A generalized wave equation for flexible structures is controlled with pointwise activators (open loop) and sensors (closed loop), both involving Dirac delta functions. The performance objective is a combination of the total energy of the structure and the penalty terms on the controls. The direct method used here is based on approximation of the open-loop controls, that converts the linear quadratic problem into a mathematical programming problem. The optimal closed loop parameters are numerically determined from the solution of energy minimization problem. A simple supported beam example is given.