Optimal Control of Load Changes for Molten Carbonate Fuel Cell Systems: A Challenge in PDE Constrained Optimization

Chudej, Kurt; Pesch, Hans Josef; Sternberg, Kati

doi:10.1137/080722102

Cited by 12 publications

(14 citation statements)

References 7 publications

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“…The optimization results are validated using an experimental 10 kW MCFC system designed for stationary, residential applications. Chudej et al [108] optimize the control strategy of a MCFC in order to balance the allowed speed of load changes and the allowed temperature differences inside the cell. The objective is to ensure Table 4 Summary of fuel cell system optimization studies: problem formulation and optimization algorithm.…”

Section: High-temperature Fuel Cell System Optimizationmentioning

confidence: 99%

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Computational design and optimization of fuel cells and fuel cell systems: A review

Secanell

Wishart²,

Dobson

2011

Journal of Power Sources

117

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Section: High-temperature Fuel Cell System Optimizationmentioning

confidence: 99%

“…Yong et al [107] Fuel consumption Multi-crossover genetic algorithm Chudej et al [108] Temperature time gradients Sparse SQP (SNOPT)…”

Section: Mcfcmentioning

confidence: 99%

Computational design and optimization of fuel cells and fuel cell systems: A review

Secanell

Wishart²,

Dobson

2011

Journal of Power Sources

117

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“…Most practical processes are described by ordinary differential equations (ODEs) coupled with partial differential equations (PDEs), such as the aerodynamic heating process of hypersonic vehicles [1] and molten carbonate fuel cell systems [2]. Recently, much attention has been paid to the coupled ODE-parabolic PDE systems, and the corresponding control theory has been developed by works of Krstic [3,4], Tang and Xie [5,6], et al The references [3][4][5][6] studied the control problems of linear ODE-parabolic PDE systems with infinite-dimensional backstepping technique.…”

Section: Introductionmentioning

confidence: 99%

“…For a symmetric matrix M , > (<) 0 M means that it is positive (negative) definite. The symbol stands for the symmetric terms in a symmetric matrix, and I , 2 I are any two elements of .…”

Section: Introductionmentioning

confidence: 99%

H<inf>∞</inf> finite-time control with a PDE state constraint for a class of nonlinear coupled ODE-PDE systems

Feng

2014

Proceedings of 2014 IEEE Chinese Guidance, Navigation and Control Conference

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This paper addresses the H finite-time control problem subject to a state constraint of the partial differential equation (PDE) for a class of coupled systems described by nonlinear ordinary differential equations (ODEs) and a linear parabolic PDE. Initially, the Karhunen-Loève decomposition (KLD) and the singular perturbation technique are applied to the PDE system to derive a finite dimensional ODE model which accurately describes the dominant dynamics of the PDE system. By combining the original ODE system with the slow model of the PDE system, a nonlinear coupled ODE system is obtained, which is subsequently represented by the Takagi-Sugeno (T-S) fuzzy model. Meanwhile, the PDE state constraint is converted into a state constraint exerted on the coupled ODE system. Then, an H fuzzy control design is developed to stabilize the original ODE system in a finite time with a terminal time as small as possible, and achieve an optimized H performance of disturbance attenuation, while the PDE state constraint is respected. Finally, the proposed design method is applied to the control of a hypersonic rocket car to illustrate its effectiveness. u denote the set of real numbers, the n -dimensional Euclidean space, and the set of all real n m u matrices, respectively. , , n and are the absolute value of scalars, the standard inner product and

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“…al. [26], Heidebrecht [10], and [6] and [24]. All these phenomena have to be simultaneously taken into account in order to describe the reallity as precise as possible and necessary.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of coupled multiphysics problems: Guidelines for real‐life applications demonstrated for a complex fuel cell model

et al. 2012

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Key wordsOptimal control of multiphysics problems, first optimize then discretize, first discretize then optimize, fuel cell systems, state constraints MSC (2000) 40-01, 49M05, 49M15, 49M25, 49M37, 65M06, 65M20, 35M10In practice one often is confronted with the simulation and optimization of dynamical processes of multiphysics systems depending on time and space. This paper shall serve as a guidebook for practioneers who wants to proceed from simulation to optimization. We are specially concerned in this paper with optimal control problems involving partial differential equations. After providing an insight into the theory of optimal control problems with partial differential equations, the focus of the paper lies on their numerical treatment to obtain approximate optimal solutions, or more precisely approximate candidate optimal solutions. The two basic approaches, first optimize then discretize (FOTD) and first discretize then optimize (FDTO) are first described in an abstract setting and then evaluated by means of the fuel cell example of this paper which can serve as a prototype problem for multiphysics processes. The example describes the dynamical behaviour inside a certain type of high temperature fuel cell where gas flows, heat distribution, and potential fields as well as chemical reactions are modelled by hyperbolic and parabolic partial differential as well as ordinary differential algebraic equations. The underlying problem is an optimal control problem where up to 28 instationary partial differential algebraic equations in one, respectively two spatial dimensions are involved. In the conclusion pros and cons of the aforementioned approaches are discussed. Hereby, not only the numerical efficiency but also the investigation of human resources are balanced against each other.

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Optimal Control of Load Changes for Molten Carbonate Fuel Cell Systems: A Challenge in PDE Constrained Optimization

Cited by 12 publications

References 7 publications

Computational design and optimization of fuel cells and fuel cell systems: A review

Computational design and optimization of fuel cells and fuel cell systems: A review

H<inf>∞</inf> finite-time control with a PDE state constraint for a class of nonlinear coupled ODE-PDE systems

Optimal control of coupled multiphysics problems: Guidelines for real‐life applications demonstrated for a complex fuel cell model

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Optimal Control of Load Changes for Molten Carbonate Fuel Cell Systems: A Challenge in PDE Constrained Optimization

Cited by 12 publications

References 7 publications

Computational design and optimization of fuel cells and fuel cell systems: A review

Computational design and optimization of fuel cells and fuel cell systems: A review

H<inf>&#x221E;</inf> finite-time control with a PDE state constraint for a class of nonlinear coupled ODE-PDE systems

Optimal control of coupled multiphysics problems: Guidelines for real‐life applications demonstrated for a complex fuel cell model

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H<inf>∞</inf> finite-time control with a PDE state constraint for a class of nonlinear coupled ODE-PDE systems