Speed Control of a Permanent Magnet Synchronous Machine (PMSM) Fed by an Inverter Voltage Fuzzy Control Approach
This paper deals with the synthesis of fuzzy controller
applied to a permanent magnet synchronous machine (PMSM) with a
guaranteed H∞ performance. To design this fuzzy controller,
nonlinear model of the PMSM is approximated by Takagi-Sugeno
fuzzy model (T-S fuzzy model), then the so-called parallel
distributed compensation (PDC) is employed. Next, we derive the
property of the H∞ norm. The latter is cast in terms of linear matrix
inequalities (LMI-s) while minimizing the H∞ norm of the transfer
function between the disturbance and the error ( ) ev T . The
experimental and simulations results were conducted on a permanent
magnet synchronous machine to illustrate the effects of the fuzzy
modelling and the controller design via the PDC.
[1] D. Driankov, H. Hellendoon and M. Reinfranck, "An introduction to
fuzzy control", Springer, Berlin Heidelberg,1993.
[2] T. M. Guerra and S. Ouattara,"Overview of the evolution of concepts
and applications of fuzzy control", first congress AFCET, pp 1-10, 1993.
[3] C. C. Lee, "Fuzzy logic in control systems", Fuzzy logic controller. part I
IEEE Transactions on systems. Man and Cybernetics, 20, pp 419-435,
1990.
[4] C. Melin and B. Vidolov, "Stabilisation of linear systems by fuzzy
controllers", part I. RAIRO-APII.JESA, volume 30, Issue 5 :pp 675-705,
French 1996.
[5] H. B. Verbruggen, H. J. Zimmermann, and R. Babuska, "Fuzzy
algorithm for control", Chapiter I. International series in Intelligent
Technologies., KAP, 1999.
[6] K. Tanaka, T.Ikeda and H. O. Wang, "fuzzy regulators and fuzzy
observers: Relaxed stability conditions and LMI-based design", IEEE
Transactions on fuzzy systems, Volume 6, Issue 2, pp. 1-16, 1998.
[7] Li C. Raymond, S. Boverie and A. Titli, "Fuzzy multivariable control
design from the fuzzy system model", proceeding Sixth IFSA, World
Congress, Sao Paulo, Brasil, 1995.
[8] X. J. Ma, Z. Q. Sun and Y. Y. He, "Analysis and design of fuzzy
controller and fuzzy observer", IEEE Transactions on fuzzy systems,
volume 6, Issue 1, pp 41-50, 1998.
[9] Y. Morere, "Implementation of control laws for T-S fuzzy models",
Doctoral thesis, University of Valencia and Hainant Combresis, 1999.
[10] M. Chaabane and M. Souissi, "Robust stability and stabilization of
systems: Application to an agricultural greenhouse", Fifth automatic
Tunisian seminar STA-2004, pp. 26-52, Hammamet, Tunisia 2004.
[11] M. Souissi, "Modeling and Control of an agricultural greenhouse",
Thesis statement in physical sciences, Faculty of science of Tunis FST,
2002.
[12] B. K. Bose, "Power electronics and AC driv". New york, Prince Hall,
first Edition, chapiter 2, pp.95, 1986.
[13] S. Hassaine, "Application of new techniques for controlling the
synchronous machine permanent magnet, Ph.D. USTO University. Oran,
Algeria, 2008.
[14] G. Feng, S. G. Cao, N. W. Rees, M. Cheng and J. Ma , H∞ control of
continuous time fuzzy dynamic systems, IEEE, Fuzzy-97, Barcelona.
[15] S. G. Cao, N. W. Rees and G. Feng, Further results about quadratic
stability of continuous time fuzzy control systems, Int. J.Systems
Science, vol 28, N┬░4 pp 397-404, 1997.
[16] S. G. Cao, N. W. Rees and G. Feng, "Quadratic stability analysis and
design of continuous time fuzzy control systems", Int. J.Systems
Science, vol 27, pp 193-203, 1996.
