Gerçek Zamanlı İki Serbestlik Dereceli Eksiksil Döner Ters Sarkaç Sisteminin Kutup Atama ile Kontrolü

Year 2021, Volume: 5 Issue: 2, 739 - 749, 31.12.2021

Servet Soygüder , Mustafa Özler

Abstract

Mühendislik problemlerinin çözümünde ve hareket analizlerinin yapılmasında eksik tahrikli iki serbestlik dereceli döner ters sarkaç mekanizması sıkça kullanılan bir mühendislik sistemidir. Bu ve benzeri sarkaç sistemleri üzerinde yapılan çalışmalar ve analizler günümüz teknolojisinde araba, uçak, uzaysal araçlar, savunma araçları, füze rampasından insan yürüyüşüne, yük taşıyan robotlardan depreme dayanıklı bina tasarımlarına kadar vb. birçok sistemin tasarım ve denetim algoritmalarının oluşturulmasında bilim adamlarına ışık tutmuştur. Eksik tahrikli iki serbestlik dereceli döner ters sarkaç mekanizması diğer adıyla Furuta ters sarkaç, kontrol mühendisliğinde kullanılan en önemli temel sistemlerden biridir. Bu çalışmada ilk olarak sistem için matematiksel model oluşturulmuştur. Bu denklemleri ifade eden dinamik denklemler Lagrange metodu ile elde edilmiştir. Dönen ters sarkaç doğrusal olmayan (Nonlinear) bir sistemdir. Elde edilen denklemlerin lineerleştirilmesi (Doğrusallaştırılması) yapılıp durum-uzay modeli elde edilmiştir. Durum-uzay modeli ile sisteme ait durum denklemleri ve durum değişkenleri elde edilmiştir. Bulunan bu verileriler ile sistemin kontrol analizi gerçekleştirilmiştir. Daha sonra gerçek zamanlı Furuta döner ters sarkaç için kutup atama(PP) kontrol algoritması tasarlanarak gerçek sistem üzerinde denetimleri başarılı olarak yapılmıştır. Sonuç olarak tasarlanan ve uygulanan bu kontrol metotu ve performansı irdelenerek gerekli kontrol analizi gerçekleştirilmiş ve sonuçlar elde edilmiştir.

Keywords

Furuta döner ters sarkaç, Eksik tahrikli sistem, Matematiksel model, Kutup yerleştirme metodu

Real-Time Control of the Two-DOF Deficient Rotating Inverted Pendulum System with Pole Placement

Abstract

Two degrees of freedom deficient rotating inverted pendulum mechanism is frequently used in the solution of engineering problems and motion analysis. Studies and analyzes on these and similar pendulum systems are used in today's technology such as cars, planes, spacecraft, defense vehicles, missile launchers, human walking, load bearing robots, earthquake resistant building designs, etc. has shed light on scientists in the design and control algorithms of many systems. The two-degree of freedom deficient rotating pendulum mechanism, also called Furuta inverted pendulum, is one of the most important basic systems used in control engineering. In this study, firstly, a mathematical model was created for the system. Dynamic equations expressing these equations were obtained by Lagrange method. The rotating inverted pendulum is a nonlinear system. Linearization of the obtained equations was done and state-space model was obtained. State equations and state variables of the system were obtained with the state-space model. Control analysis of the system was carried out with these data. Then, the pole assignment (PP) control algorithm for the Furuta rotating pendulum in real time was designed and successfully controlled on the real system. As a result, this control method and its performance was designed and applied to examine the necessary control analysis and the results were obtained.

Keywords

Deficient system, Furuta rotating inverted pendulum, Mathematical model, Pole placement method

References

• [1] Furuta K., Okutani T., and Sone H., Computer control of a double inverted pendulum, Computer and Electrical Engineering, 1978; 5.1: 67–84.
• [2] Furuta, K., Yamakita, M. and Kobayashi, S., Swing-up control of inverted pendulum using pseudo-state feedback, Journal of Systems and Control Engineering, 1992; 206, 263-269
• [3] Yoshida, K., Swing-up control of an inverted pendulum by energy-based methods, Proceedings of the American Control Conference, San Diego.1999.
• [4] Astrom, K.J. and Furuta, K., Swing up a pendulum by energy control, Automatica, 2000; 36: 287-295.
• [5] Li, H., Miao, Z. ve Wang, J., Variable universe adaptive fuzzy control on the quadruple inverted pendulum, Science in China (Series E), 2002; 45: 213-224.
• [6] Jinglai Shen, A. K. Sanyal, N. A. Chaturvedi, D. Bernstein and H. McClamroch, Dynamics and control of a 3D pendulum, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), Nassau, 2004, p. 323-328
• [7] Tsai, M. and Shen, B. H., Synchronization control of parallel dual inverted pendulums driven by linear servomotors, IET Control Theory and Applications,2007; 320-327.
• [8] Komine, T., Iwase, M., Suzuki, S. and Furuta, K., Rotational Control of Double Pendulum, IFAC Proceedings Volumes, 2004, C. 37, 325-330.
• [9] Xu, K. and Duan, X. D., Comparative study of control methods of single-rotational inverted pendulum, Proceedings. International Conference on Machine Learning and Cybernetics, Beijing, China, 2002.
• [10] Mathew, N. J., Rao K. K. and Sivakumaran, N., Swing up and stabilization control of a rotary inverted pendulum, in IFAC Proceedings Volumes (IFAC-PapersOnline), 2013, C. 37, 325-330.
• [11] Hassanzadeh, I. and Mobayen, S., Controller Design for Rotary Inverted Pendulum System Using Evolutionary Algorithms, Mathematical Problems in Engineering, C. 2011, 1-17.
• [12] Rahimi, A., Raahemifar, K., Kumar, K. and Alighanbari, H., Controller design for rotary inverted pendulum system using particle swarm optimization algorithm, in Canadian Conference on Electrical and Computer Engineering, 2013.
• [13] Shojaei, A. A., Othman, M. F., Rahmani, R. and Rani, M. R., A hybrid control scheme for a rotational ınverted pendulum, 2011 UKSim 5th European Symposium on Computer Modeling and Simulation, Madrid, Spain, 2011.
• [14] Anvar, S. M. M., Hassanzadeh, I., and Alizadeh, G., Design and implementation of sliding mode-state feedback control for stabilization of Rotary Inverted Pendulum, ICCAS 2010, Gyeonggi-do, South Korea. 2010.