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Active Disturbance Rejection Control of the Inertia Wheel Pendulum through a Tangent Linearization Approach

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  • Control Theory and Applications
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Abstract

A flatness based approach is proposed for the linear Active Disturbance Rejection Control (ADRC) stabilization of a nonlinear inertia wheel pendulum (IWP) around its unstable equilibrium point, subject to unmodelled dynamics and disturbances. The approach exploits the cascade structure, provided by the flatness property, of the tangent linearization of the underactuated system which allows designing a high gain linear cascaded Extended State Observer (ESO) of the Generalized Proportional Integral (GPI) type. This class of linear observers is employed to build an Active Disturbance Rejection Control controller with a lower order of complexity regarding other ADRC classic schemes. Experimental results demonstrate the effectiveness and feasibility of the proposed approach, as well as a better behavior with respect to a classic control technique in the presence of disturbances.

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References

  1. R. Olfati–Saber, Nonlinear Control of Underactuated Mechanical Systems with Application to Robotics and Aerospace Vehicles, Ph.D. dissertation, Massachusetts Institute of Technology, 2000.

    Google Scholar 

  2. A. S. Shiriaev, L. B. Freidovich, A. Robertsson, R. Johansson, and A. Sandberg, “Virtual–holonomic–constraintsbased design of stable oscillations of Furuta pendulum: Theory and experiments,” IEEE Transactions on Robotics, vol. 23, no. 4, pp. 827–832, 2007.

    Article  Google Scholar 

  3. P. Ordaz and A. Poznyak, “The Furuta’s pendulum stabilization without the use of a mathematical model: attractive ellipsoid method with kl–adaptation,” Proc. of Conference on Decision and Control (CDC), IEEE, pp. 7285.7290, 2012.

    Google Scholar 

  4. M. Fliess and C. Join, “Intelligent PID controllers,” Proc. of 16th Mediterrean Conference on Control and Automation, 2008.

    Google Scholar 

  5. M. Fliess and C. Join, “Model–free control,” International Journal of Control, vol. 86, no. 12, pp. 2228–2252, 2013.

    Article  MathSciNet  MATH  Google Scholar 

  6. C. Johnson, “Accomodation of external disturbances in linear regulator and servomechanism problems,” IEEE Transactions on Automatic Control, vol. 16, no. 6, pp. 635–644, 1971.

    Article  Google Scholar 

  7. J. Han, “From PID to active disturbance rejection control,” IEEE Transactions on Industrial Electronics, vol. 56, no. 3, pp. 900–906, 2009.

    Article  Google Scholar 

  8. Z. Gao, “Active disturbance rejection control: a paradigm shift in feedback control system design,” Proc. of American Control Conference, IEEE, 2006.

    Google Scholar 

  9. S. Zhao and Z. Gao, “An active disturbance rejection based approach to vibration suppression in two–inertia systems,” Asian Journal of Control, vol. 15, no. 2, pp. 350–362, 2013.

    Article  MathSciNet  MATH  Google Scholar 

  10. Z. Gao, “On the centrality of disturbance rejection in automatic control,” ISA Transactions, vol. 53, no. 4, pp. 850–857, 2014.

    Article  Google Scholar 

  11. R. Mado´nski and P. Herman, “Survey on methods of increasing the efficiency of extended state disturbance observers,” ISA transactions, vol. 56, pp. 18–27, 2015.

    Article  Google Scholar 

  12. D.–J. Zhao and D.–G. Yang, “Model–free control of quadrotor vehicle via finite–time convergent extended state observer,” International Journal of Control, Automation and Systems, vol. 14, no. 1, pp. 242–254, 2016.

    Article  Google Scholar 

  13. Y. Li, H. Sun, G. Zong, and L. Hou, “Composite antidisturbance resilient control for markovian jump nonlinear systems with partly unknown transition probabilities and multiple disturbances,” International Journal of Robust and Nonlinear Control, vol. 27, no. 14, pp. 2323–2337, 2017.

