Sliding Mode Disturbance Observer-Based Robust Prescribed Performance Tracking Control for Research Reactor

  • Myunghwan Eom
  • Dongkyoung ChwaEmail author
Original Article


This paper presents a sliding mode disturbance observer (SMDO)-based robust prescribed performance control (RPPC) method for research reactor systems with system uncertainty. The existing reactor control methods have not considered the disturbance compensation and improvement of the transient response at the same time although both of these issues are much important in the reactor control. To achieve these control objectives, the prescribed performance function is introduced and then the SMDO-based RPPC is designed for the research reactor such that the transient tracking error remains within the desired bound even in the presence of the system uncertainty. The stability of the overall research reactor control system is analyzed and simulation results are provided to demonstrate the validity of the proposed method.


Sliding mode disturbance observer Robust prescribed performance control Research reactor system System uncertainty Prescribed performance function 

List of Symbols

\(\alpha _C\)

Coolant temperature reactivity coefficient \((\hbox {mk}/^\circ \hbox {C})\)

\(\alpha _F\)

Fuel temperature reactivity coefficient \((\hbox {mk}/^\circ \hbox {C})\)

\(\alpha _R\)

Reflector temperature reactivity coefficient \((\hbox {mk}/^\circ \hbox {C})\)

\(\alpha _X\)

Equilibrium Xe reactivity coefficient at 100% FP (mk)

\( \bar{S} \)

Normalized source power (FPU: full power unit)

\(\beta _{C_i} \)

ith Group yield fraction of delayed neutrons (\(\beta _C :=\sum _ i=1^{I} \beta _{C_i} \))

\(\beta _{ D_j} \)

jth Group yield fraction of photo neutrons (\(\beta _D :=\sum _ j=1 ^{J} \beta _{ D_j} \))

\(\varLambda \)

Neutron mean generation time

\(\lambda _{C_i} \)

Decay constant of ith group delayed neutron precursor (\({\text {s}}^{-1} \))

\(\lambda _{ D_j} \)

Decay constant of jth group photo neutron precursor (\({\text {s}}^ -1 \))

\(\rho \)

Total reactivity at time (t)

\(\rho _ CR \)

Reactivity by the control rod movements

\(\rho _ C \)

Coolant temperature feedback reactivity

\(\rho _ F \)

Fuel temperature feedback reactivity

\(\rho _ R \)

Reflector temperature feedback reactivity

\(\rho _ X \)

Xenon feedback reactivity


ith Group delayed neutron precursor density


jth Group photo neutron precursor density


Neutron density in the core and reflector

\(T_ C0 \)

Coolant temperature at 100% FP (\(^\circ \hbox {C})\)

\(T_ C \)

Coolant temperature (\(^\circ \hbox {C})\)

\(T_ F0 \)

Fuel temperature at 100% FP (\(^\circ \hbox {C})\)

\(T_ F \)

Fuel element temperature (\(^\circ \hbox {C})\)

\(T_ R0 \)

Reflector temperature at 100% FP (\(^\circ \hbox {C})\)

\(T_ R \)

Reflector temperature (\(^\circ \hbox {C})\)



This work was supported by “Basic Science Research Program” through the National Research Foundation of Korea(NRF) funded by the Ministry of Science, ICT & Future Planning (2017R1A2B4009486).


