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Robust Control of Nuclear Reactors with Proportional—Integral-Derivative (PID) Controllers: The Fractional Order (FO) and Interval Approaches

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Dynamics and Control of Energy Systems

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Abstract

Control of a nuclear reactor poses a challenge to a control-system designer due to the inherent nonlinear and a time varying nature of the associated dynamics which changes with the power level and the depletion level of the radio-active fuel in the reactor core. A constraint on the rate of rise of reactor power poses an additional challenge restricting the operation of a Nuclear Power Plant (NPP) mostly as a base load station. Conventional reactor control approaches aim to achieve a stable reactor period around a designated reactor power level—which is usually 100% Full Power (FP), with refinements like flux-tilt control and zonal power level variations within a narrow range using reactivity devices distributed across the reactor core. A bulk power controller is invoked either to raise the reactor power to a steady operational level or during a sharp reduction, known as a step-back and seldom in a demand following mode.

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References

  • Ansarifar GR, Rafiei M (2015) Second-order sliding-mode control for a pressurized water nuclear reactor considering the xenon concentration feedback. Nucl Eng Technol 47(1):94–101

    Google Scholar 

  • Astrom KJ, Wittenmark B (1997) Computer-controlled systems theory and design. Tsinghua University Press, Prentice Hall

    Google Scholar 

  • Banerjee S, Halder K, Dasgupta S, Mukhopadhyay S, Ghosh K, Gupta A (2015) An interval approach for robust control of a large PHWR with PID controllers. IEEE Trans Nucl Sci 62(1):281–292

    Article  Google Scholar 

  • CRONE Tool Box. http://archive.ims-bordeaux.fr/CRONE/toolbox/pages/accueilSITE.php?guidPage=home_page

  • Chen YQ, Moore KL, Vinagre BM, Podlubny I (2004) Robust PID controller autotuning with a phase shaper. In: Proceedings of the first IFAC symposium on fractional differentiation and its application (FDA04), Bordeaux, France

    Google Scholar 

  • Das S (2008) Functional fractional calculus. Springer, Berlin. ISBN 978-3-642-20545-3

    MATH  Google Scholar 

  • Das M, Ghosh R, Goswami B, Gupta A, Tiwari AP, Balasubramanian R, Chandra AK (2006) Networked control system applied to a large pressurized heavy water reactor. IEEE Trans Nucl Sci 53(5):2948–2956, Part 2

    Google Scholar 

  • Das S, Saha S, Das S, Gupta A (2011) On the selection of tuning methodology for FOPID controllers for the control of higher order processes. ISA Trans 50(3):376–388

    Google Scholar 

  • Das S, Das S, Gupta A (2012) Fractional order modeling of a PHWR under step-back condition & control of its global power with a robust PIλDμ controller. IEEE Trans Nucl Sci 58(5):2431–2441

    Article  Google Scholar 

  • Lee YJ (1997) H-infinity robust controller design of reactor power control system. J KNS 29(4):280–290

    Google Scholar 

  • Lee YJ, Na MG (2002) Robust controller design of nuclear power reactor by parametric method. J KNS, 34(5):436–444

    Google Scholar 

  • Monje CA, Vinagre BM, Feliu V, Chen YQ (2008) Tuning and auto-tuning of fractional order controllers for industry applications. Control Eng Pract 16(7):798–812

    Google Scholar 

  • Optimization Toolbox Documentation. https://www.mathworks.com/help/optim/

  • Park MG, Cho NZ (1993) Time-optimal control of nuclear reactor power with adaptive proportional-integral-feedforward gains. IEEE Trans Nucl Sci 40(3):266–270

    Google Scholar 

  • Saha S, Das S, Ghosh R, Goswami B, Balasubramanian R, Chandra AK, Das S, Gupta A (2010a) Design of a fractional order phase shaper for iso-damped control of a PHWR under step-back condition. IEEE Trans Nucl Sci 57(3):1–11

    Google Scholar 

  • Saha S, Das S, Ghosh R, Goswami B, Balasubramanian R, Chandra AK, Das S, Gupta A (2010b) Fractional order phase shaper design with Bode’s integral for iso-damped control system. ISA Trans 49(2):196–206

    Google Scholar 

  • Suzuki K, Shimazaki J, Shinohara Y (1993) Application of H-infinity control-theory to power-control of a nonlinear reactor model. Nucl Sci Eng 115(2):142–151

    Google Scholar 

Download references

Acknowledgements

The author acknowledges the support received from his former doctoral students Dr. Suman Saha, Dr. Saptarshi Das and Dr. Shohan Banerjee in preparing the material presented in this chapter. The MATLAB codes developed by Dr. Saha and Dr. Das have been used extensively for producing the Figs. 7.4, 7.6 and 7.9. The author also acknowledges the support from IEEE for the permission to reproduce Figs. 7.7 and 7.8 and 10 from the sources referenced in the respective figures.

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Correspondence to Amitava Gupta .

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Gupta, A. (2020). Robust Control of Nuclear Reactors with Proportional—Integral-Derivative (PID) Controllers: The Fractional Order (FO) and Interval Approaches. In: Mukhopadhyay, A., Sen, S., Basu, D., Mondal, S. (eds) Dynamics and Control of Energy Systems. Energy, Environment, and Sustainability. Springer, Singapore. https://doi.org/10.1007/978-981-15-0536-2_7

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  • DOI: https://doi.org/10.1007/978-981-15-0536-2_7

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