An integral feedback linearization applied to an aeropendulum

• Autorzy: Alves Uiliam Nelson Lendzion Tomaz , Breganon Ricardo , Mendonça Márcio , Palácios Rodrigo Henrique Cunha

Identyfikatory

DOI

10.2478/candc-2025-0003

• Języki publikacji: EN

Abstrakty

EN

Aeropendulum systems are nonlinear systems, in which a motor-propeller assembly drives a rod. They are used for educational purposes and testing control laws in real systems. Feedback linearization is a nonlinear control technique that algebraically linearizes a plant’s dynamics via a feedback law and has been applied to various systems. This paper designs a feedback linearization control law incorporating an integrator into the control loop. The integrator enhances robustness in respect to constant disturbances, but alters the closed-loop dynamics, preventing it from following exactly the dynamics, associated with the desired characteristic roots under constant input. To address this, the integrator’s initial condition is treated as an additional variable, selected to ensure the expected closed-loop response. Finally, simulations and bench experiments on an Aeropendulum system validate the approach, demonstrating the integrator’s effectiveness in handling constant disturbances and the impact of selecting an appropriate initial condition.

Słowa kluczowe

EN

aeropendulum system; feedback linearization; integral control; tracking control

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2025
• Tom: Vol. 54, No. 1
• Strony: 49--77
• Opis fizyczny: Bibliogr. 26 poz., rys., tab.

Twórcy

autor

Alves Uiliam Nelson Lendzion Tomaz

• Control and Industrial Processes, IFPR – Instituto Federal do Paraná, Av. Dr. Tito, 801, Jacarezinho, 86400-000, Paraná, Brazil

autor

Breganon Ricardo

• Control and Industrial Processes, IFPR – Instituto Federal do Paraná, Av. Dr. Tito, 801, Jacarezinho, 86400-000, Paraná, Brazil

autor

Mendonça Márcio

• Graduate Program in Mechanical Engineering (PPGEM-CP), UTFPR – Universidade Tecnológica Federal do Paraná, Av. Alberto Carazzai, 1640, Cornélio Procópio, 86300-000, Paraná, Brazil

autor

Palácios Rodrigo Henrique Cunha

• Graduate Program in Mechanical Engineering (PPGEM-CP), UTFPR – Universidade Tecnológica Federal do Paraná, Av. Alberto Carazzai, 1640, Cornélio Procópio, 86300-000, Paraná, Brazil

