Rejection of nonharmonic disturbances in nonlinear systems

Shutang Liu; Yuan Jiang; Ping Liu

Kybernetika (2010)

  • Volume: 46, Issue: 5, page 785-798
  • ISSN: 0023-5954

Abstract

top
This paper proposes an asymptotic rejection algorithm on the rejection of nonharmonic periodic disturbances for general nonlinear systems. The disturbances, which are produced by nonlinear exosystems, are nonharmonic and periodic. A new nonlinear internal model is proposed to deal with the disturbances. Further, a state feedback controller is designed to ensure that the system's state variables can asymptotically converge to zero, and the disturbances can be completely rejected. The proposed algorithm can be used in many applications, e. g. active vibration control, and the avoidance of nonharmonic distortion in nonlinear circuits. An example is shown that the proposed algorithm can completely reject the nonharmonic periodic disturbances generated from a Van der Pol circuit.

How to cite

top

Liu, Shutang, Jiang, Yuan, and Liu, Ping. "Rejection of nonharmonic disturbances in nonlinear systems." Kybernetika 46.5 (2010): 785-798. <http://eudml.org/doc/197156>.

@article{Liu2010,
abstract = {This paper proposes an asymptotic rejection algorithm on the rejection of nonharmonic periodic disturbances for general nonlinear systems. The disturbances, which are produced by nonlinear exosystems, are nonharmonic and periodic. A new nonlinear internal model is proposed to deal with the disturbances. Further, a state feedback controller is designed to ensure that the system's state variables can asymptotically converge to zero, and the disturbances can be completely rejected. The proposed algorithm can be used in many applications, e. g. active vibration control, and the avoidance of nonharmonic distortion in nonlinear circuits. An example is shown that the proposed algorithm can completely reject the nonharmonic periodic disturbances generated from a Van der Pol circuit.},
author = {Liu, Shutang, Jiang, Yuan, Liu, Ping},
journal = {Kybernetika},
keywords = {disturbance rejection; nonharmonic periodic disturbances; global stability; Van der Pol circuit; vibration control; disturbance rejection; nonharmonic periodic disturbances; global stability; van der Pol circuit; vibration control},
language = {eng},
number = {5},
pages = {785-798},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Rejection of nonharmonic disturbances in nonlinear systems},
url = {http://eudml.org/doc/197156},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Liu, Shutang
AU - Jiang, Yuan
AU - Liu, Ping
TI - Rejection of nonharmonic disturbances in nonlinear systems
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 5
SP - 785
EP - 798
AB - This paper proposes an asymptotic rejection algorithm on the rejection of nonharmonic periodic disturbances for general nonlinear systems. The disturbances, which are produced by nonlinear exosystems, are nonharmonic and periodic. A new nonlinear internal model is proposed to deal with the disturbances. Further, a state feedback controller is designed to ensure that the system's state variables can asymptotically converge to zero, and the disturbances can be completely rejected. The proposed algorithm can be used in many applications, e. g. active vibration control, and the avoidance of nonharmonic distortion in nonlinear circuits. An example is shown that the proposed algorithm can completely reject the nonharmonic periodic disturbances generated from a Van der Pol circuit.
LA - eng
KW - disturbance rejection; nonharmonic periodic disturbances; global stability; Van der Pol circuit; vibration control; disturbance rejection; nonharmonic periodic disturbances; global stability; van der Pol circuit; vibration control
UR - http://eudml.org/doc/197156
ER -

