Chaotic and subharmonic oscillations in a DC–DC boost converter with PWM voltage–current hybrid controller and parallel MR load

  • Ruiye Zhang
  • Aiguo Wu
  • Zenghui Wang
  • Shijian CangEmail author
Original paper


This paper reports a pulse-width modulation voltage-mode- and current-mode-controlled DC–DC boost converter with parallel memristance and resistance loads. This circuit system has two distinct states, i.e., ON-state and OFF-state, which mainly depend on the outputs of a reset–set (RS) flip-flop that are subject to a voltage–current dual closed-loop controller and a \(T_r\)-periodic modulation signal. Based on the mathematical model and analyses of the circuit system, it is found that there exist chaotic and subharmonic dynamics for given parameters when the triggering period \(T_f\) of the RS flip-flop varies. To exhibit the existing nonlinear dynamics of the circuit system in NI Multisim, we also design a mixed-signal circuit to implement the reported system and the observed experimental results are consistent with the numerical results.


Chaotic and subharmonic oscillations DC–DC boost converter Voltage–current hybrid controller Memristance–resistance load Circuit implementation 



This work is partly supported by the National Natural Science Foundation of China (Grant Nos. 61873186 and 61773282), the Application Base and Frontier Technology Research Project of Tianjin of China (Grant Nos. 13JCQNJC03600) and South African National Research Foundation (Grant Nos. 112142 and 112108), South African National Research Foundation Incentive Grant (No. 114911) and Tertiary Education Support Programme (TESP) of South African ESKOM.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflicts of interest.


  1. 1.
    Ahrabi, R.R., Ardi, H., Elmi, M., Ajami, A.: A novel step-up multiinput DC–DC converter for hybrid electric vehicles application. IEEE Trans. Power Electron. 32(5), 3549 (2017)CrossRefGoogle Scholar
  2. 2.
    Liu, J., Laghrouche, S., Wack, M.: Observer-based higher order sliding mode control of power factor in three-phase AC/DC converter for hybrid electric vehicle applications. Int. J. Control 87(6), 1117 (2014)CrossRefMathSciNetzbMATHGoogle Scholar
  3. 3.
    Tang, Y., Khaligh, A.: Bidirectional resonant DC–DC step-up converters for driving high-voltage actuators in mobile microrobots. IEEE Trans. Power Electron. 31(1), 340 (2016)CrossRefGoogle Scholar
  4. 4.
    Katayama, N., Tosaka, S., Yamanaka, T., Hayase, M., Dowaki, K., Kogoshi, S.: New topology for DC–DC converters used in fuel cell-electric double layer capacitor hybrid power source systems for mobile devices. IEEE Trans. Ind. Appl. 52(1), 313 (2016)CrossRefGoogle Scholar
  5. 5.
    Harfman-Todorovic, M., Palma, L., Enjeti, P.: A hybrid DC–DC converter for fuel cells powered laptop computers. In: 37th IEEE Power Electronics Specialists Conference (PESC’06), pp. 1–5. IEEE (2006)Google Scholar
  6. 6.
    Sabzali, A.J., Ismail, E.H., Behbehani, H.M.: High voltage step-up integrated double boost-sepic DC–DC converter for fuel-cell and photovoltaic applications. Renew Energy 82, 44 (2015)CrossRefGoogle Scholar
  7. 7.
    Shi, Y., Li, R., Xue, Y., Li, H.: Optimized operation of current-fed dual active bridge DC–DC converter for PV applications. IEEE Trans. Ind. Electron. 62(11), 6986 (2015)CrossRefGoogle Scholar
  8. 8.
    Zainuri, M.A.A.M., Radzi, M.A.M., Soh, A.C., Rahim, N.A.: Development of adaptive perturb and observe-fuzzy control maximum power point tracking for photovoltaic boost DC–DC converter. IET Renew. Power Gener. 8(2), 183 (2014)CrossRefGoogle Scholar
  9. 9.
