Advertisement

Nonlinear H ∞  State Feedback Control of Rigid Robot Manipulators

  • Mahdi Jalili-Kharaajoo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3192)

Abstract

In this paper, nonlinear H ∞  control strategy is applied to control of a two-degree-of-freedom rigid robot manipulator. In order to obtain the nonlinear H ∞  control law, some inequalities so-called Hamilton-Jacobi-Isaacs (HJI) should be solved. It is so difficult, if not impossible, to find an explicit solution for HJI inequalities. However, there are some approximate solutions. One of these possible solutions is the use of Taylor Series expansion of nonlinear terms, which will be used in this paper. Using the obtained nonlinear robust controller, the response of the closed-loop system for tracking of fixed point and oscillating reference signals are obtained. Simulation results show better performance for higher order approximated controller than that of lower order one.

Keywords

Taylor Series Expansion Robot Manipulator State Feedback Control Disturbance Attenuation Order Controller 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Isidori, A., Astolfi, A.: Disturbance attenuation and H∞ control via measurements feedback in nonlinear systems. IEEE Trans. Automatic Control 37, 1283–1293 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Van der Schaft, A.J.: L2 gain analysis of nonlinear systems and nonlinear state feedback Control. IEEE Trans. Automatic Control 37, 770–781 (1992)zbMATHCrossRefGoogle Scholar
  3. 3.
    Isidori, A., Kang, W.: H∞ control via measurement feedback for general nonlinear systems. IEEE Trans. Automatic Control 40, 466–472 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Yazdanpanah, M.J., Khorasani, K., Patel, P.V.: Uncertainly compensation for a flexible link manipulator using nonlinear H∞ control. INT. J. Control 6, 753–771 (1998)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Jalili-Kharaajoo, M., Yazdanpanah, M.J.: Transient control and voltage regulation of power systems using approximate solution of HJB equation. In: Proc. European Control Conference (ECC 2003), Oxford, England, September2-4 (2003)Google Scholar
  6. 6.
    Lu, Q., et al.: Decentralized nonlinear H∞ excitation control based on regulation linearization. IEE Proc. Gener. Transm. Distri. 147(4), 940–946 (2000)Google Scholar
  7. 7.
    Karlsson, N., Dahleh, M., Hrovat, D.: Nonlinear H∞ control of active suspensions. In: Proc. ACC 2001, Arlington, VA, pp. 3329–3335 (2001)Google Scholar
  8. 8.
    Cai, D., Dai, Y.: A globally convergence robust controller for robot manipulator. In: Proc. IEEE Int. Conf. Control Application, Mexico City, Mexico (2001)Google Scholar
  9. 9.
    Zhihong, M., Yu, X.: Adaptive terminal Sliding Mode Tracking Control for Rigid Robotic Manipulators with Uncertain Dynamics. Journal of S. Mechanical Engineering, Series C 40(3) (1997)Google Scholar
  10. 10.
    Keleher, P.G., Stonier, R.J.: Adaptive terminal sliding mode control of a rigid robot manipulator with uncertain dynamics incorporating constrain inequalities. J. ANZIAM 43(E), E102–E157 (2002)MathSciNetGoogle Scholar
  11. 11.
    Battoliti, S., Lanari, L.: Tracking with disturbance attenuation for rigid robots. In: Proc. IEEE Int. Con. Robotics and Automation, pp. 1578–1583 (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Mahdi Jalili-Kharaajoo
    • 1
  1. 1.Young Researchers ClubIslamic Azad University, Tehran, IRANTehranIRAN

Personalised recommendations