Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2016, Article ID 1358930, 11 pages
http://dx.doi.org/10.1155/2016/1358930
Research Article

A Linear Active Disturbance Rejection Control for a Ball and Rigid Triangle System

1CIC, Instituto Politécnico Nacional, Ciudad de México, DF, Mexico
2Sección de Mecatrónica, CINVESTAV, Ciudad de México, DF, Mexico
3ESCOM, Instituto Politécnico Nacional, Ciudad de México, DF, Mexico

Received 6 May 2016; Revised 5 September 2016; Accepted 15 September 2016

Academic Editor: Alessio Merola

Copyright © 2016 Carlos Aguilar-Ibanez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. I. Fantoni and R. Lozano, Non-Linear Control for Underactuated Mechanical Systems, Springer, 2002.
  2. I. Sarras, J. Á. Acosta, R. Ortega, and A. D. Mahindrakar, “Constructive immersion and invariance stabilization for a class of underactuated mechanical systems,” Automatica, vol. 49, no. 5, pp. 1442–1448, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. S. González-Vázquez and J. Moreno-Valenzuela, “Motion control of a quadrotor aircraft via singular perturbations,” International Journal of Advanced Robotic Systems, vol. 10, article 368, 2013. View at Google Scholar
  4. C. Aguilar-Avelar and J. Moreno-Valenzuela, “A composite controller for trajectory tracking applied to the Furuta pendulum,” ISA Transactions, vol. 57, pp. 286–294, 2015. View at Publisher · View at Google Scholar
  5. M. W. Spong, “Underactuated mechanical systems,” in Control Problems in Robotics and Automation, pp. 135–150, Springer, Berlin, Germany, 1998. View at Google Scholar
  6. R. Olfati-Saber, Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles [Ph.D. thesis], Massachusetts Institute of Technology, 2000.
  7. B. Gao, H. Chen, and X. Zhang, “Control design for underactuated mechanical systems: a survey,” Electric Machines and Control, vol. 10, no. 5, p. 541, 2006. View at Google Scholar
  8. H. Sira-Ramirez, “On the control of the ‘ball and beam’ system: a trajectory planning approach,” in Proceedings of the IEEE Conference on Decision and Control, Sydney, Australia, 2000.
  9. P. Rouchon, M. Fliess, J. Lévine, and P. Martin, “Flatness, motion planning and trailer systems,” in Proceedings of the 32nd IEEE Conference on Decision and Control, pp. 2700–2705, IEEE, San Antonio, Tex, USA, December 1993. View at Scopus
  10. M. Fliess, J. Lévine, P. Martin, and P. Rouchon, “Design of trajectory stabilizing feedback for driftless at systems,” in Proceedings of the Third ECC, pp. 1882–1887, Rome, Italy, 1995.
  11. J. Lévine, Analysis and Control of Nonlinear Systems: A Flatness-Based Approach, Springer Science & Business Media, Berlin, Germany, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  12. 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. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. M. Ramírez-Neria, H. Sira-Ramírez, R. Garrido-Moctezuma, and A. Luviano-Juárez, “Linear active disturbance rejection control of underactuated systems: the case of the Furuta pendulum,” ISA Transactions, vol. 53, no. 4, pp. 920–928, 2014. View at Publisher · View at Google Scholar · View at Scopus
  14. 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. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. J. Han, “From PID to active disturbance rejection control,” IEEE Transactions on Industrial Electronics, vol. 56, no. 3, pp. 900–906, 2009. View at Publisher · View at Google Scholar · View at Scopus
  16. Z. Gao, Y. Huang, and J. Han, “An alternative paradigm for control system design,” in Proceedings of the 40th IEEE Conference on Decision and Control (CDC '01), vol. 5, pp. 4578–4585, Orlando, Fla, USA, December 2001. View at Scopus
  17. Z. Gao, S. Hu, and F. Jiang, “A novel motion control design approach based on active disturbance rejection,” in Proceedings of the 40th IEEE Conference on Decision and Control (CDC '01), vol. 5, pp. 4877–4882, Orlando, Fla, USA, December 2001. View at Publisher · View at Google Scholar · View at Scopus
  18. R. Li, T. Li, Q. Zheng, and Q. Li, “Ship tracking control based on linear active disturbance rejection control,” in Proceedings of the 2012 3rd International Conference on Intelligent Control and Information Processing (ICICIP '12), pp. 201–205, IEEE, Dalian, China, July 2012. View at Publisher · View at Google Scholar · View at Scopus
  19. R. Morales, H. Sira-Ramírez, and J. A. Somolinos, “Linear active disturbance rejection control of the hovercraft vessel model,” Ocean Engineering, vol. 96, pp. 100–108, 2015. View at Publisher · View at Google Scholar · View at Scopus
  20. H. Coral-Enriquez, J. Cortés-Romero, and G. A. Ramos, “Robust active disturbance rejection control approach to maximize energy capture in variable-speed wind turbines,” Mathematical Problems in Engineering, vol. 2013, Article ID 396740, 12 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  21. J. Cortés-Romero, H. Rojas-Cubides, H. Coral-Enriquez, H. Sira-Ramírez, and A. Luviano-Juárez, “Active disturbance rejection approach for robust fault-tolerant control via observer assisted sliding mode control,” Mathematical Problems in Engineering, vol. 2013, Article ID 609523, 12 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  22. R. Li, T. Li, R. Bu, Q. Zheng, and C. L. P. Chen, “Active disturbance rejection with sliding mode control based course and path following for underactuated ships,” Mathematical Problems in Engineering, vol. 2013, Article ID 743716, 9 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  23. H. K. Khalil, “High-gain observers in nonlinear feedback control,” in Proceedings of the International Conference on Control, Automation and Systems (ICCAS '08), pp. 47–57, IEEE, Seoul, South Korea, October 2008. View at Publisher · View at Google Scholar · View at Scopus
