Optimal actuation in vibration control

The paper addresses the problem of finding the optimal location of actuators and their relative gain so that the control effort in an actively controlled vibrating system is minimized. In technical terms the problem is finding the optimal input vector of unit norm that minimizes the norm of the control gain vector. This problem is addressed in the context of the active natural frequency modification problem associated with resonance avoidance in undamped systems, and in the context of the single-input-multi-output pole assignment problem for second order systems.

► We address the problem of optimal actuation for minimal control effort.
► In single pole assignment the optimal input vector is parallel to the mode shape.
► The equations for optimal actuation in the pole placement problem are given.