We design a leak detection, size estimation and localization algorithm for a branched pipe system, requiring flow and pressure measurements to be taken at the inlet and outlet boundaries, only. By showing that the pip...
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We design a leak detection, size estimation and localization algorithm for a branched pipe system, requiring flow and pressure measurements to be taken at the inlet and outlet boundaries, only. By showing that the pipe system model can be mapped into a system of coupled, linear hyperbolic PDEs (partial differential equations), with the parametric uncertainties caused by the leak appearing in a particular way, established methods can be applied to obtain state and parameter estimates. Analyzing the structure of the parametric uncertainties that appear in the obtained adaptive observer canonical form, we prove that total leak size can be estimated regardless of how leaks are distributed in the pipe network. Moreover, any number of point leaks can be located, provided they occur sufficiently separated in time. (c) 2022 The Author(s). Published by Elsevier Ltd.& nbsp;& nbsp
Heat exchangers are generally described by two coupled partial differential equations (PDEs), and belong to the class of systems of conservation laws. In this paper we propose a result on the regulation of heat exchan...
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Heat exchangers are generally described by two coupled partial differential equations (PDEs), and belong to the class of systems of conservation laws. In this paper we propose a result on the regulation of heat exchangers, in which we are choosing a proportional-integral (PI)-controller implemented on an output feedback from a boundary condition. First, a study on the existence and uniqueness of solutions of uncontrolled system is carried out, and we give a condition on the parameters of the system that ensures that the control-observation problem is well-posedness. Secondly we successively study the stability of the system controlled by a proportional and integral action, when the gains are adjusted following respectively a classic Lyapunov approach, and using a recent result that combines Lyapunov's approach and operator perturbation theory.
We study global finite-dimensional observer-based stabilization of a semilinear 1D heat equation with globally Lipschitz semilinearity in the state variable. We consider Neumann actuation and point measurement. Using ...
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We study global finite-dimensional observer-based stabilization of a semilinear 1D heat equation with globally Lipschitz semilinearity in the state variable. We consider Neumann actuation and point measurement. Using dynamic extension and modal decomposition we derive nonlinear ODEs for the modes of the state. We propose a controller that is based on a nonlinear finite-dimensional Luenberger observer. Our Lyapunov H-1-stability analysis leads to LMIs, which are shown to be feasible for a large enough observer dimension and small enough Lipschitz constant. Next, we consider the case of a constant input delay r > 0. To compensate the delay, we introduce a chain of M sub-predictors that leads to a nonlinear closed-loop ODE system, coupled with nonlinear infinite-dimensional tail ODEs. We provide LMIs for H-1-stability and prove that for any r > 0, the LMIs are feasible provided M and the observer dimension N are large enough and the Lipschitz constant is small enough. Numerical examples demonstrate the efficiency of the proposed approach. (C) 2022 Elsevier B.V. All rights reserved.
This paper proposes a novel fault isolation (FI) scheme for distributed parameter systems modeled by a class of parabolic partial differential equations (PDEs) with nonlinear uncertain dynamics. A key feature of the p...
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This paper proposes a novel fault isolation (FI) scheme for distributed parameter systems modeled by a class of parabolic partial differential equations (PDEs) with nonlinear uncertain dynamics. A key feature of the proposed FI scheme is its capability of dealing with the effects of system uncertainties for accurate FI. Specifically, an approximate ordinary differential equation (ODE) system is first derived to capture the dominant dynamics of the original PDE system. An adaptive dynamics identification approach using radial basis function neural network is then proposed based on this ODE system, to achieve locally-accurate identification of the uncertain system dynamics under faulty modes. A bank of FI estimators with associated adaptive thresholds are finally designed for real-time FI decision making. Rigorous analysis on the fault isolatability is provided. Simulation study on a representative transport-reaction process is conducted to demonstrate the effectiveness of the proposed approach.
We recall two recently published approaches to study stability properties of nonlinear infinite dimensional impulsive systems and apply them to finite and infinite dimensional systems. Both approaches cover the case, ...
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We recall two recently published approaches to study stability properties of nonlinear infinite dimensional impulsive systems and apply them to finite and infinite dimensional systems. Both approaches cover the case, when discrete and continuous dynamics are not stable simultaneously. We illustrate these approaches by means of several examples. In particular we demonstrate that our approaches can be used in situations where the existing results cannot be applied. In particular, we will derive sufficient conditions for the ISS property of a linear and spatially non-homogeneous parabolic system with impulsive actions.
