Design of memoryless output feedback controller of discrete-time systems with input delay

Jinhui Zhang; Yujuan Lin; Gang Feng

Design of memoryless output feedback controller of discrete-time systems with input delay

View Fulltext

Author(s): Jinhui Zhang ¹ ; Yujuan Lin ¹ ; Gang Feng ²
- Affiliations: 1: College of Information Science & Technology, Beijing University of Chemical Technology, Beijing 100029, People's Republic of China;
  2: Department of Mechanical and Biomedical Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
Source: Volume 9, Issue 8, 15 May 2015, p. 1205 – 1212
DOI: 10.1049/iet-cta.2014.0455 , Print ISSN 1751-8644, Online ISSN 1751-8652

Received 25/04/2014, Accepted 16/08/2014, Published 01/04/2015

This study addresses the output feedback stabilisation problem of discrete-time linear systems with input delay. By viewing the difference between the current input and the delayed input as a special disturbance, full- and reduced-order extended state observers are constructed, respectively, to estimate both the state and the disturbance simultaneously. Then the composite control laws are synthesised to actively compensate the input delay by using the state and disturbance estimates. Different from existing predictor-based control approaches, the proposed controllers are memoryless, and the past input information are thus not needed. Moreover, it can be observed that the information on the size of the input delay is not involved in either the observers or the controllers. Finally, simulation results are provided to illustrate the advantages and effectiveness of the proposed approaches.

References

1. 1)
  - B.Y. Zhang , S.Y. Xu , Y. Zhou . Improved stability criterion and its applications in delayed controller design for discrete time systems. Automatica , 2963 - 2967
2. 2)
  - 2. Zhang, W.: ‘Stability analysis of networked control systems’. PhD thesis, Case Western Reserve University, Case Western Reserve University, Department of Electrical Engineering and Computer Science, 2001.
3. 3)
  - 22. Zhou, B.: ‘Observer based output feedback control of discrete-time linear systems with input and output delays’, Int. J. Control, 2014, 87, (11), pp. 2252–2272..
4. 4)
  - 21. Zhou, B.: ‘Truncated predictor feedback for time-delay systems’ (Springer-Verlag, Heidelberg, Germany, 2014).
5. 5)
  - H.S. Park , Y.H. Kim , D.S. Kim , W.H. Kwon . A scheduling method for network-based control systems. IEEE Trans. Control Syst. Technol. , 3 , 318 - 330
6. 6)
  - 1. Xia, Y., Fu, M., Liu, G.-P.: ‘Analysis and synthesis of networked control systems’ (Springer-Verlag, Berlin Heidelberg, 2011).
7. 7)
  - 20. Gonzalez, A.: ‘Robust stabilization of linear discrete-time systems with time-varying input delay’, Automatica, 2013, 49, (9), pp. 2919–2922 (doi: 10.1016/j.automatica.2013.05.031).
8. 8)
  - 9. Gonzalez, A., Sala, A., Garcia, P., Albertos, P.: ‘Robustness analysis of discrete predictor-based controllers for input-delay systems’, Int. J. Syst. Sci., 2013, 44, (2), pp. 232–239 (doi: 10.1080/00207721.2011.600469).
9. 9)
  - D. Yue , Q.-L. Han , J. Lam . Network-based robust H∞ control of systems with uncertainty. Automatica , 6 , 999 - 1007
10. 10)
  - Y. Xia , G. Liu , P. Shi , J. Chen , D. Rees , J. Liang . Sliding mode control of uncertain linear discrete time systems with input delay. IET Control Theory Appl. , 4 , 1169 - 1175
11. 11)
  - 17. Niculescu, S.I.: ‘Delay effects on stability: a robust control approach’ (Springer-Verlag, London, 2001).
12. 12)
  - 23. Hespanha, J.P.: ‘Linear systems theory’ (Princeton University Press, Princeton, New Jersey, 2009).
13. 13)
  - W.H. Kwon , A.E. Pearson . Feedback stabilization of linear systems with delayed control. IEEE Trans. Autom. Control , 2 , 266 - 269
14. 14)
  - 19. Zhou, B., Lin, Z., Duan, G.: ‘Truncated predictor feedback for linear systems with long time-varying input delays’, Automatica, 2012, 48, (10), pp. 2387–2399 (doi: 10.1016/j.automatica.2012.06.032).
15. 15)
  - D. Yue . Robust stabilization of uncertain systems with unknown input delay. Automatica , 2 , 331 - 336
16. 16)
  - 24. Fantoni, I., Lozano, R.: ‘Non-linear control for underactuated mechanical systems’ (Springer, UK, 2002).
17. 17)
  - 17. Yue, D., Tian, E., Wang, Z., Lam, J.: ‘Stabilization of systems with probabilistic interval input delays and its applications to networked control systems’, IEEE Trans. Syst. Man Cybern.-Part A: Syst. Humans, 2009, 39, (4), pp. 939–945 (doi: 10.1109/TSMCA.2009.2019875).
18. 18)
  - R.C. Luo , L.Y. Chung . Stabilization for linear uncertain system with time latency. IEEE Trans. Ind. Electron. , 4 , 905 - 910
19. 19)
  - N. Poursafar , H. Taghirad , M. Haeri . Model predictive control of non-linear discrete time systems: a linear matrix inequality approach. IET Control Theory Appl. , 10 , 1922 - 1932
20. 20)
  - 22. Zhou, B., Li, Z., Lin, Z.: ‘Observer based output feedback control of linear systems with input and output delays’, Automatica, 2013, 49, (7), pp. 2039–2052 (doi: 10.1016/j.automatica.2013.03.031).
21. 21)
  - 26. Gonzalez, A., Sala, A., Albertos, P.: ‘Predictor-based stabilization of discrete time-varying input-delay systems’, Automatica, 2012, 48, (2), pp. 454–457 (doi: 10.1016/j.automatica.2011.10.005).
22. 22)
  - D.S. Kim , Y.S. Lee , W.H. Kwon , H.S. Park . Maximum allowable delay bounds of networked control systems. Control Eng. Practice , 1301 - 1313
23. 23)
  - Y.S. Moon , P. Park , W.H. Kwon . Robust stabilization of uncertain input-delayed systems using reduction method. Automatica , 2 , 307 - 312
24. 24)
  - H. Chen , X. Zheng . On improved robust stabilization of uncertain systems with unknown input delay. Automatica , 6 , 1067 - 1072

Login

Not registered yet?

Share

Tools

Login to add to favourites

Key

Design of memoryless output feedback controller of discrete-time systems with input delay

References

Related content