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Observer Design for a Class of Nonlinear Discrete Time Systems: Real Time Application to the One-link Flexible Joint Robot

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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2018
Authors:
Assem Thabet, Noussaiba Gasmi
10.5120/ijca2018916875

Assem Thabet and Noussaiba Gasmi. Observer Design for a Class of Nonlinear Discrete Time Systems: Real Time Application to the One-link Flexible Joint Robot. International Journal of Computer Applications 179(37):1-6, April 2018. BibTeX

@article{10.5120/ijca2018916875,
	author = {Assem Thabet and Noussaiba Gasmi},
	title = {Observer Design for a Class of Nonlinear Discrete Time Systems: Real Time Application to the One-link Flexible Joint Robot},
	journal = {International Journal of Computer Applications},
	issue_date = {April 2018},
	volume = {179},
	number = {37},
	month = {Apr},
	year = {2018},
	issn = {0975-8887},
	pages = {1-6},
	numpages = {6},
	url = {http://www.ijcaonline.org/archives/volume179/number37/29279-2018916875},
	doi = {10.5120/ijca2018916875},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}
}

Abstract

This paper demonstrates the observer design for large class of nonlinear discrete time systems. The use of the differential mean value theorem (DMVT) allows transforming the nonlinear error dynamics into a linear parameter varying (LPV) system. This has the advantage of introducing a general condition on the nonlinear functions. To ensure asymptotic stability, sufficient conditions are expressed in terms of linear matrix inequalities (LMIs). For comparison, an observer based on the use of the one-sided Lipschitz condition is introduced. High performances are shown through real time implementation of the one-link flexible joint robot to ARDUINO MEGA 2560 device.

References

  1. Masoud Abbaszadeh and Horacio J. Marquez. Nonlinear observer design for one-sided lipschitz systems. In Proc. American Control Conf., pages 5284–5289, Marriott Waterfront, Baltimore, MD, USA, June 30-July 02, 2010.
  2. A. Alessandri. Design of observers for lipschitz nonlinear systems using lmi. In NOLCOS, IFAC Symposium on Nonlinear Control Systems, Stuttgart, Germany, 2004.
  3. M. Benallouch, M. Boutayeb, and M. Zasadzinski. Observers design for one-sided lipschitz discrete-time systems. Syst. Control Letters, 61:879–886, 2012.
  4. M. Boutayeb. Identification of nonlinear systems in the presence of unknown but bounded disturbances. IEEE Trans. on Autom. Control, 45:1503–1507, 2000.
  5. M. Boutayeb and C. Aubry. A strong tracking extended kalman observer for nonlinear discrete-time systems. IEEE Trans. on Autom. Control, 44:1550–1556, 1999.
  6. S. Boyd, L. El Ghaoui, E. Ferron, and V. Balakrishnan. Linear matrix inequalities in systems and control theory. Studies in Applied Mathematics SIAM, Philadelphia, 15 edition, 1994.
  7. Q.P. Ha and H. Trinh. State and input simultaneous estimation for a class of nonlinear systems. Automatica, 40:1779–1785, 2004.
  8. Pan Jinfeng, Meng Min, and Feng Jun-e. A note on observers design for one-sided lipschitz nonlinear systems. In Control Conference (CCC), 2015 34th Chinese, pages 1003–1007, July 2015.
  9. Linlin Li, Ying Yang, Yong Zhang, and S.X. Ding. Fault estimation of one-sided lipschitz and quasi-one-sided lipschitz systems. In Control Conference (CCC), 2014 33rd Chinese, pages 2574–2579, July 2014.
  10. W. Lin and C. Byrnes. Remarks on linearization of discretetime autonomous systems and nonlinear observer design. Syst. Control Letters, 25:31–40, 1995.
  11. P.R. Pagilla and Y. Zhu. Controller and observer design for lipschitz nonlinear systems. In Proc. American Control Conf., pages 2379–2384, Boston, Massachusetts,USA, 2004.
  12. R. Rajamani. Observer for lipschitz nonlinear systems. IEEE Trans. on Autom. Control, 43:397–401, 1998.
  13. M. Spong. Modeling and control of elastic joint robots. Trans. ASME, J. Dyn. Syst., Meas. Control, 109:310–319, 1987.
  14. A. Thabet, M. Boutayeb, and M. N. Abdelkrim. On the modeling and state estimation for dynamic power system. Int. J. of Electronics Science and Engineering, 7 (2):181–190, 2013.
  15. A. Thabet, M. Boutayeb, and M.N. Abdelkrim. Real time dynamic state estimation for power system. Int J. of Computer Applications, 38-2:11–18, 2012.
  16. A. Thabet, G.B.H Frej, and M. Boutayeb. Observer-based feedback stabilization for lipschitz nonlinear systems with extension to h1 performance analysis: Design and experimental results. IEEE Trans. on Control Systems Technology, 26 (1):321–328, 2018.
  17. ChunyanWang, Zongyu Zuo, Zongli Lin, and Zhengtao Ding. Consensus control of a class of lipschitz nonlinear systems with input delay. Circuits and Systems I: Regular Papers, IEEE Transactions on, 62(11):2730–2738, Nov 2015.
  18. A. Zemouch and M. Boutayeb. A unified H1 adaptive observer synthesis method for a class of systems with both lipschitz and monotone nonlinearities. Syst. Control Letters, 58:282–288, 2009.
  19. A. Zemouch, M. Boutayeb, and G.I. Bara. Observers for a class of lipschitz systems with extension to H1 performance analysis. Syst. Control Letters, 57:18–27, 2008.
  20. F. Zhu and Z.Han. A note on observers for lipschitz nonlinear systems. IEEE Trans. on Autom. Control, 47:1751–1754, 2002.

Keywords

Discrete time systems, DMVT, One-sided Lipschitz condition, Quadratic inner-boundedness, LMIs