Bibliografia

• Alves, U.N.L.T. (2025) An Integral Feedback Linearization Applied to an Aeropendulum – Models, Parameters, and Measurement Data. Publisher: Mendeley Data. https://doi.org/10.17632/9vx366bfm3.2
• Bagheri, M., Naseradinmousavi, P. and Krstić, M. (2019) Feedback linearization based predictor for time delay control of a high-dof robot manipulator. Automatica 108, 108485 https://doi.org/10.1016/j.automatica.2019.06.037
• Breganon, R., Alves, U.N.L.T., Almeida, J.P.L.S., Ribeiro, F.S.F., Mendonça, M., Palácios, R.H.C. and Montezuma, M.A.F. (2021) Loop-shaping H∞ control of an aeropendulum model. International Journal of Applied Mechanics and Engineering 26(4), 1–16 https://doi.org/10.2478/ ijame-2021-0046
• Breganon, R., Alves, U.N.L.T., Ribeiro, F.S.F., Barbara, G.V., Almeida, J.P.L.S., Pivovar, L.E., Montezuma, M.A.F. and Mendonça, M. (2021a) Development of inverted pendulum systems as didactical tools in courses of control and automation engineering. Holos 5, 1–14 https://doi. org/10.15628/holos.2021. 10351. In Portuguese.
• Breganon, R., Alves, U.N.L.T., Almeida, J.P.L.S., Ribeiro, F.S.F., Mendonça, M., Palácios, R.H.C. and Montezuma, M.A.F. (2023) Model identification and H control of an aeropendulum. Journal of Applied Research and Technology 21(4), 526–534 https://doi.org/10.22201/icat.24486736e.2023.21.4.1741
• Chen, Y.T., Yu, C.S. and Chen, P.N. (2020) Feedback linearization based robust control for linear permanent magnet synchronous motors. Energies 13 https://doi. org/10.3390/en13205242
• Csizmadia, M., Kuczmann, M. and Orosz, T. (2022) A novel control scheme based on exact feedback linearization achieving robust constant voltage for boost converter. Electronics 12, 57 https://doi.org/10.3390/electronics12010057
• Enikov, E.T. and Campa, G. (2012) Mechatronic aeropendulum: Demonstration of linear and nonlinear feedback control principles with matlab/simulink real-time windows target. IEEE Transactions on Education 55, 538–545 https://doi.org/10.1109/TE.2012. 2195496
• Kayacan, E. and Fossen, T.I. (2019) Feedback linearization control for systems with mismatched uncertainties via disturbance observers. Asian Journal of Control 21, 1064–1076 https://doi.org/10.1002/asjc.1802
• Khalil, H.K. (2001) Nonlinear Systems, 3rd edn. Prentice Hall, Upper Saddle River, NJ.
• Lathi, B.P. (2005) Linear Systems and Signals, 3rd edn. Oxford University Press, New York.
• Lu, Y.-S. and Cheng, C.-M. (2005) Design of a non-overshooting pid controller with an integral sliding perturbation observer for motor positioning systems. JSME International Journal Series C 48, 103–110 https://doi.org/10.1299/jsmec.48.103
• Lucena, E.R., Luiz, S.O.D. and Lima, A.M.N. (2021) Modeling, parameter estimation, and control of an aero-pendulum. In: Procedings do XV Simp´osio Brasileiro de Automa¸c˜ao Inteligente. SBA Sociedade Brasileira de Automática, Rio Grande, Brazil, 1984–1989. https://doi.org/10.20906/sbai.v1i1.2837
• Mahmood, A. and Kim, Y. (2017) Decentrailized formation flight control of quadcopters using robust feedback linearization. Journal of the Franklin Institute 354, 852– 871 https://doi.org/10.1016/j.jfranklin.2016. 10.039
• Martins, L., Cardeira, C. and Oliveira, P. (2021) Feedback linearization with zero dynamics stabilization for quadrotor control. Journal of Intelligent and Robotic Systems 101, 7 https://doi.org/10.1007/s10846-020-01265-2
• Meng, X., Yu, H., Zhang, J., Xu, T., Wu, H. and Yan, K. (2022) Disturbance observer-based feedback linearization control for a quadruple-tank liquid level system. ISA Transactions 122, 146–162 https://doi.org/10.1016/j.isatra.2021.04.021
• Mehndiratta, M., Kayacan, E., Reyhanoglu, M. and Kayacan, E. (2020) Robust tracking control of aerial robots via a simple learning strategybased feedback linearization. IEEE Access 8, 1653–1669 https://doi.org/10.1109/ACCESS.2019.2962512
• Neto, R.C., Trindade, F.L.A., Marques, B.R.A., Azevedo, G.M.S., Barbosa, E.J. and Barbosa, E.A.O. (2023) An aeropendulum-based didactic platform for the learning of control engineering. Journal of Control, Automation and Electrical Systems https://doi.org/10. 1007/s40313-022-00981-4
• Nise, N.S. (2019) Control Systems Engineering, 8th edn. Wiley, Pomona, CA
• Oliveira, L., Bento, A., Leite, V.J.S. and Gomide, F. (2020) Evolving granular feedback linearization: Design, analysis, and applications. Applied Soft Computing Journal 86 https://doi.org/10.1016/j.asoc.2019.105927
• Oliveira, L., Bento, A., Leite, V.J.S. and Gomide, F. (2020b) Comparisons of robust methods on feedback linearization through experimental tests. IFAC-PapersOnLine 53, 7983–7988 https://doi.org/10.1016/j.ifacol.2020.12.2218
• Rafiuddin, N. and Khan, Y.U. (2022) Nonlinear controller design for mechatronic aeropendulum. International Journal of Dynamics and Control https://doi.org/10.1007/s40435-022-01080-7
• Saleem, O., Rizwan, M., Zeb, A.A., Ali, A.H. and Saleem, M.A. (2020) Online adaptive pid tracking control of an aero-pendulum using pso-scaled fuzzy gain adjustment mechanism. Soft Computing 24, 10629–10643 https://doi.org/10.1007/s00500-019-04568-1
• Silva, H.R.M., Ramos, I.T.M., Cardim, R., Assunção, E. and Teixeira, M.C.M. (2020) Identification and switched control of an aeropendulum system. In: Proceedings of the XXIII Congresso Brasileiro de Automática. SBA Sociedade Brasileira de Automática, Porto Alegre, Brazil, 1–6. https://www.sba.org.br/open journal systems/index.php /cba/article/view/1429
• Slotine, J.-J.E. and Li, W. (1991) Applied Nonlinear Control. Prentice Hall, Englewood Cliffs, NJ.
• Yamanaka, H.F., Bispo, C.A.S., Breganon, R., Ribeiro, F.S.F., Almeida, J.P.L.S. and Alves, U.N.L.T. (2022) Constru¸cão e controle seguidor via lqr de um sistema aeropêndulo. In: Proceedings of the XXIV Congresso Brasileiro de Automática. SBA Sociedade Brasileira de Automática, Fortaleza, Brazil, 1–7. https://doi.org/10.20906/CBA2022/3193. In Portuguese