Abstract We study a Crank–Nicolson type time discretisation (known as Tustin's method in engineering literature) for a conservative, infinite-dimensional linear dynamical system whose transfer function is scalar ...
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Abstract We study a Crank–Nicolson type time discretisation (known as Tustin's method in engineering literature) for a conservative, infinite-dimensional linear dynamical system whose transfer function is scalar and inner. We show that this discretisation approximates the state trajectory at any given time. We first prove the result for canonical Hankel range realisations, and the general case is then obtained using the state space isomorphism.
Abstract A semilinear one-dimensional convection-diffusion equation with distributed control, coupled to the Dirichlet or to the mixed boundary conditions, is considered. A sampled-data controller design is developed,...
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Abstract A semilinear one-dimensional convection-diffusion equation with distributed control, coupled to the Dirichlet or to the mixed boundary conditions, is considered. A sampled-data controller design is developed, where the sampled-data (in time) measurements of the state are taken in a finite number of fixed sampling points in the spatial domain. Sufficient conditions for the exponential convergence of the state dynamics are derived in terms of Linear Matrix Inequalities (LMIs) depending on the bounds of the sampling intervals. The new method is based on the direct Lyapunov approach via Wirtinger's and Halanay's inequalities.
Abstract In this paper we develop a model describing the ballistic transport of chemical precursor species for an atomic layer deposition process (ALD). Because of the large Knudsen number corresponding to ALD over na...
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Abstract In this paper we develop a model describing the ballistic transport of chemical precursor species for an atomic layer deposition process (ALD). Because of the large Knudsen number corresponding to ALD over nanoporous materials, the gas-phase transport inside the nanostructures takes place in a purely ballistic manner. Precursor transmission probability functions describing the fluxes between the pore surface features are developed and then are coupled to ALD surface reaction models, spatially discretized, and integrated over each precursor exposure period to determine the pore spatial surface reaction extent profile. Predictions from our dynamic model then are compared to a previously published study of ALD in nanopores to validate our simulator. The utility of physically based models of the type we develop can be exploited to determine optimal precursor exposure levels for ALD based nanomanufacturing operations.
Abstract In this work, the boundary control of a distributedparameter system (DPS) modeled by parabolic partial differential equations with spatially varying coefficients is studied. An infinite dimensional state spa...
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Abstract In this work, the boundary control of a distributedparameter system (DPS) modeled by parabolic partial differential equations with spatially varying coefficients is studied. An infinite dimensional state space setting is formulated and an exact transformation of the boundary actuation is realized to obtain an evolutionary model. The evolutionary model is used for subsequent linear quadratic regulator synthesis which incorporates the spatially varying coefficients of the underlying set of the PDEs. The formulated LQR controller is applied to the nonlinear model of the system and its performance is studied.
Abstract We consider dynamical systems defined on graph structures. The dynamics on the edges are governed by partial differential equations that are interconnected at the graph vertices through algebraic conditions i...
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Abstract We consider dynamical systems defined on graph structures. The dynamics on the edges are governed by partial differential equations that are interconnected at the graph vertices through algebraic conditions involving the boundary conditions of the PDEs. We show that a variety of such wave propagation problems on networks are solvable (forward in time) and energy passive or conservative — given that the governing PDEs are solvable on the separate edges. We treat these problems in the operator theoretic boundary control system framework.
Nowadays, distributedsystems are increasingly present, for public software applications as well as critical systems. software applications as well as critical systems. This title and distributedsystems: Design and A...
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ISBN:
(数字)9781118602638
ISBN:
(纸本)9781848213142
Nowadays, distributedsystems are increasingly present, for public software applications as well as critical systems. software applications as well as critical systems. This title and distributedsystems: Design and Algorithms – from the same editors – introduce the underlying concepts, the associated design techniques and the related security *** objective of this book is to describe the state of the art of the formal methods for the analysis of distributedsystems. Numerous issues remain open and are the topics of major research projects. One current research trend consists of profoundly mixing the design, modeling, verification and implementation stages. This prototyping-based approach is centered around the concept of model *** book is more specifically intended for readers that wish to gain an overview of the application of formal methods in the design of distributedsystems. Master’s and PhD students, as well as engineers in industry, will find a global understanding of the techniques as well as references to the most up-to-date works in this area.
In this work, we present some concepts recently introduced in the analysis and control of distributed parameter systems: Spreadability, vulnerability, regional viability and protector control. These concepts permit to...
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In this work, we present some concepts recently introduced in the analysis and control of distributed parameter systems: Spreadability, vulnerability, regional viability and protector control. These concepts permit to describe many biogeographical phenomena, as those of pollution, desertification or epidemics, which are characterized by a spatio-temporal evolution. We give some connection between such concepts. To illustrate these concepts an example is presented.
Active control of a flexible beam is investigated using time-delayed piezoelectric actuator. A minimization problem is formulated that consists of finding the control voltage applied to a piezoelectric patch actuator ...
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ISBN:
(纸本)9781457700033
Active control of a flexible beam is investigated using time-delayed piezoelectric actuator. A minimization problem is formulated that consists of finding the control voltage applied to a piezoelectric patch actuator which suppresses the dynamic responses of the beam at a specified terminal time with least control effort. The solution method is based on a combination of modal expansion and direct approximation approaches. The modal expansion approach is used to convert the optimal control problem of distributedparameter system (DPS) into the optimal control problem of a linear time-invariant lumped parameter system (LPS). A direct state-control parametrization approach is proposed where wavelets are employed to solve time delayed LPS. The operational matrices of integration and delay are utilized to reduce the solution of linear time-varying delayed systems to the solution of algebraic equations. An illustrative example is included to demonstrate the applicability and the efficiency of the proposed method and the results are quite satisfactory.
This paper addresses the design of a distributed, second-order sliding-mode based, tracking controller for a class of uncertain diffusion-reaction processes. Spatially varying uncertain parameters and mixed boundary c...
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ISBN:
(纸本)9781612848006
This paper addresses the design of a distributed, second-order sliding-mode based, tracking controller for a class of uncertain diffusion-reaction processes. Spatially varying uncertain parameters and mixed boundary conditions, along with the presence of an uncertain distributed disturbance, characterize the considered class of processes. The paper presents a constructive Lyapunov-based stability analysis which leads to simple tuning conditions for the controller parameters, The good performance of the proposed control systems are verified by means of computer simulations.
This paper proposes a recursive least mean squared error fixed-interval smoothing algorithm in distributed parameter systems. It is assumed that the state-space model of the signal to be estimated is unknown, and the ...
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This paper proposes a recursive least mean squared error fixed-interval smoothing algorithm in distributed parameter systems. It is assumed that the state-space model of the signal to be estimated is unknown, and the algorithm only requires the second-order moments of the signal and the white noise perturbing its observations. Practical application of the proposed algorithm is illustrated with a restoration image problem. (c) 2005 Elsevier Inc. All rights reserved.
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