  24. S. Puga, M. Bonilla, M. Malabre, and R. Lozano, “Singularly perturbed implicit control law for linear time varying SISO systems,” International Journal of Robust and Nonlinear Control, vol. 24, no. 10, pp. 1530–1549, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. S. Puga, M. Bonilla, C. H. Moog, M. Malabre, and R. Lozano, “Singularly perturbed feedback linearization for SISO nonlinear systems with measurement of the state,” in Proceedings of the European Control Conference (ECC '15), pp. 3250–3255, Linz, Austria, July 2015. View at Publisher · View at Google Scholar
  26. J. D. J. Rubio, G. Ochoa, R. Balcazar, and J. Pacheco, “Uniform stable observer for the disturbance estimation in two renewable energy systems,” ISA Transactions, vol. 58, pp. 155–164, 2015. View at Publisher · View at Google Scholar · View at Scopus
  27. A. M. Bloch, N. E. Leonard, and J. E. Marsden, “Matching and stabilization by the method of controlled lagrangians,” in Proceedings of the 37th IEEE Conference on Decision and Control, vol. 2, pp. 1446–1451, IEEE, Piscataway, NJ, USA, 1998.
  28. R. Ortega, M. W. Spong, F. Gómez-Estern, and G. Blankenstein, “Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment,” IEEE Transactions on Automatic Control, vol. 47, no. 8, pp. 1218–1233, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. R. Ortega and E. Garcia-Canseco, “Interconnection and damping assignment passivity-based control: a survey,” European Journal of Control, vol. 10, no. 5, pp. 432–450, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. Q. Gao, Y. Hou, K. Li, Z. Sun, C. Wang, and R. Hou, “Neural network based active disturbance rejection control of a novel electrohydraulic servo system for simultaneously balancing and positioning by isoactuation configuration,” Shock and Vibration, vol. 2016, Article ID 4921095, 9 pages, 2016. View at Publisher · View at Google Scholar
  31. S. Galvan-Colmenares, M. A. Moreno-Armendáriz,, J. de Jesús Rubio, F. Ortíz-Rodriguez, W. Yu, and C. F. Aguilar-Ibáñez, “Dual PD control regulation with nonlinear compensation for a ball and plate system,” Mathematical Problems in Engineering, vol. 2014, Article ID 894209, 10 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. Q. Zheng, L. Q. Gao, and Z. Gao, “On validation of extended state observer through analysis and experimentation,” Journal of Dynamic Systems, Measurement and Control, vol. 134, no. 2, Article ID 024505, 2012. View at Publisher · View at Google Scholar · View at Scopus
  33. B.-Z. Guo and Z.-L. Zhao, “Weak convergence of nonlinear high-gain tracking differentiator,” IEEE Transactions on Automatic Control, vol. 58, no. 4, pp. 1074–1080, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  34. B.-Z. Guo and Z.-L. Zhao, “On the convergence of an extended state observer for nonlinear systems with uncertainty,” Systems & Control Letters, vol. 60, no. 6, pp. 420–430, 2011. View at Publisher · View at Google Scholar · View at Scopus
  35. B.-Z. Guo and Z.-L. Zhao, “On convergence of the nonlinear active disturbance rejection control for MIMO systems,” SIAM Journal on Control and Optimization, vol. 51, no. 2, pp. 1727–1757, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  36. W.-H. Chen, J. Yang, L. Guo, and S. Li, “Disturbance-observer-based control and related methods—an overview,” IEEE Transactions on Industrial Electronics, vol. 63, no. 2, pp. 1083–1095, 2016. View at Publisher · View at Google Scholar
  37. R. Madoński and P. Herman, “Survey on methods of increasing the efficiency of extended state disturbance observers,” ISA Transactions, vol. 56, pp. 18–27, 2015. View at Publisher · View at Google Scholar · View at Scopus
  38. A. N. Atassi and H. K. Khalil, “A separation principle for the stabilization of a class of nonlinear systems,” IEEE Transactions on Automatic Control, vol. 44, no. 9, pp. 1672–1687, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  39. W. Zhou, S. Shao, and Z. Gao, “A stability study of the active disturbance rejection control problem by a singular perturbation approach,” Applied Mathematical Sciences, vol. 3, no. 9–12, pp. 491–508, 2009. View at Google Scholar · View at MathSciNet · View at Scopus
  40. H. K. Khalil and L. Praly, “High-gain observers in nonlinear feedback control,” International Journal of Robust and Nonlinear Control, vol. 24, no. 6, pp. 993–1015, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  41. R. Bhatia and P. Rosenthal, “How and why to solve the operator equation AX-XB=Y,” The Bulletin of the London Mathematical Society, vol. 29, no. 1, pp. 1–21, 1997. View at Publisher · View at Google Scholar · View at MathSciNet