Chaos suppression for a Buck converter with the memristive load


The memristor is a nonlinear device with a particular memory function and is widely used in various circuit researches. This work studies the peak current mode controlled (PCMC) buck converter with the memristive load at the continuous current mode (CCM). Firstly, a state equation for a buck converter with the memristive load is derived and a generic voltage-controlled memristor simulator is constructed by using a nonlinear function model; Secondly, facing the system chaos caused by changing bifurcation parameters, we introduce ramp compensation to stabilize the system at period-1. The chaos is effectively suppressed, this provides a guide for parameters choosing in buck converters with nonlinear loads in practical applications. The simulation is implemented by using MATLAB and PSIM.

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  1. 1.

    Chen, J., & Kang, Y. (2011). Power electronic-power electronic transform and control technique. Beijing: High Education Press.

    Google Scholar 

  2. 2.

    Brown, M. (1990). Practical switching power supply design. Cambridge: Academic Press.

    Google Scholar 

  3. 3.

    Ma, X. K., Li, M., Dai, D., Zhang, H., & Zou, J. L. (2006). Reviews of research on complex behavior of power electronic circuits and systems. Transactions of China Electrotechnical Society, 021(012), 1–11.

    Google Scholar 

  4. 4.

    Brockett R.W., Wood J.R. (1984). Understanding power converterchaotic behavior mechanism in protective and abnormal modes. In Proceedings of 11th Annual International Power Electronics Conference, 14–15.

  5. 5.

    Tse, C. K., & Di Bernardo, M. (2002). Complex behavior in switching power converters. Proceedings of the IEEE, 90(5), 768–781.

    Article  Google Scholar 

  6. 6.

    Hu, W., Zhang, F. Y., Long, X. L., Chen, X. B., & Deng, W. T. (2014). Stability analysis and control of nonlinear behavior in V2 switching buck converter. Journal of Power Electronics, 14(6), 1208–1216.

    Article  Google Scholar 

  7. 7.

    Demirbas, S., Fidanboy, H., & Kurt, E. (2016). Exploration of the chaotic behaviour in a buck–boost converter depending on the converter and load elements. Journal of Electronic Materials, 45(8), 3889–3899.

    Article  Google Scholar 

  8. 8.

    Zhioua, M., El Aroudi, A., Belghith, S., Bosque-Moncusí, J. M., Giral, R., Al Hosani, K., & Al-Numay, M. (2016). Modeling, dynamics, bifurcation behavior and stability analysis of a DC–DC boost converter in photovoltaic systems. International Journal of Bifurcation and Chaos, 26(10), 1650166.

    MathSciNet  Article  Google Scholar 

  9. 9.

    Tosaka, S., Yamanaka, T., Katayama, N., Hayase, M., Dowaki, K., & Kogoshi, S. (2014). Developing a new topology for the DC-DC converter used in fuel cell-electric double layer capacitor hybrid power source system for mobile devices. International Power Electronics Conference, 2014, 1207–1213.

    Google Scholar 

  10. 10.

    Zhou, G. H., Xu, J. P., Bao, B. C., Wang, J. P., & Jin, Y. Y. (2011). Complex subharmonic oscillation phenomenon of peak current controlled buck converter with current source load. Acta Physica Sinica, 01, 51–58.

    Google Scholar 

  11. 11.

    Strukov, D. B., Snider, G. S., Stewart, D. R., & Williams, R. S. (2008). The missing memristor found. Nature, 453(7191), 80–83.

    Article  Google Scholar 

  12. 12.

    Wang, R., Yang, J., Mao, J., Wang, Z., Wu, S., Zhou, M., et al. (2020). Recent advances of volatile memristors: devices, mechanisms, and applications. Advanced Intelligent Systems, 2(9), 2000055.

    Article  Google Scholar 

  13. 13.

    Wang, X. P., Shen, Y., Wu, J. S., & Sun, J. W. (2013). Review on memristor and its applications. Acta Automatica Sinica, 39(008), 1170–1184.

    MathSciNet  Article  Google Scholar 

  14. 14.

    Chua, L. (2011). Resistance switching memories are memristors. Applied Physics A, 102, 765–783.

    Article  Google Scholar 

  15. 15.

    Valov, I., Linn, E., Tappertzhofen, S., Schmelzer, S., van den Hurk, J., Lentz, F., & Waser, R. (2013). Nanobatteries in redox-based resistive switches require extension of memristor theory. Nature Communications, 4(1), 1771.

    Article  Google Scholar 

  16. 16.

    Cha, J. H., Yang, S. Y., Oh, J., et al. (2020). Conductive- bridging random-access memories for emerging neuromorphic computing. Nanoscale, 12(27), 14339–14368.

    Article  Google Scholar 

  17. 17.

    Yao, P., Wu, H. Q., Gao, B., et al. (2020). Fully hardware- implemented memristor convolutional neural network. Nature, 577, 641–646.

    Article  Google Scholar 

  18. 18.

    Zhang, R. Y., Wu, A. G., Zhang, S. R., et al. (2018). Dynamical analysis and circuit implementation of a DC/DC single-stage boost converter with memristance load. Nonlinear Dynamics, 93, 1741–1755.

    Article  Google Scholar 

  19. 19.

    Bao, B., Zhang, X., Bao, H., Wu, P., Wu, Z., & Chen, M. (2019). Dynamical effects of memristive load on peak current mode buck-boost switching converter. Chaos, Solitons & Fractals, 122, 69–79.

