Abstract
AbstractThis paper considers a pole assignment problem to cluster all poles of a closed‐loop system into some specified regions by introducing the complex state for systems having an isotropic property and by using the Riccati equation. The algebraic relations for the distribution of the eigenvalues of a complex matrix are used in order to cluster the poles into specified regions, which guarantees the relative stability margin, e.g. uniform damping or uniform damping ratio. The proposed scheme is essentially a combination of the pole assignment approach and linear quadratic design, taking the advantages of both. A block modal control method—an extension of recursive pole assignment—is also developed for the vibration control of rotating systems by clustering the forward and backward modes in order. Vibration control simulations with an isotropic rotor—bearing system, a magnetic bearing system and a rotating circular disc are treated in order to demonstrate the advantages of the proposed method.
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