Boundary control for two-link flexible manipulator with input constraints based on partial differential equation model

Abstract This work tackles boundary controller design and analysis for input-saturated two-link flexible manipulators. The system dynamics, incorporating boundary force effects, are modeled using Partial Differential Equations (PDEs) defined within local body-fixed coordinate frames. To simultaneously achieve angular position regulation and suppress flexible link vibrations under actuator saturation limitations, we have presented a novel boundary control strategy. This strategy employs a smooth hyperbolic function to explicitly constrain the control input within a predetermined upper bound. Assuming a sufficiently small flexural displacement allows the approximation of its relationship with the axial rate of flexural displacement as linear. Utilizing LaSalle’s invariance principle and this approximation, the system’s stability is rigorously proved. Finally, Simulation results illustrate the efficacy of the controller in regulating the angular position and suppressing vibrations in the links.