Robust H∞ stabilization of a large flexible structure via normalized coprime factor plant description

The concept of robust stabilization via normalized left coprime factor description of the plant uncertainty has been successfully applied to the DLR genetic flexible test structure. The method for the design of the robust H_∞ controllers involves shaping the open-loop singular values with a precompensator and/or postcompensator and then designing a coprime factorization of this weighted plant model. Its main features are that the weighting can be performed directly on the rate and position outputs of the flexible structure and that there is no undesirable cancellation of the plant poles by the controller. Some simple guidelines for specifying the desired loop shapes in the designs are also provided. The effect of the weighting selection and the distance to the optimality (suboptimality) are investigated. The robustness and the performance of the controllers are analyzed using the singular values of the related closed-loop transfer functions