Skip to main content

Part of the book series: Energy Systems in Electrical Engineering ((ESIEE))

  • 315 Accesses

Abstract

Controlling of large nuclear reactors is a challenging task due to the simultaneous presence of both the slow and the fast varying dynamic modes. However, as demonstrated in this chapter, the two-time-scale property of the system can be taken advantage of. In particular, the design of linear quadratic regulator for spatial power control of Advanced Heavy Water Reactor (AHWR) has been presented in this chapter. The singularly perturbed two-time-scale model of AHWR is decomposed into two comparatively lower order subsystems, namely, slow and fast subsystems of orders 73 and 17, respectively. Two individual optimal controllers are developed for both the subsystems and then a composite controller is obtained for original higher order system. This composite controller is applied to the vectorized nonlinear model of AHWR. From dynamic simulations of the nonlinear model of the reactor in representative transients, the suggested control scheme is found to be superior to other methods.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Chang, K.W.: Singular perturbations of a general boundary value problem. SIAM J. Math. Anal. 3(3), 520–526 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chang, K.W.: Diagonalization method for a vector boundary problem of singular perturbation type. J. Math. Anal. Appl. 48(3), 652–665 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chow, J.H., Kokotovic, P.V.: A decomposition of near-optimum regulators for systems with slow and fast modes. IEEE Trans. Autom. Control 21(5), 701–705 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gaitsgory, V., Nguyen, M.T.: Averaging of three time scale singularly perturbed control systems. Syst. Control Lett. 42(5), 395–403 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. Gajic, Z., Lim, M.-T.: Optimal Control of Singularly Perturbed Linear Systems and Applications: High Accuracy Techniques. Marcel Dekker Inc., New York (2001)

    Book  MATH  Google Scholar 

  6. Kokotovic, P.V., Khalil, H.K., Reilly, J.O.: Singular Perturbation Methods in Control, Analysis and Design. Academic, New York (1986)

    Google Scholar 

  7. Kokotovic, P.V., O’Malley, R.E., Sannuti, P.: Singular perturbation and order reduction in control theory - an overview. Automatica 12, 123–132 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ladde, G.S., Rajalakshmi, S.G.: Diagonalization and stability of multi-time-scale singularly perturbed linear systems. Appl. Math. Comput. 16(2), 115–140 (1985)

    MathSciNet  MATH  Google Scholar 

  9. Munje, R.K., Patre, B.M.: Spatial power control of singularly perturbed nuclear reactor. Control Eng. Appl. Inform. 18(3), 22–29 (2016)

    Google Scholar 

  10. Naidu, D.S.: Singular Perturbation Methodology in Control Systems. Peter Peregrinus Ltd., London (1988)

    Book  MATH  Google Scholar 

  11. Naidu, D.S.: Singular perturbations and time scales in control theory and applications: overview. Dyn. Contin. Discrete Impuls. Syst. 9, 233–278 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  12. Phillips, R.G.: A two stage design of linear feedback controls. IEEE Trans. Autom. Control 25, 1220–1223 (1980)

    Article  Google Scholar 

  13. Saberi, A., Khalil, H.: Stabilization and regulation of nonlinear singularly perturbed systems-composite control. IEEE Trans. Autom. Cotrol 30, 739–747 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  14. Saksena, V.R., O’Reilly, J., Kokotovic, P.V.: Singular perturbation and time-scale methods in control theory: survey 1976–1983. Automatica 20, 273–293 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  15. Sannuti, P., Kokotovic, P.V.: Near optimum design of linear systems by a singular perturbation method. IEEE Trans. Autom. Control 14(1), 15–22 (1969)

    Article  MATH  Google Scholar 

  16. Shimjith, S.R., Tiwari, A.P., Bandyopadhyay, B.: A three-time-scale approach for design of linear state regulator for spatial control of advanced heavy water reactor. IEEE Trans. Nucl. Sci. 58(3), 1264–1276 (2011)

    Article  Google Scholar 

  17. Singh, N.P., Singh, Y.P., Ahson, S.I.: An iterative approach to reduced-order modeling of synchronous machines using singular perturbation. Proc. IEEE 74, 892–893 (1986)

    Article  Google Scholar 

  18. Suzuki, M.: Composite controls for singularly perturbed systems. Proc. IEEE Int. Conf. Control Appl. 26(2), 123–124 (1981)

    MathSciNet  MATH  Google Scholar 

  19. Syrcos, G., Sannuti, P.: Singular perturbation modeling of continuous and discrete physical systems. Int. J. Control 37, 1007–1022 (1983)

    Article  MATH  Google Scholar 

  20. Tiwari, A.P., Bandyopadhyay, B., Werner, H.: Spatial control of a large pressurize heavy water reactor by piecewise constant periodic output feedback. IEEE Trans. Nucl. Sci. 47, 389–402 (2000)

    Article  Google Scholar 

  21. Yan, Z., Naidu, D.S., Cai, C., Zou, Y.: Singular perturbations and time scales in control theories and applications: an overview 2002–2012. Int. J. Inf. Syst. Sci. 9, 1–36 (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ravindra Munje .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this chapter

Cite this chapter

Munje, R., Patre, B., Tiwari, A. (2018). State Feedback Control Using Linear Quadratic Regulator. In: Investigation of Spatial Control Strategies with Application to Advanced Heavy Water Reactor. Energy Systems in Electrical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-10-3014-7_4

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-3014-7_4

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-3013-0

  • Online ISBN: 978-981-10-3014-7

  • eBook Packages: EnergyEnergy (R0)

Publish with us

Policies and ethics