Skip to main content

Robust Control of Linear Continuous-Time Polytopic Systems and Application to an Electro-Hydraulic Servo System

  • Conference paper
Book cover Intelligent Robotics and Applications (ICIRA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5314))

Included in the following conference series:

Abstract

Sufficient conditions for the robust stability and stabilizability of linear continuous-time polytopic systems are proposed in this paper. These conditions are based on a parameter-dependent Lyapunov matrix obtained from the feasibility of a set of matrix inequalities defined at the vertices of polytopic systems. Noting that an electro-hydraulic servo system can be modeled as a linear continuous-time polytopic system, the controller derived from the proposed condition is applied to the control of this system. A numerical example demonstrates that this method has satisfactory performance.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dasgupta, S., Chockalingam, G., Anderson, B.D.O., Fu, M.: Lyapunov functions for uncertain systems with applications to the stability of time varying systems. IEEE Trans. Circuits and Systems I: Fundamental Theory and Applications 41(2), 93–106 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  2. Gahinet, P., Apkarian, P., Chilali, M.: Affine parameter-dependent Lyapunov functions and real parametric uncertainty. IEEE Trans. Automatic Control 41(3), 436–442 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  3. de Oliveira, M.C., Bernussou, J., Geromel, J.C.: A new discrete-time robust stability condition. System & Control Letters 37(4), 261–265 (1999)

    Article  MATH  Google Scholar 

  4. Daafouz, J., Bernussou, J.: Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties. System & Control Letters 43(5), 355–359 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  5. Peaucelle, D., Arzelier, D., Bachelier, O., Bernussou, J.: A new robust D-stability condition for real convex polytopic uncertainty. Systems & Control Letters 40, 21–30 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. Leite, V.J.S., Peres, P.L.D.: An improved LMI condition for robust D-stability of uncertain polytopic systems. IEEE Trans. Automatic Control 48(3), 500–504 (2003)

    Article  MathSciNet  Google Scholar 

  7. Arzelier, D., Henrion, D., Peaucelle, D.: Robust D stabilization of a polytope of matrices. Int. J. Control 75(10), 744–752 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Colaneri, P., Geromel, J.C., Locatelli, A.: Control theory and design: an RH2 and RH ∞  viewpoint. Academic Press, London (1997)

    Google Scholar 

  9. Wijnheijmer, F., Naus, G., Post, W., Steinbuch, M., Teerhuis, P.: Modelling and LPV control of an electro-hydraulic servo system. In: 2006 IEEE International Conference on Control Applications, pp. 3116–3121. IEEE Press, New York (2006)

    Chapter  Google Scholar 

  10. Kim, M.Y., Lee, C.-O.: An experimental study on the optimization of controller gains for an electro-hydraulic servo system using evolution strategies. Control Engineering Practice 14, 137–147 (2006)

    Article  Google Scholar 

  11. Yao, B., Bu, F., Chiu, G.T.C.: Non-linear adaptive robust control of electro-hydraulic systems driven by double-rod actuators. Int. J. Control 74(8), 761–775 (2001)

    Article  MATH  Google Scholar 

  12. Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V.: Linear matrix inequalities in system and control theory. SIAM, Philadelphia (1994)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mao, WJ., Zhang, YY. (2008). Robust Control of Linear Continuous-Time Polytopic Systems and Application to an Electro-Hydraulic Servo System. In: Xiong, C., Huang, Y., Xiong, Y., Liu, H. (eds) Intelligent Robotics and Applications. ICIRA 2008. Lecture Notes in Computer Science(), vol 5314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88513-9_43

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-88513-9_43

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88512-2

  • Online ISBN: 978-3-540-88513-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics