Arabalı Ters Sarkaç Sisteminin Dengelenmesi için Farklı Oransal-Türevsel Denetim Tabanlı Bulanık Üyelik Fonksiyonlarının Başarımlarının İncelenmesi

Yıl 2022, Cilt: 38 Sayı: 3, 483 - 499, 30.12.2022

Ahmet Gani Hasan Rıza Özçalık

Öz

Bu çalışmada, arabalı bir ters sarkaç (TS) sisteminin oransal-türevsel denetim tabanlı farklı üyelik fonksiyonlu (MF) bulanık denetleyiciler kullanılarak dengelenmesi amaçlanmıştır. Bu amaçla araba yatay konumda (çizgisel konum) arzu edilen yörüngeyi takip ederken, sarkacın da dikey konumda (açısal konum) dengede kalması sağlanmıştır. Tasarlanan denetim sistemine ait benzetim çalışmaları Matlab/Simulink ortamında yapılmış olup sarkacın dikey ve arabanın yatay konum denetimi için elde edilen başarım değerleri ayrı ayrı verilmiştir. Benzetim çalışmasından edilen denetim başarım değerleri incelendiğinde sarkacın dikey konumu için yükselme zamanı, yerleşme zamanı ve aşım bakımından üçgen bulanık üyelik fonksiyonunun gauss bulanık üyelik fonksiyonuna göre sırasıyla %8, %4.35 ve %7.7 oranlarında iyileştirme yaptığı görülmüştür. Benzer şekilde arabanın yatay konumu için de yükselme zamanı, yerleşme zamanı ve aşım bakımından üçgen bulanık üyelik fonksiyonunun (ÜF) gauss bulanık ÜF’ye göre sırasıyla %3.8, %3 ve %30 oranlarında daha iyi denetim başarımına sahip olduğu görülmüştür. Sarkacın dikey konum ve arabanın yatay konum denetimi için tüm denetim başarım değerleri analiz edildiğinde üçgen bulanık ÜF’nin gauss bulanık ÜF’ye göre daha tatmin edici sonuçlar verdiği açıkça görülmüştür.

Anahtar Kelimeler

Arabalı Ters Sarkaç, Oransal-Türevsel Denetim, Farklı Bulanık üyelik fonksiyonları

The Investigation of Performances of Different Proportional-Derivative Control Based Fuzzy Membership Functions in Balancing the Inverted Pendulum (IP) System on Cart

Öz

The present study aims to balance an inverted pendulum (IP) system on cart using fuzzy controllers with different membership functions (MFs) based on proportional-derivative control. To this end, the cart was designed to track an intended trajectory in a horizontal (linear) position, while the IP was balanced in a vertical (angular) position. The designed controller system was simulated in Matlab/Simulink, and performance rates were measured for the IP’s vertical position and the cart’s horizontal position. The obtained simulation results demonstrated that triangular fuzzy membership function (MF) improved rise time, settling time and overshoot for the IP’s vertical position by 8%, 4.35% and 7.7%, respectively, compared to gaussian fuzzy MF. Similarly, for the cart’s horizontal position, triangular fuzzy MF improved rise time, settling time and overshoot by 3.8%, 3 and 30%, respectively, compared to gaussian fuzzy MF. When all performance rates are analyzed in terms of the IP’s vertical position and the cart’s horizontal position, it was found that triangular fuzzy MF displayed a more satisfactory performance compared to Gaussian fuzzy MF.

Anahtar Kelimeler

Inverted Pendulum on Cart, Different Fuzzy Membership Functions, Proportional- Derivative Control