    Article  MathSciNet  MATH  Google Scholar 

  14. H. Sun, Y. Li, G. Zong, and L. Hou, “Disturbance attenuation and rejection for stochastic markovian jump system with partially known transition probabilities,” Automatica, vol. 89, pp. 349–357, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  15. B. Xu, “Composite learning control of flexible–link manipulator using NN and DOB,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 48, no. 11, pp. 1979–1985, 2017.

    Article  Google Scholar 

  16. B. Xu and P. Zhang, “Composite learning sliding mode control of flexible–link manipulator,” Complexity, vol. 2017. 2017.

  17. B. Xu and F. Sun, “Composite intelligent learning control of strict–feedback systems with disturbance,” IEEE Transactions on Cybernetics, vol. 48, no. 2, pp. 730–741, 2018.

    Article  Google Scholar 

  18. H. Sira–Ramírez, C. A. Núñez, and N. Visairo, “Robust sigma–delta generalised proportional integral observer based control of a’ buck’ converter with uncertain loads,” International Journal of Control, vol. 83, no. 8, pp. 1631–1640, 2010.

    Article  MathSciNet  MATH  Google Scholar 

  19. H. Sira–Ramírez, C. López–Uribe, and M. Velasco–Villa, “Linear observer–based active disturbance rejection control of the omnidirectional mobile robot,” Asian Journal of Control, vol. 15, no. 1, pp. 51–63, 2013.

    Article  MathSciNet  MATH  Google Scholar 

  20. H. Sira–Ramírez, J. Linares–Flores, A. Luviano–Juarez, and J. Cortés–Romero, “Ultramodelos globales y el control por rechazo activo de perturbaciones en sistemas no lineales diferencialmente planos,” Revista Iberoamericana de Automática e Informática Industrial RIAI, vol. 12, no. 2, pp. 133–144, 2015.

    Article  Google Scholar 

  21. Y. Li, M. Sun, Z. Wang, and Z. Chen, “Quantitative analysis of critical limitation in using extended state observer,” International Journal of Control, Automation and Systems, vol. 14, no. 3, pp. 876–882, 2016.

    Article  Google Scholar 

  22. M. W. Spong, P. Corke, and R. Lozano, “Nonlinear control of the reaction wheel pendulum,” Automatica, vol. 37, no. 11, pp. 1845–1851, 2001.

    Article  MATH  Google Scholar 

  23. I. Fantoni and R. Lozano, Non–linear Control for Underactuated Mechanical Systems, Springer Science & Business Media, 2002.

    Book  Google Scholar 

  24. A. Zhang, C. Yang, S. Gong, and J. Qiu, “Nonlinear stabilizing control of underactuated inertia wheel pendulum based on coordinate transformation and time–reverse strategy,” Nonlinear Dynamics, vol. 84, no. 4, pp. 2467–2476, 2016.

    Article  MathSciNet  MATH  Google Scholar 

  25. B. Lu, Y. Fang, and N. Sun, “Global stabilization of inertia wheel systems with a novel sliding mode–based strategy,” Proc. of 14th InternationalWorkshop on Variable Structure Systems, IEEE, pp. 200–205, 2016.

    Google Scholar 

  26. V. Hernandez and H. Sira–Ramirez, “Generalized PI control for swinging up and balancing the inertia wheel pendulum,” Proc. of the American Control Conference, vol. 4, IEEE, pp. 2809.2814, 2003.

    Google Scholar 

  27. R. Iriarte, L. T. Aguilar, and L. Fridman, “Second order sliding mode tracking controller for inertia wheel pendulum,” Journal of the Franklin Institute, vol. 350, no. 1, pp. 92–106, 2013.

    Article  MathSciNet  MATH  Google Scholar 

  28. H. Gritli and S. Belghith, “Robust feedback control of the underactuated inertia wheel inverted pendulum under parametric uncertainties and subject to external disturbances: LMI formulation,” Journal of the Franklin Institute, 2017.

