In this paper we are interested in the thermodynamic analysis of a counterflow heat exchanger, when the dynamics are described by two hyperbolic partial differential equations (PDEs). First from the first and second l...
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ISBN:
(纸本)9781713872344
In this paper we are interested in the thermodynamic analysis of a counterflow heat exchanger, when the dynamics are described by two hyperbolic partial differential equations (PDEs). First from the first and second law of thermodynamics we derive the different models of the heat exchanger. Next we perform an analysis of the equilibrium profiles from a certain condition on the system parameters that guarantees the existence and uniqueness of the solution of the PDEs model. In this analysis we show the importance of the thermal pinch as an energy efficiency factor. Finally we study the passivity and the asymptotic stability of the considered heat exchanger essentially basing ourselves on the entropy as a storage function, entropy production as a dissipation function, and the thermodynamic availability function as a Lyapunov function. Copyright (c) 2023 The Authors.
Synchronization in networks of dynamical systems is of importance in biological, chemical, physical and social systems. This paper investigates an observer-based synchronization scheme for a class of networked distrib...
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Synchronization in networks of dynamical systems is of importance in biological, chemical, physical and social systems. This paper investigates an observer-based synchronization scheme for a class of networked distributed parameter systems under an abstract framework. As in reality the system states may not be available and different subsystems (agents) share information through a communication network, we estimate the states based on a distributed observer in the case of partial network connectivity. Then a synchronizing controller combining a state feedback is constructed and the well-posedness of the closed-loop system is examined. Numerical simulations are provided to illustrate the effectiveness of the proposed results.
The primary concern of the present paper is to give an overview of the available results and methods in the field of second-order sliding mode based boundary control synthesis for uncertain and perturbed distributed p...
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The primary concern of the present paper is to give an overview of the available results and methods in the field of second-order sliding mode based boundary control synthesis for uncertain and perturbed distributed parameter systems. We particularly aim at showing how the same basic algorithm (the combined Twisting/PD algorithm) can be applied to solve different problems involving parabolic and hyperbolic-type equations. Then, we deal with a reaction-diffusion process by also providing some novelty in that a destabilizing mixed-type boundary condition, which was not considered in the previous work [14], is taken into account. The effectiveness of the developed controller is supported by simulation results.
Exponential stability for the singular distributed parameter systems is discussed in the light of functional analysis and the theory of GE-semigroup in Hilbert space. Some necessary and sufficient conditions concernin...
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Exponential stability for the singular distributed parameter systems is discussed in the light of functional analysis and the theory of GE-semigroup in Hilbert space. Some necessary and sufficient conditions concerning the exponential stability of the singular distributed parameter systems are given. The results that we obtained are theoretically important for studying the stability of the singular distributed parameter systems.
This paper deals with a novel model-based fault diagnostics and prognostics scheme for distributed parameter systems (DPSs) expressed by a series of partial differential equations (PDEs). Assume that system states are...
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ISBN:
(纸本)9781467360890
This paper deals with a novel model-based fault diagnostics and prognostics scheme for distributed parameter systems (DPSs) expressed by a series of partial differential equations (PDEs). Assume that system states are available, an observer is developed based on the PDE model of the system and to compare the detection residual, which is characterized as the different value between the output of the physical system and the observer, with a predefined threshold a fault can be detected. Then, the fault dynamics is approximated and its parameters are learned by a proposed update law using system state information. The parameter magnitudes together with the tuning update law are used to estimate the time to failure (TTF). Two output filters and one input filter are proposed to relax the demand of system state measurable. Finally, the act of the state and filter based diagnosis and prognosis scheme is demonstrated by using a heated rod with an actuator fault.
Many systems, arising in electrical and electronic engineering may be represented as an interconnection of LTI system and a periodic nonlinear block, as exemplified by phase-locked loops (PLL) and more general systems...
