Control of Axially Moving Strings and Beams

Using the models developed in Chaps. 2 and 3, we investigate various control schemes for axially moving strings and beams. First, the control methods using an approximate ODE model, such as the model-based feedback control and variable structure control, are presented. Subsequently, various control schemes using the PDE models, including the transfer function method, wave cancellation method, boundary control based on the Lyapunov method, adaptive control method, and hybrid control methods, are discussed. Numerical simulations are provided to illustrate the performance of the control schemes.