    Google Scholar 

  29. J. Moreno–Valenzuela and C. Aguilar–Avelar, Motion Control of Underactuated Mechanical Systems, Springer, 2018.

    Book  Google Scholar 

  30. H. Sussmann and P. Kokotovic, “The peaking phenomenon and the global stabilization of nonlinear systems,” IEEE Transactions on Automatic Control, vol. 36, no. 4, pp. 424–440, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  31. H. Sira–Ramirez and S. K. Agrawal, Differentially Flat Systems, CRC Press, 2004.

    Book  MATH  Google Scholar 

  32. H. Sira–Ramirez, A. Luviano–Juárez, M. Ramírez–Neria, and E. W. Zurita–Bustamante, Active Disturbance Rejection Control of Dynamic Systems: A Flatness Based Approach, Butterworth–Heinemann, 2018.

    Google Scholar 

  33. R. Olfati–Saber, “Global stabilization of a flat underactuated system: the inertia wheel pendulum,” Proc. of IEEE Conference on Decision and Control, vol. 4, Citeseer, pp. 3764.3765, 2001.

    Google Scholar 

  34. M. Fliess, J. Lévine, P. Martin, and P. Rouchon, “Flatness and defect of non–linear systems: introductory theory and examples,” International Journal of Control, vol. 61, no. 6, pp. 1327–1361, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  35. Z. Qing and G. Zhiqiang, “On practical applications of active disturbance rejection control,” Proc. of Chinese Control Conference (CCC), IEEE, pp. 6095.6100, 2010.

    Google Scholar 

  36. Y. C. Kim, L. H. Keel, and S. P. Bhattacharyya, “Transient response control via characteristic ratio assignment,” IEEE Transactions on Automatic Control, vol. 48, no. 12, pp. 2238–2244, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  37. M. Ramirez–Neria, J. L. Garcia–Antonio, H. Sira–Ramirez, M. Velasco–Villa, and R. Castro–Linares, “An active disturbance rejection control of leaer–follower Thomson’s jumping rings,” Control Theory & Applications, vol. 30, no. 12, pp. 1564–1572, 2013.

    Google Scholar 

  38. J. Cortés–Romero, G. A. Ramos, and H. Coral–Enriquez, “Generalized proportional integral control for periodic signals under active disturbance rejection approach,” ISA Transactions, vol. 53, no. 6, pp. 1901–1909, 2014.

    Article  Google Scholar 

  39. X.–J. Li and G.–H. Yang, “Adaptive fault–tolerant synchronization control of a class of complex dynamical networks with general input distribution matrices and actuator faults,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 3, pp. 559–569, 2017.

    Article  MathSciNet  Google Scholar 

  40. X.–J. Li and G.–H. Yang, “Fault detection in finite frequency domain for Takagi–Sugeno fuzzy systems with sensor faults,” IEEE Transactions on Cybernetics, vol. 44, no. 8, pp. 1446–1458, 2014.

    Article  Google Scholar 

  41. F. Wang, B. Chen, C. Lin, J. Zhang, and X. Meng, “Adaptive neural network finite–time output feedback control of quantized nonlinear systems,” IEEE Transactions on Cybernetics, vol. 48, no. 6, pp. 1839–1848, 2018.

    Article  Google Scholar 

  42. F. Wang, B. Chen, Y. Sun, and C. Lin, “Finite time control of switched stochastic nonlinear systems,” Fuzzy Sets and Systems, in press, 2018. DOI: 10.1016/j.fss.2018.04.016

    Google Scholar 

  43. X.–J. Li and G.–H. Yang, “Fls–based adaptive synchronization control of complex dynamical networks with nonlinear couplings and state–dependent uncertainties,” IEEE transactions on Cybernetics, vol. 46, no. 1, pp. 171–180, 2016.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Universidad Tecnológica de México - UNITEC MEXICO - Campus Atizapán, Blvd. Calacoaya No.7 Col. La Ermita Atizapán, de Zaragoza México C.P., 52999, México

    Mario Ramírez-Neria

  2. Mechatronics Section of the Electrical Engineering Department of Cinvestav-IPN. Apartado postal 14740, México City C.P., 07360, México

    Hebertt Sira-Ramírez

  3. Departament of Cinvestav-IPN, México City, Apartado postal 14740, Mexico C.P., 07360, México

    Rubén Garrido-Moctezuma

  4. Instituto Politécnico Nacional - UPIITA Av. IPN 2580 Col. Barrio La Laguna Ticomán Mexico City, Mexico C.P., 07340, México

    Alberto Luviano-Juárez

Authors
  1. Mario Ramírez-Neria
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  2. Hebertt Sira-Ramírez
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  3. Rubén Garrido-Moctezuma
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  4. Alberto Luviano-Juárez
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Corresponding author

Correspondence to Alberto Luviano-Juárez.

