Fractional neutron point kinetics equations for nuclear reactor dynamics

Espinosa-Paredes, Gilberto; Polo-Labarrios, M.A.; Espinosa-Martínez, É.-G.; Gallegos, Edmundo del Valle

doi:10.1016/j.anucene.2010.10.012

Cited by 124 publications

(18 citation statements)

References 97 publications

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“…The physical justification for opting FO modeling strategy for the reactor is discussed next. Recent research [14]- [17] shows the neutron diffusion equation in nuclear reactor is nonFickian in nature and the reactor point kinetic equations can be accurately described using FO differential equations (the fractional order appearing in space as well as time). So, the motivation of the present work is based on the fact that FO description of the reactor dynamics is a more realistic scenario for neutron diffusion equation and point reactor kinetics.…”

Section: Fractional Order Modeling Of a Phwr Undermentioning

confidence: 99%

Fractional Order Modeling of a PHWR Under Step-Back Condition and Control of Its Global Power With a Robust ${\rm PI}^{\lambda} {\rm D} ^{\mu}$ Controller

Das

Gupta

2011

IEEE Trans. Nucl. Sci.

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Abstract-Bulk reduction of reactor power within a small finite time interval under abnormal conditions is referred to as step-back. In this paper, a 500MWe Canadian Deuterium Uranium (CANDU) type Pressurized Heavy Water Reactor (PHWR) is modeled using few variants of Least Square Estimator (LSE) from practical test data under a control rod drop scenario in order to design a control system to achieve a dead-beat response during a stepped reduction of its global power. A new fractional order (FO) model reduction technique is attempted which increases the parametric robustness of the control loop due to lesser modeling error and ensures iso-damped closed loop response with a PI λ D μ or FOPID controller. Such a controller can, therefore, be used to achieve active step-back under varying load conditions for which the system dynamics change significantly. For closed loop active control of the reduced FO reactor models, the PI λ D μ controller is shown to perform better than the classical integer order PID controllers and present operating Reactor Regulating System (RRS) due to its robustness against shift in system parameters.

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Section: Fractional Order Modeling Of a Phwr Undermentioning

confidence: 99%

Fractional Order Modeling of a PHWR Under Step-Back Condition and Control of Its Global Power With a Robust ${\rm PI}^{\lambda} {\rm D} ^{\mu}$ Controller

Das

Gupta

2011

IEEE Trans. Nucl. Sci.

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“…The FNPK model with six groups of delayed neutron precursors, which was initially described for one group in [8] and extended to six groups in [11], may be given by fractional differential equations:…”

Section: The Fractional Neutron Point Kinetics Modelmentioning

confidence: 99%

“…In recent years, however, the FNPK model has become the subject of research [8,11]. In [8] the fractional point kinetics model with one group of delayed neutron precursors was proposed.…”

Section: Introductionmentioning

confidence: 99%

“…Point models for nuclear reactors have been commonly used for many years [1,2,5,6,8,15]. In order to improve control better methods of approximating processes taking place in the nuclear reactor have been researched.…”

Section: Introductionmentioning

confidence: 99%

“…In [8] the fractional point kinetics model with one group of delayed neutron precursors was proposed. In this paper, the authors extended the model for six groups.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Solution of Fractional Neutron Point Kinetics Model in Nuclear Reactor

Nowak

Duzinkiewicz

Piotrowski

2014

Archives of Control Sciences

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This paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme in the FOMCON Toolbox in MATLAB environment. Third is the method proposed by Edwards. The impact of selected parameters on the model's response was examined. The results for typical input were discussed and compared.

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