Concurrent Design of Active Control and Structural Modifications for Eigenstructure Assignment on a Cantilever Beam

This paper proposes the experimental application of a novel hybrid control technique to perform eigenstructure assignment in vibrating systems. The method takes advantage of the concurrent use of passive modifications of the elastic and inertial parameters, and of state-feedback active control. The system modifications are computed through the solution of a rank minimization problem to shape the space of the allowable eigenvectors that can be achieved through active control. The test consists of a cantilever beam, which is modified and controlled to feature a second vibrational mode whose vibrations are confined to the part of the beam near the free end. The beam is controlled through a piezoelectric actuator and a Kalman filter is adopted to estimate the state vector for state-feedback control. The method proposed is able to overcome the limitations of the use of either passive modifications or active control alone, by significantly enlarging the set of assignable eigenpairs in vibrating systems.