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A Novel Polynomial Tracking Differentiator

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Proceedings of 2019 Chinese Intelligent Systems Conference (CISC 2019)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 594))

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Abstract

A novel polynomial tracking differentiator is presented in this paper to obtain the continuous signal and its derivative from the reference signal in real time. The proposed differentiator is a robust scheme and can suppress the chattering effect. The stability of the differentiator is verified by using the Lyapunov theory. Simulations are carried out and the results demonstrate that the tracking and differential errors can converge faster and a higher precision is achieved.

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References

  1. Jana AK (2010) A nonlinear exponential observer for a batch distillation. In: 2010 11th International Conference on Control Automation Robotics & Vision, pp 1393–1396. IEEE

    Google Scholar 

  2. Ali JM et al (2015) Review and classification of recent observers applied in chemical process systems. Comput Chem Eng 76:27–41

    Article  Google Scholar 

  3. Wang X, Shirinzadeh B (2014) High-order nonlinear differentiator and application to aircraft control. Mech Syst Signal Process 46(2):227–252

    Article  Google Scholar 

  4. Ma R, Zhang G, Krause O (2018) Fast terminal sliding-mode finite-time tracking control with differential evolution optimization algorithm using integral chain differentiator in uncertain nonlinear systems. Int J Robust Nonlinear Control 28(2):625–639

    Article  MathSciNet  Google Scholar 

  5. Tian D, Shen H, Dai M (2014) Improving the rapidity of nonlinear tracking differentiator via feedforward. IEEE Trans Industr Electron 61(7):3736–3743

    Article  Google Scholar 

  6. Feng J, Wang W, Chen Yu (2018) An improved tracking-differentiator filter based on Taylor’s formula. Optik 158:1026–1033

    Article  Google Scholar 

  7. Hong Y, Huang J, Yangsheng X (2001) On an output feedback finite-time stabilization problem. IEEE Trans Autom Control 46(2):305–309

    Article  MathSciNet  Google Scholar 

  8. Wang X, Chen Z, Yang G (2007) Finite-time-convergent differentiator based on singular perturbation technique. IEEE Trans Autom Control 52(9):1731–1737

    Article  MathSciNet  Google Scholar 

  9. Levant A (1998) Robust exact differentiation via sliding mode technique. Automatica 34(3):379–384

    Article  MathSciNet  Google Scholar 

  10. Levant A (2003) Higher-order sliding modes, differentiation and output-feedback control. Int J Control 76(9–10):924–941

    Article  MathSciNet  Google Scholar 

  11. Levant A (2005) Homogeneity approach to high-order sliding mode design. Automatica 41(5):823–830

    Article  MathSciNet  Google Scholar 

  12. Levant A (2009) Non-homogeneous finite-time-convergent differentiator. In: Proceedings of the 48th IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, pp 8399–8404. IEEE

    Google Scholar 

  13. Levant A (2014) Globally convergent fast exact differentiator with variable gains. In: 2014 European Control Conference (ECC), pp 2925–2930. IEEE

    Google Scholar 

  14. Livne M, Levant A (2014) Proper discretization of homogeneous differentiators. Automatica 50(8):2007–2014

    Article  MathSciNet  Google Scholar 

  15. Bu X et al (2015) Tracking differentiator design for the robust backstepping control of a flexible air-breathing hypersonic vehicle. J Franklin Inst 352(4):1739–1765

    Article  MathSciNet  Google Scholar 

  16. Shao X, Wang H (2016) Back-stepping robust trajectory linearization control for hypersonic reentry vehicle via novel tracking differentiator. J Franklin Inst 353(9):1957–1984

    Article  MathSciNet  Google Scholar 

  17. Liu Z, Jiang Y (2017) Design of a modified tracking differentiator. World J Eng Technol 5(04):668

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the key field fund (grant No. 61400020401).

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Correspondence to Jiao Jia .

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Jia, J., Zhou, S. (2020). A Novel Polynomial Tracking Differentiator. In: Jia, Y., Du, J., Zhang, W. (eds) Proceedings of 2019 Chinese Intelligent Systems Conference. CISC 2019. Lecture Notes in Electrical Engineering, vol 594. Springer, Singapore. https://doi.org/10.1007/978-981-32-9698-5_75

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