Boundary control of a rotating flexible body-beam system

We consider the problem of controlling a rotating flexible body-beam system composed of a rigid disk at the clamped-end of a Euler-Bernoulli beam and a point mass at its free-end. First, we design an exact model knowledge control law which exponentially stabilizes the beam´s displacement while also ensuring the body-beam system rotates at a desired speed exponentially fast. We then design an adaptive control law which achieves the same control objective asymptotically fast. The boundary control laws are composed of a control torque applied to the disk and a control force applied at the beam´s free-end.