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Modeling and stability analysis methods of neutrosophic transfer functions

  • Jun YeEmail author
  • Wenhua Cui
Methodologies and Application
  • 15 Downloads

Abstract

Uncertainty is inherent property in actual control systems because parameters in actual control systems are no constants and changeable under some environments. Therefore, actual systems imply their indeterminate parameters, which can affect the control behavior and performance. Then, a neutrosophic number (NN) presented by Smarandache is very easy expressing determinate and/or indeterminate information because a NN p = c + dI is composed of its determinate term c and its indeterminate term dI for c, dR (R is all real numbers), where the symbol “I” denotes indeterminacy. Unfortunately, all uncertain modeling and analysis of practical control systems in existing literature do not provide any concept of NN models and analysis methods till now. Hence, this study firstly proposes a neutrosophic modeling method and defines a neutrosophic transfer function and a neutrosophic characteristic equation. Then, two stability analysis methods of neutrosophic linear systems are established based on the bounded range of all possible characteristic roots and the neutrosophic Routh stability criterion. Finally, the proposed methods are used for two practical examples on the RLC circuit and mass–spring–damper systems with NN parameters. The analysis results demonstrate the effectiveness and feasibility of the proposed methods.

Keywords

Neutrosophic transfer function Neutrosophic characteristic equation Neutrosophic Routh stability criterion Neutrosophic characteristic root 

Notes

Acknowledgment

This paper was supported by the National Natural Science Foundation of China (No. 61703280).

Compliance with ethical standards

Conflict of interest

The authors declare that we have no conflict of interest regarding the publication of this paper.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

References

  1. Chen JQ, Ye J, Du SG (2017a) Scale effect and anisotropy analyzed for neutrosophic numbers of rock joint roughness coefficient based on neutrosophic statistics. Symmetry 9(10):208.  https://doi.org/10.3390/sym9100208 CrossRefGoogle Scholar
  2. Chen JQ, Ye J, Du SG, Yong R (2017b) Expressions of rock joint roughness coefficient using neutrosophic interval statistical numbers. Symmetry 9(7):123.  https://doi.org/10.3390/sym9070123 CrossRefGoogle Scholar
  3. Czarkowski D, Pujara LR, Kazimierczuk MK (1995) Robust stability of state feedback control of PWM DC-DC push-pull converter. IEEE Trans Ind Electron 42(1):108–111CrossRefGoogle Scholar
  4. Dazzo JJ, Houpis CH (1995) Linear control system analysis and design, 4th edn. McGraw-Hill, USAGoogle Scholar
  5. Elkaranshawy HA, Bayoumi EHE, Soliman HM (2009) Robust control of a flexible-arm robot using Kharitonov theorem. Electromotion 16:98–108Google Scholar
  6. Hote YV, Roy Choudhury D, Gupta JRP (2009) Robust stability analysis PWM push-pull DC-DC converter. IEEE Trans Power Electron 24(10):2353–2356CrossRefGoogle Scholar
  7. Hote YV, Gupta JRP, Roy Choudhury D (2010) Kharitonov’s theorem and Routh criterion for stability margin of interval systems. Int J Control Autom Syst 8(3):647–654CrossRefGoogle Scholar
  8. Hussein MT (2005) A novel algorithm to compute all vertex matrices of an interval matrix: computational approach. Int J Comput Inf Sci 2(2):137–142Google Scholar
  9. Hussein MT (2010) An efficient computational method for bounds of eigenvalues of interval system using a convex hull algorithm. Arab J Sci Eng 35(1B):249–263Google Scholar
  10. Hussein MT (2011) Assessing 3-D uncertain system stability by using MATLAB convex hull functions. Int J Adv Comput Sci Appl 2(6):13–18CrossRefGoogle Scholar
  11. Hussein MT (2015) Modeling mechanical and electrical uncertain systems using functions of robust control MATLAB Toolbox®3. Int J Adv Comput Sci Appl 6(4):79–84Google Scholar
  12. Jiang WZ, Ye J (2016) Optimal design of truss structures using a neutrosophic number optimization model under an indeterminate environment. Neutrosophic Sets Syst 14:93–97Google Scholar
  13. Kharitonov VL (1979) Asymptotic stability of an equilibrium position of a family of systems of linear differential equations. Differ Equ 14:1483–1485zbMATHGoogle Scholar
  14. Kolev LV (1988) Interval mathematics algorithms for tolerance analysis. IEEE Trans Circuits Syst 35:967–975MathSciNetCrossRefGoogle Scholar
  15. Kong LW, Wu YF, Ye J (2015) Misfire fault diagnosis method of gasoline engines using the cosine similarity measure of neutrosophic numbers. Neutrosophic Sets Systems 8:43–46Google Scholar
  16. Meressi T, Chen D, Paden B (1993) Application of Kharitonov’s theorem to mechanical systems. IEEE Trans Autom Control 38(3):488–491MathSciNetCrossRefGoogle Scholar
  17. Precup RE, Preitl S (2006) PI and PID controllers tuning for integral-type servo systems to ensure robust stability and controller robustness. Springer J Electr Eng 88:149–156CrossRefGoogle Scholar
  18. Smarandache F (1998) Neutrosophy: neutrosophic probability, set, and logic. American Research Press, RehobothzbMATHGoogle Scholar
  19. Smarandache F (2013) Introduction to neutrosophic measure, neutrosophic integral, and neutrosophic probability. Sitech & Education Publisher, Craiova—ColumbuszbMATHGoogle Scholar
  20. Smarandache F (2014) Introduction to neutrosophic statistics. Sitech & Education Publishing, CraiovazbMATHGoogle Scholar
  21. Ye J (2016a) Multiple-attribute group decision-making method under a neutrosophic number environment. J Intell Syst 25(3):377–386Google Scholar
  22. Ye J (2016b) Fault diagnoses of steam turbine using the exponential similarity measure of neutrosophic numbers. J Intell Fuzzy Syst 30:1927–1934CrossRefGoogle Scholar
  23. Ye J (2017a) Bidirectional projection method for multiple attribute group decision making with neutrosophic numbers. Neural Comput Appl 28:1021–1029CrossRefGoogle Scholar
  24. Ye J (2017b) Neutrosophic linear equations and application in traffic flow problems. Algorithms 10(4):133.  https://doi.org/10.3390/a10040133 MathSciNetCrossRefzbMATHGoogle Scholar
  25. Ye J (2018) Neutrosophic number linear programming method and its application under neutrosophic number environments. Soft Comput 22(14):4639–4646CrossRefGoogle Scholar
  26. Ye J, Yong R, Liang QF, Huang M, Du SG (2016) Neutrosophic functions of the joint roughness coefficient (JRC) and the shear strength: a case study from the pyroclastic rock mass in Shaoxing City, China. Mathem Problems Eng 2016, Article ID 4825709, 9 pages. http://dx.doi.org/10.1155/2016/4825709
  27. Ye J, Chen JQ, Yong R, Du SG (2017) Expression and analysis of joint roughness coefficient using neutrosophic number functions. Information 8(2):69.  https://doi.org/10.3390/info8020069 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Electrical and Information EngineeringShaoxing UniversityShaoxingPeople’s Republic of China

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