Skip to main content
SpringerLink
Log in

Observability and controllability analysis for sandwich systems with dead-zone

  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

In this paper, an approach to analyze the observability and controllability of sandwich systems with dead-zone is proposed. In this method, a non-smooth state-space function is proposed to describe the sandwich systems with dead-zone which are also non-smooth nonlinear systems. Then, a linearization method based on non-smooth optimization is proposed to derive a linearized state-space function to approximate the non-smooth sandwich systems within a bounded region around the equilibrium points that we are interested in. Afterwards, both observability and controllability matrices are constructed and the methods to analyze the observability as well as controllability of sandwich system with dead-zone are derived. Finally, a numerical example is presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Vörös, “Recursive identification of Hammerstein systems with discontinuous nonlinearities containing deadzones,” IEEE Trans. Autom.Control, vol. 48, no. 12, pp. 2203–2206, Dec. 2003. [click]

    Article  Google Scholar 

  2. R. Kalman, P. Falb, and M. Arbib, Topics in Mathematical System Theory, Mc Graw-Hill Company, New York, 1969.

    MATH  Google Scholar 

  3. H. Sussmann, “Single-input observability of continuoustime systems,” Mathematical Systems Theory, vol. 12, no. 3, pp.371–393, 1979. [click]

    MathSciNet  MATH  Google Scholar 

  4. A. J. Van der Schaft, “Observability and controllability for smooth nonlinear systems,” SIAM Journal of Control and Optimization, vol. 20, no. 3, pp. 338–354, 1982. [click]

    Article  MATH  Google Scholar 

  5. A. Isidori, Nonlinear Control Systems, Springer, London, 1989.

    Book  MATH  Google Scholar 

  6. R. Herman and A. Krener, “Nonlinear controllability and observability,” IEEE Transactions on Automatic Control, vol. 22, no. 5, pp. 728–740, 1977. [click]

    Article  Google Scholar 

  7. J. Klamka, “On the global controllability of perturbed nonlinear systems,” IEEE Transactions on Automatic Control, vol. 20, no. 1, pp. 170–172, 1975. [click]

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Klamka, “Controllability of nonlinear discrete systems,” Proc. of American Control Conference, Anchorage, AK, USA, pp. 4670–4671, 2002. [click]

    Google Scholar 

  9. E. Sontag, “On the observability of polynomial systems, I: Finite-time problems,” SIAM Journal of Control and Optimization, vol.17, no. 1, pp. 139–151, 1979. [click]

    Article  MathSciNet  MATH  Google Scholar 

  10. G. Jank, “Controllability, observability and optimal control of continuous-time 2-D systems,” International Journal of Applied Mathematic and Computer Science, vol. 12, no. 2, pp. 181–195, 2012.

    MathSciNet  Google Scholar 

  11. R. Koplon and E. Sontag, “Linear systems with sign observations,” SIAM Journal Control and Optimization, vol. 31, no.12, pp. 1245–1266, 1993. [click]

    Article  MathSciNet  MATH  Google Scholar 

  12. L. Mincheko and S. Sirotko, “Controllability of nonsmooth discrete systems with delay,” Optimization, vol. 51, no. 1, pp. 161–174, 2002. [click]

    Article  MathSciNet  Google Scholar 

  13. T. Murphey and J. Burdick, “Nonsmooth controllability theory and an example,” Proc. of 41st IEEE Conference on Decision and Control, Shanghai, China, pp. 370–376, 2002. [click]

    Google Scholar 

  14. A. Zhirabok, and A. Shumsky, “An approach to the analysis of observability and controllability in nonlinear Systems via linear methods,” International Journal of Applied Mathematic and Computer Science, vol. 22, no. 3, pp. 507–522., 2012. [click]

    MathSciNet  MATH  Google Scholar 

  15. F. H. Clarke, Optimization and Nonsmooth Analysis, John Wiley, New York, 1983.

    MATH  Google Scholar 

  16. L. Qi and J. Sun, “A non-smooth version of Newton’s method,” Mathematical Programming, vol. 58, pp. 353–367, 1993. [click]