Additional information

Recommended by Associate Editor Ding Zhai under the direction of Editor Jessie (Ju H.) Park. This article was supported by Conacyt-Mexico and SIP IPN under research grant 20181665.

Mario Ramírez-Neria received the B.S. degree in Mechatronics Engineering from the Professional Interdisciplinary Unit of Engineering and Advanced Technologies of the National Polytechnic Institute, Mexico City, Mexico, the M.S. degree in Electrical Engineering from the Mechatronics Section of the Electrical Engineering Department of CINVESTAV IPN, and the Ph.D. in Automatic Control from the Automatic Control Departament of CINVESTAV-IPN. Currently, he is with the department of mechatronics at Universidad Tecnológica de México Campus Atizapán. He is the author of 5 technical articles in refereed journals, has participated in 14 International Conferences and he is the coauthor of 1 book. His current research interest are applications of control theory, active disturbance rejection control and robotics.

Hebertt Sira-Ramírez received the degree of Electrical Engineer from the Universidad de Los Andes (ULA) in Mérida (Venezuela) in 1970. He obtained his M.Sc. in Electrical Engineering in 1974 and the Ph.D. in EE in 1977 all from the Massachusetts Institute of Technology (Cambrdige, Massachussetts, USA). He worked for 28 years at the ULA from where he is Retired Professor. Since 1998, he is a Titular Researcher in the Mechatronics Section of the Electrical Engineering Department of CINVESTAV-IPN in México City. He is the author of 163 technical articles in refereed journals, has written 31 book chapters, has participated in 271 International Conferences and he is the coauthor of 6 books. Dr. Sira-Ramírez is interested in the switched control of nonlinear systems. In particular, on the control of power electronics systems. He has been involved in the development of algebraic approaches to state and parameter estimation for the control of uncertain systems and active disturbance rejection control.

Rubén Garrido-Moctezuma received the B.Eng. degree in electrical engineering from the Escuela Superior de Ingeniería Mecánica y Eléctrica Instituto Politécnico Nacional, Mexico City, Mexico, in 1983, the M.Sc. degree in electrical engineering from the Center for Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV-IPN), Mexico City, in 1987, and the Ph.D. degree from the Université de Technology de Compiègne, Compiègne, France, in 1993. He is currently a Professor with the Departamento de Control Automático, CINVESTAV-IPN. His research interests include robot control; parallel robots; visual servoing; parameter identification; electric, pneumatic, and hydraulic servomechanisms; adaptive control; and neural network control.

Alberto Luviano-Juárez received the B.S. degree in mechatronics engineering from the Instituto Politécnico Nacional, México, in 2003, the M.Sc. degree in Automatic Control from the Department of Automatic Control, Centro de Investigación y de Estudios Avanzados (CINVESTAV), del Instituto Politécnico Nacional (IPN), in 2006, and the Ph.D. degree in electrical engineering from the Mechatronics section, Departament of Electrical Engineering at CINVESTAV, IPN, in 2011. Since 2011, he has been with the Postgraduate and Research Section at Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, IPN. His research interests include robust estimation and control in mechatronic systems, robotics, and algebraic methods in the estimation and control of mechatronic systems.

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Ramírez-Neria, M., Sira-Ramírez, H., Garrido-Moctezuma, R. et al. Active Disturbance Rejection Control of the Inertia Wheel Pendulum through a Tangent Linearization Approach. Int. J. Control Autom. Syst. 17, 18–28 (2019). https://doi.org/10.1007/s12555-017-0428-0

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  • DOI: https://doi.org/10.1007/s12555-017-0428-0

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