Active boundary control of an Euler–Bernoulli beam for generating vibration-free state

This paper presents active boundary control—ABC—of an Euler–Bernoulli beam, which enables one to generate a desired boundary condition at any designated position of a target beam structure, thereby permitting the structure to possess desired properties characterized by the boundary condition. Furthermore, ABC has potential to create a completely vibration-free state in the designated area of a beam. This paper begins by presenting the principle of ABC using a transfer matrix method, the optimal control law of the ABC system being derived. It is found that, in addition to conventional four classical boundary conditions: free, pinned, clamped and sliding support, ABC can generate two more boundary conditions that may not be observed in real systems but realized by ABC. It is also found that as a result of applying ABC to a specific location, including a current conventional boundary of a beam, a completely vibration-free state in the target region of a beam can be realized. Finally, an experiment using an adaptive feedforward control was conducted, demonstrating that ABC enables the generation of a desired boundary condition at the designated location of a target beam, and of a completely vibration-free state of a beam.