A new approach to the synthesis of modal control laws in active structural vibration control

Many systems have, by their nature, a small damping and they are therefore potentially subjected to dangerous vibratory phenomena. The aim of active vibration control is to contain these phenomena, increasing the natural damping of the system and its fatigue life, preferably without changing its natural frequencies and vibration modes. The modal control technique is the favorite amongst mechanical and structural engineers because of its representation in modal coordinates. However, especially in the field of active vibration control, the traditional design of the controller developed in state coordinates makes it difficult to understand how the mechanical parameters of the system are modified. The present paper introduces a new approach to the synthesis of a modal controller to suppress vibrations in structures. It turns away from the traditional formulation of the problem showing how the performance of the designed controller can be evaluated through the analysis of the resulting modal damping matrix of the controlled system. The approach is based on the relationship existing between the shape of the matrix and the possibility that the control forces are dissipative (and, thus, ensuring the system stability). This analysis allows us to easily evaluate spillover effects, due to the presence of unmodeled modes, the stability of the control and the consequent effectiveness in reducing vibration. The opportunity to easily manage this information allows the synthesis of an efficient modal controller. Theoretical aspects are supported by numerical simulations and experimental tests.