Real gyroscopic uncertainties in robust control of flexible rotors

Control laws for flexible high-speed rotors need to account for gyroscopic effects, resulting in a dependency of linear plant models on the rotational speed of the rotor. When these variations are captured by uncertainties in a robust control manner, it is common to employ unstructured or structured complex model perturbations. In order to reduce design-induced conservatism, the synthesis setup presented in this paper deploys a real parametric uncertainty to account for speed-dependent terms of the plant model. The resulting Linear Fractional Transformation (LFT) decomposition of the system can be tackled appropriately using mixed μ synthesis techniques. Suitable approaches for explicit treatment of such problems include (D,G)-K and μ-K algorithms, modifications of the latter being suggested in this paper. To demonstrate potential improvements achievable when using real parametric uncertainties for active vibration control of flexible high-speed rotors via mixed μ synthesis, the methodology is applied with respect to a particular test rig exposed to severe gyroscopic effects. At the hand of this system, efficient performance measures are suggested, leading to promising results both in simulations and validating experiments.