多項式入力に対する定常値を補償した代表根低次元モデル

概要

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Methods for approximating a complex system of high order to a model of low order are refered to as reduced-order modelings. One of the ways of obtaining such an approximate model is to disregard the eigenvalues of the original system which are farthest from the origin and retain only dominant eigenvalues. The Davison model and the Marshall model are renowned reduced-order models by dominant eigenvalue technique. A defect of these methods is that a steady-state value of these models does not coincide with that of the original system for polynomial inputs.In this paper, we consider a dominant eigenvalue reduced-order model which eliminates this defect. First, we derive the reduced-order model which compensates for a steady-state value for polynomial inputs. This model is the same as the Davison model or the Marshall model for special inputs. Next, we prove that the steady-state value of the model coincides with that of the original system for polynomial inputs. Finally, we show that the model, which involves differential terms of the inputs, can be applied to a control problem by using the polynomial input suboptimal control method.
公益社団法人計測自動制御学会の論文