Kaynakça

• [1] Peker, F., Kaya, İ., 2017. PID tip denetleyiciler kullanılarak yapılan bir ters sarkaç stabilizasyonunun performans analizi. Dicle Üniversitesi Mühendislik Fakültesi Mühendislik Dergisi, 8(3), (2017). 563-574.
• [2] Yoshida, K., 1999.Swing-up control of an inverted pendulum by energy-based methods. In Proceedings of the 1999 American Control Conference, 02-04 June 1999. (Vol. 6, pp. 4045-4047). IEEE.
• [3] Razzaghi, K., Jalali, A. A., 2012. A new approach on stabilization control of an inverted pendulum, using PID controller. In Advanced Materials Research, Vol. 403, (2012), 4674-4680. Trans Tech Publications Ltd.
• [4] Gani, A., 2014. Lineer olmayan dinamik sistemlerin denetiminde bulanık mantık esaslı denetim yöntemlerinin performansının incelenmesi. Kahramanmaraş Sütçü İmam Üniversitesi, Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi, 95s, Kahramanmaraş.
• [5] Furuta, K., Okutani, T., Sone, H., 1978. Computer control of a double inverted pendulum. Computers & Electrical Engineering, 5(1), 67-84.
• [6] Jaiwat, P., Ohtsuka, T., 2014. Real-time swing-up of double inverted pendulum by nonlinear model predictive control. In 5th International Symposium on Advanced Control of Industrial Processes (pp. 290-295).
• [7] Åström, K. J., Furuta, K., 2000. Swinging up a pendulum by energy control. Automatica, 36(2), (2000), 287-295.
• [8] Gordillo, F., Acosta, J. A., Aracil, J.2003. A new swing-up law for the Furuta pendulum. International Journal of Control, 76(8), (2003), 836-844.
• [9] Peker, F., & Kaya, İ., 2016. Performance analysis of an inverted pendulum stabilisation based on PID Controllers. In Proceedings International Engineering, Science and Education Conference, 01-03 December 2016 (pp. 640-646).
• [10] Peker, F., 2017. Ters sarkaç sisteminin PI-PD denetleyici kullanılarak kontrol edilmesi. Dicle Üniversitesi, Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi, 80s. Diyarbakır.
• [11] Samara, R., Hikmarika, H., Dwijayanti, S., & Suprapto, B. Y. 2019. Comparison of Inverted Pendulum control system using Proportional–Integral–Derivative (PID) and Proportional–Integral (PI). In 2019 International Conference on Electrical Engineering and Computer Science (ICECOS) (pp. 316-320). IEEE.
• [12] Peker, F., & Kaya, I., 2017. Identification and real time control of an inverted pendulum using PI-PD controller. In 2017 21st International Conference on System Theory, Control and Computing (ICSTCC) (pp. 771-776). IEEE.
• [13] Kuśmierz, B., Gromaszek, K., & Kryk, K., 2018. Inverted pendulum model Linear–Quadratic Regulator (LQR). In Photonics Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2018 (Vol. 10808, pp. 1921-1928). SPIE.
• [14] Lee, H. W., 2017. Performance the balance of circular inverted pendulum by using lqr controlled theory. In 2017 IEEE International Conference on Consumer Electronics-Taiwan (ICCE-TW) (pp. 415-416). IEEE.
• [15] Wan, L. L., Lei, J., & Wu, H. X. 2014. Design of LQR Controller for the Inverted Pendulum. In Advanced Materials Research (Vol. 1037, pp. 221-224). Trans Tech Publications Ltd.
• [16] Kumar, C., Lal, S., Patra, N., Halder, K., & Reza, M., 2012. Optimal controller design for inverted pendulum system based on LQR method. In 2012 IEEE International Conference on Advanced Communication Control and Computing Technologies (ICACCCT) (pp. 259-263). IEEE.
• [17] Fang, H., Tang, W., & Zheng, E., 2012. Research on inverted pendulum control based on LQR. In Advances in Mechanical and Electronic Engineering (pp. 375-380). Springer, Berlin, Heidelberg.
