Two Degrees of Freedom in the Control of a DC-DC Boost Converter, Fuzzy Identified Explicit Model in Feed-forward Line

  • Robert Baždarić
  • Igor Škrjanc
  • Drago Matko


We present a novel approach to the fuzzy control of a DC-DC Boost Converter. Using heuristic partitioning of the main control parameters and focusing on global knowledge of the open-loop, stable system’s equilibriums, the new method is developed based on an offline fuzzy identification of the steadystate duty cycle. The explicit and the fuzzy identified global model of the duty cycle robustly contribute to the system’s stability, even in the presence of large changes to the process parameters. In comparison with the analytically derived duty cycle using two different methods, the identified model prediction of an infinity horizon duty cycle shows better precision. These results are achieved in an analysis of the converter’s hybrid-simulation model where the assumptions made in the mathematical modelling are minor in comparison with similar assumptions in physical examples. The steady-state error compensation relies on the optimized PI controller, which is independently constructed and involved in the final Two-Degreesof-Freedom (TDOF) controller. The successful simulation results agree with the robustness and present a DC-DC converter with stable operation, even in the dynamic exchange of the DCM (Discontinuous Conduction Mode) and CCM (Continuous Conduction Mode). The method is widely applicable as it minimizes the real time of processing and avoids over-determined solutions.


DC-DC boost converter Hybrid modelling Fuzzy identification Robust control of nonlinear dynamical system Explicit Fuzzy Model Predictive Control (EFMPC) Two Degrees of Freedom (TDOF) 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Mariéthoz, S., Almér, S., Bâja, M., Beccuti, A.G., Patino, D., Wernrud, A., Buisson, J., Cormerais, H., Geyer, T., Fujioka, H., Jönsson, U.T., Kao, C.-Y., Morari, M., Papafotiou, G., Rantzer, A., Riedinger, P.: Comparison of Hybrid Control Techniques for Buck and Boost DC-DC Converters. IEEE, Trans. Control Syst. Technol. 18(5) (2010)Google Scholar
  2. 2.
    Beccuti, A.G., Papafotiou, G., Frasca, R., Morari, M.: Explicit Hybrid Model Predictive Control of the dc-dc Boost Converter. In: IEEE, PECS 2007., pp. 2503–2509Google Scholar
  3. 3.
    Fujioka, H., Kao, C.-Y., Almér, S., Jönsson, U.: LQ optimal control for a class of pulse width modulated systems. Automatica 43(6), 1009–1020 (2007)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Fujioka, H., Kao, C.-Y., Almér, S., Jönsson, U.: Robust tracking with H performance for PWM systems. Automatica 45, 1808–1818 (2009)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Lincoln, B., Rantzer, A.: Relaxing dynamic programming. IEEE, Trans. Autom. Control 51(5), 1249–1260 (2006)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Rong-Jong, W., Li-Chung, S.: Design of voltage tracking control for dc-dc boost converter via total sliding-mode technique. IEEE, Trans. Ind. Electron. 58(6) (2011)Google Scholar
  7. 7.
    Vidal-Idiarte, E., Carrejo, C.E., Calvente, J., Martínez-Salamero, L.: Two-Loop Digital Sliding Mode Control of DC-DC Power Converters Based on Predictive Interpolation. IEEE, Trans Ind. Electron. 58(6) (2011)Google Scholar
  8. 8.
    Di Bernardo, M., Budd, C.J., Champneys, A.R., Kowalczyk, P.: Piecewise-smooth Dynamical Systems – Theory and Applications. In: Springer-Verlag London Limited (2008)Google Scholar
  9. 9.
    Tse, C.K.: Flip Bifurcations and Chaos in Three-State Boost Switching Regulators. IEEE, Trans. Circ. Syst.-1; Fundam. Theory Aplications 41(1) (1994)Google Scholar
  10. 10.
    Yanfeg, C., Tse, C.K., Wong, S.s.-C.: Interaction of Fast-Scale and Slow-Scale Bifurcation in Current-Mode Controlled DC/DC Converters. Int. J. Bifurcation Chaos 17(5), 1609–1622 (2007)Google Scholar
  11. 11.
    Middlebrook, R.D., Slobodan, Ć.: A General Unified Approach to Modeling Switching-Converter Power Stages. In: IEEE, 1976 Record, pp. 18-34 (IEEE Publication 76CH1084-3 AES)Google Scholar
  12. 12.
    Erickson, R.W., Ćuk, S., Middlebrook, R.D.: Large-Signal Modelling and Analysis of Switching Regulators. In: IEEE, 1982 PESC Rec., pp. 240-250Google Scholar
  13. 13.
    Guesmi, K., Essounbouli, N., Hamzaoui, A., Zaytoon, J., Manamanni, N.: Shifting nonlinear phenomena in a DC-DC converter using fuzzy logic controller, Elsevier (2007)Google Scholar
  14. 14.
    Mehran, K., Giaouris, D., Zahawi, B.: Stability analysis and control of nonlinear phenomena in boost converters using model-based takagi–sugeno fuzzy approach. IEEE, Trans. Circ. Syst. —I: Reg. Papers 57(1) (2010)Google Scholar
  15. 15.
    van der Schaft, A.J., Schumacher, J.M.: Complementarity modeling of hybrid systems. IEEE, Trans. Autom. Control 43(4) (1998)Google Scholar
  16. 16.
    Vasca, F., Iannelli, L., Kanat Camlibel, M., Frasca, R.: A New Perspective for Modeling Power Electronic Converters: Complementarity Framework. IEEE, Trans. Power Electron. 24(2) (2009)Google Scholar
  17. 17.
    Santos, M.I.: Chapter 2: Modelling switched power converters using the complementarity formalism, doctoral thesis. Universitat Politècnica Catalunya (2006)Google Scholar
  18. 18.
    Goffman, C., Pedrick, G.: First Course in Functional Analysis. In: Prentice-Hall Inc. Englewood Cliffs, N.J. (1965)MATHGoogle Scholar
  19. 19.
    Stoorvogel, A.A., Van den Boom, T.J.J.: Model Predictive Control. In: DISC Course Lecture Notes (2010)Google Scholar
  20. 20.
    Geyer, T., Papafotiou, G., Morari, M.: Hybrid model predictive control of the step-down DC-DC converter. IEEE, Trans. Control Syst. Technol. 16(6), 1112–1124 (2008)CrossRefGoogle Scholar
  21. 21.
    Alessio, A., Bemporad, A.: A Survey on Explicit Model Predictive Control in Nonlinear Model Predictive Control, pp. 345–369. Springer-Verlag, Berlin Heidelberg, LNCIS 384 (2009)Google Scholar
  22. 22.
    The MathWorks Inc: MATLAB, R2009a, (2009)Google Scholar
  23. 23.
    Passino, K.M., Yurkovich, S.: Fuzzy Control. In: Addison Wesley Longman, Inc. (1998)Google Scholar
  24. 24.
    Ogata, K.: Modern Control Engineering-Fifth Edition. In: Prentice Hall (2010)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Faculty of Electrical EngineeringUniversity of LjubljanaLjubljanaSlovenija

Personalised recommendations