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Adaptive observer design for uncertain hyperbolic PDEs coupled with uncertain LTV ODEs; Application to refrigeration systems
Automatica ( IF 6.4 ) Pub Date : 2023-06-01 , DOI: 10.1016/j.automatica.2023.111096
Mohammad Ghousein, Emmanuel Witrant

The problem of estimating the temperatures and the heat transfer coefficient of a concentric tube heat exchanger coupled with a heater is considered in this work. Measurements collected from the extremities of the exchanger tube are used to estimate the heat distribution over the length of the exchanger, which induces a boundary estimation problem. This system, which is part of any standard cooling plant, is particularly challenging due to the distributed nature of its variables. It is modeled by a system of (2 × 2) hyperbolic PDEs, coupled with an ODE at the boundary. To solve the estimation problem, we consider a general class of systems consisting of a (2 × 2) hyperbolic system coupled with a set of nX linear time-varying (LTV) ODEs at the boundary. Both the PDE and the ODEs have uncertain parameters to be estimated. The objective is to estimate the PDE states, the ODE states, and the parameters simultaneously with no assumption on the ODEs stability. We design a Luenberger state observer, and our method is mainly based on the decoupling of the PDE estimation error states from that of the ODEs via swapping design. We then derive the observer gains from the Lyapunov analysis of the decoupled system after proving the boundedness of the swapping filters. We give sufficient conditions of the exponential convergence of the adaptive observer through differential Lyapunov inequalities (DLIs). Finally, we apply the developed theory on the coupled heat exchanger–heater model to evaluate the performance of the observer in numerical simulations.



中文翻译:

不确定双曲 PDE 与不确定 LTV ODE 耦合的自适应观测器设计;应用于制冷系统

在这项工作中考虑了估计与加热器耦合的同心管换热器的温度和传热系数的问题。从换热器管的末端收集的测量值用于估计换热器长度上的热分布,这会引发边界估计问题。该系统是任何标准冷却设备的一部分,由于其变量的分布式特性,因此特别具有挑战性。它由 (2 × 2) 双曲 PDE 的系统建模,并在边界处耦合 ODE。为了解决估计问题,我们考虑一类由 (2 × 2) 双曲系统和一组nX边界处的线性时变 (LTV) ODE。PDE 和 ODE 都有待估计的不确定参数。目标是在不假设 ODE 稳定性的情况下同时估计 PDE 状态、ODE 状态和参数。我们设计了一个 Luenberger 状态观察器,我们的方法主要基于通过交换设计将 PDE 估计误差状态与 ODE 的状态解耦。然后,在证明交换滤波器的有界性之后,我们从解耦系统的 Lyapunov 分析中得出观察者增益。我们通过微分李雅普诺夫不等式 (DLI) 给出了自适应观测器指数收敛的充分条件。最后,我们将已开发的理论应用于耦合换热器-加热器模型,以评估观测器在数值模拟中的性能。

更新日期:2023-06-01
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