Modeling and Analysis of Linear Hyperbolic Systems of Balance Laws

Bartecki, Krzysztof

doi:10.1007/978-3-319-27501-7

Cited by 7 publications

(14 citation statements)

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“…Let us consider a linear 2 × 2 system issued from first principles balances described by the following hyperbolic coupled PDEs (Bartecki, 2016)…”

Section: Problem Formulationmentioning

confidence: 99%

“…An important class of DPSs encountered in a wide variety of practical applications is described by coupled linear hyperbolic PDEs issued from first principles (Bartecki, 2016). In this case, two kinds of DPSs can be distinguished: strongly and weakly coupled (Bartecki, 2016). When both temporal and spatial derivatives of different state variables are involved in each equation of the model, the system is said to be strongly coupled.…”

Section: Introductionmentioning

confidence: 99%

“…In the other case, when each equation of the model contains only the temporal and spatial derivatives of the same state variable, the system is weakly coupled. Note that, under certain assumptions, a strongly coupled system can be transformed into a weakly one by means of a decoupling procedure (Bartecki, 2016).…”

Section: Introductionmentioning

confidence: 99%

“…Heat exchangers, electrical transmission lines, irrigation channels and transportation pipelines are some examples of DPSs whose dynamic behavior is described by coupled hyperbolic PDEs (Xu and Dubljevic, 2016;Bartecki, 2016). For these DPSs, for certain practical considerations, some parameters of the model are taken as control variables.…”

Section: Introductionmentioning

confidence: 99%

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Feedback control of bilinear distributed parameter system by input-output linearisation

Habrache

Maidi

Corriou

2019

IJMIC

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In this paper, a control law that enforces the tracking of a boundary controlled output for a bilinear distributed parameter system is developed in the framework of geometric control. The dynamic behavior of the system is described by two weakly coupled linear hyperbolic partial differential equations. The stability of the resulting closed-loop system is investigated based on eigenvalues of the spatial operator of a weakly coupled system of balance equations. It is shown that, under some reasonable assumptions, the stability condition is related to the choice of the tuning parameter of the control law. The performance of the developed control law is demonstrated, through numerical simulation, in the case of a co-current heat exchanger. The control objective is to control the outlet cold fluid temperature by manipulating its velocity. Both tracking and disturbance rejection problems are considered.

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“…Let us consider a linear 2 × 2 system issued from first principles balances described by the following hyperbolic coupled PDEs (Bartecki, 2016)…”

Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Feedback control of bilinear distributed parameter system by input-output linearisation

Habrache

Maidi

Corriou

2019

IJMIC

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“…The Euler's equations represent a purely hyperbolic system of equations ( [25]- [26]), and so the number of boundary conditions to be imposed on the domain is determined by the theory of characteristics depending on the incoming/outgoing waves. The details of the boundary conditions that yield a well-posed problem are discussed in [25].…”

Section: Boundary Conditionsmentioning

confidence: 99%

Numerical Simulation of the Vortex Shedding Behind an Airfoil-Spoiler Configuration

Guaily¹,

Abdelrahman²

2018

AJAE

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Spoilers are widely used on aircrafts as lateral control devices. Despite their wide usage, very little numerical and theoretical information exist. Numerical simulation of the full unsteady, compressible Euler's equations over the NACA 23012 airfoil with spoiler is performed using a hybrid Least-Squares finite element/finite difference method coupled to the Newton-Raphson's linearization technique. The flow patterns behind the spoiler are presented. The pressure coefficient over the upper and lower surfaces are successfully compared to previously published experimental work. The vortex shedding due to the existence of the spoiler is strong specially at high deflection angles. Convection of the vortices will affect the performance of the tail and so a future study of the wing-tail interaction is needed.

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Late‐lumping fuzzy boundary geometric control of nonlinear partial differential systems

Raab

Habbi

Maidi

2020

Intl J Robust & Nonlinear

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In this article, a fuzzy boundary geometric controller that stabilizes a class of nonlinear distributed parameter systems (DPSs) is proposed. The design procedure relies on the use of Takagi-Sugeno (T-S) type fuzzy partial differential equation (PDE) model, which approximates the dynamical behavior of the nonlinear DPS. The T-S fuzzy PDE model is constructed through "fuzzy blending" of local linear PDE models of infinite characteristic indexes. This is a challenging task in the design procedure of fuzzy PDE model-based boundary controller in the framework of the well-established geometric control theory. To overcome this constraint, it is proposed in this article to resort to the concept of extended operator in order to transform the T-S fuzzy PDE model with boundary control to an equivalent fuzzy PDE model with punctual control and finite characteristic index. Based on the developed fuzzy model, a fuzzy boundary geometric controller is derived and sufficient conditions of exponential stability of the resulting closed-loop system are established by employing the Lyapunov direct method. The stabilizing performance of the proposed fuzzy PDE model-based boundary geometric controller is evaluated on benchmark control problems and compared with other existing control methods via numerical simulations.

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Modeling and Analysis of Linear Hyperbolic Systems of Balance Laws

Cited by 7 publications

References 0 publications

Feedback control of bilinear distributed parameter system by input-output linearisation

Feedback control of bilinear distributed parameter system by input-output linearisation

Numerical Simulation of the Vortex Shedding Behind an Airfoil-Spoiler Configuration

Late‐lumping fuzzy boundary geometric control of nonlinear partial differential systems

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