On Loop Transfer Recovery for Discrete-Time Non-Minimum Phase Systems

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  • 離散時間非最小位相系に対するループ伝達関数回復について
  • リサン ジカン ヒ サイショウ イソウケイ ニ タイスル ループ デンタツ カ

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Abstract

For discrete-time non-minimum phase plants, the feedback property achieved by enforcing the conventional loop transfer recovery technique is discussed in this paper. Considering digital implementation accounting the computation delay in the controller, we use a discrete-time LQG controller including a prediction type Kalman filter. For simplicity, we assume that a non-minimum phase plant has a single real unstable zero. First, we give an explicit representation of the sensitivity matrix achieved by enforcing the conventional loop transfer recovery procedure at the plant input. The directional property between the target and the achievable sensitivity matrices is clarified. In addition, we show that the sensitivity matrix obtained by enforcing the conventional procedure coincides with that obtained by the partial loop transfer recovery technique which attempts to recover the feedback property related to the minimum phase part of the plant. This fact provides a clear system-theoretic meaning to the enforcement of the loop transfer recovery technique for non-minimum phase plants.

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