• [18] Peng, Y., & Liu, Z. N., 2012. Optimal Design of LQR Controller for Single Inverted Pendulum. In Advanced Materials Research (Vol. 472, pp. 1505-1509). Trans Tech Publications Ltd.
• [19] Wang, H., Dong, H., He, L., Shi, Y., & Zhang, Y. 2010. Design and simulation of LQR controller with the linear inverted pendulum. In 2010 international conference on electrical and control engineering (pp. 699-702). IEEE.
• [20] Lingyan, H., Guoping, L., Xiaoping, L., & Hua, Z. 2009. The computer simulation and real-time stabilization control for the inverted pendulum system based on LQR. In 2009 Fifth International Conference on Natural Computation (Vol. 6, pp. 438-442). IEEE.
• [21] Czyżniewski, M., Łangowski, R., Klassa, D., & Matwiszyn, M., 2021. A case study of robust sliding mode control applied to inverted pendulum on a cart. In 2021 25th International Conference on Methods and Models in Automation and Robotics (MMAR) (pp. 156-161). IEEE.
• [22] Osman, N., Fareh, R., Tha'er, O. S., Khalid, H. M., & Ghommam, J. 2021. Inverted Pendulum System Disturbance and Uncertainty Effects Reduction using Sliding Mode-Based Control Design. In 2021 18th International Multi-Conference on Systems, Signals & Devices (SSD) (pp. 186-193). IEEE.
• [23]Cui, J., 2019. Numerical Design Method for Nonlinear Sliding Mode Control of Inverted Pendulum. In 2019 Chinese Control Conference (CCC) (pp. 2646-2649). IEEE.
• [24]Bsili, I., Ghabi, J., & Messaoud, H., 2015. Discrete sliding mode control of inverted pendulum. In 2015 World Symposium on Mechatronics Engineering & Applied Physics (WSMEAP) (pp. 1-6). IEEE.
• [25]Rudra, S., & Barai, R. K., 2012. Robust adaptive backstepping control of inverted pendulum on cart system. International journal of control and automation, 5(1), 13-26.
• [26]Deng, L., & Gao, S.,2011. The design for the controller of the linear inverted pendulum based on backstepping. In Proceedings of 2011 International Conference on Electronic & Mechanical Engineering and Information Technology (Vol. 6, pp. 2892-2895). IEEE.
• [27] Ebrahim, A., & Murphy, G. V.2005. Adaptive backstepping controller design of an inverted pendulum. In Proceedings of the Thirty-Seventh Southeastern Symposium on System Theory, 2005. SSST'05. (pp. 172-174). IEEE.
• [28]Singh, V. K., & Kumar, V., 2014. Adaptive backstepping control design for stabilization of inverted pendulum. In 2014 Students Conference on Engineering and Systems (pp. 1-5). IEEE.
• [29]Korkmaz, D., Bal, C., & Gökbulut, M.,2015. Modeling of inverted pendulum on a cart by using Artificial Neural Networks. In 2015 23nd Signal Processing and Communications Applications Conference (SIU) (pp. 2642-2645). IEEE.
• [30]Mladenov, V.,2011. Application of neural networks for control of inverted pendulum. WSEAS Transactions on circuits and systems, 10(2), 49-58.
• [31] Noh, J. S., Lee, G. H., Choi, H. J., & Jung, S.,2009. Robust control of a mobile inverted pendulum robot using a RBF neural network controller. In 2008 IEEE International Conference on Robotics and Biomimetics (pp. 1932-1937). IEEE.
• [32]Kim, S. S., Lee, G. H., & Jung, S.,2008. Implementation of a neural network controller on a DSP for controlling an inverted pendulum system on an XY plane. IFAC Proceedings Volumes, 41(2), 5439-5443.
• [33]Kharola, A., 2016. Design of a hybrid adaptive neuro fuzzy inference system (ANFIS) controller for position and angle control of inverted pendulum (IP) systems. International Journal of Fuzzy System Applications (IJFSA), 5(1), 27-42.
• [34]Tatikonda, R. C., Battula, V. P., & Kumar, V.,2010. Control of inverted pendulum using adaptive neuro fuzzy inference structure (ANFIS). In Proceedings of 2010 IEEE international symposium on circuits and systems (pp. 1348-1351). IEEE.
