Optimal Control of Beams With Dynamic Loading and Buckling

The vibration of beams can be suppressed by a set of discrete actuators associated with a causal optimal, coupled-modal control algorithm which is derived from minimizing a time-dependent weighted sum of the kinetic energy, potential energy, and the control effort. The control gains are functions of the control interval and couple the modes that participate in the control. The controller can be applied to control a beam subjected to a resonant cyclic load, a moving load, and a beam column subjected to a unit impuse at midspan before buckling.