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

• Published in: Mathematical problems in engineering Vol. 2015; no. 2015; pp. 1 - 10
• Main Authors: Ramos Fernandez, Julio Cesar, Garcia Barrientos, Abel, Espinoza Quesada, Eduardo Steed, Ordaz Oliver, Jesus Patricio
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 01.01.2015; Hindawi Limited
• Subjects: Compensators; Control theory; Controllers; Disturbances; Dynamical systems; Ellipsoids; Mathematical analysis; Mathematical models; Mechanical systems; Nonlinear control; Nonlinear dynamics; Nonlinear systems; Nonlinearity; Ordinary differential equations; Proportional integral derivative; Rejection; Stability analysis; Tribology; Uncertainty analysis; Mexico
• ISSN: 1024-123X; 1563-5147
• DOI: 10.1155/2015/701415

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.