A design method for robust stabilizing simple multi-period repetitive controllers for time-delay plants

Yamada, Kou; Ando, Yoshinori; Hagiwara, Takaaki; Kobayashi, Masahiko; Sakanushi, Tatsuya

doi:10.1109/ecticon.2009.5137031

Cited by 2 publications

(1 citation statement)

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“…However, it is striking that the generalized ℋ︁ 2 method has not been applied to solve the model approximation for LRPs yet, while there is no doubt that the research on this topic is both theoretically interesting and challenging. Recently, there are some results reported on the repetitive control, see, for example, 21–23.…”

Section: Introductionmentioning

confidence: 99%

Generalized ℋ︁₂ model approximation for differential linear repetitive processes

Zheng

2011

Optim Control Appl Methods

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This paper investigates the generalized H 2 model approximation for differential linear repetitive processes (LRPs). For a given LRP, which is assumed to be stable along the pass, we are aimed at constructing a reduced-order model of the LRP such that the generalized H 2 gain of the approximation error LRP between the original LRP and the reduced-order one is less than a prescribed scalar. A sufficient condition to characterize the bound of the generalized H 2 gain of the approximation error LRP is presented in terms of linear matrix inequalities (LMIs). Two different approaches are proposed to solve the considered generalized H 2 model approximation problem. One is the convex linearization approach, which casts the model approximation into a convex optimization problem, while the other is the projection approach, which casts the model approximation into a sequential minimization problem subject to LMI constraints by employing the cone complementary linearization algorithm. A numerical example is provided to demonstrate the proposed theories. 66 L. WU, W. X. ZHENG AND X. SU method [1][2][3][4][5], the optimal Hankel-norm approximation method [6,7], and the optimal H 2 model approximation [8,9], just to mention a few. As is well known, H ∞ and L 2 -L ∞ (called also generalized H 2 ) settings have been considerably used in optimal synthesis over the past decades [10][11][12]. They have been well recognized to be most appropriate for systems with noise input, whose stochastic information is not precisely known. H ∞ setting minimizes the worst-case energy gain from the noise inputs to the system output; whereas L 2 -L ∞ setting minimizes the worst-case energy to peak gain from the noise inputs to the system output. In this paper, we are interested in the generalized H 2 model approximation method, which was studied in [13] for time-varying delay systems. One of its main advantages is the fact that this method is insensitive to the exact knowledge of the statistics of the noise signals. The generalized H 2 model approximation procedure ensures that the generalized H 2 gain from the input signal to the approximation error will be less than a prescribed level, where the noise input is an arbitrary energy-bounded signal.Linear repetitive processes (LRPs) are a distinct class of 2-D systems (that is, information propagation in two independent directions) of both system-theoretic and application interests [14]. The essential unique characteristic of a repetitive, or multipass, process is a series of sweeps, termed passes, through a set of dynamics defined over a fixed finite duration known as the pass length. On each pass, an output, termed the pass profile, is produced which acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile [14]. To introduce a formal definition, let <+∞ denote the pass length (assumed constant). Then in an LRP the pass profile y k (t), 0 t , generated on pass k acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile y k+1...

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