References

top
  1. Arcak, M., Kokotovic, P., 10.1016/S0005-1098(01)00160-1, Automatica 37 (2001), 1923–1930. (2001) MR2110678DOI10.1016/S0005-1098(01)00160-1
  2. Benedetto, M. D. Di, 10.1080/00207178708933784, Internat. J. Control 45 (1987), 1023–1034. (1987) MR0880281DOI10.1080/00207178708933784
  3. Bodson, M., Douglas, S. C., 10.1016/S0005-1098(97)00149-0, Automatica 33 (1997), 2213–2221. (1997) MR1604113DOI10.1016/S0005-1098(97)00149-0
  4. Byrnes, C. I., Isidori, A., 10.1109/TAC.2004.838492, IEEE Trans. Automat. Control 49 (2004), 2244–2247. (2004) MR2106753DOI10.1109/TAC.2004.838492
  5. Chen, C., Ding, Z., Lennox, B., 10.1109/TCSII.2008.2009962, IEEE Trans. Circuits. Syst. II: Expr. Briefs 55 (2008), 1289–1293. (2008) DOI10.1109/TCSII.2008.2009962
  6. Chen, Z., Huang, J., 10.1016/j.automatica.2005.03.015, Automatica 41 (2005), 1447–1454. (2005) Zbl1086.93013MR2160490DOI10.1016/j.automatica.2005.03.015
  7. Davison, E. J., 10.1109/TAC.1976.1101137, IEEE Trans. Automat. Control 21 (1976), 25–34. (1976) Zbl0326.93007MR0406616DOI10.1109/TAC.1976.1101137
  8. Desoer, C. A., Lin, C. A., 10.1109/TAC.1985.1104078, IEEE Trans. Automat. Control 30 (1985), 861–867. (1985) Zbl0573.93027MR0799479DOI10.1109/TAC.1985.1104078
  9. Ding, Z., Global output regulation of uncertain nonlinear systems with exogenous signals, Automatica 37 (2001),113–119. (2001) Zbl0964.93057MR1832885
  10. Ding, Z., 10.1109/TAC.2005.864199, IEEE Trans. Automat. Control 51 (2006), 498–503. (2006) MR2205690DOI10.1109/TAC.2005.864199
  11. Ding, Z., 10.1016/j.automatica.2006.08.006, Automatica 43 (2007), 174–177. (2007) MR2266785DOI10.1016/j.automatica.2006.08.006
  12. Ding, Z., Decentralized output regulation of large scale nonlinear systems with delay, Kybernetika 45 (2009), 33–48. (2009) Zbl1158.93303MR2489579
  13. Feng, G., Zhang, T., 10.1109/TCSII.2005.862178, IEEE Trans. Circuits. Syst. II: Expr. Briefs 53 (2006), 249–253. (2006) DOI10.1109/TCSII.2005.862178
  14. Francis, D. A., Wonham, W. M., 10.1007/BF01447855, Appl. Math. Optim. 2 (1975), 170–194. (1975) Zbl0351.93015MR0389331DOI10.1007/BF01447855
  15. Hu, T., Teel, A. R., 10.1109/TCSI.2007.895530, IEEE Trans. Circuits. Syst. I: Reg. Paper 54 (2007), 1367–1379. (2007) MR2370594DOI10.1109/TCSI.2007.895530
  16. Huang, J., 10.1109/9.388697, IEEE Trans. Automat. Control 40 (1995), 1118–1122. (1995) Zbl0829.93027MR1345975DOI10.1109/9.388697
  17. Huang, J., Nonlinear Output Regulation: Theroy and Application, SIAM, Philadelphia 2004. (2004) MR2308004
  18. Huang, J., Chen, Z., 10.1109/TAC.2004.839236, IEEE Trans. Automat. Control 49 (2004), 2203–2218. (2004) MR2106750DOI10.1109/TAC.2004.839236
  19. Huang, J., Lin, C-F., 10.1109/9.299646, IEEE Trans. Automat. Control 39 (1994), 1510–1513. (1994) Zbl0800.93290MR1283933DOI10.1109/9.299646
  20. Huang, J., Rugh, W. J., 10.1016/0005-1098(90)90081-R, Automatica 26 (1990), 963–972. (1990) Zbl0717.93019MR1080983DOI10.1016/0005-1098(90)90081-R
  21. Isidori, A., Nonlinear Control Systems, Third edition. Springer, Berlin 1995. (1995) Zbl0878.93001MR1410988
  22. Isidori, A., Byrnes, C. I., 10.1109/9.45168, IEEE Trans. Automat. Control 35 (1990), 131–140. (1990) Zbl0704.93034MR1038409DOI10.1109/9.45168
  23. Jiang, Y., Liu, S., Rejection of nonharmonic disturbances in a class of nonlinear systems with nonlinear exosystems, Asian J. Control. Submitted for publication. 
  24. Johnson, C. D., 10.1109/TAC.1971.1099830, IEEE Trans. Automat. Control 16 (1971), 635–644. (1971) DOI10.1109/TAC.1971.1099830
  25. Khalil, H. K., Nonlinear Systems, Third edition. Prentice-Hall, NJ 2002. (2002) Zbl1003.34002
  26. Liu, L., Chen, Z., Huang, J., Parameter convergence and minimal internal model with an adaptive output regulation problem, Automatica 45 (2009), 1206–1311. (2009) Zbl1162.93363MR2531610
  27. Marino, R., Santosuosso, G. L., Tomei, P., 10.1016/S0005-1098(03)00170-5, Automatica 39 (2003), 1755–1761. (2003) MR2142091DOI10.1016/S0005-1098(03)00170-5
  28. Priscoli, F. D., 10.1016/j.sysconle.2004.04.003, Systems Control Lett. 53 (2004), 177–185. (2004) Zbl1157.93412MR2092508DOI10.1016/j.sysconle.2004.04.003
  29. Ramos, L. E., C̆elikovský, S., Kuc̆era, V., 10.1109/TAC.2004.835404, IEEE Trans. Automat. Control 49 (2004), 1737–1742. (2004) MR2091325DOI10.1109/TAC.2004.835404
  30. Rehák, B., Čelikovský, S., Ruiz-León, J., Orozco-Mora, J., A comparison of two fem-based methods for the solution of the nonlinear output regulation problem, Kybernetika 45 (2009), 427–444. (2009) Zbl1165.93320MR2543132
  31. Serrani, A., Isidori, A., 10.1016/S0167-6911(99)00099-7, Systems Control Lett. 39 (2000), 133–139. (2000) Zbl0948.93027MR1826676DOI10.1016/S0167-6911(99)00099-7
  32. Serrani, A., Isidori, A., Marconi, L., 10.1109/9.940923, IEEE Trans. Automat. Control 46 (2001), 1178–1194. (2001) Zbl1057.93053MR1847323DOI10.1109/9.940923
  33. Sun, W., Huang, J., Output regulation for a class of uncertain nonlinear systems with nonlinear exosystems and its application, Science in China, Ser. F: Information Sciences. 52 (2009), 2172–2179. (2009) Zbl1182.93072MR2566641
  34. Xi, Z., Ding, Z., 10.1016/j.automatica.2006.08.011, Automatica 43 (2007), 143–149. (2007) Zbl1140.93462MR2266780DOI10.1016/j.automatica.2006.08.011
  35. Ye, X., Huang, J., 10.1109/TAC.2002.808480, IEEE Trans. Automat. Control 48 (2003), 276–281. (2003) MR1957326DOI10.1109/TAC.2002.808480

NotesEmbed ?

top

You must be logged in to post comments.