Optimal gains for active vibration control by the beam analogy

A numerical approach to determine optimal gains for active optimal vibration control of continuous structures by the finite element method is presented. The approach uses an analogy between the optimality equations for control in the time domain and the governing equations for a set of static beams in the spatial domain. The finite element model of control is generated and analyzed in a fictitious spatial domain. The results are then transferred to the time domain to describe the optimal dynamic response of the system. The analogy (referred to as the beam analogy) allows for an efficient application of the finite element method to solve two-point-boundary-value problems for the finite time control cases. Here it is applied to the infinite time control cases. An algorithm for a direct calculation of optimal gains for closed loop control of time-invariant problems without using Riccati’s equation is discussed in detail.