International Journal of Computer Science & Network Security

International Journal of Computer Science & Network Security (국제컴퓨터통신보호논문지학회)
권호 표지
DOI QR코드

DOI QR Code

Internal Model Control for Unstable Overactuated Systems with Time Delays

  • Mahmoud, Ines (University of Tunis El Manar Tunis, Automatic Research Laboratory, LA.R. A, National Engineering School of Tunis, ENIT) ;
  • Saidi, Imen (University of Tunis El Manar Tunis, Automatic Research Laboratory, LA.R. A, National Engineering School of Tunis, ENIT)
  • Received : 2021.01.05
  • Published : 2021.01.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we have proposed a new internal model control structure (IMC). It is aimed at unstable overactuated multivariable systems whose transfer matrices are singular and unstable. The model inversion problem is essential to understand this structure. Indeed, the precision between the output of the process and the setpoint is linked to the quality of the inversion. This property is preserved in the presence of an additive disturbance at the output. This inversion approach proposed in this article can be applied to multivariable systems with no minimum phase or minimum phase shift with or without delays in their transfer matrices. It is proven by an example of simulation through which we have shown its good performance as a guarantee of stability, precision as well as rapidity of system responses despite the presence of external disturbances and we have tested this control structure in the frequency domain hence the robustness of the IMC.

Keywords

References

  1. C. G. Economou, M. Morari, B. O. Palsson," Internal model control: Extension to nonlinear systems," Industrial & Engineering Chemistry Process Design and Development, vol. 25, n°. 2, pp. 403-411, (1986). https://doi.org/10.1021/i200033a010
  2. V. A Cirtoaje, "quasi-universal practical IMC algorithm," Automatika, vol. 58, pp. 168-181, (2017). https://doi.org/10.1080/00051144.2017.1383581
  3. Q.B. Jin and B.Y. Jiang, "Pseudo-feed-forward decoupling internal model control for singularity plants with time delays. Transactions of the Institute of Measurement and Control, vol. 36, n°. 4, pp. 403565-576, (2013).
  4. B. Francis and W. Wonham, "The internal model principle of control theory," Automatica, vol. 12, pp. 457-465, (1976). https://doi.org/10.1016/0005-1098(76)90006-6
  5. A. Hammami, I. Saidi and D. Soudani, "Comparative study of PMSG controllers for variable wind turbine power optimization," International Journal of Advanced Computer Science and Applications, vol. 9, n°. 8, (2018).
  6. A. Dhahri, I. Saidi and D. Soudani "A New internal model control Method for MIMO over-Actuated systems," International Journal of Advanced Computer Science and Applications, vol. 7, n°. 10, (2016).
  7. I. Saidi, N. Touati, A. dhahri and D. Soudani, "A comparative study on existing and new methods to design internal model controllers for non-square systems, " Transactions of the Institute of Measurement and Control, vol. 41, n°.13, pp. 3637-3650, (2019). https://doi.org/10.1177/0142331219834608
  8. N. Touati, I. Saidi, A. dhahri and D. Soudani, "Internal multimodel control for nonlinear overactuated systems, " Arabian Journal for Science and Engineering, vol. 44, n°. 3, pp. 2369-2377, (2019). https://doi.org/10.1007/s13369-018-3515-5
  9. H. Shibasaki, J. Endo, Y. Hikichi, R. Tanaka, K. Kawaguchi and Y. Ishida, "A modified internal model control for an unstable plant with an integrator in continuous-time system. International Journal of Information and Electronics Engineering, 3, 357-360, (2013).
  10. L. Quan, H. Zhang and Y. Yang, "A novel internal model control method for non-square system", Applied Mechanics and Materials, vol. 238, pp. 66-70, (2012). https://doi.org/10.4028/www.scientific.net/AMM.238.66
  11. P. Y. Chen, L. L. Ou, J. Sun and W. D. Zhang,"Modified internal model control and its application in non-square processes," Control and Decision, vol. 23, pp. 581-584, 2008. https://doi.org/10.3321/j.issn:1001-0920.2008.05.022
  12. I. Bejaoui, I. Saidi, M. G. Xibilia and D. Soudani, "Internal model control of discrete non-minimum phase over-actuated systems with multiple time delays and uncertain parameters", Journal of Engineering Science and Technology Review, vol. 12, n°. 2, pp. 111-118, (2019). https://doi.org/10.25103/jestr.122.16
  13. Z.X. Chen, K. Yamada, N. T. Mai, I. Murakami, Y. Ando, T. Hagiwara and T. Hoshikawa, "A Design method for internal model controllers for minimum-phase unstable plants," ICIC Express Letters, vol.4, n°. 6, p. 2045-2050, (2010).
  14. N. Touati, D. Soudani, M. Naceur and M. Benrejeb, " On an internal multimodel control for nonlinear multivariable systems - A comparative study," International Journal of Advanced Computer Science and Applications, vol. 4, n°. 7, pp. 66-71, (2013).
  15. W. Tan, H. J. Marquez and T. Chen, "IMC design for unstable processes with time delays," Journal of Process Control, vol. 13, n°. 3, pp. 203-213, (2003). https://doi.org/10.1016/S0959-1524(02)00058-6
  16. E. Maherzi, W. Arouri and M. Besbes, " Switched control of a time delayed compass gait robot," International Journal of Advanced Computer Science and Applications, vol. 7, n°. 7, pp. 99-104, (2016).
  17. W. Belhaj and O. Boubaker, "MIMO PI controllers for LTI systems with multiple time delays based on ILMIs and sensitivity functions," Mathematical Problems in Engineering, vol. 2017, n°. 2, (2017).
  18. S. Adlipour, A. Abooee, A. and M. Haeri, LMI-based sufficient conditions for robust stability and stabilization of LTI-fractional-order systems subjected to interval and polytopic uncertainties," Transactions of the Institute of Measurement and Control, vol. 25, n°. 10, pp. 1207-1216, (2015).
  19. N. Maamri, J. C. Trigeassou, M. Bentayeb and O. Bachelier, "PID controllers design for MIMO plants with time specifications LMI-Approach, " 5th IFAC Symposium on Robust Control Design, vol. 39, n°. 9, pp. 178-184, France: Toulouse, (2006).