The Observer-Based Controller Design of the Discrete-Time Singularly Perturbed Systems

Oloomi, Hossein M.; Sawan, M.E.

doi:10.23919/acc.1986.4789257

Cited by 4 publications

(5 citation statements)

References 3 publications

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“…27 The observer problem was first brought up by Porter 28 for linear systems with fast and slow modes; and has been thereafter thoroughly studied for both linear and nonlinear systems, mostly within the singular perturbation framework. 18,27,[29][30][31][32][33][34][35][36][37][38][39][40] Particularly, for linear two-time-scale systems, Yoo and Gajic 40 have recently proposed a linear observer design method. In their approach, the observer poles can be independently placed for the two fast and slow subsystems, by decomposing a singularly perturbed system through a series of linear transformations.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear observer design for two‐time‐scale systems

Duan

Kravaris

2020

AIChE Journal

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A two-time-scale system involves both fast and slow dynamics. This article studies observer design for general nonlinear two-time-scale systems and presents two alternative nonlinear observer design approaches, one full-order and one reduced-order.The full-order observer is designed by following a scheme to systematically select design parameters, so that the fast and slow observer dynamics are assigned to estimate the corresponding system modes. The reduced-order observer is derived based on a lower dimensional model to reconstruct the slow states, along with the algebraic slow-motion invariant manifold function to reconstruct the fast states. Through an error analysis, it is shown that the reduced-order observer is capable of providing accurate estimation of the states for the detailed system with an exponentially decaying estimation error. In the last part of the article, the two proposed observers are designed for an anaerobic digestion process, as an illustrative example to evaluate their performance and convergence properties.

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Section: Introductionmentioning

confidence: 99%

Nonlinear observer design for two‐time‐scale systems

Duan

Kravaris

2020

AIChE Journal

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“…Jiang et al [17] use a reducedorder high-gain observer to obtain semiglobal stabilization for a nonlinear benchmark example. However, to the best of authors' knowledge, there is only little attention paid to the observer-based feedback control for singularly perturbed systems [18][19][20][21][22]. Reference [19] considers the robust stability of linear shift-invariant discrete-time singularly perturbed systems; a composite observer-based controller is given such that the closed-loop system is stable.…”

Section: Introductionmentioning

confidence: 99%

“…However, to the best of authors' knowledge, there is only little attention paid to the observer-based feedback control for singularly perturbed systems [18][19][20][21][22]. Reference [19] considers the robust stability of linear shift-invariant discrete-time singularly perturbed systems; a composite observer-based controller is given such that the closed-loop system is stable. In [21], an observerbased output feedback control for singularly perturbed linear systems is considered under the model-based framework.…”

Section: Introductionmentioning

confidence: 99%

Robust Observer-Based Feedback Control for Lipschitz Singularly Perturbed Systems

Wang

Liu

2015

Mathematical Problems in Engineering

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The observer-based feedback control for singularly perturbed systems (SPSs) with Lipschitz constraint is addressed. A sufficient condition, independent of the perturbation parameter, for a full-order observer is presented in terms of linear matrix inequality (LMI) such that observation error is exponentially stable for all sufficiently small perturbation parameters. Then, for observer-based feedback control, a proper controller is constructed to guarantee the input-to-state stability of the system with regard to the observation error. Considering the convergence of observation error, the stability of the system can be obtained based on the input-to-state stability property. It is shown that the proposed method is simple and easy to operate. Moreover, the upper bound of the small perturbation parameter for stability of systems can be explicitly estimated with a workable computation way. Finally, two numerical examples show the effectiveness of the proposed method.

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“…Usually, there are three kinds of controllers: (1) state feedback controllers, (2) output feedback controllers [l], [4] and (3) observerbased controllers [2], [5]. Many papers concentrate on output feedback controllers and observer-based controllers, because state variables of systems are not always available for measurement.…”

Section: Introductionmentioning

confidence: 99%

Digital control strategy on decentralized large-scale actuator systems

Yao

2002

Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301)

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The goal of this research is to develop a new control scheme for digital computer control of decentralized largescale systems. Such a control system can be taken as a decentralized singularly-perturbed systems, because of the faster responses of the subsystems. Digital control of robust reduced-order controllers and reduced-order observer-based controllers are expected to be found for stabilization and reliable control of linear large-scale systems via decentralized control. The developed control techniques will be suitable for large-scale and high-dimension systems with strong potential for practical applications, such as power distribution and communication networks.

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The Observer-Based Controller Design of the Discrete-Time Singularly Perturbed Systems

Cited by 4 publications

References 3 publications

Nonlinear observer design for two‐time‐scale systems

Nonlinear observer design for two‐time‐scale systems

Robust Observer-Based Feedback Control for Lipschitz Singularly Perturbed Systems

Digital control strategy on decentralized large-scale actuator systems

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