Stabilizing Controller Design for Quasi-Resonant Converters Described by a Class of Piecewise Linear Models

This paper presents a stabilizing controller design method for quasi resonant (QR) converters described by a class of piecewise linear (PWL) models. The generalized state-space averaging technique (GSSA) is applied for the modeling and analysis of the half-wave zero current switching quasi-resonant (HW-ZCS-QR) buck converter. The nonlinear GSSA model of the converter is reconstructed using a piecewise linearizing technique. Subsequently, the piecewise linear models are combined together, to form a unified model, using a fuzzy modeling approach. The stability of the applied method has been investigated using Lyapunov method. Finally, a linear H∞ controller synthesis method is applied to the converter described by the proposed model. The experimental results on the converter are presented to verify the performance of the applied method for modeling the dynamics of the converter and designing the appropriate controller.

[1]  Yasunori Mitani,et al.  Robust control design for a ZCS converter , 2002, IEEE 2002 28th Annual Conference of the Industrial Electronics Society. IECON 02.

[2]  Zhendong Sun,et al.  Switched Stabilization of Higher-order Switched Linear Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[3]  F. Tahami,et al.  Piecewise Affine Large Signal Modeling of PFC Rectifiers , 2007, 2007 IEEE International Symposium on Industrial Electronics.

[4]  Ibrahim N. Hajj,et al.  Steady-state analysis of piecewise-linear dynamic systems , 1981 .

[5]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[6]  Hirohito Funato,et al.  Stability analysis of nonlinear power electronic systems utilizing periodicity and introducing auxiliary state vector , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[7]  István Nagy,et al.  Stability analysis of a feedback-controlled resonant DC-DC converter , 2003, IEEE Trans. Ind. Electron..

[8]  Francisco D. Freijedo,et al.  Analysis and Design of Resonant Current Controllers for Voltage-Source Converters by Means of Nyquist Diagrams and Sensitivity Function , 2011, IEEE Transactions on Industrial Electronics.

[9]  Biswarup Basak,et al.  Exploration of Bifurcation and Chaos in Buck Converter Supplied From a Rectifier , 2010, IEEE Transactions on Power Electronics.

[10]  Ashwin M. Khambadkone,et al.  Quasi-resonant-converters-based high-efficiency spindle motor drives for magnetic data storage , 2004, IEEE Transactions on Industrial Electronics.

[11]  Reza Ghazi,et al.  Robust control of DC/DC PWM converters: a comparison of H/sub /spl infin//, /spl mu/, and fuzzy logic based approaches , 2003, Proceedings of 2003 IEEE Conference on Control Applications, 2003. CCA 2003..

[12]  Abraham Pressman,et al.  Switching Power Supply Design , 1997 .

[13]  F. Tahami,et al.  On Piecewise Affined Large-Signal Modeling of PWM converters , 2006, 2006 IEEE International Conference on Industrial Technology.

[14]  Steven Frank Glover,et al.  Modeling and stability analysis of power electronics based systems , 2003 .

[15]  M. Morari,et al.  Stability and stabilization of piecewise affine and hybrid systems: an LMI approach , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[16]  D. C. Hamill,et al.  Instability, subharmonics and chaos in power electronic systems , 1989 .

[17]  Marcelo C. M. Teixeira,et al.  Stabilizing controller design for uncertain nonlinear systems using fuzzy models , 1999, IEEE Trans. Fuzzy Syst..

[18]  M. Çamlibel,et al.  A New Perspective for Modeling Power Electronics Converters: Complementarity Framework , 2009, IEEE Transactions on Power Electronics.

[19]  Sergey Edward Lyshevski.  Resonant converters: nonlinear analysis and control , 2000, IEEE Trans. Ind. Electron..

[20]  Stephen P. Boyd,et al.  Piecewise-affine state feedback for piecewise-affine slab systems using convex optimization , 2005, Syst. Control. Lett..

[21]  A. L. Baranovski,et al.  Bifurcation and statistical analysis of DC-DC converters , 2003 .

[22]  K. Glover.  All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds† , 1984 .

[23]  Jun-ichi Imura,et al.  Well-posedness analysis of switch-driven piecewise affine systems , 2003, IEEE Trans. Autom. Control..

[24]  M. Morari,et al.  Constrained Optimal Control of the Step-Down DC–DC Converter , 2008, IEEE Transactions on Power Electronics.

[25]  Jonathan P. How,et al.  Synthesis of piecewise-affine controllers for stabilization of nonlinear systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[26]  C. Q. Lee,et al.  A unified averaging technique for the modeling of quasi-resonant converters , 1998 .

[27]  V. Vorperian,et al.  Quasi-square-wave converters: topologies and analysis , 1988 .

[28]  F. Tahami,et al.  A fuzzy modeling and control method for PWM converters , 2010, Proceedings of 14th International Power Electronics and Motion Control Conference EPE-PEMC 2010.