An adaptive iterative learning algorithm for boundary control of a flexible manipulator

In this study, we consider the boundary control problem of a flexible manipulator in the presence of system parametric uncertainty and external disturbances. The dynamic behavior of the flexible manipulator is represented by partial differential equations (PDEs). Based on the Lyapunov method, we propose an adaptive iterative learning control scheme for trajectory tracking and vibration suppressing of a flexible manipulator. The proposed control scheme is designed using both a proportional-derivative feedback structure and an iterative term. The learning convergence of iterative learning control is achieved through rigorous analysis without any simplification or discretization of the PDE dynamics. Finally, the results are illustrated using numerical simulations for control performance verification.