Numerical and experimental validation with bifurcation diagrams for a controlled DC–DC converter with quasi-sliding control
This paper presents a stability analysis of a buck converter using a Zero Average Dynamics (ZAD) controller and Fixed-Point Induction Control (FPIC) when the control parameter 𝑁, the reference voltage υref, and the source voltage 𝐸 are changed. The study was based on a previous analysis in which the control parameter was adjusted to 𝑁=1 and the parameter 𝐾𝑠 was changed during the simulation, finding the stability zone and regions with chaotic behavior. Thus, this new study presents the transient and steady-state behaviors and robustness of the buck converter when the control parameter 𝑁 changes. Moreover, numerical simulation results are compared with experimental observations. The results show that the system regulates the output voltage with low error when the voltage is changed in the source E. Besides, the voltage overshoot increases, and the settling time decreases when the control parameter 𝑁 is augmented and the control parameter 𝐾𝑠 is constant. Furthermore, the buck converter controlled by ZAD and FPIC techniques is effective in regulating the output voltage of the circuit even when there are two delay periods and voltage input disturbances.
 D. W. Hart, Electrónica de potencia. Madrid: Prentice Hall, 2001.
 N. Mohan, Advanced electric drives : analysis, control, and modeling using MATLAB/Simulink. Wiley, 2014.
 M. H. Rashid, Power electronics handbook : devices, circuits, and applications. Butterworth-Heinemann, 2011.
 A. V Peterchev and S. R. Sanders, “Quantization resolution and limit cycling in digitally controlled PWM converters,” IEEE Trans. Power Electron., vol. 18, no. 1, pp. 301–308, 2003.
 H. Peng, A. Prodic, E. Alarcon, and D. Maksimovic, “Modeling of Quantization Effects in Digitally Controlled DC–DC Converters,” IEEE Trans. Power Electron., vol. 22, no. 1, pp. 208–215, Jan. 2007.
 F. Angulo, F. Hoyos, and G. Olivar, “Experimental results on the quantization in the ADC device for a ZAD-strategy controlled DC-DC buck converter,” in 7th European Nonlinear Dynamics Conference, 2011, pp. 1–6.
 Haitao Hu, V. Yousefzadeh, and D. Maksimovic, “Nonuniform A/D Quantization for Improved Dynamic Responses of Digitally Controlled DC-DC Converters,” IEEE Trans. Power Electron., vol. 23, no. 4, pp. 1998–2005, Jul. 2008.
 F. E. Hoyos, D. Burbano, F. Angulo, G. Olivar, N. Toro, and J. A. Taborda, “Effects of Quantization, Delay and Internal Resistances in Digitally ZAD-Controlled Buck Converter,” Int. J. Bifurc. Chaos, vol. 22, no. 10, p. 9, Oct. 2012.
 M. Algreer, M. Armstrong, and D. Giaouris, “Adaptive PD+I Control of a Switch-Mode DC–DC Power Converter Using a Recursive FIR Predictor,” IEEE Trans. Ind. Appl., vol. 47, no. 5, pp. 2135–2144, Sep. 2011.
 M. Shirazi, R. Zane, and D. Maksimovic, “An Autotuning Digital Controller for DC–DC Power Converters Based on Online Frequency-Response Measurement,” IEEE Trans. Power Electron., vol. 24, no. 11, pp. 2578–2588, Nov. 2009.
 C. W. Fung, C. P. Liu, and M. H. Pong, “A Diagrammatic Approach to Search for Minimum Sampling Frequency and Quantization Resolution for Digital Control of Power Converters,” in 2007 IEEE Power Electronics Specialists Conference, 2007, pp. 826–832.
 J. A. Taborda, F. Angulo, and G. Olivar, “Estimation of parameters in Buck converter with Digital-PWM control based on ZAD strategy,” in 2011 IEEE Second Latin American Symposium on Circuits and Systems (LASCAS), 2011, pp. 1–4.
 F. E. Hoyos Velasco, N. T. García, and Y. A. Garcés Gómez, “Adaptive Control for Buck Power Converter Using Fixed Point Inducting Control and Zero Average Dynamics Strategies,” Int. J. Bifurc. Chaos, vol. 25, no. 4, p. 13, Apr. 2015.
 E. Fossas, R. Griño, and D. Biel, “Quasi-Sliding control based on pulse width modulation, zero averaged dynamics and the L2 norm,” in Advances in Variable Structure Systems, 2000, pp. 335–344.
 S. Ashita, G. Uma, and P. Deivasundari, “Chaotic dynamics of a zero average dynamics controlled DC–DC Ćuk converter,” IET Power Electron., vol. 7, no. 2, pp. 289–298, Feb. 2014.
 F. Angulo, G. Olivar, J. Taborda, and F. Hoyos, “Nonsmooth dynamics and FPIC chaos control in a DC-DC ZAD-strategy power converter,” in ENOC, 2008, pp. 1–6.
 F. Angulo, J. E. Burgos, and G. Olivar, “Chaos stabilization with TDAS and FPIC in a buck converter controlled by lateral PWM and ZAD,” in 2007 Mediterranean Conference on Control & Automation, 2007, pp. 1–6.
 J. A. Taborda, S. Santini, M. di Bernardo, and F. Angulo, “Active Chaos Control of a Cam-Follower Impacting System using FPIC Technique*,” IFAC Proc. Vol., vol. 42, no. 7, pp. 327–332, 2009.
 D. G. Montoya, C. A. Ramos-Paja, and R. Giral, “Improved Design of Sliding-Mode Controllers Based on the Requirements of MPPT Techniques,” IEEE Trans. Power Electron., vol. 31, no. 1, pp. 235–247, Jan. 2016.