State-Feedback Nonlinear H∞ Boundary Control for a Gantry Crane with Flexible Cable

Abstract

We have solved the state-feedback nonlinear ${\mathcal{H}_\infty }$ boundary control to stabilize a flexible cable of a gantry crane. The cable is not assumed rigid; therefore, we represented the cable dynamics as a hyperbolic partial differential equation. We proved the asymptotical stability of the unperturbed closed-loop system through a strict Lyapunov functional. Moreover, we demonstrated the disturbance attenuation level through the ℒ2-gain analysis. We corroborate the theoretical results by numerical simulations developed in a dynamic model of a laboratory gantry crane.