Adaptive boundary control for flexible two-link manipulator based on partial differential equation dynamic model

In this studies, adaptive boundary control for a flexible two-link manipulator with a changeable payload at the free-end. Taking into account the infinite-dimensionality of the flexural dynamics, this study proposes a partial differential equation (PDE) model, so that the problem of possible spillover instability caused by the neglect of flexible modes can be avoided. Based on the PDE model, an adaptive boundary control scheme is designed to regulate joint position and suppress elastic vibration while compensating for parametric uncertainties. The asymptotic stability of the closed-loop system is validated theoretically. The effectiveness of the control scheme is also verified by the numerical simulations.