• [35]Al-Mekhlafi, M. A., Wahid, H., & Aziz, A. A., 2018. Adaptive neuro-fuzzy control approach for a Single Inverted Pendulum System. International Journal of Electrical & Computer Engineering (2088-8708), 8(5).
• [36]Meenakshi, R., & Manimozhi, M.,2016. Adaptive neuro-fuzzy inference system controller design for single stage inverted pendulum. In 2016 International Conference on Computation of Power, Energy Information and Commuincation (ICCPEIC) (pp. 472-476). IEEE.
• [37] Tatikonda, R. C., Battula, V. P., & Kumar, V.,2010. Control of inverted pendulum using adaptive neuro-fuzzy inference structure (ANFIS). In Proceedings of 2010 IEEE international symposium on circuits and systems (pp. 1348-1351). IEEE.
• [38]Mousa, M. E., Ebrahim, M. A., Zaky, M. M., Saied, E. M., & Kotb, S. A., 2021. Hybrid optimization technique for enhancing the stability of inverted pendulum system. International Journal of Swarm Intelligence Research (IJSIR), 12(1), 77-97.
• [39]Maity, S., & Luecke, G. R., 2019. Stabilization and optimization of design parameters for control of inverted pendulum. Journal of dynamic systems, measurement, and control, 141(8).
• [40]Singhal, N. K., & Swarup, A.,2019. Performance improvement of inverted pendulum using optimization algorithms. In 2019 3rd international conference on electronics, communication and aerospace technology (ICECA) (pp. 316-322). IEEE.
• [41] Hou, X. L., & Xu, X. H. 2006. Optimization of feedback control parameters of equilibrium point about nonlinear inverted pendulum. Kongzhi Lilun yu Yingyong/ Control Theory & Applications, 23(3), 467-470.
• [42]Chmielewski, A., Gumiński, R., Maciąg, P., & Mączak, J. (2016). The use of fuzzy logic in the control of an inverted pendulum. In Dynamical Systems: Theoretical and Experimental Analysis (pp. 71-82). Springer, Cham.
• [43]Huang, Y. H., Zhang, L., Zhang, P. P., Ru, F. F., & Wang, K. Q.,2015. Fuzzy control and simulation of single inverted pendulum. In Control Engineering and Information Systems: Proceedings of the 2014 International Conference on Control Engineering and Information Systems (ICCEIS 2014, Yueyang, Hunan, China, 20-22 June 2014). (p. 109). CRC Press.
• [44]Pal, A. K., & Chakrabarty, J., 2014. Adaptive fuzzy control of inverted pendulum with a fuzzy-based set-point weighting scheme. In 2014 Fourth International Conference of Emerging Applications of Information Technology (pp. 46-51). IEEE.
• [45]Tripathi, S. K., Panday, H., & Gaur, P.,2013. Robust control of Inverted Pendulum using fuzzy logic controller. In 2013 Students Conference on Engineering and Systems (SCES) (pp. 1-6). IEEE.
• [46]Wang, H., & Bai, Y.,2013. Application of fuzzy control in the inverted pendulum. In Proceedings of 2013 2nd International Conference on Measurement, Information and Control (Vol. 2, pp. 1354-1357). IEEE.
• [47]Prasad, L. B., Gupta, H. O., & Tyagi, B.,2011. Intelligent control of nonlinear inverted pendulum dynamical system with disturbance input using fuzzy logic systems. In 2011 International Conference on Recent Advancements in Electrical, Electronics and Control Engineering (pp. 136-141). IEEE.
• [48]Roose, A. I., Yahya, S., & Al-Rizzo, H., 2017. Fuzzy-logic control of an inverted pendulum on a cart. Computers & Electrical Engineering, 61, 31-47.
• [49]Pham, D. B., Pham, D. T., Dao, Q. T., & Nguyen, V. A.,2022. Takagi-Sugeno fuzzy control for stabilizing nonlinear inverted pendulum. In Intelligent Systems and Networks (pp. 333-341). Springer, Singapore.