In this work, a boundary tracking control scheme is investigated for the stabilization of a floating platform connected to a traditional mooring system. The system is composed of a floating platform and several moorin...
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In this work, a boundary tracking control scheme is investigated for the stabilization of a floating platform connected to a traditional mooring system. The system is composed of a floating platform and several mooring lines which are designed for station keeping of the former on the sea surface. Since the floating platform is subject to excitation forces from waves and currents, a coupled boundary-tracking controller is proposed for the tip payload of mooring lines in two-dimensional direction to reduce the effect of boundary vertical and horizontal displacement. Firstly, a boundary controller is proposed to the boundary oscillation in horizontal direction. Secondly, in order to efficiently suppress the heave motions of the platform, an auxiliary exo-system is introduced to generate the desired time-varying reference trajectory in the vertical direction. Furthermore, a tracking error system is derived by integrating the reference trajectory. According to this error system, the boundary motion of mooring lines in vertical direction can track the reference trajectory which is to achieve the target of vibration suppression. In addition, the stability of the system is guaranteed by Lyapunov's method. Finally, numerical simulation results show that efficacy of the proposed control scheme, that is, the boundary displacement of z-axis can accurately track a bounded periodic time-varying reference trajectory and the horizontal boundary vibration can be suppressed within a small range.
The article deals with the output feedback regulation of exponentially stable systems by an integral controller. We propose appropriate Lyapunov functionals to prove exponential stability of the closed-loop system. An...
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The article deals with the output feedback regulation of exponentially stable systems by an integral controller. We propose appropriate Lyapunov functionals to prove exponential stability of the closed-loop system. An example of parabolic partial differential equation (PDE) systems and an example of hyperbolic systems are worked out to show how exponentially stabilizing integral controllers are designed. The proof is based on a novel Lyapunov functional construction that employs the forwarding techniques.
In this paper, we proposed a model-based abnormality detection scheme for a class of nonlinear parabolic distributed parameter systems (DPSs). The proposed methodology consists of the design of an observer and an abno...
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In this paper, we proposed a model-based abnormality detection scheme for a class of nonlinear parabolic distributed parameter systems (DPSs). The proposed methodology consists of the design of an observer and an abnormality detection filter (ADF) based on the backstepping technique and a limited number of in-domain measurements plus one boundary measurement. By taking the difference between the measured and estimated outputs from observer, a residual signal is generated for fault detection. For the detection purpose, the residual is evaluated in a lumped manner and we propose an explicit expression for the time-varying threshold. The convergence properties of the PDE observer and the residual are analyzed by Lyapunov stability theory. Eventually, the proposed abnormality detection scheme is demonstrated on a nonlinear DPS.
We investigate the state observer design problem for thermoacoustic instabilities in a Rijke tube using an infinite dimensional perspective. The observer, whose design is based on the backstepping methodology with Vol...
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We investigate the state observer design problem for thermoacoustic instabilities in a Rijke tube using an infinite dimensional perspective. The observer, whose design is based on the backstepping methodology with Volterra and full integral terms, consists of a copy of the linearized plant model plus output injection terms and relies only on a single boundary acoustic pressure sensor. The exponential convergence, in the L-2 sense, of the observed error dynamics is proved, and the analytic expression of the observer gains are derived explicitly. The results are tested in an experimental Rijke tube prototype in order to illustrate the effectiveness of the method.
In this work, we aim at addressing thermodynamic modeling and passivity properties of a class of distributed parameter systems (DPSs) with dispersion that are described by partial differential equations (PDEs). The cl...
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In this work, we aim at addressing thermodynamic modeling and passivity properties of a class of distributed parameter systems (DPSs) with dispersion that are described by partial differential equations (PDEs). The class of distributed parameter systems account for a general class of thermodynamic models with spatial-temporal characteristics. For this class of distributedsystems, various contributions on stability analysis, control and estimator designs have been made in the existing literature. On a different note, this contribution aims at providing a thermodynamic perspective on the modeling of the transport processes and passivity using flux expressions based on thermodynamical driving forces. A linearized model is derived and an invertible linear transformation is applied to further simplify the model by eliminating the transport terms. A case study on an adiabatic tubular reactor with dispersion is used as an example.
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