheng, Z., Chen, G., & Li, C. (2015). Model predictive Flocking control for Second-order multi-agent systems with input constraints. IEEE Transactions on Circuits and Systems I: Regular Papers, 62(6), 1599-1606. doi:10.1109/tcsi.2015.2418871
  • Wang, J., Cui, N., & Wei, C. (2019). Optimal rocket landing guidance using convex optimization and model predictive control. Journal of Guidance, Control, and Dynamics, 42(5), 1078-1092. doi:10.2514/1.g003518

Optimal Control of Input Constrained Inverted Pendulum

Year 2021, Issue: 25, 247 - 255, 31.08.2021
https://doi.org/10.31590/ejosat.898753

Abstract

Rapid developments in today's actuator and sensor technologies have pioneered the development of platforms containing very different actuator and sensor combinations. In order to utilize the potentials of the platforms in the best way, it has become a necessity to develop new methods in control systems and new control methods have begun to be gathered under the name of modern control. The optimal control, which is one of the subtitles of modern control, has started to be used widely today with the increase in the processing power of computers. In this study, applications of finite horizon LQR, infinite horizon LQR, finite horizon MPC and dual mode prediction MPC controllers, which are four of the subtitles of optimal control, which have various advantages compared to classical control methods, have been investigated. This investigation was carried out in discrete time space in accordance with the nature of digital computers. An inverted pendulum system model is used to observe the control performances of the four controllers. The inverted pendulum mechanism is an inclusive dynamic model due to its nonlinear, unstable and underactuated nature. After reviewing this study, the reader will have an idea of which of these four control systems should be applied in which situations.

References

  • Akgul, E., Mutlu, M., Saranli, A., & Yazicioglu, Y. (2012). A comparative evaluation of adaptive and non-adaptive Sliding Mode, LQR & PID control for platform stabilization. 2012 IEEE International Conference on Control Applications. doi:10.1109/cca.2012.6402701
  • Arifianto, O., & Farhood, M. (2015). Optimal control of a small fixed-wing UAV about concatenated trajectories. Control Engineering Practice, 40, 113-132. doi:10.1016/j.conengprac.2015.03.007
  • Batkovic, I., Zanon, M., Ali, M., & Falcone, P. (2019). Real-time constrained trajectory planning and vehicle control for proactive autonomous driving with road users. 2019 18th European Control Conference (ECC). doi:10.23919/ecc.2019.8796099
  • Çeven, S , Albayrak, A . (2020). Çift Ters Sarkaç Sisteminin Kontrolü için PID ve LQR Kontrolcü Tasarımlarının Modellenmesi . Avrupa Bilim ve Teknoloji Dergisi , Ejosat Özel Sayı 2020 (HORA) , 323-330 . DOI: 10.31590/ejosat.780070
  • Ding, Y., Pandala, A., & Park, H. (2019). Real-time Model Predictive Control for Versatile Dynamic Motions in Quadrupedal Robots. 2019 International Conference on Robotics and Automation (ICRA). doi:10.1109/icra.2019.8793669
  • Frasch, J. V., Gray, A., Zanon, M., Ferreau, H. J., Sager, S., Borrelli, F., & Diehl, M. (2013). An auto-generated nonlinear mpc algorithm for real-time obstacle avoidance of ground vehicles. 2013 European Control Conference (ECC). doi:10.23919/ecc.2013.6669836
  • Greer, W. B., & Sultan, C. (2020). Shrinking horizon model predictive control method for helicopter–ship touchdown. Journal of Guidance, Control, and Dynamics, 43(5), 884-900. doi:10.2514/1.g004374
  • Kamel, M., Burri, M., & Siegwart, R. (2017). Linear vs Nonlinear MPC for Trajectory Tracking Applied to Rotary Wing Micro Aerial Vehicles. IFAC-PapersOnLine, 50(1), 3463-3469. doi:10.1016/j.ifacol.2017.08.849
  • Kirk, D. E. (2004). Optimal control theory: An introduction. Mineola, NY: Dover Publications.
  • Villarreal, O., Barasuol, V., Wensing, P. M., Caldwell, D. G., & Semini, C. (2020). MPC-based controller with terrain insight for DYNAMIC legged locomotion. 2020 IEEE International Conference on Robotics and Automation (ICRA). doi:10.1109/icra40945.2020.9197312
  • Zhang, H., Cheng, Z., Chen, G., & Li, C. (2015). Model predictive Flocking control for Second-order multi-agent systems with input constraints. IEEE Transactions on Circuits and Systems I: Regular Papers, 62(6), 1599-1606. doi:10.1109/tcsi.2015.2418871
  • Wang, J., Cui, N., & Wei, C. (2019). Optimal rocket landing guidance using convex optimization and model predictive control. Journal of Guidance, Control, and Dynamics, 42(5), 1078-1092. doi:10.2514/1.g003518
There are 12 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Sait Sovukluk 0000-0002-8698-8835

Mert Ankaralı 0000-0002-1235-5373

Publication Date August 31, 2021
Published in Issue Year 2021 Issue: 25

Cite

APA Sovukluk, S., & Ankaralı, M. (2021). Giriş Kısıtlı Ters Sarkaç Mekanizmasının Optimal Kontrolü. Avrupa Bilim Ve Teknoloji Dergisi(25), 247-255. https://doi.org/10.31590/ejosat.898753