Passivity Based Adaptive Control of a Single-Link Flexible Manipulator

This paper deals mainly with an adaptive passivity based control of a single-link flexible manipulator with parametric uncertainties. The combined Euler–Lagrange formalism and assumed modes method is employed to derive the dynamics of the system. The resulting model is extremely nonlinear and depends on the number of modes shapes adopted. Passivity based control strategy is used to achieve good trajectory tracking at the joint space and to damp the end effector undesirable vibrations. In the purpose of improving the robustness of the proposed controller against both robot flexibility and parametric uncertainties, an adaptive control law using the passivity approach is designed to overcome this problem. The global stability of the closed-loop system is verified using Lyapunov theory by taking into consideration the passivity property of the flexible manipulator. The simulation results using Matlab/Simulink are given to show the excellent performances of the adaptive controller such as asymptotic trajectory tracking and fast parameters convergence.