Summary
Motivated by an engineering application in cable mining elevators, we address a new problem on stabilization of 2×2 coupled linear first‐order hyperbolic PDEs sandwiched between 2 ODEs. A ...novel methology combining PDE backstepping and ODE backstepping is proposed to derive a state‐feedback controller without high differential terms. The well‐posedness and invertibility properties of the PDE backstepping transformation are proved. All states, including coupled linear hyperbolic PDEs and 2 ODEs, are included in the closed‐loop exponential stability analysis. Moreover, boundedness and exponential convergence of the designed controller are proved. The performance is investigated via numerical simulation.
This article deals with the backstepping design of observer-based compensators for parabolic ODE-PDE-ODE systems. The latter consist of <inline-formula><tex-math notation="LaTeX">\boldsymbol ...{n}</tex-math></inline-formula> coupled parabolic PDEs with distinct diffusion coefficients and spatially-varying coefficients, that are bidirectionally coupled to ODEs at both boundaries. The actuation and sensing appears through these ODEs resulting in a challenging control problem. For this setup a systematic backstepping approach is proposed, in order to determine a state feedback controller and an observer. In particular, the state feedback loop and the observer error dynamics are mapped into stable ODE-PDE-ODE cascades by making use of a sequence of transformations. With this, the design can be traced back to the solution of kernel equations already found in the literature as well as initial and boundary value problems, that can be solved numerically. Exponential stability of the closed-loop system is verified, wherein the decay rate can be directly specified in the design. The results of the article are illustrated by the output feedback control of an unstable ODE-PDE-ODE system with two coupled parabolic PDEs.
Due to their dynamic properties such as irregular sampling rate and high-frequency sampling, Continuous Time Series (CTS) are found in many applications. Since CTS with irregular sampling rate are ...difficult to model with standard Recurrent Neural Networks (RNNs), RNNs have been generalised to have continuous-time hidden dynamics defined by a Neural Ordinary Differential Equation (Neural ODE), leading to the ODE-RNN model. Another approach that provides a better modelling is that of the Latent ODE model, which constructs a continuous-time model where a latent state is defined at all times. The Latent ODE model uses a standard RNN as the encoder and a Neural ODE as the decoder. However, since the RNN encoder leads to difficulties with missing data and ill-defined latent variables, a Latent ODE-RNN model has recently been proposed that uses a ODE-RNN model as the encoder instead.
Both the Latent ODE and Latent ODE-RNN models are difficult to train due to the vanishing and exploding gradients problem. To overcome this problem, the main contribution of this paper is to propose and illustrate a new model based on a new Latent ODE using an ODE-LSTM (Long Short-Term Memory) network as an encoder - the Latent ODE-LSTM model. To limit the growth of the gradients, the Norm Gradient Clipping strategy was embedded on the Latent ODE-LSTM model.
The performance evaluation of the new Latent ODE-LSTM (with and without Norm Gradient Clipping) for modelling CTS with regular and irregular sampling rates is then demonstrated. Numerical experiments show that the new Latent ODE-LSTM performs better than Latent ODE-RNNs and can avoid the vanishing and exploding gradients during training.
Code implementations developed in this work are available at github.com/CeciliaCoelho/LatentODELSTM.
OpenSMOKE++ is a general framework for numerical simulations of reacting systems with detailed kinetic mechanisms, including thousands of chemical species and reactions. The framework is entirely ...written in object-oriented C++ and can be easily extended and customized by the user for specific systems, without having to modify the core functionality of the program. The OpenSMOKE++ framework can handle simulations of ideal chemical reactors (plug-flow, batch, and jet stirred reactors), shock-tubes, rapid compression machines, and can be easily incorporated into multi-dimensional CFD codes for the modeling of reacting flows. OpenSMOKE++ provides useful numerical tools such as the sensitivity and rate of production analyses, needed to recognize the main chemical paths and to interpret the numerical results from a kinetic point of view. Since simulations involving large kinetic mechanisms are very time consuming, OpenSMOKE++ adopts advanced numerical techniques able to reduce the computational cost, without sacrificing the accuracy and the robustness of the calculations.
In the present paper we give a detailed description of the framework features, the numerical models available, and the implementation of the code. The possibility of coupling the OpenSMOKE++ functionality with existing numerical codes is discussed. The computational performances of the framework are presented, and the capabilities of OpenSMOKE++ in terms of integration of stiff ODE systems are discussed and analyzed with special emphasis. Some examples demonstrating the ability of the OpenSMOKE++ framework to successfully manage large kinetic mechanisms are eventually presented.
Program title: OpenSMOKE++
Catalogue identifier: AEVY_v1_0
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEVY_v1_0.html
Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland
Licensing provisions: GNU General Public License, version 3
No. of lines in distributed program, including test data, etc.: 146353
No. of bytes in distributed program, including test data, etc.: 4890534
Distribution format: tar.gz
Programming language: C++.
Computer: Any computer that can run a C++ Compiler.
Operating system: Tested on Microsoft Windows 7, Ubuntu 14.4.
RAM: From a few Mb to several Gb depending on the size of the system being simulated.
Classification: 22.
External routines: Eigen, Boost C++ Libraries, RapidXML
Nature of problem: Evolution of reacting gas mixtures with detailed description of thermodynamic, kinetic and transport data.
Solution method: Stiff systems of Ordinary differential Equations, whose solution is obtained using methods based on the Backward Differentiation Formulas (BDF) (LU factorization of dense matrices is required).
