On Gain Design in Virtual Output Feedback for Model Updating

The set of equations to be solved for parameter estimation in model updating has no unique solution when, as will typically be the case in structural applications, the dimensionality of the model exceeds the number of target parameters estimated from experiments. One approach for enlarging the target space is to create multiple closed-loop systems that, in addition, can be designed with pole sensitivities favorable for updating the model. The present paper will focus on designing gains for model updating using a recently proposed virtual implementation of output feedback, which allows computation of several closed-loop systems from a single open-loop realization and removes the constraint of closed-loop stability. The gains are designed through an eigenstructure assignment procedure, in which the model parameters to be updated are divided into two different classes; one where the pole sensitivities with respect to the parameter are to be enhanced and one where they are to be reduced. A numerical examination with a structural system is presented that demonstrates the merit of the proposed gain design procedure.