Adaptive boundary observer design for linear hyperbolic systems; Application to estimation in heat exchangers

Ghousein, Mohammad; Witrant, Emmanuel; Bhanot, Viren; Petagna, P.

doi:10.1016/j.automatica.2020.108824

Cited by 23 publications

(23 citation statements)

References 24 publications

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“…which immediately implies (17). The finite-dimensional system (A M , B M ) is controllable and we can apply a pole placement theorem to find a matrix gain K such that A M +B M K is Hurwitz.…”

Section: Stabilization Of the Finite-dimensional Partmentioning

confidence: 90%

“…As a consequence, to use the proposed method, one needs to measure the state R on all the domain, which is sometimes impossible in industrial applications (see [10] for example). Some works [5,11,15,17,31] solve this difficulty designing a boundary observer of the state R. Here for simplicity, it is assumed that the observation of the state is complete in order to focus only on the effect of the control.…”

Section: Literature Reviewmentioning

confidence: 99%

“…which reduces the analysis to eigenspaces only (and not generalized eigenspaces). In order to prove (17), the eigenvalues of A are calculated. This is equivalent to solve:…”

Section: Stabilization Of the Finite-dimensional Partmentioning

confidence: 99%

See 2 more Smart Citations

Spectral stabilization of linear transport equations with boundary and in-domain couplings

Dus¹,

Ferrante²,

Prieur³

2022

Comptes Rendus. Mathématique

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In this work, the problem of stabilization of general systems of linear transport equations with indomain and boundary couplings is investigated. It is proved that the unstable part of the spectrum is of finite cardinal. Then, using the pole placement theorem, a linear full state feedback controller is synthesized to stabilize the unstable finite-dimensional part of the system. Finally, by a careful study of semigroups, we prove the exponential stability of the closed-loop system. As a by product, the linear control constructed before is saturated and a fine estimate of the basin of attraction is given.

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Section: Stabilization Of the Finite-dimensional Partmentioning

confidence: 90%

Section: Literature Reviewmentioning

confidence: 99%

See 1 more Smart Citation

Spectral stabilization of linear transport equations with boundary and in-domain couplings

Dus¹,

Ferrante²,

Prieur³

2022

Comptes Rendus. Mathématique

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show abstract

“…[12][13][14][15][16][17] In that framework, exact parametric estimation is not necessary for the achievement of reference tracking. It is relatively recently that boundary adaptive observers featuring exponential convergence have been developed for PDEs with (constant) uncertain parameters in the domain or boundaries, (e.g., 18,19 ) for linear and semi linear parabolic PDEs, 20,21 for nonlinear wave PDEs, 22,23 for coupled first-order linear hyperbolic PDEs. Adaptive observers for ODE-PDE cascades, with parameter uncertainties in the ODE and/or the PDE, have been developed in references 24,25.…”

Section: Introductionmentioning

confidence: 99%

Adaptive observer design for uncertain nonlinear ODE‐PDE cascades

Benabdelhadi

Giri

Krstić

et al. 2022

Adaptive Control & Signal

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We are revisiting the problem of adaptive observer design for systems that are constituted of an Ordinary Differential Equation (ODE), containing a globally Lipschitz function of the state, and a linear Partial Differential Equation (PDE) of a diffusion-reaction heat type. The ODE and PDE are connected in series and both are subject to parametric uncertainties. In addition to nonlinearity and uncertainty, the system complexity also lies in the fact that no sensor can be implemented at the junction point between the ODE and the PDE. In the absence of parameter uncertainty, nonadaptive state observers are available featuring exponential convergence. However, convergence is guaranteed only under the condition that either the Lipschitz coefficient is sufficiently small or the PDE domain length is sufficiently small. To get around this limitation, and also to account for parameter uncertainty, we develop a design that involves two concatenated adaptive observers, covering the two subintervals of the PDE domain. The proposed design employs one extra sensor, providing the measurement of the PDE state at an inner position close to the ODE-PDE junction point.Both observers are shown to be exponentially convergent, under ad-hoc persistent excitation (PE) conditions, with no limitation on the Lipschitz coefficient and domain length.

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“…The advanced versions Kalman filter can be used for uncertain distributed parameter estimation, for example Villegas et al (2019) have used EnKF for solving the history matching inverse problem of matching pressure-production data. Ghousein et al (2020) introduced an adaptive boundary observer to design an observer for a linear hyperbolic system in the heat exchanger to estimate the temperature distribution along the flows from measurements at the tubes boundaries only. Hong and Shi (2020) designed an adaptive sliding mode observer for placement pressure control system to control irregularity and asymmetry pressure fluctuation and their impacts to the density in the composite products.…”

Section: Introductionmentioning

confidence: 99%

Multi-phase flow measurement in a gas refinery using decentralized Lyapunov–based adaptive observer

Farahani

Montazeri

2020

Transactions of the Institute of Measurement and Control

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This paper presents a new Lyapunov-based nonlinear adaptive observer and joint unscented Kalman filter to precisely estimate the states and the parameters for the low-order lumped model of the multi-phase flow at the gas refinery. The main focus of the study is to estimate the discharge coefficient of the orifice meter installed on the interconnection lines of the subsystems (parameters) and the total oil and gas mass flows (states). The adaptive estimation is conducted using the real-time measurements including choke pressure, bottom line pressure, single-phase gas flow, and single-phase liquid flow in the refinery outlet. To check the stability and performance of the system against changes, the Lyapunov theory has been used. In all stages, the investigations were based on the data collected from the actual process in the South Pars Gas Complex, Iran. Using the dynamic HYSYS simulation, it is found that the proposed adaptive observer is capable of estimating the oil and gas flows and identifying the discharge coefficient of the flow meter at issue. To show the performance of the proposed adaptive observer, it is evaluated against and compared with the unscented Kalman filter. The comparison of the results obtained from the proposed observer, unscented Kalman filter, and dynamic HYSYS simulation with data collected from the actual process of the refinery shows the appropriate performance of the both estimation algorithms in detecting the changes in liquid and gas flow rates and the consistency of their results with the real process in the South Pars Gas Complex. The simulations reveal that low-order lumped model is sufficient for estimation of parameters and states of the multiphase flow entering the gas refinery.

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Adaptive boundary observer design for linear hyperbolic systems; Application to estimation in heat exchangers

Cited by 23 publications

References 24 publications

Spectral stabilization of linear transport equations with boundary and in-domain couplings

Spectral stabilization of linear transport equations with boundary and in-domain couplings

Adaptive observer design for uncertain nonlinear ODE‐PDE cascades

Multi-phase flow measurement in a gas refinery using decentralized Lyapunov–based adaptive observer

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