  1. 1.
    Dong Z (2011) Nonlinear state-feedback dissipation power level control for nuclear reactors. IEEE Trans Nucl Sci 58(1):241–257CrossRefGoogle Scholar
  2. 2.
    Dong Z (2013) Nonlinear adaptive power-level control for modular high temperature gas-cooled reactors. IEEE Trans Nucl Sci 60(2):1332–1345CrossRefGoogle Scholar
  3. 3.
    Dasgupta S, Routh A, Banerjee S, Agilageswari K, Balasubramanian R, Bhandarkar S, Chattopadhyay S, Kumar M, Gupta A (2013) Networked control of a large pressurized heavy water reactor PHWR with discrete proportional-integral-derivative PID controllers. IEEE Trans Nucl Sci 60(5):3879–3888CrossRefGoogle Scholar
  4. 4.
    Dong Z (2015) Model-free power-level control of MHTGRs against input saturation and dead-zone. IEEE Trans Nucl Sci 62(6):3297–3310CrossRefGoogle Scholar
  5. 5.
    Vegh J, Gajdos F, Horvath C, Matisz A, Nyisztor D (2015) Improving research reactor accident response capability at the Hungarian nuclear safety authority. IEEE Trans Nucl Sci 62(1):187–194CrossRefGoogle Scholar
  6. 6.
    Dong Z (2012) Dynamic output feedback power-level control for the MHTGR based on iterative damping assignment. Energies 5(6):1782–1815CrossRefGoogle Scholar
  7. 7.
    Munje R, Patre B, Shimjith S, Tiwari A (2013) Sliding mode control for spatial stabilization of advanced heavy water reactor. IEEE Trans Nucl Sci 60(4):3040–3050CrossRefGoogle Scholar
  8. 8.
    Patre B, Londhe P, Nagarale R (2015) Fuzzy sliding mode control for spatial control of large nuclear reactor. IEEE Trans Nucl Sci 62(5):2255–2265CrossRefGoogle Scholar
  9. 9.
    Li G, Wan J, Zhao F (2014) New strategies with multi-model, statefeedback control and stability analysis for load-follow PWR core. Progr Nucl Energy 75:168–179CrossRefGoogle Scholar
  10. 10.
    Davijani NZ, Jahanfarnia G, Abharian AE (2017) Nonlinear fractional sliding mode controller based on reduced order FNPK model for output power control of nuclear research reactors. IEEE Trans Nucl Sci 64(1):713–723CrossRefGoogle Scholar
  11. 11.
    Yang M (2019) Distributed parameter control method for axial neutron flux in fast nuclear reactor. IEEE Trans Nucl Sci 66(6):899–910CrossRefGoogle Scholar
  12. 12.
    Jo H, Cha H (2017) Sequence control verification of a central solenoid converter for nuclear fusion reactors by using a hardware-in-the-loop. IEEE Trans Nucl Sci 64(9):6864–6873Google Scholar
  13. 13.
    Vajpayee V, Mukhopadhyay S, Tiwari AP (2018) Data-driven subspace predictive control of a nuclear reactor. IEEE Trans Nucl Sci 65(2):666–679CrossRefGoogle Scholar
  14. 14.
    Tee KP, Ge SS (2009) Control of nonlinear systems with full state constraint using a barrier Lyapunov function. In: Proceedings of the 48h IEEE conference on decision and control held jointly with 2009 28th Chinese control conference, Shanghai, China, pp 8618–8623Google Scholar
  15. 15.
    Tee KP, Ge SS, Tay EH (2009) Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica 45(4):918–927MathSciNetCrossRefGoogle Scholar
  16. 16.
    Tee KP, Ren B, Ge SS (2011) Control of nonlinear systems with timevarying output constraints. Automatica 47(11):2511–2516MathSciNetCrossRefGoogle Scholar
  17. 17.
    Liu Y-J, Ma L, Liu L, Tong S, Chen CLP (2019) Adaptive neural network learning controller design for a class of nonlinear systems with timevarying state constraints. IEEE Trans Neural Netw Learn Syst (Early Access). CrossRefGoogle Scholar
  18. 18.
    Wang C, Wu Y, Wang F, Zhao Y (2019) TABLF-based adaptive control for uncertain nonlinear systems with time-varying asymmetric full state constraints. Int J Control (Early Access). CrossRefGoogle Scholar
  19. 19.
    Tang L, Li D (2019) Time-varying barrier Lyapunov function based adaptive neural controller design for nonlinear pure-feedback systems with unknown Hysteresis. Int J Control Autom Syst 17(7):1642–1654CrossRefGoogle Scholar
  20. 20.
    Zuo Z, Wang C (2014) Adaptive trajectory tracking control of output constrained multi-rotors systems. IET Control Theory Appl 8(13):1163–1174CrossRefGoogle Scholar
  21. 21.
    Ilchmann A, Ryan EP, Trenn S (2005) Tracking control: performance funnels and prescribed transient behaviour. Syst Control Lett 54(7):655–670MathSciNetCrossRefGoogle Scholar
  22. 22.
    Kostarigka AK, Doulgeri Z, Rovithakis GA (2013) Prescribed performance tracking for flexible joint robots with unknown dynamics and variable elasticity. Automatica 49(5):1137–1147MathSciNetCrossRefGoogle Scholar
