Boundary Control for a Nonlinear Two-link Rigid-flexible Manipulator in Three-dimensional Workspace with Full State Constraints

This paper discusses the vibration control for a two-link rigid-flexible manipulator in 3D space with angular position and speed constraints. A nonlinear hybrid PDE-ODE model is derived and based on asymmetric barrier Lyapunov functions, a boundary feedback controller is proposed to realize joint states control, vibration suppression, and full state constraints. The asymptotic stability of the closed-loop system is verified by analyzing PDE solutions. Moreover, to improve robustness, a robust boundary controller using the sign function is presented to restrain input disturbances. Numerical simulations are conducted to illustrate the effectiveness and robust performance of the proposed controllers.