Uncertainty Models and Robust Complex-Rational Controller Design for Flexible Structures

Real parametric uncertainties in themodal dampingratios and frequencies of  exible structures are represented by complex uncertainties that can lead to robust controller designs satisfying robust performance speciŽ cations. These complex uncertaintyblocksare useful in a1-synthesis controllerdesignprocedure. Twomodels are proposed for modal parameter uncertainties. The Ž rst model uses a coprime factorization representation of the perturbed plant, whereas in the second model, a diagonal representation with complex eigenvalues is used. The innovation in the second method proposed is the use of a complex-rational controller design strategy, which offers tight uncertainty bounds and leads to a robust performance controller. The frequency response of the complex-rational controller is then approximated by a real-rational controller achieving the robust performance speciŽ cations.