  23. 23.
    Bechlioulis CP, Rovithakis GA (2013) Approximation-free prescribed performance control for unknown SISO pure feedback systems. In: Proceedings of the European Control Conference, Zurich, Switzerland, pp 4544–4549Google Scholar
  24. 24.
    Karayiannidis Y, Doulgeri Z (2012) Model-free robot joint position regulation and tracking with prescribed performance guarantees. Robot Auton Syst 60(2):214–226CrossRefGoogle Scholar
  25. 25.
    Han S-I, Lee J-M (2014) Recurrent fuzzy neural network backstepping control for the prescribed output tracking performance of nonlinear dynamic systems. ISA Trans 53(1):33–43CrossRefGoogle Scholar
  26. 26.
    Na J, Chen Q, Ren X, Guo Y (2014) Adaptive prescribed performance motion control of servo mechanisms with friction compensation. IEEE Trans Ind Electron 61(1):486–494CrossRefGoogle Scholar
  27. 27.
    Huang Y, Na J, Wu X, Liu X, Guo Y (2015) Adaptive control of nonlinear uncertain active suspension systems with prescribed performance. ISA Trans 54:145–155CrossRefGoogle Scholar
  28. 28.
    Sui S, Tong S, Li Y (2015) Observer-based fuzzy adaptive prescribed performance tracking control for nonlinear stochastic systems with input saturation. Neurocomputing 158:100–108CrossRefGoogle Scholar
  29. 29.
    Bechlioulis CP, Doulgeri Z, Rovithakis GA (2010) Neuro-adaptive force/position control with prescribed performance and guaranteed contact maintenance. IEEE Trans Neural Netw 21(12):1857–1868CrossRefGoogle Scholar
  30. 30.
    Zhu L, Zhou Y, Liu Y (2018) Robust adaptive neural prescribed performance control for MDF continuous hot pressing system with input saturation. IEEE Access 6:9099–9113CrossRefGoogle Scholar
  31. 31.
    Qin H, Wu Z, Sun Y, Zhang C, Lin C (2019) Fault-tolerant prescribed performance control algorithm for underwater acoustic sensor network nodes with thruster saturation. IEEE Access 7:69504–69515CrossRefGoogle Scholar
  32. 32.
    Zhu Y, Qiao J, Guo L (2019) Adaptive sliding mode disturbance observerbased composite control with prescribed performance of space manipulators for target capturing. IEEE Trans Ind Electron 66(3):1973–1983CrossRefGoogle Scholar
  33. 33.
    Joo Y, Back J (2012) Power regulation of variable speed wind turbines using pitch control based on disturbance observer. J Electr Eng Technol 7(2):273–280CrossRefGoogle Scholar
  34. 34.
    Kim J-S, Menon PP, Back J, Shim H (2017) Disturbance observer based boundary tracking for environment monitoring. J Electr Eng Technol 12(3):1299–1306CrossRefGoogle Scholar
  35. 35.
    Wang S, Fu J, Yang Y, Shi J (2017) An improved predictive functional control with minimum-order observer for speed control of permanent magnet synchronous motor. J Electr Eng Technol 12(1):272–283CrossRefGoogle Scholar
  36. 36.
    Shansi Z, Shuyuan M, Wang Weiming (2018) Sliding mode control based on disturbance observer for magnetic levitation positioning stage. J Electr Eng Technol 13(5):2116–2124Google Scholar
  37. 37.
    Eom M, Chwa D, Baang D (2015) Robust disturbance observer-based feedback linearization control for a research reactor considering a power change rate constraint. IEEE Trans Nucl Sci 62(3):1301–1312CrossRefGoogle Scholar
  38. 38.
    Duderstadt JJ, Hamilton LJ (1976) Nuclear reactor analysis. Wiley, New YorkGoogle Scholar
  39. 39.
    Kim S (2011) Dane-Bang, Program description and functional test of RRSSIM, JR-TR-SA-013, Rev. 0, Korea Atomic Energy Research Institute, Tech. RepGoogle Scholar
  40. 40.
    Bechlioulis CP, Rovithakis GA (2008) Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance. IEEE Trans Autom Control 53(9):2090–2099MathSciNetCrossRefGoogle Scholar
  41. 41.
    Bechlioulis CP, Rovithakis GA (2009) Adaptive control with guaranteed transient and steady state tracking error bounds for strict feedback systems. Automatica 45(2):532–538MathSciNetCrossRefGoogle Scholar
  42. 42.
    Khalil HK (2002) Nonlinear systems, 3rd edn. Prentice hall, Upper Saddle RiverzbMATHGoogle Scholar

Copyright information

© The Korean Institute of Electrical Engineers 2019

Authors and Affiliations

  1. 1.COO Defense Systems Division Defense System R&DDoosan Corporation MottrolChangwonSouth Korea
  2. 2.Department of Electrical and Computer EngineeringAjou UniversitySuwon-siSouth Korea

Personalised recommendations