Investigation of the Problem of Stabilisation of the Overturned Equilibrium Position of the Furuta Pendulum

Qunkai Niu

doi:10.62051/ijcsit.v4n3.12

Authors

Qunkai Niu

DOI:

https://doi.org/10.62051/ijcsit.v4n3.12

Keywords:

Pendulum on a trolley, Double pendulum, Furuta's Pendulum, Inear control, Non-linear control, Intelligent control

Abstract

Research goal: Investigation of the problem of' stabilisation of' the overturned equilibr ium position of the Furuta Pendulum Tasks to be solved in WRC / Research tasks: (1) Analvtical! review of incomplete-drive robots, their model representations and structural properties. (2) Analysis of kinematics and dynamic properties of incomplete-drive robots. (3) Research methods and control algorithms for incomplete-drive robots. (4) Synthesis of a control algorithm for stabilising F uruta's pendul um relative to an unstable overtumned equilibrium position. Experimental modelling. (5) Analysis of dynamic properties and qualitative indicators of the obtained svstem. The aim of this final qualification work is to investigate incompletely driven systems, analyse their dynamic properties and control methods. Furuta's pendulum is investigated as an example of an incompletely driven system. In the work the model of the system is compiled, the control algorithm is synthesised, mathematical modelling in Simulink MATLAB environment is carried out.

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References

[1] Choukchou-Braham A. ct al. Analysis and control of underactuated mechanical systems. - Springer Science & Business Media, 2013.

[2] Krener A. et al. Poincaré's linearisation method applied to the design of nonlinear compensators //AIgebraic Computing in Control: Proceedings of the First European Conference Paris, March 13-15, 1991. - Springer Berlin Heidelberg, 1991.-C. 76-114.

[3] Pfeifer, R., Lungarella, M., & Iida, F. (2007). Self-organisation, embodiment,and biologically inspired robotics. Science, 3 18(5853), 1088-1093.

[4] Rauskolb, T., Beikirch, H., Schiller, R., & Vahrenkamp, N. (2018). MPC-based energy-efficient driving for hybrid electric vehicles with uncertain traffic information. IEEE Transactions on Intelligent Transportation Systems, 20(8)，3029-3042.

[5] Anderle M., Čelikovský S. On the controller implementation in the real underactuated walking robot model //2019 12th Asian Control Conference (ASCC). - IeEE, 2019. - C. 1125-1130.

[6] Noh M. M. et al. Robust Controller Design for Autonomous Underwater Glider Using Backstepping Super Twisting /Proceedings of the 10th National Technical Seminar on Underwater System Technology 2018: NUSYS'18 Springer, 2019. - T. 538. - C. 79.

[7] Das A., Nabi M. A review on soft robotics: Modeling, control and applications in human-robot interaction //2019 International Conference on Computing. Communication, and Intelligent Systems (ICCCIS). - IEEE, 2019. - C. 306-311.

[8] Kwakernaak H, Sivan R. Linear optimal control systems. - M.: Mir, 1977.- 653 C.

[9] Russ Tedrake. Underactuated Robotics: Algorithms for Walking, Running, Swimming, Flying, and Manipulation (Course Notes for MIT 6.832). URL: http://underactuated.mit.edu/acrobot.html (Date of access: 15.04.2023)

[10] Richard M. Murray and John Hauser. A case study in approximate linearisation The acrobot example, April 1991.

[11] Van Kats C, J, A. A, Nonlinear control of a Furuta Rotary inverted pendulum //DCT report. - 2004. - No. 2004.69.

[12] Spong, M.W.: 'Partial feedback linearisation of underactuated mechanical systems', Proc, IEEE/RSJ/GI Int. Conf, Intelligent Robots and Systems, Munich Germany, 1994, pp. 314-321.

[13] Rudra S., Barai R. K., Maitra M. Block backstepping design of nonlinear state feedback control law for underactuated mechanical systems. - Springer Singapore.2017.-C.1.

[14] Cheng C. C., Ho C.H.Design of adaptive sliding mode controllers for mismatched perturbed systems with application to underactuated systems //2017 36th Chinese Control Conference (CCC). - IEEE, 2017. - C. 1329-1336.

[15] Xin X., Yamasaki T. Energy-based swing-up control for a remotely driven Acrobot: Theoretical and experimental results //IEEE Transactions on Control Systems Technology. - 2011. - T. 20. - N. 4.- C. 1048-1056.

[16] Shiriaev A. S. et al. On global properties of passivity-based control of an inverted pendulum //International Journal of Robust and Nonlinear Control IF AC- Affiliated Journal. - 2000. - T. 10. - No. 4.- C. 283-300.

[17] Huynh X. D. ct al. Application of fuzzy algorithm in optimizing hierarchical sliding mode control for pendubot system //Robotica and Management. - 2017.T.22.- No. 2.- C. 8-12.

[18] Spong M. W. Underactuated mechanical systems /Control problems in robotics and automation., - Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. C.135-150.

[19] Spong M. W. Energy based control of a class of underactuated mechanical systems //IFAC Proceedings Volumes. -1996.-T. 29.-N@, 1.-C. 2828-2832.

[20] Fantoni l., Lozano R., Spong M. W. Energy based control of the pendubot //EEE Transactions on Automatic Control.- 2000. -T. 45.-N@, 4.-C. 725-729.

[21] Araki N. ct al. Parameter identitfication and swing-up control of an acrobot system //2005 IEEE Intemnational Conference on Industrial Technology.- IEEE, 2005 C. 1040-1045.

[22] Uspensky V. B. B, Shipulina L. V. Modern Theory of Control. Methods of synthesis and optimisation of control systems. -2013.

[23] Pegat A. Fuzzy Modelling and Control. 2nd ed. -M. Moscow BINOM. Laboratory of Knowledge, 2013. 798 c.

[24] Sugeno M., Takagi T. Fuzzy identification of systems and its applications to modelling and control //Readings in Fuzzy Sets for Intelligent Systems. - 1993 T. 15.-No. 1. - C. 387-403.

[25] Mamdani E. H., Assilian S. An experiment in linguistic synthesis with a fuzzy logic controller //International journal of man-machine studies. - 1975.- T. 7.-No 1.- C. 1-13.

[26] Li Y. et al. Study of 3-dimension trajectory eectory tracking tracking of underactuated autonomous underwater vehicle //Ocean Engineering. - 2015. - T. 105.- C. 270-274.

[27] Li W., Tanaka K., Wang H. O. Acrobatic control of a pendubot //IEEE Transactions on Fuzzy Systems. - 2004. - T. 12. - Ne. 4. - C. 549-554.

[28] Lin J., Ding Y. S., Chang J. Balancing and swinging-up control for cart-pendulum- seesaw system by decomposed fuzzy coordination control // Journal of Vibration and Control. - 2014. - T. 20.- Ne. 6. - C. 925-942.

[29] Fan X., Zhang N., Teng S. Trajectory planning and tracking of ball and plate system using hierarchical fuzzy control scheme //Fuzzy Sets and Systems 2004.-T. 144. - No 2.- C. 297-312.

[30] Xu J. X., Guo Z. Q.., Lee T, H. Design and implementation of a Takagi-Sugeno-type fuzzy logic controller on a two-wheeled mobile robot //IEEE Transactions on industrial electronics. - 2012.-T. 60.- N. 12.-C. 5717-5728.

[31] Yang C. et al. Neural network-based motion control of an underactuated wheeled.