Control of a class of single-link flexible robot arms with bounded unknown pay-load is addressed in this paper. The Lyapunov's direct method is used to prove the asymptotical stability of the closed-loop system under the proposed linear controller. The stability analysis is performed directly on the system's partial differential governing equation, so that no approximation is involved. Thus the 'spillover' problem, which is caused by using finite dimensional (truncated) models to approximate the infinite dimensional models of distributed parameter systems, is eliminated. It is theoretically shown that a simple linear controller with feedback of only joint variables is sufficient to stabilize asymptotically the complex system of a flexible arm with bounded unknown payload. A numerical example of a single-link flexible arm with bounded unknown payload is presented for illustration.
"Control of single-link flexible arms with bounded unknown payload", Proc. SPIE 2620, International Conference on Intelligent Manufacturing, (28 August 1995); doi: 10.1117/12.217559; https://doi.org/10.1117/12.217559