Pole assignment in rotating disk vibration control using complex modal state feedback

Abstract

Modal state feedback controls of rotating disk vibrations in real and complex fields are formulated and compared. Pole assignment in real modal space necessitates the simultaneous assignment of eigenvalues and eigenvectors to uniquely determine the feedback gain matrix. Pole assignment in complex modal space, however, uniquely determines the feedback gain matrix, because preservation of the isotropic nature in the uncontrolled and controlled modal systems only allows the assignment of the isotropic eigenstructure. The proposed complex modal control scheme reduces the order of the system to be dealt with. It also minimises the required control energy and the transient magnitudes of the state.