Simultaneous active and passive control for eigenstructure assignment in lightly damped systems

The assignment of the eigenstructure (i.e. eigenvalues and eigenvectors) in vibrating systems is an effective way to improve their dynamic performances. System controllability ensures that the poles of the controlled system are exactly assigned but it does not allow to assign arbitrary desired eigenvectors. To this purpose, this paper proposes a novel method for vibration control in lightly damped systems through the concurrent synthesis of passive structural modifications and active state (or state derivative) feedback control gains. Indeed, the suitable modification of the inertial and elastic parameters allows to enlarge the range of assignable eigenvectors. The problem is formulated as an optimization problem, where constraints are introduced to assure the feasibility of the physical system modifications while avoiding spillover phenomena. The experimental application to the eigenstructure assignment on a manipulator proves the method effectiveness.