    Article  MathSciNet  MATH  Google Scholar 

  17. S. Roman, Advanced Linear Algebra, Springer, New York, 2008. [click]

    MATH  Google Scholar 

  18. G. Tao, J. Burkholder and J. Guo, “Adaptive state feedback actuator nonlinearity compensation for multivariable systems,” Int. J. Adapt. Control Signal Process, vol. 27, pp. 82–107, 2013. [click]

    Article  MathSciNet  MATH  Google Scholar 

  19. Y. Tseng and Y. Wang,“Model following variable structure control design in reciprocal state space framework with dead-zone nonlinearity and lumped uncertainty,” Proc. of 7th IEEE Conference on Industrial Electronics and Applications, pp. 1627–1632, 2012. [click]

    Google Scholar 

  20. J. Liu, W. Chen, M. Wu, J. She, Y. He, “Compensation in Repetitive Control System for Aperiodic Disturbances and Input Dead Zone,” Preprints of the 19th IFAC World Congress, Cape Town, South Africa, August, pp. 2752–2757, 2014.

    Google Scholar 

  21. Y. Tan, R. Dong, and R. Li, “Recursive identification of sandwich systems with dead zone and application,” IEEE Transactions on Control Systems Technology, vol. 17, no. 4, pp. 945–951, 2009. [click]

    Article  Google Scholar 

  22. R. Dong and Y. Tan, “On-line identification algorithm and convergence analysis for sandwich systems with backlash,” International Journal of Control, Automation and Systems, vol. 9, no. 3, pp. 588–594, 2011. [click]

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Na Luo

  2. School of General Education, Sanda University, 2727 Jinhai Road, Shanghai, 201209, China

    Na Luo

  3. Department of Electrical Engineering, Shanghai Normal University, Shanghai, 200234, China

    Yonghong Tan & Ruili Dong

Authors
  1. Na Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yonghong Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ruili Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yonghong Tan.

Additional information

Recommended by Associate Editor Do Wan Kim under the direction of Editor Myotaeg Lim. This work is partially supported by the Research Projects of Science and Technology Commission of Shanghai (Grant Nos. 14140711200 and and 14ZR1430300) and the National Science Foundation of China (NSFC Grant Nos.: 61571302, 61371145, 61203108, and 61171088).

Na Luo is a Ph.D. candidate of Mathematics and Science College in Shanghai Normal University. Presently, she is also a lecturer at the School of General Education, Sanda University, Shanghai, China. Her research interests are in analysis and control for nonlinear dynamic systems.

Yonghong Tan received his Ph.D. degree in electrical engineering in 1996 from the University of Ghent, Ghent, Belgium. He was a postdoctoral fellow at Simon Fraser University, Vancouver, BC, Canada from 1996 to 1998. He is currently a Professor in the College of Information, Mechanical and Electrical Engineering, Shanghai Normal University, Shanghai, China. Dr. Tan was once a visiting professor at Colorado State University, Fort Collins, USA; Concordia University, Montreal, QC, Canada; Shibaura Institute of Technology, Japan; and University ofWindsor, Canada. He also once held professorships at Guilin University of Electronic Technology and the University of Electronic Science and Technology of China, and moreover, he was an adjunct professor at Shanghai Jiaotong University, Nankai Univerity and Xidian University, respectively. His research interests include modeling and control of nonlinear systems, mechatronics, signal processing and intelligent control. He is the author or co-author of more than 220 articles published in peer review journals and referenced conferences, and he is also the holder of twelve patents.

Ruili Dong received her Ph.D. degree from Shanghai Jiaotong University, Shanghai, China. She is currently an Associate Professor in the College of Information, Mechanical and Electrical Engineering, Shanghai Normal University, Shanghai. Dr. Dong was once a visiting scholar at Dept. of Mechanical and Industrial Enigineering, Illinois University at Chicago, USA, from 2012 to 2013. Presently, she is a visiting professor at Dresden University of Technology, Germany. Her research interests include mechatronics and identification and control of nonlinear systems. Dr. Dong has published more than 50 papers in peerreview journals and referenced conferences. She also holds six patents.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Luo, N., Tan, Y. & Dong, R. Observability and controllability analysis for sandwich systems with dead-zone. Int. J. Control Autom. Syst. 14, 188–197 (2016). https://doi.org/10.1007/s12555-015-0015-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-015-0015-1

Keywords

Search

Navigation