Lyapunov functions and the control of the Euler-Bernoulli beam

Abstract

A controller for the Euler-Bernoulli beam is derived using the complete distributed model along with a Lyapunov function approach. Model structure is therefore preserved in the control law whose parameters can be used to balance two different types of behaviour: the gross motion of the beam and the vibration superimposed on it. In the limiting case of a rigid beam, these two types of behaviour become indistinguishable and so the controller reduces to a proportional feedback law. This approach also guarantees that the controller provides asymptotic trajectory tracking for smooth initial conditions. Also, since it is not constrained to linear systems it could, in principle, be used for multi-link flexible robot systems.