Non-collocated tracking for an Euler–Bernoulli beam subject to disturbances with unknown frequencies

In this work, we study the output tracking problem of an Euler–Bernoulli beam subject to non-collocated boundary controls and harmonic disturbances with unknown frequencies. We restructure the measurable tracking error by the auxiliary system and the internal model dynamic. An adaptive method is used to estimate the unknown parameters. Finally, we present an adaptive error-based dynamic compensator to realize tracking and compensate disturbance. The well-posedness and stability of closed-loop system are proved by employing the semigroup theory and energy multiplier method. In order to confirm the effectiveness of the proposed control schemes, the numerical simulations are presented.