Effect of switching uncertainty on a boost converter under a coloured noise influence



The noise processes associated with dynamical systems have limited bandwidth having finite, non-zero correlation time enabling us to model them as the Ornstein–Uhlenbeck process. The confluence of the deterministic system dynamics with these noisy forcing functions may trigger a series of unwarranted complex, peculiar phenomenon or stability issues in the system under different initial conditions and noise intensities. Thus, revisiting the system dynamics in the Ornstein–Uhlenbeck setting using the estimation and filtration algorithms seems an accurate and imperative choice. The Itô calculus, a very powerful classical tool, is used to evaluate the performance of stochastic differential equations. However, the Itô calculus cannot be directly applied to the systems under the influence of the Ornstein–Uhlenbeck process and we come across what is more fondly called as the curse of dimensionality, the augmented state vector approach. This paper develops a system theoretic-estimation algorithm for a switched-mode DC–DC power converter driven by the Ornstein–Uhlenbeck process. This is a novel attempt in this research direction. The algorithm is tested under a various data set and initial conditions to validate the findings.


Switched-mode DC–DC power converters Ornstein–Uhlenbeck process Itô theory State estimations 



The authors are grateful to finer and in-depth comments of anonymous qualified Reviewers. Corrections on the lines of the suggestions of the Reviewers and the Editor led to the error-less content of the ‘revised paper’.


  1. 1.
    Chatterjee D (2007) Studies on stability and stabilization of randomly switched systems. Ph.D. Dissertation, Electrical and Computer Engineering, University of Illinois at Urbana–Champaign, lL, USAGoogle Scholar
  2. 2.
    Mazumdar SK, Nayfeh AH, Boroyevich D (2001) Theoretical and experimental investigation of fast and slow-scale instabilities of a DC–DC converter. IEEE Trans Power Electron 16(2):201– 216CrossRefGoogle Scholar
  3. 3.
    Scholten AJ, Tiemeijer LF, Langevelde RV, Havens RJ, Zegers-van DATA, Venezia VC (2003) Noise modeling for RF CMOS circuit simulation. IEEE Trans Electron Devices 50(3):618–632CrossRefGoogle Scholar
  4. 4.
    Midya P, Krein PT (2000) Noise properties of pulse-width modulated power converters: open loop effects. IEEE Trans Power Electron 15(6):1134–1143CrossRefGoogle Scholar
  5. 5.
    Leyva-Ramos J, Morales-Saldaña JA (2000) Uncertainty models for switch-mode DC–DC converters. IEEE Trans Circuit Syst Part I Fundam Theory Appl 47(2):200–203CrossRefGoogle Scholar
  6. 6.
    Sangswang A, Nwankpa CO (2003) Effects of switching-time uncertainties on pulse width-modulated power converters: modeling and analysis. IEEE Trans Circuit Syst Part I Fundam Theory Appl 50(8):1006–1012CrossRefGoogle Scholar
  7. 7.
    Sangswang A (2003) Uncertainty modeling of power electronic converter dynamics. Ph.D. thesis, Centre for Electric Power Engineering, Drexel University, Philadelphia, PA, USAGoogle Scholar
  8. 8.
    Kawasaki N, Nomura H, Masuhiro M (1995) A new control law of bilinear DC–DC converters. IEEE Trans Power Electron 10(3):318–325CrossRefGoogle Scholar
  9. 9.
    Willsky AS (1976) Analysis of bilinear noise models in circuits and devices. J Franklin Inst 301(1–2):103–122MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Sun W, Chen RMM, Jiang Y (2002) Tolerance analysis for electronic circuit design using the method of moments. Int Symp Circuits Syst 1:565–568Google Scholar
  11. 11.
    Wang L, Hong J, Scherer R, Bai F (2009) Dynamics and variational integrators of stochastic Hamiltonian systems. Int J Numer Anal Model 6(4):586–602MathSciNetGoogle Scholar
  12. 12.
    Ober-Blöbaum S, Tao M, Cheng M, Owhadi H, Marsden JE (2011) Variational integrators for electric circuits. J Comput Phys 242:498–530Google Scholar
  13. 13.
    Su Q, Strunz K (2005) Stochastic circuit modeling with hermite polynomial chaos. Electron Lett 41(21):1163–1165. doi: 10.1049/el:20052415 CrossRefGoogle Scholar
  14. 14.
    Jung P, Hänggi P (1987) Dynamical systems: a unified colored-noise approximation. Phys Rev A 35(10):4464–4466CrossRefGoogle Scholar
  15. 15.
    Luo Z, Zhu S (2002) Colored noise in a two-dimensional nonlinear system. Eur Phys J D 19:111–117CrossRefGoogle Scholar
  16. 16.
    Bobryk RV, Chrzeszczyk A (2002) Colored-noise-induced parametric resonance. Phys A 316:225–232CrossRefMATHGoogle Scholar
  17. 17.
    Chen RM, Chang S (1991) State and parameter estimations for dynamic systems with colored noise: an accuracy approach based on the minimum discrepancy measure. IEEE Trans Autom Control 36(7):813–823Google Scholar
  18. 18.
    Zhou Y, Fang C (2010) Stochastic resonance in a DC–DC converter with colored noise. International Conference on Communications, Circuits and Systems (ICCCAS), Chengdu City, China 28–30 Jul 2010, pp. 581–584Google Scholar
  19. 19.
    Sira-Ramirez H, Delgado de Nieto M (1996) A Lagrangian approach to average modeling of pulse width-modulation controlled DC-to-DC power converters. IEEE Trans Circuits Syst I Fundam Theory Appl 43:427–430CrossRefGoogle Scholar
  20. 20.
    Scherpen JMA, Jeltsema D, Klaassens JB (2003) Lagrangian modeling of switched electrical networks. Syst Control Lett 48:365–374CrossRefMATHGoogle Scholar
  21. 21.
    Lehman B, Bass RM (1996) Switching frequency dependent averaged models for PWM DC–DC converters. IEEE Trans Power Electron 11(1):89–98CrossRefGoogle Scholar
  22. 22.
    Stanković AM, Verghese GC, Perreault D (1995) Analysis and synthesis of randomized modulation schemes for power converters. IEEE Trans Power Electron 10(6):680–693CrossRefGoogle Scholar
  23. 23.
    Sharma SN, Parthasarathy H (2007) Dynamics of a stochastically perturbed two-body problem. Proc Royal Soc A Math Phys Eng Sci 463:979–1003MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Jazwinski AH (1970) Stochastic processes and filtering theory. Academic Press, New YorkMATHGoogle Scholar
  25. 25.
    Sage AP, Melsa JL (1971) Estimation theory with applications to communications and control. McGraw-Hill, New YorkMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.National Institute TechnologySuratIndia

Personalised recommendations