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Piecewise Affine Control Design for Power Factor Correction Rectifiers

  • Received : 2010.10.09
  • Published : 2011.05.20

Abstract

Single-phase power factor correction (PFC) converter circuits are non-linear systems due to the contribution of their multiplier. This non-linearity causes difficulties in analysis and design. Models that reduce the system to a linear system involve considerable approximation, and produce results that are susceptible to instability problems. In this paper a piecewise affine (PWA) system is introduced for describing the nonlinear averaged model. Then robust output feedback controllers are established in terms of the linear matrix inequality (LMI). Simulation and experiments results show the effectiveness of the proposed control method.

Keywords

References

  1. R. W. Erickson and D. Maksimovic, Fundamentals of Power Electronics, 2nd ed., Kluwer Academic Publishers, 2000.
  2. V. Vorperian, "Simplified analysis of PWM converters using the model of the PWM switch: Part I and II," IEEE Trans. Aerosp. Electron. Syst., Vol. AES-26, pp. 409-505, May 1990.
  3. A. Fernandez, J. Sebastian, P. Villegas, M. M. Hernando, and J. Garcia, "Dynamic limits of a power factor pre-regulator," in Proc. IEEE PESC'03, pp. 1697-1602, 2003.
  4. M. Alfayyoumi, A. H. Nayfeh, and D. Boroyevich, "Input filter interactions in DC-DC switching regulators," in Records of PESC'99, pp. 926-932, 1999.
  5. M. Chen, A. Mathew, and J. Sun, "Nonlinear current control of single-phase PFC converters," IEEE Trans. Power Electron., Vol. 22, No. 6, pp. 2187-2194, Nov. 2007. https://doi.org/10.1109/TPEL.2007.909410
  6. V. M. Rao, A. K. Jain, K. K. Reddy, and A. Behal, "Nonlinear control of a single phase unity power factor rectifier: design, analysis, and experimental results," IEEE Trans. Contr. Syst. Technol., Vol. 16, No. 6, pp.1301-1307, Nov. 2008. https://doi.org/10.1109/TCST.2008.917877
  7. F.-Z. Chen and D. Maksimovic, "Digital control for improved efficiency and reduced harmonic distortion over wide load range in boost PFC rectifiers," Applied Power Electronics Conference and Exposition, 2009.
  8. A. Prodic, D. Maksimovic, and R. W. Erickson, "Dead-zone digital controllers for improved dynamic response of low harmonic rectifiers," IEEE Trans. Power Electron., Vol. 21, No. 1, pp. 173-181, Jan. 2006. https://doi.org/10.1109/TPEL.2005.861157
  9. A. Hassibi, S. P. Boyd, and J. P. How, "A class of lyapunov functionals for analyzing hybrid dynamical systems," in Proc. American Control Conference, Jun. 1999.
  10. F. Tahami and B. Molaei, "Piecewise affined system modeling and control of PWM converters," Journal of Circuits, Systems and Computers (JCSC), Vol. 16, No. 1, pp.113-128, Feb. 2007. https://doi.org/10.1142/S0218126607003526
  11. L. Rodrigues and J. P. How. "Automated control design for a piecewise affine approximation of a class of nonlinear systems," in Proc. 2001 America Control Conference, 2001.
  12. J. C. Crebier, B. Revol, and J. Paul Ferrieux, "Boost-chopper-derived PFC rectifiers: Interest and reality," IEEE trans. Ind. Electron., Vol. 52, No. 1, pp. 36-45, Feb. 2005. https://doi.org/10.1109/TIE.2004.841143
  13. A. Rantzer and M. Johansson, "Piecewise linear quadratic optimal control," IEEE Trans. Autom. Control, Vol. 45, No. 4, pp. 629-237, Apr. 2000. https://doi.org/10.1109/9.847100
  14. F. Tahami and H. M. Ahmadian, "Piecewise affine large signal modeling of PFC rectifiers," in Proc. 2007 IEEE International Symposium on Industrial Electronics (ISIE 2007), Jun. 2007.
  15. S. P. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnam, Linear Matrix Inequalities in System and Control Theory, Philadelphia, StatePA: SIAM, 1994.
  16. C. Scherer, P. Gahinet, and M. Chilali, "Multiobjective output-feedback control via LMI optimization," IEEE Trans. on Autom. Control, Vol. 42, No. 7, pp 896-911, Jul. 1997. https://doi.org/10.1109/9.599969
  17. P. Gahinet, A. Nemirovski, A. Laub, and M. Chilali, The LMI Control Toolbox, The Mathworks Inc., 1995.
  18. R Ghosh and G. Narayanan, "A simple method to improve the dynamic response of single-phase PWM rectifiers," IEEE Trans. Ind. Electron., Vol. 55, No. 10, pp. 3627-3634, Oct. 2008. https://doi.org/10.1109/TIE.2008.928113
  19. L. Rodrigues, A. Hassibi, and J. P. How, "Output feedback controller synthesis for piecewise-affine systems with multiple equilibria," in Proc. American Control Conference, 2000.
  20. C. H. Houpis and G. B. Lamont, Digital Control systems, New York: McGraw-Hill, 1985.

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