[17] Z. X. Hang, G. Feng and T. H. Lee, "Stability analysis and design of
fuzzy control systems using LMI techniques", Proc.Control 97, Sydney,
Australia.
[18] S. G. Cao, N. W. Rees, G. Feng, H-infinity control of nonlinear
continuous time systems based on dynamical fuzzy models, Int.
J.Systems Sci.27 pp 821-830, 1996.
[19] B. S. Chen, C. S. Tseng, H. J. Uang, "Robustness design of nonlinear
dynamic systems via fuzzy control", IEEE Trans. Fuzzy Systems, vol 7,
pp 571-585, 1999.
[20] B. S. Chen, C. S. Tseng, H. J. Uang, "Mixed H2/H∞ Fuzzy output
feedback control design for nonlinear dynamic systems: An LMI
approach", IEEE Trans .Fuzzy Systems vol 8, pp 249-265, 2000.
[21] T. M. Guerra, L. Vermeiren, "Control law for Takagi-Sugeno fuzzy
models", Fuzzy Sets and Systems Vol. 120, pp 95-108, 2001.
[22] X.Liu, Q.Zhang, New approach to controller designs based on fuzzy
observers for T-S systems via LMI. Automatica vol 39, pp 1571-1582,
2003.
[23] K. S., Narendra and A. M. Annaswanny, "Stable Adaptive Systems".
Englewood Cliffs, NJ: Prentice-Hall 1989.
[24] K. Tanaka, T. Ikeda and H. O. Wang, "Fuzzy regulators and fuzzy
observers: Relaxed stability conditions and LMI-based design", .IEEE
Transaction on Fuzzy Systems, Vol. 6, N┬░1, pp 1-16, 1998.
[25] G. O. Young, "Synthetic structure of industrial plastics (Book style with
paper title and editor)," in Plastics, 2nd ed. vol. 3, J. Peters, Ed. New
York: McGraw-Hill, 1964, pp. 15-64.
[1] D. Driankov, H. Hellendoon and M. Reinfranck, "An introduction to
fuzzy control", Springer, Berlin Heidelberg,1993.
[2] T. M. Guerra and S. Ouattara,"Overview of the evolution of concepts
and applications of fuzzy control", first congress AFCET, pp 1-10, 1993.
[3] C. C. Lee, "Fuzzy logic in control systems", Fuzzy logic controller. part I
IEEE Transactions on systems. Man and Cybernetics, 20, pp 419-435,
1990.
[4] C. Melin and B. Vidolov, "Stabilisation of linear systems by fuzzy
controllers", part I. RAIRO-APII.JESA, volume 30, Issue 5 :pp 675-705,
French 1996.
[5] H. B. Verbruggen, H. J. Zimmermann, and R. Babuska, "Fuzzy
algorithm for control", Chapiter I. International series in Intelligent
Technologies., KAP, 1999.
[6] K. Tanaka, T.Ikeda and H. O. Wang, "fuzzy regulators and fuzzy
observers: Relaxed stability conditions and LMI-based design", IEEE
Transactions on fuzzy systems, Volume 6, Issue 2, pp. 1-16, 1998.
[7] Li C. Raymond, S. Boverie and A. Titli, "Fuzzy multivariable control
design from the fuzzy system model", proceeding Sixth IFSA, World
Congress, Sao Paulo, Brasil, 1995.
[8] X. J. Ma, Z. Q. Sun and Y. Y. He, "Analysis and design of fuzzy
controller and fuzzy observer", IEEE Transactions on fuzzy systems,
volume 6, Issue 1, pp 41-50, 1998.
[9] Y. Morere, "Implementation of control laws for T-S fuzzy models",
Doctoral thesis, University of Valencia and Hainant Combresis, 1999.
[10] M. Chaabane and M. Souissi, "Robust stability and stabilization of
systems: Application to an agricultural greenhouse", Fifth automatic
Tunisian seminar STA-2004, pp. 26-52, Hammamet, Tunisia 2004.
[11] M. Souissi, "Modeling and Control of an agricultural greenhouse",
Thesis statement in physical sciences, Faculty of science of Tunis FST,
2002.
