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. Accepted for publication: February 2005. AMS Subject Classifications: 93C20, 93D15, 35B35, 35P10. The first author was supported by the National Natural Science Foundation of China and the National Research Foundation of South Africa. 1013 1014 Bao-Zhu Guo, Jun-Min Wang, and Siu-Pang Yung