    MathSciNet  Article  Google Scholar 

  20. 20.

    Liu, W., Wang, F. Q., & Ma, X. K. (2016). Slow-scale instability in voltage-mode controlled H-Bridge inverter with memristive Load. International Journal of Bifurcation and Chaos, 26(12), 1650200–1651193.

    MathSciNet  Article  Google Scholar 

  21. 21.

    Chua, L. (1971). Memristor-The missing circuit element. IEEE Transactions on Circuit Theory, 18(5), 507–519.

    Article  Google Scholar 

  22. 22.

    Adhikari, S. P., Sah, M., Kim, H., & Chua, L. (2013). Three fingerprints of memristor. IEEE Transactions on Circuits and Systems I, 60(11), 3008–3021.

    Article  Google Scholar 

  23. 23.

    Wang, D., Zhang, S., Gan, M., & Qiu, J. (2020). A novel EM identification method for Hammerstein systems with missing output data. IEEE Transactions on Industrial Informatics, 16, 2500–2508.

    Article  Google Scholar 

  24. 24.

    Wang, D., Li, L., Ji, Y., & Yan, Y. (2018). Model recovery for Hammerstein systems using the auxiliary model based orthogonal matching pursuit method. Applied Mathematical Modelling, 54, 537–550.

    MathSciNet  Article  Google Scholar 

  25. 25.

    Wang, D., Yan, Y., Liu, Y., & Ding, J. (2019). Model recovery for Hammerstein systems using the hierarchical orthogonal matching pursuit method. Journal of Computational and Applied Mathematics, 345, 135–145.

    MathSciNet  Article  Google Scholar 

  26. 26.

    Pal, I., Kumar, V., Aishwarya, N., Nayak, A., & Islam, A. (2020). A VDTA-based robust electronically tunable memristor emulator circuit. Analog Integrated Circuits and Signal Processing, 104, 47–59.

    Article  Google Scholar 

  27. 27.

    Muthuswamy, B. (2010). Implementing memristor based chaotic circuits. International Journal of Bifurcation and Chaos, 20(05), 1335–1350.

    Article  Google Scholar 

  28. 28.

    Chua, L. (2015). Everything You wish to know about memristors but are afraid to ask. Radio Engineering, 24(2), 319–368.

    Google Scholar 

  29. 29.

    Chang, C. Y., Zhao, X., Yang, F., & Wu, C. E. (2016). Bifurcation and chaos in high-frequency peak current mode Buck converter. Chinese Physics B, 25(7), 070504.

    Article  Google Scholar 

  30. 30.

    Zamani, N., Ataei, M., & Niroomand, M. (2015). 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, 20–29.

    MathSciNet  Article  Google Scholar 

  31. 31.

    He, L., Fang, Y., Li, J., & Xing, Y. (2006). Over current protection for peak current controlled DC-DC converter. Transactions of China Electrotechnical Society, 21(010), 86–89.

    Google Scholar 

  32. 32.

    Zhou, Y., Wang, Y., Wang, K., Kang, L., Peng, F., Wang, L., & Pang, J. (2020). Hybrid genetic algorithm method for efficient and robust evaluation of remaining useful life of supercapacitors. Applied Energy, 260, 114169.

    Article  Google Scholar 

  33. 33.

    Zhou, Y., Huang, Y., Pang, J., & Wang, K. (2019). Remaining useful life prediction for supercapacitor based on long short-term memory neural network. Journal of Power Sources, 440, 227149.

    Article  Google Scholar 

  34. 34.

    Jiao, M., Wang, D. Q., & Qiu, J. L. (2020). A GRU-RNN based momentum optimized algorithm for SOC estimation. Journal of Power Sources, 459, 228051.

    Article  Google Scholar 

  35. 35.

    Li, W. Q., Yang, Y., Wang, D. Q., & Yin, S. Q. (2020). The multi- innovation extended Kalman filter algorithm for battery SOC estimation. Ionics.

    Article  Google Scholar 

  36. 36.

    Wang, N., Zhang, G. S., Kuznetsov, N. V., & Bao, H. (2021). Hidden attractors and multistability in a modified Chua’s circuit. Communications in Nonlinear Science and Numerical Simulation, 92, 105494.

    MathSciNet  Article  Google Scholar 

  37. 37.

    Wang, N., Zhang, G. S., & Bao, H. (2020). A Simple Autonomous Chaotic Circuit with Dead-Zone Nonlinearity. IEEE Transactions on Circuits and Systems II: Express Briefs.

    Book  Google Scholar 

  38. 38.

    Wang, N., Zhang, G. S., & Bao, H. (2020). Infinitely many coexisting conservative flows in a 4D conservative system inspired by LC circuit. Nonlinear Dynamics, 99, 3197–3216.

    Article  Google Scholar 

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This work was supported by the National Natural Science Foundation of China (No. 61873138), and in part by the Taishan Scholar Project Fund of Shandong Province of China.

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Correspondence to Qiuhua Fan or Dongqing Wang.

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Zhu, B., Fan, Q., Li, G. et al. Chaos suppression for a Buck converter with the memristive load. Analog Integr Circ Sig Process 107, 309–318 (2021).

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  • Buck converter
  • Memristive load
  • Ramp compensation
  • Chaos