Closed-loop swing-up and stabilization of inverted pendulum by finite-horizon LQR applied in 2-DOF concept

• Autorzy: Docekal Tomas , Ozana Stepan , Pal Singh Abhaya , Kawala-Sterniuk Aleksandra
• Języki publikacji: EN

Abstrakty

EN

The general framework of this paper is the control design of complex nonlinear systems. The proposed approach is demonstrated with the use of a case study regarding a typical mechatronic system - control design of inverted pendulum on the cart. The methodology used for the solution of this problem is based on two- degree of freedom control structure (2-DOF) with feed-forward and feedback terms. Feed-forward term represents a solution of trajectory generation problem and feedback term stands for a state controller. Both of these parts generally fall into the category of optimal control problems. The article focuses on the design of a finite-horizon linear quadratic controller and its application in 2-DOF structure with the use of customized LQR computation procedure, showing all necessary steps of the design, including source codes. It is proposed that the developed methodology is general and can be adopted for most of other nonlinear mechatronic systems, including unstable or non-minimum phase systems. This has been already tested successfully for models of both double and triple inverted pendulums. The functionality of the concept under real conditions can also be seen in Ozana (2018a) and Ozana (2018b) showing preliminary experiments with real apparatus.

Słowa kluczowe

EN

finite-horizon LQR; closed-loop swing-up; 2-DOF structure; inverted pendulum

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2020
• Tom: Vol. 49, No. 1
• Strony: 109--122
• Opis fizyczny: Bibliogr. 15 poz., rys., tab.

Twórcy

autor

Docekal Tomas

• Faculty of Electrical Engineering and Computer Science, VSB-TU Ostrava, 17. listopadu 15, 708 00 Ostrava, Czech Republic

autor

Ozana Stepan

• Faculty of Electrical Engineering and Computer Science, VSB-TU Ostrava, 17. listopadu 15, 708 00 Ostrava, Czech Republic

autor

Pal Singh Abhaya

• Symbiosis Institute of Technology, Symbiosis International (Deemed University), Pune, India

autor

Kawala-Sterniuk Aleksandra

• Faculty of Electrical Engineering, Automatic Control and Informatics, Opole University of Technology, Opole, Poland

Bibliografia

• Cizniar, M., Fikar, M. and Latifi, A. M. (2017) MATLAB Dynamic Optimisation Code DYNOPT. User’s Guide, Technical Report, KIRP FCHPT STU, Bratislava, Slovak Republic, https://bitbucket.org/dynopt/dynopt code hg/ src/default/dynopt guide.pdf
• Durand, S., Castellanos, F. G., Marchand, N. and Sanchez, W. F. G. (2013) Event-based control of the inverted pendulum: Swing up and stabilization. Journal of Control Engineering and Applied Informatics, 15(3), 96.
• Hercus, R., Wong, K.-Y., Shee, S.-K. and Ho, K.-F. (2013) Control of an inverted pendulum using the neurabase network model. In: M. Lee, A. Hirose, Z.-G. Hou, & R. M. Kil, eds., Neural Information Processing. Springer, 605-615. https://doi.org/10.1007/978-3-642-42042-9 75
• Ichtev, A. K. (2008) Fuzzy controller for swing-up and stabilization of inverted pendulum. 2008 4th International IEEE Conference Intelligent Systems, 1, 2-57-2–62. https://doi.org/10.1109/IS.2008.4670408
• Kelly, M. P. (2018) OptimTraj Users Guide. User’s Guide, https://github.com/MatthewPeterKelly/OptimTraj/blob/master/docs /UsersGuide/ OptimTraj UsersGuide.pdf
• Kennedy, D. and Conlon, J. (2011) Inverted pendulum swing up controller. Conference Papers. Mechanical Technologies and Structural Materials 2011, Split, Croatia. https://arrow.tudublin.ie/engschmeccon/47
• Kunze, A. (2016) Pytrajectory’s documentation. User’s Guide, https://pytrajectory.readthedocs.io/en/master/
• Ozana, S. (2018a) Swing-up and Control of Linear Simple Inverted Pendulum [Video]. https://youtu.be/Sqhr8fYhMfg
• Ozana, S. (2018b) Swing-up and Control of Linear Triple Inverted Pendulum [Video]. https://youtu.be/meMWfva-Jio
• Ozana, S. and Docekal, T. (2017) The concept of virtual laboratory and PIL modeling with REX control system. 2017 21st International Conference on Process Control (PC), 98–103. https://doi.org/10.1109/PC.2017.7976196
• Ozana, S., Pies, M. and Hajovsky, R. (2014) Computation of swing-up signal for inverted pendulum using dynamic optimization. In: K. Saeed & V. Snasel, eds., Computer Information Systems and Industrial Management. Springer, 301-314. https://doi.org/10.1007/978-3-662-45237-0 29
• Ozana, S. and Schlegel, M. (2018) Computation of reference trajectories for inverted pendulum with the use of two-point bvp with free parameters. IFAC-PapersOnLine, 51(6), 408–413. https://doi.org/10.1016/j. ifacol.2018.07.119
• Tum, M., Gyeong, G., Park, J. H. and Lee, Y. S. (2014) Swing-up control of a single inverted pendulum on a cart with input and output constraints. 2014 11th International Conference on Informatics in Control, Automation and Robotics (ICINCO), 01, 475–482. https://doi.org/10.5220/0005018604750482
• Yang, X. and Zheng, X. (2018) Swing-up and stabilization control design for an underactuated rotary inverted pendulum system: Theory and experiments. IEEE Transactions on Industrial Electronics, 65(9), 7229–7238. https://doi.org/10.1109/TIE.2018.2793214
• Yokoyama, J., Mihara, K., Suemitsu, H. and Matsuo, T. (2011) Swing-up control of an inverted pendulum by two step control strategy. 2011 IEEE/SICE International Symposium on System Integration (SII), 1061–1066. https://doi.org/10.1109/SII.2011.6147596

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).