    Zhioua, M., El Aroudi, A., Belghith, S., Bosque-Moncusí, J.M., Giral, R., Al Hosani, K., Al-Numay, M.: Modeling, dynamics, bifurcation behavior and stability analysis of a DC–DC boost converter in photovoltaic systems. Int. J. Bifurc. Chaos 26(10), 1650166 (2016)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Merabet, A., Ahmed, K.T., Ibrahim, H., Beguenane, R., Ghias, A.M.: Energy management and control system for laboratory scale microgrid based wind-PV-battery. IEEE Trans. Sustain. Energy 8(1), 145 (2017)CrossRefGoogle Scholar
  11. 11.
    Peña Asensio, A., Arnaltes Gómez, S., Rodriguez-Amenedo, J.L., García Plaza, M., Eloy-García Carrasco, J., de las Morenas, J.M.Alonso-Martínez: A voltage and frequency control strategy for stand-alone full converter wind energy conversion systems. Energies 11(3), 474 (2018)CrossRefGoogle Scholar
  12. 12.
    Naayagi, R., Forsyth, A., Shuttleworth, R.: Bidirectional control of a dual active bridge DC–DC converter for aerospace applications. IET Power Electron. 5(7), 1104 (2012)CrossRefGoogle Scholar
  13. 13.
    Naayagi, R., Forsyth, A.J., Shuttleworth, R.: High-power bidirectional DC–DC converter for aerospace applications. IEEE Trans. Power Electron. 27(11), 4366 (2012)CrossRefGoogle Scholar
  14. 14.
    Toribio, E., El Aroudi, A., Olivar, G., Benadero, L.: Numerical and experimental study of the region of period-one operation of a PWM boost converter. IEEE Trans. Power Electron. 15(6), 1163 (2000)CrossRefGoogle Scholar
  15. 15.
    El Aroudi, A., Debbat, M., Giral, R., Olivar, G., Benadero, L., Toribio, E.: Bifurcations in DC–DC switching converters: review of methods and applications. Int. J. Bifurc. Chaos 15(05), 1549 (2005)CrossRefMathSciNetzbMATHGoogle Scholar
  16. 16.
    Wu, C., Si, G., Zhang, Y., Yang, N.: The fractional-order state-space averaging modeling of the buck-boost DC/DC converter in discontinuous conduction mode and the performance analysis. Nonlinear Dyn. 79(1), 689 (2015)CrossRefGoogle Scholar
  17. 17.
    Benmiloud, M., Benalia, A.: Finite-time stabilization of the limit cycle of two-cell DC/DC converter: hybrid approach. Nonlinear Dyn. 83(1–2), 319 (2016)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Wang, L., Meng, Z., Sun, Y., Guo, L.: Bifurcation and chaos analysis of power converter for switched reluctance motor drive. Int. J. Electron. 104(1), 157 (2017)CrossRefGoogle Scholar
  19. 19.
    Jia, Z., Liu, C.: Fractional-order modeling and simulation of magnetic coupled boost converter in continuous conduction mode. Int. J. Bifurc. Chaos 28(05), 1850061 (2018)CrossRefMathSciNetzbMATHGoogle Scholar
  20. 20.
    Deane, J.H.: Chaos in a current-mode controlled boost DC–DC converter. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 39(8), 680 (1992)CrossRefGoogle Scholar
  21. 21.
    Cafagna, D., Grassi, G.: Experimental study of dynamic behaviors and routes to chaos in DC–DC boost converters. Chaos Solitons Fractals 25(2), 499 (2005)CrossRefzbMATHGoogle Scholar
  22. 22.
    Cafagna, D., Grassi, G.: Bifurcation analysis and chaotic behavior in boost converters: experimental results. Nonlinear Dyn. 44(1–4), 251 (2006)CrossRefzbMATHGoogle Scholar
  23. 23.