Additional comments: The code was specifically conceived for managing homogeneous, reacting mixtures including thousands of species and reactions.
Running time: Problem-dependent, from seconds (small kinetics) to hours
As an effective method to analyze complex catalytic reaction networks, microkinetic modeling is gaining increasing popularity in the catalytic activity evaluation and rational design of heterogeneous ...catalysts. An automated simulator with stable and reliable performance is especially useful and in great request. Here we introduce the CATKINAS package developed for large‐scale microkinetic modeling and analysis. Featuring with a multilevel solver and a multifunctional analyzer, CATKINAS can provide both accurate solutions and various quantitative and automatic analysis for a wide range of catalytic systems. The structure and the basic workflow are overviewed with the multilevel solver particularly illustrated. Also, we take the CO methanation reaction as an example to illustrate the application and efficiency of the CATKINAS package.
CATKINAS is a high‐performance catalytic microkinetic analysis software aimed for large‐scale mechanism auto‐analysis and catalyst screening. The software consists of a user‐friendly input module, a multilevel solver, and a multidimensional analyzer. Parallel processing and machine learning acceleration are also implemented to ensure fast and robust solving process. CATKINAS can be used for solving, analyzing, and visualizing microkinetic simulations of various catalytic systems and greatly facilitate the rational design of heterogeneous catalysts.
This paper considers the backstepping design of observer-based compensators for general linear heterodirectional hyperbolic ODE–PDE–ODE systems, where the ODEs are coupled to the PDEs at both ...boundaries and the input appears in an ODE. A state feedback controller is designed by mapping the closed-loop system into a stable ODE–PDE–ODE cascade. This is achieved by representing the ODE at the actuated boundary in Byrnes–Isidori normal form. The resulting state feedback is implemented by an observer for a collocated measurement of the PDE state, for which a systematic backstepping approach is presented. The exponential stability of the closed-loop system is verified in the ∞-norm. It is shown that all design equations can be traced back to kernel equations known from the literature, to simple Volterra integral equations of the second kind and to explicitly solvable boundary value problems. This leads to a systematic approach for the boundary stabilization of the considered class of ODE–PDE–ODE systems by output feedback control. The results of the paper are illustrated by a numerical example.
In this article, we are devoted to the global stabilization for ordinary differential equation (ODE)-parabolic partial differential equation (PDE)-ODE-coupled systems subject to spatially varying ...coefficient, where a nonlinear ODE is located at the driving end and a linear ODE is located at the other end. By means of infinite-dimensional and finite-dimensional backstepping transformations, both state-feedback and output-feedback controllers are established to assure the global exponential stability of the resulting closed-loop system. Besides, the boundedness and exponential convergence of the controllers are also investigated. Finally, the availability of the theoretical results is illustrated by simulation data.
Copper sulfides (Cu2–xS), are a novel kind of photothermal material exhibiting significant photothermal conversion efficiency, making them very attractive in various energy conversion related ...devices. Preparing high quality uniform Cu2‐xS nanocrystals (NCs) is a top priority for further energy‐and sustainability relevant nanodevices. Here, a shape‐controlled high quality Cu7S4 NCs synthesis strategy is reported using sulfur in 1‐octadecene as precursor by varying the heating temperature, as well as its forming mechanism. The performance of the Cu7S4 NCs is further explored for light‐driven water evaporation without the need of heating the bulk liquid to the boiling point, and the results suggest that as‐synthesized highly monodisperse NCs perform higher evaporation rate than polydisperse NCs under the identical morphology. Furthermore, disk‐like NCs exhibit higher water evaporation rate than spherical NCs. The water evaporation rate can be further enhanced by assembling the organic phase Cu7S4 NCs into a dense film on the aqueous solution surface. The maximum photothermal conversion efficiency is as high as 77.1%.
Monodisperse Cu7S4 nanocrystals, as highly efficient photothermal materials, exhibit extraordinary performance in water evaporation when assembled into a film on the surface of liquid solution under light illumination.
Mathematical models play an increasing role in understanding and predicting machining processes, in particular milling. However, despite the considerable efforts that have been dedicated to this ...problem, a majority of milling models still rely on simplifying assumptions to calculate the chip thickness. In this paper, the chip thickness is determined without these simplifications, based on a surface function that describes the milled surface and on information about the workpiece boundary. By combining the partial differential equation (PDE) governing the evolution of this surface function with the ordinary differential equations (ODE) governing the tool/machine dynamics, a mixed PDE-ODE formulation is proposed to describe the dynamics of the milling process. The coupled system of differential equations is solved using an algorithm that combines finite difference (ODE) and finite volume (PDE) methods. A case study is presented to compare the proposed approach with the classical delay differential equations (DDE) model formulation for milling processes based on a simplified chip thickness model. The PDE-ODE formulation represents an explicit mathematical model for milling process dynamics; it yields a theoretically exact chip thickness and offers a means to assess the validity of models based on DDE formulation. Moreover, the proposed formulation is capable of simulating transient tool behaviors when the tool is milling the outer region of the workpiece, which is in general neglected by the DDE-based models.
•Accurate mathematical description of the milling process.•Evolution of the machined surface around the tool is described.•Chip thickness model affects the accuracy of milling simulation in certain scenarios.•Transient tool behaviors are captured while milling the outer part of the workpiece.
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