Decoupling Control Using a Limiting Property of Linear Optimum Regulators and Application to Controlthe Shinansha

Decoupling control with a limiting form of linear optimal regulator for a non-minimum phase system

“…(18) holds for the scalar system A, B, P from Lemma 3.4 [10] (see also the proof of Theorem 4.1), and consequently is the decoupled system, where Ĝ is A, B, P is minimum phase from Lemma 5.1, and satisfies Lemma 3. Q.E.D.…”

“…It is assumed the CB = 0 and rank CAB = rank C, but the discussion is extended to a general invertible system. The relationships between the limiting form of the LQR and the asymptotic decoupled system for minimum phase systems are well known [10]. Our purpose in this paper is to discuss the following two problems.…”

“…10. For the system A, B, C, however, we should discuss in more detail condition A3 on the fixed poles for the decoupled system that was used to prove Theorem 4.1.…”

“…[Lemma 3.4] [10] Suppose that the minimum phase system A, B, C has a block diagonal interactor matrix as follows:…”

“…Our research group has shown that a closed-loop system with limiting feedback consisting of feedback and feedforward gain can be decoupled by letting only the weighting matrix of the outputs tend to infinity, by virtue of the output zeroing property [7] and the disturbance decoupling property [8] of the limiting property of the LQR [9,10]. The indirect relationship between the asymptotic property of the LQR and decoupling control has also been discussed from the ILQ design point of view [11,12].…”