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Many systems, arising in electrical and electronic engineering may be represented as an interconnection of LTI system and a periodic nonlinear block, as exemplified by phase-locked loops (PLL) and more general systems, based on controlled phase synchronization of several periodic processes (“phase synchronization” systems, or PSS). Typically such systems are featured by the gradient-like behavior, i.e. the system has infinite sequence of equilibria points, and any solution converges to one of them (which may be interpreted as the phase locking). This property however says nothing about the transient behavior of the system, whose important qualitative index is the maximal phase error. Before the phase is locked, the error may increase up to several periods, which phenomenon is known as cycle slipping and was introduced by J. Stoker for the model of mathematical pendulum. Since the cycle slipping is considered to be undesired behavior of PLLs, it is important to find efficient estimates for the number of slipped cycles. In the present paper, we address the problem of cycle-slipping for phase synchronization systems with infinite-dimensional linear part. New effective estimates for a number of slipped cycles are obtained by means of Popov's method of “a priori integral indices”, which was originally developed for proving absolute stability of nonlinear systems.
In this paper, the disturbance decoupling observer design problem for a class of distributed parameter systems with unknown disturbance in the state and in the measurement equations is considered. The disturbance dist...
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In this paper, the disturbance decoupling observer design problem for a class of distributed parameter systems with unknown disturbance in the state and in the measurement equations is considered. The disturbance distribution is an unknown signal, but the operator describing the disturbance is known. All operators for systems and observers are bounded operators. A novel disturbance decoupling observers design scheme is proposed via the algebraic transformation. The solvability of the problem hinges on the solution to a corresponding operator equation. The existence conditions for the disturbance decoupling observers are presented. Finally, a numerical example of a 1-D parabolic system is used to illustrate the results of the disturbance decoupling observers..
The optimization and adaptation of the synchronization gains for a class of networked systems is presented in which the state of each of the networked nodes is governed by a distributedparameter system. The design ob...
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ISBN:
(纸本)9781479932757
The optimization and adaptation of the synchronization gains for a class of networked systems is presented in which the state of each of the networked nodes is governed by a distributedparameter system. The design objectives aim at ensuring that all pairwise state differences of the networked systems converge to zero in an appropriate norm and that the states of these systems satisfy the control objective. The proposed static output feedback controllers thus contain a term that addresses the control objective and a consensus term that ensures synchronization. The synchronization gains of the resulting aggregate systems can be viewed as the strengths of the interconnections among the network nodes. Two different optimization schemes for the non-zero entries of the associated graph Laplacian are proposed. An alternate design proposes the on-line adjustment of the entries of the graph Laplacian matrix via an adaptation involving available output signals of the networked systems. The proposed results are demonstrated by a numerical example for a 1D partial differential equation.
This paper study the sampled-data control problem of a class of distributed parameter systems. A novel sampled-data control scheme is presented using mobile actuator-sensor networks. By utilizing a Lyapunov functional...
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This paper study the sampled-data control problem of a class of distributed parameter systems. A novel sampled-data control scheme is presented using mobile actuator-sensor networks. By utilizing a Lyapunov functional which depend on spatial parameter, a controller combine to decentralized static output feedback control scheme and the point measurement of the mobile sensor is designed to derive several sufficient criteria ensuring the distributed parameter systems to be globally asymptotically stable. The criteria are given in the form of linear operator inequalities and the velocity law of each mobile actuator/sensor. It is also shown that static sampled-data control of distributed parameter systems is just a special case of our main results. A numerical simulations illustrate the effectiveness of the proposed control scheme in enhancing system performance.
We focus on model-based networked control of general linear dissipative distributed parameter systems, the infinite dimensional representation of which can be decomposed to finite-dimensional slow and infinite-dimensi...
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ISBN:
(纸本)9781479932757
We focus on model-based networked control of general linear dissipative distributed parameter systems, the infinite dimensional representation of which can be decomposed to finite-dimensional slow and infinite-dimensional fast and stable subsystems. The controller synthesis of such systems is addressed using adaptive proper orthogonal decomposition (APOD). Specifically, APOD is used to recursively construct locally accurate low dimensional reduced order models (ROMs). The ROM is included in the control structure to reduce the frequency of spatially distributed sensor measurements over the network by suspending communication. The main objective of the current work is to identify a criterion for minimizing communication bandwidth (snapshots transfer rate) from the distributed sensors to the control structure considering closed-loop stability. The proposed approach is successfully used to regulate the thermal dynamics in a tubular chemical reactor.
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