Preview control for a class of linear discrete-time periodic systems

Li, Li; Lu, Yanrong; Gu, Lisi

doi:10.1080/00207179.2019.1618497

Cited by 8 publications

(12 citation statements)

References 36 publications

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“…In terms of the periodic system, persistent efforts have been made to solve preview control problems. 39,40 However, these studies cannot satisfactorily address the preview tracking control problem for a given periodic reference signal because an RC is not available in the preview controller. Furthermore, compared with a previous study, 39 the second difference is the size of the system.…”

Section: Design Of Output-feedback Ppr Controllermentioning

confidence: 99%

“…39,40 However, these studies cannot satisfactorily address the preview tracking control problem for a given periodic reference signal because an RC is not available in the preview controller. Furthermore, compared with a previous study, 39 the second difference is the size of the system. The augmented system in this study has n + (M R + 1) + 1 states, whereas the system in the aforementioned reference has n + (M R + N + 1) × q + q.…”

Section: Design Of Output-feedback Ppr Controllermentioning

confidence: 99%

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Preview repetitive control for linear discrete‐time periodic systems

2021

Adaptive Control & Signal

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A discrete-time preview repetitive control (PRC) scheme was proposed for linear discrete-time periodic systems that were subjected to previewable reference signals. First, the state augmentation technique was used to derive an augmented system that included future information on previewable signals. Second, a two-dimensional (2D) model was developed for the augmented system so that the control and leaning actions can be adjusted preferentially by using control gains. Sufficient conditions that guarantee the closed-loop stability of the augmented 2D systems were derived, and the design of a periodic controller with preview action and repetitive control was proposed using the linear matrix inequality approach. Finally, the effectiveness of the proposed PRC was established by using two numerical simulation examples.

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Section: Design Of Output-feedback Ppr Controllermentioning

confidence: 99%

Section: Design Of Output-feedback Ppr Controllermentioning

confidence: 99%

Preview repetitive control for linear discrete‐time periodic systems

2021

Adaptive Control & Signal

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“…Theorem 2. Consider the closed-loop system (26). For given 𝛽 and N-periodic matrices Q(k) ∈ R q×n , system (26) is asymptotically stable, if there exist N-periodic positive definite matrices X 1 (k) ∈ R 𝛼×𝛼 , X 2 (k) ∈ R n×n , N-periodic matrices Y (k) ∈ R m×𝛼 , S(k) ∈ R q×q and W(k) ∈ R n×q and 𝜀 > 0 such that the following matrix inequalities hold:…”

Section: Observer-based State Feedback Preview Controlmentioning

confidence: 99%

“…However, only a few papers have discussed the preview control problems for periodic systems. For example, a servomechanism with preview action was designed for periodic systems in Reference 26, where the preview controller synthesis was transformed into a output‐feedback controller synthesis based on augmentation modeling technique. The optimal preview control was proposed for a class of linear discrete‐time periodic system through lifting method and LQR theory in Reference 27.…”

Section: Introductionmentioning

confidence: 99%

“…The optimal preview control was proposed for a class of linear discrete‐time periodic system through lifting method and LQR theory in Reference 27. It should be mentioned that the system model considered in this article is more general, which includes linear periodic systems in Reference 26,27 as a special case when

δ A (k) = 0

and

δ B (k) = 0

. Furthermore, compared with the lifting design method in Reference 27, the proposed preview controller synthesis approaches in Theorems 2 and 4 are quite simple and straight forward, which reduce the design complexity and the computational load.…”

Section: Introductionmentioning

confidence: 99%

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Preview control for uncertain discrete‐time periodic systems

Zhang

Liao

2021

Intl J Robust & Nonlinear

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This article concerns the designing observer‐based feedback preview control and static output feedback preview control for linear uncertain discrete‐time periodic systems subject to previewable reference signal. First, a difference operator approach and a state augmentation technique are employed to derive an augmented error system. Second, considering the state unmeasured and previewable reference signal, a state observer and a preview controller are designed to achieve signal tracking performance. Then, by the Lyapunov stability theory, some sufficient conditions are obtained for the closed‐loop systems in linear matrix inequality form. Finally, two numerical simulation examples are presented to illustrate the effectiveness of the proposed method.

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Preview controller synthesis for a class of linear parameter periodic systems

Li,

Liao,

Zhang

2024

Adaptive Control & Signal

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SummaryIn this study, the problem of preview tracking control (PTC) was considered with regard to the linear parameter periodic systems (LPPSs) subject to previewed signals. First, the difference operator approach was extended to derive an augmented error system (AES). As a result, the PTC problem was transformed into a stabilization problem via state/output feedback. Second, sufficient conditions guaranteeing the closed‐loop stability of the augmented error systems were derived, and the design of a periodic controller with preview actions was proposed through the approach of linear matrix inequalities (LMIs). Finally, a numerical simulation was performed to illustrate the effectiveness of the proposed periodic controller.

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Preview control for a class of linear discrete-time periodic systems

Cited by 8 publications

References 36 publications

Preview repetitive control for linear discrete‐time periodic systems

Preview repetitive control for linear discrete‐time periodic systems

Preview control for uncertain discrete‐time periodic systems

Preview controller synthesis for a class of linear parameter periodic systems

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