Adaptive boundary control of a flexible-link flexible-joint manipulator under uncertainties and unknown disturbances

In this article, we consider the trajectory tracking and vibration suppression of a flexible-link flexible-joint manipulator under uncertainties and external time-varying unknown disturbances. The coupled ordinary differential equation and partial differential equation model dynamic of the system is presented by employing the Hamilton principle. Using the singular perturbation theory, the dynamic is decomposed into a no-underactuated slow ordinary differential equation and fast partial differential equation subsystem, which solves the problem of the underactuated ordinary differential equation subsystem of the ordinary differential equation and partial differential equation cascade and reduces the analytical complexity. For the slow subsystem, to guarantee the trajectory tracking of the joint, an adaptive global sliding mode controller without gain overestimation is designed, which can guarantee the global stability of the slow system and reduce the chattering of the sliding mode control. For the fast subsystem, an adaptive boundary controller is developed to suppress the elastic vibration of the flexible link during the trajectory tracking. The stability of the whole closed-loop system is rigorously proved via the Lyapunov analysis method. Simulation results show the effectiveness of the proposed controller.