Abstract and Applied Analysis

Robust Position Control of PMSM Using Fractional-Order Sliding Mode Controller

Jiacai Huang, Hongsheng Li, YangQuan Chen, and Qinghong Xu

Full-text: Open access

Abstract

A new robust fractional-order sliding mode controller (FOSMC) is proposed for the position control of a permanent magnet synchronous motor (PMSM). The sliding mode controller (SMC), which is insensitive to uncertainties and load disturbances, is studied widely in the application of PMSM drive. In the existing SMC method, the sliding surface is usually designed based on the integer-order integration or differentiation of the state variables, while in this proposed robust FOSMC algorithm, the sliding surface is designed based on the fractional-order calculus of the state variables. In fact, the conventional SMC method can be seen as a special case of the proposed FOSMC method. The performance and robustness of the proposed method are analyzed and tested for nonlinear load torque disturbances, and simulation results show that the proposed algorithm is more robust and effective than the conventional SMC method.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 512703, 33 pages.

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365168359

Digital Object Identifier
doi:10.1155/2012/512703

Mathematical Reviews number (MathSciNet)
MR2999890

Zentralblatt MATH identifier
1256.93053

Citation

Huang, Jiacai; Li, Hongsheng; Chen, YangQuan; Xu, Qinghong. Robust Position Control of PMSM Using Fractional-Order Sliding Mode Controller. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 512703, 33 pages. doi:10.1155/2012/512703. https://projecteuclid.org/euclid.aaa/1365168359


