Boundary Controllers for Euler-Bernoulli Beam with Arbitrary Decay Rate

摘要

We consider a problem of stabilization of the Euler-Bernoulli beam. The beam is controlled at one end (using position and moment actuators) and has the "sliding" boundary condition at the opposite end. We design the controllers that achieve any prescribed decay rate of the closed loop system, improving upon the existing "boundary damper" controllers. The idea of the control design is to use the well-known representation of the Euler-Bernoulli beam model through the Schrodinger equation, and then adapt recently developed back-stepping designs for the latter in order to stabilize the beam. We derive the explicit integral transformation (and its inverse) of the closed-loop system into an exponentially stable target system. The transformation is of a novel Volterra/Fredholm type. The design is illustrated with simulations.