On the loop transfer recovery

Abstract

One method of model-based compensator design for linear multivariate systems consists of state-feedback design and observer design (Athans 1971). A key step in recent work in multivariate synthesis involves selecting an observer gain so the final loop-transfer function is the same as the state-feedback loop transfer function (Doyle and Stein 1979, Goodman 1984). This is called loop transfer recovery (LTR). This paper shows how identification of the eigenstructure of the compensators that achieve LTR makes possible a design procedure for observer gain (Luenberger 1971). This procedure is based on the eigenstructure assignment of the observers. The sufficient condition for LTR and the stability of the closed-loop system is that the plant be minimum-phase. The limitation of this method might arise when the plant has multiple transmission zeros.