    Li, H., Tang, W.K.S., Li, Z., Halang, W.A.: A chaotic peak current-mode boost converter for EMI reduction and ripple suppression. IEEE Trans. Circuits Syst. II Express Br. 55(8), 763 (2008)CrossRefGoogle Scholar
  24. 24.
    Giaouris, D., Banerjee, S., Stergiopoulos, F., Papadopoulou, S., Voutetakis, S., Zahawi, B., Pickert, V., Abusorrah, A., Al Hindawi, M., Al-Turki, Y.: Foldings and grazings of tori in current controlled interleaved boost converters. Int. J. Circuit Theory Appl. 42(10), 1080 (2014)CrossRefGoogle Scholar
  25. 25.
    Cheng, W., Song, J., Li, H., Guo, Y.: Time-varying compensation for peak current-controlled PFC boost converter. IEEE Trans. Power Electron. 30(6), 3431 (2015)CrossRefGoogle Scholar
  26. 26.
    El Aroudi, A., Benadero, L., Toribio, E., Olivar, G.: Hopf bifurcation and chaos from torus breakdown in a PWM voltage-controlled DC–DC boost converter. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 46(11), 1374 (1999)CrossRefGoogle Scholar
  27. 27.
    El Aroudi, A., Leyva, R.: Quasi-periodic route to chaos in a PWM voltage-controlled DC–DC boost converter. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 48(8), 967 (2001)CrossRefGoogle Scholar
  28. 28.
    Jiang, W., Chincholkar, S.H., Chan, C.Y.: Investigation of a voltage-mode controller for a DC–DC multilevel boost converter. IEEE Trans. Circuits Syst. II Express Br. 65(7), 908 (2018)CrossRefGoogle Scholar
  29. 29.
    di Bernardo, M., Garefalo, F., Glielmo, L., Vasca, F.: Switchings, bifurcations, and chaos in DC/DC converters. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 45(2), 133 (1998)CrossRefGoogle Scholar
  30. 30.
    Li, H., Li, Z., Zhang, B., Zheng, Q., Halang, W.: The stability of a chaotic PWM boost converter. Int. J. Circuit Theory Appl. 39(5), 451 (2011)CrossRefGoogle Scholar
  31. 31.
    Morcillo, J.D., Burbano, D., Angulo, F.: Adaptive ramp technique for controlling chaos and subharmonic oscillations in DC–DC power converters. IEEE Trans. Power Electron. 31(7), 5330 (2016)CrossRefGoogle Scholar
  32. 32.
    Zhang, H., Li, W., Ding, H., Luo, P., Wan, X., Hu, W.: Nonlinear model analysis of transient behavior in cascade DC–DC boost converters. Int. J. Bifurc. Chaos 27(09), 1750140 (2017)CrossRefzbMATHGoogle Scholar
  33. 33.
    Corradini, L., Orietti, E., Mattavelli, P., Saggini, S.: Digital hysteretic voltage-mode control for DC–DC converters based on asynchronous sampling. IEEE Trans. Power Electron. 24(1), 201 (2009)CrossRefGoogle Scholar
  34. 34.
    Gavagsaz-Ghoachani, R., Phattanasak, M., Zandi, M., Martin, J.P., Pierfederici, S., Nahid-Mobarakeh, B., Davat, B.: Estimation of the bifurcation point of a modulated-hysteresis current-controlled DC–DC boost converter: stability analysis and experimental verification. IET Power Electron. 8(11), 2195 (2015)CrossRefGoogle Scholar
  35. 35.
    Zamani, N., Ataei, M., Niroomand, M.: Analysis and control of chaotic behavior in boost converter by ramp compensation based on Lyapunov exponents assignment: theoretical and experimental investigation. Chaos Solitons Fractals 81, 20 (2015)CrossRefMathSciNetzbMATHGoogle Scholar
  36. 36.
    Hu, W., Zhang, B., Yang, R., Qiu, D.: Dynamic behaviours of constant on-time one-cycle controlled boost converter. IET Power Electron. 11(1), 160 (2017)CrossRefGoogle Scholar
  37. 37.
