Boundary stabilization of a flexible manipulator with rotational inertia

We design a stabilizing linear boundary feedback control for a one-link flexible manipulator with rotational inertia.The system is modelled as a Rayleigh beam rotating around one endpoint, with the torque at this endpoint as the control input.The closed-loop system is nondissipative, so that its well posedness is not easy to establish.We study the asymptotic properties of the eigenvalues and eigenvectors of the corresponding operator A and establish that the generalized eigenvectors form a Riesz basis for the energy state space.It follows that A generates a C0-semigroup that satisfies the spectrum-determined growth assumption.This semigroup is exponentially stable under certain conditions on the feedback gains.If the higher-order feedback gain is set to zero, then we obtain a polynomial decay rate for the semigroup.