Skip to main content
Log in

Robust-stabilizing controller horizons on the basis of predictive model with truncated pulse transient function

  • Adaptive and Robust Systems
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

Abstract

Consideration was given to the problem of determining the robust-stabilizing values of the control (M) and prediction (P) horizons for the systems with predictive controllers. The specified z-image of the controller with predictive model allows one to examine the asymptotic characteristics of the closed loop and determine the condition for system robust stability in the case of astatic delay plants. The advantage of the proposed method of determination of M and P was demonstrated by way of example.

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

Access this article

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. Krasovskii, A.A., Bukov, V.N., and Shendrik, V.S., Universal’nye algoritmy optimal’nogo upravleniya nepreryvnymi protsessami (Universal Algorithms of Optimal Control of Continuous Processes), Moscow: Nauka, 1977.

    Google Scholar 

  2. Kwon, W.H. and Han, S.H., Receding Horizon Control: Model Predictive Control for State Models, Berlin: Springer, 2005.

    Google Scholar 

  3. Morary, M. and Lee, J.H., Model Predictive Control: Past, Present and Future, Comput. Chemical Eng., 1999, no. 4–5, pp. 667–682.

  4. Qin, S.J. and Badgwell, T.A., A Survey of Industrial Model Predictive Control Technology, Control Eng. Practice, 2003, vol. 11, no. 7, pp. 733–764.

    Article  Google Scholar 

  5. Kothare, M.V., Balakrishnan, V., and Morary, M., Robust Constrained Model Predictive Control Using Linear Matrix Inequalities, Automatica, 1996, vol. 32, no. 10, pp. 1361–1379.

    Article  MATH  Google Scholar 

  6. Langson, W., Chryssochoos, I., Racovic, S.V., and Mayne, D.Q., Robust Model Predictive Control Using Tubes, Automatica, 2004, vol. 40, pp. 125–133.

    Article  MATH  Google Scholar 

  7. Yan, J. and Bitmead, R.R., Incorporating State Estimation into Model Predictive Control and Its Application to Network Traffic Control, Automatica, 2005, vol. 41, pp. 595–604.

    Article  MATH  Google Scholar 

  8. Liu, Ch.-Sh. and Peng, H., Inverse-dynamics Based State and Disturbance Observers for Linear Time-invariant Systems, J. Dynam. Syst., Measurement, Control, 2002, vol. 124, pp. 375–381.

    Article  Google Scholar 

  9. Richard, J.-P., Time-delay Systems: An Overview of Some Recent Advances and Open Problems, Automatica, 2003, vol. 39, pp. 1667–1694.

    Article  MATH  Google Scholar 

  10. Dougherty, D. and Cooper, D., A Practical Multiple Model Adaptive Strategy for Single-loop MPC, Control Eng. Practice, 2003, vol. 11, pp. 141–159.

    Article  Google Scholar 

  11. Luyben, W., Practical Distillation Control, New York: Van Nostrand Reinhold, 1992.

    Google Scholar 

  12. Badgwell, T.A., Robust Stability Conditions for SISO Model Predictive Control Algorithms, Automatica, 1997, vol. 33, no. 7, pp. 1357–1361.

    Article  MATH  Google Scholar 

  13. Shen, T. and Zhu, J., Necessary and Sufficient Conditions for Robust Stability of DMC, in Proc. 5 th World Congr. Intelligent Control Automat., Hangzhou, P.R. China, 2004, pp. 624–627.

  14. Gantmakher, F.R., Teoriya matrits (Matrix Theory), Moscow: Nauka, 1967.

    Google Scholar 

  15. Lundstrom, P., Lee, J.H., Morari, M., and Skogestad, S., Limitations of Dynamic Matrix Control, Comput. & Chemical Eng., 1995, vol. 19, no. 4, pp. 409–421.

    Article  Google Scholar 

  16. Li, Zh., Liu, J., Fu, C., and Tan, W., A Modified Dynamic Matrix Control for Integrating Processes, in Proc. Int. Conf. Control Appl., Taipei, Taiwan, 2004, pp. 1674–1678.

  17. Morari, M. and Zafiriou, E., Robust Process Control, Englewood Cliffs: Prentice Hall, 1989.

    Google Scholar 

  18. Kong, F. and Keyser, R.D., Criteria for Choosing the Horizon in Extended Horizon Predictive Control, IEEE Trans. Automat. Control, 1994, vol. 39, no. 7, pp. 1467–1470.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © A. Yu. Torgashov, 2007, published in Avtomatika i Telemekhanika, 2007, No. 7, pp. 90–102.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Torgashov, A.Y. Robust-stabilizing controller horizons on the basis of predictive model with truncated pulse transient function. Autom Remote Control 68, 1201–1212 (2007). https://doi.org/10.1134/S0005117907070089

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117907070089

PACS number

Navigation