Higher Order Sliding Controller Parameter Determining Method: A Research

Year : 2024 | Volume :14 | Issue : 02 | Page : 51-66
By

HyonChol Kim,

KyongMin Yun,

ChangKol Chal,

  1. Faculty, Kim Il Sung University, Pyongyang, North Korea
  2. Student, Kim Il Sung University, Pyongyang, North Korea
  3. Student, Kim Il Sung University, Pyongyang, North Korea

Abstract

In this paper, it is generally believed that sliding switching surfaces should reflect the design parameters of the system in variable structure control, and the control characteristics are the way to constrain the state on sliding switching surfaces. In the literature, classical sliding (primary sliding) is considered that sliding-switching surface is the same as the characteristic equation of the closed-loop system, and the design of the control system is reflected in accordance with the characteristic equation of the sliding-switching surface. The corresponding modes are referred to as SMs, and the technique is centred on high-frequency (or theoretically infinite frequency) control switching. SMs are often established in a finite amount of time, are accurate, and are insensitive to matching disturbances. The primary disadvantage of the technique is the potential for hazardous system vibrations caused by the control switching, sometimes known as the “chattering effect.” Additionally, sliding variables of relative degree 1 and relay control form the foundation of standard SMs. But it is very difficult to set up to reflect the characteristics of the control system due to the differentiability because the switching surface is represented by discrete nonlinear (natural nonlinear) differential equations. So, in the previous sections, controller structures of high order sliding mode were introduced but the method of determining the controller parameters was not presented. Therefore, we propose the method of determining parameters in the use of high order sliding mode which is superior to classical sliding mode for free vibration and the shortest time problems with the help of simple mathematical knowledge. As a result, this paper will concretize the design of controllers more exactly.

Keywords: Nonlinear control system; Sliding mode (SM); Robustness; High-order sliding mode (HOSM); Single-input single-output (SISO); Multiple-input multiple-output (MIMO)

[This article belongs to Trends in Electrical Engineering(tee)]

How to cite this article: HyonChol Kim, KyongMin Yun, ChangKol Chal. Higher Order Sliding Controller Parameter Determining Method: A Research. Trends in Electrical Engineering. 2023; 14(02):51-66.
How to cite this URL: HyonChol Kim, KyongMin Yun, ChangKol Chal. Higher Order Sliding Controller Parameter Determining Method: A Research. Trends in Electrical Engineering. 2023; 14(02):51-66. Available from: https://journals.stmjournals.com/tee/article=2023/view=168980

References

  1. Levant, “Homogeneity approach to high-order sliding mode design,” Automatica, vol. 41, no. 5, pp. 823–830, 2005.
  2. I. Utkin, Sliding Modes in Optimization and Control Problems. New York: Springer, 1992. Springer Science & Business Media, 12 Mar 2013; Technology & Engineering.
  3. Zinober, A.S.I. (1994). An introduction to sliding mode variable structure control. In: Zinober, A.S.I. (eds) Variable Structure and Lyapunov Control. Lecture Notes in Control and Information Sciences, vol 193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0033676
  4. Edwards, C., & Spurgeon, S.K. (1998). Sliding Mode Control: Theory And Applications (1st ed.). CRC Press. https://doi.org/10.1201/9781498701822
  5. Fridman and U. Shaked, “An LMI approach to stability of discrete delay systems,” 2003 European Control Conference (ECC), Cambridge, UK, 2003, pp. 1477-1482, doi: 10.23919/ECC.2003.7085170.
  6. Fridman, “A LMI approach to stability of descriptor systems with delay,” 2001 European Control Conference (ECC), Porto, Portugal, 2001, pp. 2871-2876, doi: 10.23919/ECC.2001.7076368.
  7. Slotine JJ, Li W. Applied nonlinear control. Englewood Cliffs, NJ: Prentice hall; 1991 Jan.
  8. Pan Y, Furuta K, Suzuki S, Hatakeyama S. Design of variable structure controller-from sliding mode to sliding sector. InProceedings of the 39th IEEE Conference on Decision and Control (Cat. No. 00CH37187) 2000 Dec 12 (Vol. 2, pp. 1685-1690). IEEE.
  9. Emel’yanov, Stanislav V., Sergey K. Korovin and L. V. Levantovskii. “Higher-order sliding modes in binary control systems.” (1986).
  10. LEVANT, A. (1993). Sliding order and sliding accuracy in sliding mode control. International Journal of Control, 58(6), 1247–1263. https://doi.org/10.1080/00207179308923053
  11. Levant, “Universal SISO sliding-mode controllers with finite-time convergence,” IEEE Trans. Autom. Control, Sep. 2001; 46(9): 1447–1451.
  12. Levant. Principles of 2-sliding mode design. Automatica, 2007; 43: 576-586.
  13. Levant, “Finite-time stability and high relative degrees in sliding-mode control,” Lecture Notes Control Inform. Sci., vol. 412, pp.59–92, 2012.
  14. Levant, “Construction principles of 2-sliding mode design, Automatica, vol. 43, no. 4, pp. 576–586, 2007.
  15. Utkin and H. Lee, “Chattering analysis,” in Advances in Variable Structure and Sliding Mode Control, Lecture Notes in Control and Information Sciences, C. Edwards, E. Fossas Colet, and L. Fridman, Eds. Berlin, Germany: Springer Verlag, 2006, vol. 334, pp. 107–123.
  16. Levant, “Sliding order and sliding accuracy in sliding mode control,” Int. J. Control, vol. 58, no. 6, pp. 1247–1263, 1993.
  17. Levant, “Finite-time stability and high relative degrees in sliding mode control”. Lecture Notes Control Inform. Sci., vol. 412, pp. 59–92, 2012.
  18. Levant, “Quasi-continuous high-order sliding-mode controllers”. IEEE Trans. Autom. Control, vol. 50, no. 11, pp. 1812–1816, Nov. 2005.
  19. Levant, “Higher-order sliding modes, differentiation and output feedback control,” Int. J. Contr., vol. 76, no. 9/10, pp. 924–941, 2003
  20. B. Shtessel and I. A. Shkolnikov, “Aeronautical and space vehicle control in dynamic sliding manifolds,” Int. J. Contr., vol. 76, no. 9/10,pp. 1000–1017, 2003.
  21. B. Shtessel, I. A. Shkolnikov, and M. D. J. Brown, “An asymptotic second-order smooth sliding mode control,” Asian J. Control, vol. 5, no.4, pp. 498–504, 2004.
Regular Issue Subscription Original Research
Volume 14
Issue 02
Received July 16, 2024
Accepted August 8, 2024
Published November 24, 2023
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