Dependent modal space control

This paper presents a new control technique for reducing vibration in flexible structures. It is based on the modal approach and is called dependent modal space control (DMSC). The well-known independent modal space control (IMSC) method, devised in the 1980s, allows the frequency and damping of the controlled modes to be changed using diagonal control gain matrices, leaving the mode shapes unaltered. DMSC, on the other hand, can impose not only frequency and damping but also the controlled mode shapes by using full control gain matrices. In many applications, owing to the limited number of sensors–actuators available for control and the increasing spillover effects, generic assignment of eigenvectors is not possible. However, an optimal eigenstructure assignment can be computed to reduce structure vibration by minimizing an input–output performance index. To demonstrate the advantages of this new method, we compare IMSC and DMSC using numerical simulation on a finite element method model of a cantilevered beam.