Summary: Vibration suppression of a structurally damped beam via open and closed-loop controls is investigated. In doing so, minimization of a weighted, energy-based performance measure leads to closed-form expressions for optimal open-loop parameters in terms of feedback gains. The control problem is then completed by optimizing these feedback parameters numerically. Methods to determine optimal terminal time of control are also presented. Furthermore, techniques are established to optimize the response and performance of a system experiencing a known feedback time delay. Different types of optimization are proposed and, for each one, the trade-off between performance and computational efficiency is fully discussed.