[12] B. K. Bose, "Power electronics and AC driv". New york, Prince Hall,
first Edition, chapiter 2, pp.95, 1986.
[13] S. Hassaine, "Application of new techniques for controlling the
synchronous machine permanent magnet, Ph.D. USTO University. Oran,
Algeria, 2008.
[14] G. Feng, S. G. Cao, N. W. Rees, M. Cheng and J. Ma , H∞ control of
continuous time fuzzy dynamic systems, IEEE, Fuzzy-97, Barcelona.
[15] S. G. Cao, N. W. Rees and G. Feng, Further results about quadratic
stability of continuous time fuzzy control systems, Int. J.Systems
Science, vol 28, N┬░4 pp 397-404, 1997.
[16] S. G. Cao, N. W. Rees and G. Feng, "Quadratic stability analysis and
design of continuous time fuzzy control systems", Int. J.Systems
Science, vol 27, pp 193-203, 1996.
[17] Z. X. Hang, G. Feng and T. H. Lee, "Stability analysis and design of
fuzzy control systems using LMI techniques", Proc.Control 97, Sydney,
Australia.
[18] S. G. Cao, N. W. Rees, G. Feng, H-infinity control of nonlinear
continuous time systems based on dynamical fuzzy models, Int.
J.Systems Sci.27 pp 821-830, 1996.
[19] B. S. Chen, C. S. Tseng, H. J. Uang, "Robustness design of nonlinear
dynamic systems via fuzzy control", IEEE Trans. Fuzzy Systems, vol 7,
pp 571-585, 1999.
[20] B. S. Chen, C. S. Tseng, H. J. Uang, "Mixed H2/H∞ Fuzzy output
feedback control design for nonlinear dynamic systems: An LMI
approach", IEEE Trans .Fuzzy Systems vol 8, pp 249-265, 2000.
[21] T. M. Guerra, L. Vermeiren, "Control law for Takagi-Sugeno fuzzy
models", Fuzzy Sets and Systems Vol. 120, pp 95-108, 2001.
[22] X.Liu, Q.Zhang, New approach to controller designs based on fuzzy
observers for T-S systems via LMI. Automatica vol 39, pp 1571-1582,
2003.
[23] K. S., Narendra and A. M. Annaswanny, "Stable Adaptive Systems".
Englewood Cliffs, NJ: Prentice-Hall 1989.
[24] K. Tanaka, T. Ikeda and H. O. Wang, "Fuzzy regulators and fuzzy
observers: Relaxed stability conditions and LMI-based design", .IEEE
Transaction on Fuzzy Systems, Vol. 6, N┬░1, pp 1-16, 1998.
[25] G. O. Young, "Synthetic structure of industrial plastics (Book style with
paper title and editor)," in Plastics, 2nd ed. vol. 3, J. Peters, Ed. New
York: McGraw-Hill, 1964, pp. 15-64.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:54381", author = "Jamel Khedri and Mohamed Chaabane and Mansour Souissi and Driss Mehdi", title = "Speed Control of a Permanent Magnet Synchronous Machine (PMSM) Fed by an Inverter Voltage Fuzzy Control Approach", abstract = "This paper deals with the synthesis of fuzzy controller
applied to a permanent magnet synchronous machine (PMSM) with a
guaranteed H∞ performance. To design this fuzzy controller,
nonlinear model of the PMSM is approximated by Takagi-Sugeno
fuzzy model (T-S fuzzy model), then the so-called parallel
distributed compensation (PDC) is employed. Next, we derive the
property of the H∞ norm. The latter is cast in terms of linear matrix
inequalities (LMI-s) while minimizing the H∞ norm of the transfer
function between the disturbance and the error ( ) ev T . The
experimental and simulations results were conducted on a permanent
magnet synchronous machine to illustrate the effects of the fuzzy
modelling and the controller design via the PDC.", keywords = "Feedback controller, Takagi-Sugeno fuzzy model,Linear Matrix Inequality (LMI), PMSM, H∞ performance.", volume = "4", number = "8", pages = "633-7", }