Export citation

References

  • \setlengthemsep0.7pt K. K. Shyu, C. K. Lai, Y. W. Tsai, and D. I. Yang, “A newly robust controller design for the position control of permanent-magnet synchronous motor,” IEEE Transactions on Industrial Electronics, vol. 49, no. 3, pp. 558–565, 2002.
  • F. J. Lin, “Real-time IP position controller design with torque feedforward control for PM synchronous motor,” IEEE Transactions on Industrial Electronics, vol. 44, no. 3, pp. 398–407, 1997.
  • F. J. Lin and Y. S. Lin, “A robust PM synchronous motor drive with adaptive uncertainty observer,” IEEE Transactions on Energy Conversion, vol. 14, no. 4, pp. 989–995, 1999.
  • C. K. Lai and K. K. Shyu, “A novel motor drive design for incremental motion system via sliding-mode control method,” IEEE Transactions on Industrial Electronics, vol. 52, no. 2, pp. 499–507, 2005.
  • R. Errouissi and M. Ouhrouche, “Nonlinear predictive controller for a permanent magnet synchronous motor drive,” Mathematics and Computers in Simulation, vol. 81, no. 2, pp. 394–406, 2010.
  • A. M. Harb, “Nonlinear chaos control in a permanent magnet reluctance machine,” Chaos, Solitons & Fractals, vol. 19, no. 5, pp. 1217–1224, 2004.
  • S. Zhao and K. K. Tan, “Adaptive feedforward compensation of force ripples in linear motors,” Control Engineering Practice, vol. 13, no. 9, pp. 1081–1092, 2005.
  • J. Zhou and Y. Wang, “Real-time nonlinear adaptive backstepping speed control for a PM synchronous motor,” Control Engineering Practice, vol. 13, no. 10, pp. 1259–1269, 2005.
  • T. L. Hsien, Y. Y. Sun, and M. C. Tsai, “${H}^{\infty }$ control for a sensor less permanent magnet synchronous drive,” IEE Proceedings–-Electric Power Applications, vol. 144, no. 3, pp. 173–181, 1997.
  • A. R. Ghafari-Kashani, J. Faiz, and M. J. Yazdanpanah, “Integration of non-linear ${H}^{\infty }$ and sliding mode control techniques for motion control of a permanent magnet synchronous motor,” IET Electric Power Applications, vol. 4, no. 4, pp. 267–280, 2010.
  • T. S. Lee, C. H. Lin, and F. J. Lin, “An adaptive ${H}_{\infty }$ controller design for permanent magnet synchronous motor drives,” Control Engineering Practice, vol. 13, no. 4, pp. 425–439, 2005.
  • A. Mezouar, M. K. Fellah, and S. Hadjeri, “Adaptive sliding mode observer for induction motor using two-time-scale approach,” Electric Power Systems Research, vol. 77, no. 5-6, pp. 604–618, 2007.
  • N. Inanc and V. Ozbulur, “Torque ripple minimization of a switched reluctance motor by using continuous sliding mode control technique,” Electric Power Systems Research, vol. 66, no. 3, pp. 241–251, 2003.
  • C. F. J. Kuo, C. H. Hsu, and C. C. Tsai, “Control of a permanent magnet synchronous motor with a fuzzy sliding-mode controller,” The International Journal of Advanced Manufacturing Technology, vol. 32, no. 7-8, pp. 757–763, 2007.
  • C. Elmas and O. Ustun, “A hybrid controller for the speed control of a permanent magnet synchronous motor drive,” Control Engineering Practice, vol. 16, no. 3, pp. 260–270, 2008.
  • F. F. M. El-Sousy, “Robust wavelet-neural-network sliding-mode control system for permanent magnet synchronous motor drive,” IET Electric Power Applications, vol. 5, no. 1, pp. 113–132, 2011.
  • Y. Feng, J. F. Zheng, X. H. Yu, and N. V. Truong, “Hybrid terminal sliding-mode observer design method for a permanent-magnet synchronous motor control system,” IEEE Transactions on Industrial Electronics, vol. 56, no. 9, pp. 3424–3431, 2009.
  • S. H. Chang, Y. H. Ting, P. Y. Chen, and S. W. Hung, “Robust current control-based sliding mode control with simple uncertainties estimation in permanent magnet synchronous motor drive systems,” IET Electric Power Applications, vol. 4, no. 6, pp. 441–450, 2010.
  • I. Podlubny, “Fractional-order systems and $P{I}^{\lambda }{D}^{\mu }$-controllers,” IEEE Transactions on Automatic Control, vol. 44, no. 1, pp. 208–214, 1999.
  • Y. Q. Chen, I. Petras, and D. Y. Xue, “Fractional order control–-a tutorial,” in Proceedings of the American Control Conference (ACC '09), pp. 1397–1411, June 2009.
  • A. Oustaloup, F. Levron, B. Mathieu, and F. M. Nanot, “Frequency-band complex noninteger differentiator: characterization and synthesis,” IEEE Transactions on Circuits and Systems I, vol. 47, no. 1, pp. 25–39, 2000.
  • K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, NY, USA, 1974.
  • I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, Calif, USA, 1999.
  • Y. Q. Chen, H. S. Ahn, and I. Podlubny, “Robust stability check of fractional order linear time invariant systems with interval uncertainties,” Signal Processing, vol. 86, no. 10, pp. 2611–2618, 2006.
  • M. Ö. Efe, “Fractional fuzzy adaptive sliding-mode control of a 2-DOF direct-drive robot arm,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 38, no. 6, pp. 1561–1570, 2008.
  • H. Delavari, A. N. Ranjbar, R. Ghaderi, and S. Momani, “Fractional order control of a coupled tank,” Nonlinear Dynamics, vol. 61, no. 3, pp. 383–397, 2010.
  • H. S. Li, Y. Luo, and Y. Q. Chen, “A fractional order proportional and derivative (FOPD) motion controller: tuning rule and experiments,” IEEE Transactions on Control Systems Technology, vol. 18, no. 2, pp. 516–520, 2010.
  • Y. Li, Y. Q. Chen, and I. Podlubny, “Stability of fractional-order nonlinear dynamic systems: lyapunov direct method and generalized Mittag-Leffler stability,” Computers & Mathematics with Applications, vol. 59, no. 5, pp. 1810–1821, 2010.
  • D. Baleanu, H. Mohammadi, and S. Rezapour, “Positive solutions of an initial value problem for nonlinear fractional differential equations,” Abstract and Applied Analysis, vol. 2012, Article ID 837437, 7 pages, 2012.
  • D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, World Scientific, New York, NY, USA, 2012.
  • D. Bleanu, O. G. Mustafa, and R. P. Agarwal, “Asymptotically linear solutions for some linear fractional differential equations,” Abstract and Applied Analysis, vol. 2010, Article ID 865139, 8 pages, 2010.
  • F. Jarad, T. Abdeljawad, and D. Baleanu, “On Riesz-Caputo formulation for sequential fractional variational principles,” Abstract and Applied Analysis, vol. 2012, Article ID 890396, 15 pages, 2012.
  • M. O. Efe, “A fractional order adaptation law for integer order sliding mode control of a 2DOF robot,” in Proceedings of the International Workshops on New Trends in Science and Technology (NTST 08) and the Workshop Fractional Differentiation and Its Applications (FDA 09), Ankara, Turkey, November 2008.
  • S. H. Hosseinnia, R. Ghaderi, N. A. Ranjbar, M. Mahmoudian, and S. Momani, “Sliding mode synchronization of an uncertain fractional order chaotic system,” Computers & Mathematics with Applications, vol. 59, no. 5, pp. 1637–1643, 2010.
  • B. T. Zhang and Y. Pi, “Robust fractional order proportion-plus-differential controller based on fuzzy inference for permanent magnet synchronous motor,” IET Control Theory & Applications, vol. 6, no. 6, pp. 829–837, 2012.
  • Y. Luo, Y. Q. Chen, H. S. Ahn, and Y. Pi, “Fractional order robust control for cogging effect compensation in PMSM position servo systems: stability analysis and experiments,” Control Engineering Practice, vol. 18, no. 9, pp. 1022–1036, 2010.
  • Y. Q. Chen, “Impulse response invariant discretization of fractional order integrators/differentiators is to compute a discrete-time finite dimensional (z) transfer function to approximate s$^{r}$ with r a real number,” Category: Filter Design and Analysis, MATLAB Central, 2008, http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do objectId=21342 objectType=FILE.