Reduced Model inH∞Vibration Control Using Linear Matrix Inequalities

Many practical problems in structural dynamics are modeled with a high number of degrees of freedom in order to properly describe the structure. A formulation to design robust controllers is theH∞technique where the controller has the same order of the mathematical model and this becomes unpractical and infeasible for most practical problems where the number of degrees of freedom is not small. One way to overcome this difficulty is to employ a model reduction technique, and design a reduced order controller based on this reduced model. In this case, it is required that the reduced controller ensures a good performance also for the nominal model (reduced) and for the real model (non-reduced) of the structure. Since the reduced controller is designed based on a truncated dynamic model, the non-modeled vibration modes can be excited causing the spillover phenomena, which is a severe undesirable effect. This work investigates the behavior of a reduced order controller obtained based on a reduced model through the Guyan reduction. TheH∞robust control and Linear Matrix Inequalities (LMI) formulations are employed to the problem of controlling a flexible structure subjected to an external disturbance. Some simulations are performed using a cantilever beam modeled by the finite element method. The results show that the Guyan reduced order model can be used to design a controller to the non-reduced model with success.