Thermodynamic approach to the structural stability of process plants

Hangos, Katalin M.; Alonso, Antonio A.; Perkins, John D.; Ydstie, B. Erik

doi:10.1002/aic.690450414

Cited by 89 publications

(58 citation statements)

References 12 publications

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“…A similar line of arguments was employed by Farschman et al (1998) to derive mass and energy inventory control concepts. Hangos et al (1999) applied them to define structural stability conditions for separation process networks. Thermodynamics was also central in the work by Bao et al (2002) to design passivity-based decentralized control of failure-tolerant systems.…”

Section: Introductionmentioning

confidence: 99%

A systematic approach to plant-wide control based on thermodynamics

Antelo

Otero-Muras

Banga

et al. 2007

Computers & Chemical Engineering

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In this work, a systematic approach to plant-wide control design is proposed. The method combines ingredients from process networks, thermodynamics and systems theory to derive robust decentralized controllers that will ensure complete plant stability. As a first step, the considered process system is decomposed into abstract mass and energy inventory networks. In this framework, conceptual inventory control loops are then designed for the mass and energy layers to guarantee that the states of the plant, both in terms of extensive and intensive properties, will converge to a compact convex region defined by constant inventories. This result by itself does not ensure the convergence of intensive variables to a desired operation point as complex dynamic phenomena such as multiplicities may appear in the invariant set. In order to avoid these phenomena, thermodynamics naturally provides the designer, in these convex regions, with a legitimate storage or Lyapunov function candidate, the entropy, that can be employed to ensure global stability. Based on this, the control structure design procedure is completed with the realization of the conceptual inventory and intensive variable control loops over the available degrees of freedom in the system. To that purpose, both PI and feedback linearization control are employed. The different aspects of the proposed methodology will be illustrated on a non-isothermal chemical reaction network.

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Section: Introductionmentioning

confidence: 99%

A systematic approach to plant-wide control based on thermodynamics

Antelo

Otero-Muras

Banga

et al. 2007

Computers & Chemical Engineering

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“…An entropy-based Lyapunov function candidate serves as a tool for proving structural stability for closed reaction kinetic system obeying the MAL. The equivalence of the special form of this Lyapunov function used in reaction kinetics [20] was shown to be equivalent to the thermodynamically motivated Lyapunov function used in process systems engineering [7,8].…”

Section: Discussionmentioning

confidence: 99%

“…The basic idea behind the above function is to use the second law of thermodynamics [8] to derive a Lyapunov function of the form…”

Section: Stabilitymentioning

confidence: 99%

“…The above approach of general systems and control theory can be usefully complemented with a thermodynamic approach taking into account that reaction kinetic systems are special types of process systems [6], where most often stability is well-established in the thermodynamic approach to analyse their dynamical properties (see e.g., [7,8,9]). The thermodynamic approach recognizes, that the reaction kinetic equations originate from dynamic conservation balances constructed for component masses, and utilizes the second law of thermodynamics [10] to associate an entropy-based Lyapunov function candidate to investigate the stability of the system.…”

Section: Introductionmentioning

confidence: 99%

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Engineering Model Reduction and Entropy-based Lyapunov Functions in Chemical Reaction Kinetics

Hangos

2010

Entropy

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In this paper, the structural properties of chemical reaction systems obeying the mass action law are investigated and related to the physical and chemical properties of the system. An entropy-based Lyapunov function candidate serves as a tool for proving structural stability, the existence of which is guaranteed by the second law of thermodynamics. The commonly used engineering model reduction methods, the so-called quasi equilibrium and quasi steady state assumption based reductions, together with the variable lumping are formally defined as model transformations acting on the reaction graph. These model reduction transformations are analysed to find conditions when (a) the reduced model remains in the same reaction kinetic system class, (b) the reduced model retains the most important properties of the original one including structural stability. It is shown that both variable lumping and quasi equilibrium based reduction preserve both the reaction kinetic form and the structural stability of reaction kinetic models of closed systems with mass action law kinetics, but this is not always the case for the reduction based on quasi steady state assumption.

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“…This theory could be applied to various types of networked systems previously examined with other methods, such as plant-wide (integrated) process networks (Luyben et al, 1999), (Hangos et al, 1999), (Gilles, 1998), (Kumar & Daoutidis, 2002), chemical reaction networks (Fishtik et al, 2004), or biological networks (Majewski & Domach, 1989), (Hatzimanikatis et al, 1996).…”

Section: Introductionmentioning

confidence: 99%

Complex Process Networks: Passivity and Optimality

Jillson

Ydstie

2005

IFAC Proceedings Volumes

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We introduce a novel modelling framework for studying dynamics, distributed control, and optimization of complex networks made up of chemical processes. We are interested in developing self-organizing structures so that stability and optimality follows as a consequence of how the networks are put together and how they are connected with boundary conditions or other networks. By considering only the topology of the system and basic conservation principles, a result analogous to Tellegen's Theorem of electrical circuit theory is produced. Using this result and passivity theory, a network is shown to converge to a stationary point when the flow relationships are positive. Also, under similar conditions, it is shown that the network is self-optimizing in that the entropy production is minimized.

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Thermodynamic approach to the structural stability of process plants

Cited by 89 publications

References 12 publications

A systematic approach to plant-wide control based on thermodynamics

A systematic approach to plant-wide control based on thermodynamics

Engineering Model Reduction and Entropy-based Lyapunov Functions in Chemical Reaction Kinetics

Complex Process Networks: Passivity and Optimality

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