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PID Based on Attractive Ellipsoid Method for Dynamic Uncertain and External Disturbances Rejection in Mechanical Systems

Author

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  • Jesus Patricio Ordaz Oliver
  • Eduardo Steed Espinoza Quesada
  • Abel Garcia Barrientos
  • Julio Cesar Ramos Fernandez

Abstract

This paper presents a stability analysis for LNDS (Lagrangian nonlinear dynamical systems) with dynamic uncertain using a PID controller with external disturbances rejection based on attractive ellipsoid methods, since the PID-CT (proportional integral derivative computed torque) compensator has been used for the nonlinear trajectory tracking of an LNDS, when there are external perturbations and system uncertainties. The global system convergence of the trivial solution has not been proved. In this sense, we propose an approach to find the gains of the nonlinear PID-CT controller to guarantee the boundedness of the trivial solution by means of the concept of the UUB (uniform-ultimately bounded) stability. In order to show the effectiveness of the methodology proposed, we applied it in a real 2-DoF robot system.

Suggested Citation

  • Jesus Patricio Ordaz Oliver & Eduardo Steed Espinoza Quesada & Abel Garcia Barrientos & Julio Cesar Ramos Fernandez, 2015. "PID Based on Attractive Ellipsoid Method for Dynamic Uncertain and External Disturbances Rejection in Mechanical Systems," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-10, May.
    • Handle: RePEc:hin:jnlmpe:701415
    DOI: 10.1155/2015/701415
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