Multistage Output-lifting Eigenstructure Assignment: A Multirate Ball and Plate Example

By exploiting both the left and the right allowable subspaces in consecutive stages, this paper extends a recently-developed output-lifting eigenstructure assignment approach into a multistage eigenstructure assignment scheme. In this scheme, design degrees of freedom, enlarged via output-lifting, are further exploited to improve eigenvector assignment. To mitigate the inherent conflicts between the theoretical development of eigenstructure assignment and inherent physical system characteristics, the paper also clearly demonstrates how to derive an ideal eigenstructure, particularly the desired eigenvectors, to distribute and decouple the natural modes among appropriate states or outputs, based upon an example: a novel multirate Ball and Plate system. The design and simulation results show the efficacy of the scheme.