• [50]Patra, A. K., Mishra, A. K., Agrawal, R., & Nahak, N.,2021. Stabilizing and trajectory tracking of inverted pendulum based on fuzzy logic control. In Intelligent and Cloud Computing (pp. 563-573). Springer, Singapore.
• [51] Kulikova, I. V.,2020. Control the movement of an inverted pendulum by using a first-order type Takagi-Sugeno-Kang fuzzy controller. In Journal of Physics: Conference Series (Vol. 1546, No. 1, p. 012088). IOP Publishing.
• [52]Gani, A., Açikgoz, H., Kiliç, E., & Sit, S., 2014. Fuzzy logic based control of inverted pendulum. Elektrik - Elektronik, Bilgisayar ve Biyomedikal Mühendisliği Sempozyumu, 27, 29 November 2014. Bursa.
• [53]Gani, A., Kececioglu, O. F., Acikgoz, H., & Sekkeli, M.,2017. Fuzzy logic controller design based on Sugeno inference method for nonlinear inverted pendulum dynamical system. Sigma Journal of Engineering and Natural Sciences-Sigma Muhendislik ve Fen Bilimleri Dergisi, 8(1), 19-30.
• [54]Gani, A., Baş, Z., Acikgoz, H., & Kececioglu, O., 2014. Control of nonlinear dynamic inverted pendulum system using fuzzy logic based control methods. International Journal of Engineering Research & Technology, 3(9), 1400-1404.
• [55]Nguyen, N. , Pham, V., Ho, T., & Dao, T., 2022. Designing an effective hybrid control strategy to balance a practical inverted pendulum system. International Journal of Engineering Trends and Technology, 70(5), 80-87. doi:10.14445/22315381/IJETT-V70I5P210.
• [56]Kharola, A., 2016. Design of a hybrid adaptive neuro fuzzy inference system (ANFIS) controller for position and angle control of inverted pendulum (IP) systems. International Journal of Fuzzy System Applications (IJFSA), 5(1), 27-42.
• [57]Sit, S., Kilic, E., Ozcalik, H. R., Alhasan, H. A., & Gani, A.,2016. Modelling and performance comparison of PD and Takagi-Sugeno type fuzzy logic controllers for inverted pendulum system. Bitlis Eren University Journal of Science and Technology, 6(2), (2016), 76-84.
• [58]Patel, N., & Nigam, M. J.,2013. Design of fuzzy PD controller for inverted pendulum in real time. In Proceedings of International Conference on Advances in Computing (pp. 955-962). Springer, New Delhi.
• [59]Gani, A., Açikgoz, H., Kiliç, E., & Sit, S. PD-Bulanık mantık denetleyici ve PD denetleyici kullanarak ters sarkaç sisteminin dinamik performans analizi Uluslararasi Hakemli Mühendislik ve Fen Bilimleri Dergisi 2(1), 2014.
• [60]Gani, A., Ozcalik, H. R., Sekkeli, M., Kececioglu, O. F., & Sit, S., 2016. Dynamic performance comparison of PD and PD-fuzzy logic controllers for inverted pendulum system. International Conference on Natural Science and Engineering (ICNASE’16), March 19-20, 2016, Kilis.
• [61] Gani A., Kececioglu O.F., Baş Z., Acikgoz H., and Sekkeli M. Dynamic performance analysis of self-tuning fuzzy-PID controller for the inverted pendulum system. 4th International Fuzzy Systems Symposium November, 5-6, 2015-İstanbul, Turkey. pp.32-35.
• [62]Gani A., Kececioglu O.F., Dogmuş O., Gunes M., Öz Ayarlamalı Bulanık-PID, PID ve LQR Denetleyiciler ile Ters Sarkaç Sisteminin Denetimi. Otomatik Kontrol Ulusal Toplantısı , 10-12 Eylül 2015-Denizli, Turkey. pp.540-545.
• [63]Ogata, K., 1990. Modern Control Engineering, Prentice-Hall Inc.
• [64]Yıldız. C., 2008. Genetik algoritma destekli bulanık denetim kullanarak vektör esaslı asenkron motor kontrolü, Yüksek Lisans Tezi. Kahramanmaraş Sütçü İmam Üniversitesi. Fen Bilimleri Enstitüsü. Kahramanmaraş.
• [65]Prasad, Lal Bahadur., Gupta, Hari Om., Tyagi, Barjeev., 2011.Intelligent Control of Nonlinear Inverted Pendulum Dynamical System with Disturbance Input using Fuzzy Logic Systems. International Conference on Recent Advancements in Electrical, Electronics and Control Engineering.