    Karamanakos, P., Geyer, T., Manias, S.: Direct voltage control of DC–DC boost converters using enumeration-based model predictive control. IEEE Trans. Power Electron. 29(2), 968 (2014)CrossRefGoogle Scholar
  38. 38.
    Wang, B., Kanamarlapudi, V.R.K., Xian, L., Peng, X., Tan, K.T., So, P.L.: Model predictive voltage control for single-inductor multiple-output DC–DC converter with reduced cross regulation. IEEE Trans. Ind. Electron. 63(7), 4187 (2016)CrossRefGoogle Scholar
  39. 39.
    Wei, Q., Wu, B., Xu, D., Zargari, N.R.: Model predictive control of capacitor voltage balancing for cascaded modular DC–DC converters. IEEE Trans. Power Electron. 32(1), 752 (2017)CrossRefGoogle Scholar
  40. 40.
    Gurbina, M., Ciresan, A., Lascu, D., Lica, S., Pop-Calimanu, I.M.: A new exact mathematical approach for studying bifurcation in DCM operated DC–DC switching converters. Energies 11(3), 663 (2018)CrossRefGoogle Scholar
  41. 41.
    Sriramalakshmi, P., Kavitha, A., Sanjeevikumar, P., Sutikno, T., Maroti, P.K., Ramachandaramurthy, V.K.: Control of chaos in a current mode controlled buck boost converter using weak periodic perturbation method. Int. J. Power Electron. Driv. Syst. 8(4), 1467 (2017)Google Scholar
  42. 42.
    Zhang, R., Wu, A., Zhang, S., Wang, Z., Cang, S.: Dynamical analysis and circuit implementation of a DC/DC single-stage boost converter with memristance load. Nonlinear Dyn. 93(3), 1741 (2018)CrossRefGoogle Scholar
  43. 43.
    Chua, L.: Memristor-the missing circuit element. IEEE Trans. Circuit Theory 18(5), 507 (1971)CrossRefGoogle Scholar
  44. 44.
    Strukov, D.B., Snider, G.S., Stewart, D.R., Williams, R.S.: The missing memristor found. Nature 453(7191), 80 (2008)CrossRefGoogle Scholar
  45. 45.
    Abuelma’atti, M.T., Khalifa, Z.J.: A new floating memristor emulator and its application in frequency-to-voltage conversion. Analog Integr. Circuits Signal Process. 86(1), 141 (2016)CrossRefGoogle Scholar
  46. 46.
    Iu, H.H.C., Yu, D., Fitch, A.L., Sreeram, V., Chen, H.: Controlling chaos in a memristor based circuit using a twin-T notch filter. IEEE Trans. Circuits Syst. I Regul. Pap. 58(6), 1337 (2011)CrossRefMathSciNetGoogle Scholar
  47. 47.
    Fouda, M.E., Radwan, A.G.: Memristor-based voltage-controlled relaxation oscillators. Int. J. Circuit Theory Appl. 42(10), 1092 (2014)CrossRefGoogle Scholar
  48. 48.
    Tse, C.K., Di Bernardo, M.: Complex behavior in switching power converters. Proc. IEEE 90(5), 768 (2002)CrossRefGoogle Scholar
  49. 49.
    Zhou, G., Xu, J., Jin, Y.: Elimination of subharmonic oscillation of digital-average-current-controlled switching DC–DC converters. IEEE Trans. Ind. Electron. 57(8), 2904 (2010)CrossRefGoogle Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Maintenance BranchState Grid Jibei Electric Power Company LimitedBeijingChina
  2. 2.School of Electrical and Information EngineeringTianjin UniversityTianjinChina
  3. 3.Department of Electrical and Mining EngineeringUniversity of South AfricaFloridaSouth Africa
  4. 4.Department of Product DesignTianjin University of Science and TechnologyTianjinChina

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