Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 410873, 9 pages
http://dx.doi.org/10.1155/2015/410873
Research Article

Analysis and Synthesis of Global Nonlinear Controller for Robot Manipulators

1Instituto Politécnico Nacional, Centro de Investigación y Desarrollo de Tecnología Digital, Avenida Instituto Politécnico Nacional 1310, Mesa de Otay, 22510 Tijuana, BC, Mexico
2Departamento de Ingeniería Eléctrica y Electrónica, Instituto Tecnológico de Tijuana, Calzada Tecnológico S/N, Fraccionamiento Tomas Aquino, 22414 Tijuana, BC, Mexico

Received 23 December 2014; Revised 10 March 2015; Accepted 11 March 2015

Academic Editor: Dan Ye

Copyright © 2015 Carlos Alberto Chavez Guzmán 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. S. Arimoto, Control Theory of Non-Linear Mechanical Systems: A Passivity-Based and Circuit-Theoretic Approach, Oxford University Press, London, UK, 1996.
  2. R. Kelly, V. Santibanez, and A. Loria, Control of Robot Manipulators in Joint Space, Springer, London, UK, 2005.
  3. M. Spong and M. Vidyasagar, Robot Dynamics and Control, John Wiley & Sons, New York, NY, USA, 1989.
  4. V. I. Utkin, Sliding Modes in Control Optimization, Springer, Berlin, Germany, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  5. V. Utkin, J. Guldner, and J. Shi, Sliding Modes in Electromechanical Systems, Taylor & Francis, London, UK, 1999.
  6. W. Chung, L.-C. Fu, and S.-H. Hsu, “Motion control,” in Handbook of Robotics, B. Siciliano and O. Khatib, Eds., pp. 133–159, Springer, London, UK, 2008. View at Google Scholar
  7. L. Acho, Y. Orlov, and V. Solis, “Non-linear measurement feedback H-control of time-periodic systems with application to tracking control of robot manipulators,” International Journal of Control, vol. 74, no. 2, pp. 190–198, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. J. A. Ball, J. W. Helton, and M. L. Walker, “H control for nonlinear systems with output feedback,” IEEE Transactions on Automatic Control, vol. 38, no. 4, pp. 546–559, 1993. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. J. Helton and M. James, Extending H Control to Nonlinear Systems—Control of Nonlinear Systems to Achieve Performance Objectives, SIAM, Philadelphia, Pa, USA, 1999.
  10. Y. V. Orlov and L. T. Aguilar, Advanced H Control: Towards Nonsmooth Theory and Applications, Birkhäuser, New York, NY, USA, 2014.
  11. A. J. van der Schaft, “L2-gain analysis of nonlinear systems and nonlinear state feedback H control,” IEEE Transactions on Automatic Control, vol. 37, no. 6, pp. 770–784, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. A. Isidori and A. Astolfi, “Disturbance attenuation and H-control via measurement feedback in nonlinear systems,” IEEE Transactions on Automatic Control, vol. 37, no. 9, pp. 1283–1293, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. M. Krstic and H. Deng, Stabilization of Nonlinear Uncertain Systems, Communications and Control Engineering, Springer, London, UK, 1998. View at MathSciNet
  14. A. I. Subbotin, Generalized Solutions of First-Order PDE's—the Dynamical Optimization Perspective, Birkhäauser, Boston, Mass, USA, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  15. Y. Orlov and L. Aguilar, “Non-smooth H-position control of mechanical manipulators with frictional joints,” International Journal of Control, vol. 77, no. 11, pp. 1062–1069, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. I. Meza, L. Aguilar, A. Shiriaev, L. Freidovich, and Y. Orlov, “Periodic motion planning and nonlinear H tracking control of a 3-DOF underactuated helicopter,” International Journal of Systems Science, vol. 42, no. 5, pp. 829–838, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. D. L. Lukes, “Optimal regulation of nonlinear dynamical systems,” SIAM Journal on Control and Optimization, vol. 7, pp. 75–100, 1969. View at Publisher · View at Google Scholar · View at MathSciNet
  18. S. T. Glad, “Robustness of nonlinear state feedback: a survey,” Automatica, vol. 23, no. 4, pp. 425–435, 1987. View at Publisher · View at Google Scholar · View at Scopus
  19. M. D. S. Aliyu, “An approach for solving the Hamilton-Jacobi-Isaacs equation (HJIE) in nonlinear H control,” Automatica, vol. 39, no. 5, pp. 877–884, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. H. C. Ferreira, P. H. Rocha, and R. M. Sales, “Galerkin method and weight function applied to nonlinear H control with output feedbac,” Journal of Vibration and Control, vol. 16, no. 12, pp. 1817–1843, 2008. View at Google Scholar · View at MathSciNet · View at Scopus
  21. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Studies in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 1994.
  22. E. Fridman and Y. Orlov, “An LMI approach to H boundary control of semilinear parabolic and hyperbolic systems,” Automatica, vol. 45, no. 9, pp. 2060–2066, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. J. Yim and J. H. Park, “Nonlinear H control of robotic manipulator,” in Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, pp. 866–871, IEEE, Tokyo, Japan, October 1999. View at Publisher · View at Google Scholar · View at Scopus
  24. M. D. S. Aliyu, Nonlinear H Control, Hamiltonian Systems, and Hamilton Jacobi Equations, CRC Press, Boca Raton, Fla, USA, 2011.
  25. M. Hardt, J. W. Helton, and K. Kreutz-Delgado, “Numerical solution of nonlinear H2 and H control problems with application to jet engine compressors,” IEEE Transactions on Control Systems Technology, vol. 8, no. 1, pp. 98–111, 2000. View at Publisher · View at Google Scholar · View at Scopus
  26. V. Santibanez and R. Kelly, “Strict Lyapunov functions for control of robot manipulators,” Automatica, vol. 33, no. 4, pp. 675–682, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  27. T. Basar and P. Bernhard, H-Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach, Birkhäuser, Boston, Mass, USA, 2nd edition, 1995. View at MathSciNet
  28. J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “State-space solutions to standard H2 and H control problems,” IEEE Transactions on Automatic Control, vol. 34, no. 8, pp. 831–847, 1989. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. Sensoray Model 626, Sensoray Co., Inc., Tigard, Ore, USA, January 2004, http://www.sensoray.com/downloads/man_626_1.0.5.pdf.