Skip to main content

Towards a Hybrid Symbolic/Numeric Computational Approach in Controller Design

  • Conference paper
  • First Online:
  • 324 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2385))

Abstract

Application of general computer algebra systems like MAPLE V® can prove advantageous over conventional ‘numerical’ simulation approach for controller design. In this paper, an approach for the application of hybrid symbolic/numeric computations to obtain explicit equations leading to the design of an output feedback controller is presented. The methodology for controller design using symbolic algebra is exemplified by considering the design of an excitation controller for a simplified model of the synchronous generator connected to an infinite bus. The output feedback controller is obtained from a symbolic full-state feedback controller by eliminating feedback from unmeasurable states using the free parameters in the symbolic feedback gain expressions. The entire analysis is carried out using the MATLAB® symbolic algebra toolbox that supports MAPLE V®.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. G.(Bram) de Jager, Applications of zero dynamics with symbolic computation, UKACC international conference on control’98, September 1998, pp. 1311–1316.

    Google Scholar 

  2. H. Baki and N. Munro, Implementation of balanced realisation algorithms in a symbolic environment, UKACC International conference on control’98, pp. 1317–1321.

    Google Scholar 

  3. E. Kontogiannis and N. Munro, The use of symbolic algebra in robust control, UKACC International conference on control’98, September 1998. pp. 1328–1332.

    Google Scholar 

  4. D.J. Balance and W. Chen, Symbolic computation in value sets of plants with uncertain parameters, UKACC International Conference on Control’98, September 98, pp. 1322–1327.

    Google Scholar 

  5. M.T. Soylemez and N. Munro, Pole assignment and symbolic algebra: A new way of thinking, UKACC International Conference on Control’98, September 1998, pp. 1306–1310.

    Google Scholar 

  6. M. Chetty and K.P Dabke, Symbolic computations: An overview and application to controller design, proceedings of international conference on Information, Decision and Control, Adelaide, 8th-10th February, 1999, pp. 451–456.

    Google Scholar 

  7. K. P. Dabke, Linear control with incomplete state feedback and known initial-state statistics, Int. J. Control, vol. 11, No. 1, pp. 133–141, 1970.

    Article  MATH  MathSciNet  Google Scholar 

  8. G. Zames, Input-Output Feedback Stability and Robustness, 1959-85, IEEE Control Systems, vol. 16, No. 3, pp. 61–66, June 1996.

    Article  Google Scholar 

  9. T. Kailath, Linear systems, Prentice Hall, Englewood cliffs, New Jersey, 1980.

    MATH  Google Scholar 

  10. B. Porter and M.A. Woodhead, Performance of optimal control systems when some of the state variables are not measurable, Int. Jr. of Control, vol. 8, pp. 191–195, 1968.

    Article  MATH  Google Scholar 

  11. The Mathworks Inc., Symbolic math tool for use with MATLAB, user’s guide, Version 2.

    Google Scholar 

  12. M.L. Kothari, J. Nanda and K. Bhattacharya, Discrete-mode power system stabilisers, Proc. IEE part-C, Generation Transmission and Distribution, November, 1993, pp. 523–531.

    Google Scholar 

  13. M. Aldeen and M. Chetty, A dynamic output power system stabiliser, Control’95, October 1997, vol. 2, pp. 575–579.

    Google Scholar 

  14. D.D. Moerder and A.J Calise, Convergence of a numerical algorithm for calculating optimal output feedback gains, IEEE Trans. On Automatic Control, Vol. AC-30, No. 9, pp. 900–903, September 1985.

    Article  Google Scholar 

  15. W.S. Levine and M. Athans, On the determination of optimal output feedback gains for linear multivariable systems, IEEE Trans on Automatic Control, Vol. AC-15, pp.44–48, 1970.

    Article  MathSciNet  Google Scholar 

  16. S.S Choi and H.R. Sirisena, Computation of optimal output feedback controls for unstable linear multivariable systems, IEEE Trans on Automatic Control, Vol. AC-22, pp.134–136, Feb 1977.

    Article  Google Scholar 

  17. P.M. Anderson and A.A. Fouad, Power system control and stability, New York, IEEE press, 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chetty, M. (2002). Towards a Hybrid Symbolic/Numeric Computational Approach in Controller Design. In: Calmet, J., Benhamou, B., Caprotti, O., Henocque, L., Sorge, V. (eds) Artificial Intelligence, Automated Reasoning, and Symbolic Computation. AISC Calculemus 2002 2002. Lecture Notes in Computer Science(), vol 2385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45470-5_5

Download citation

  • DOI: https://doi.org/10.1007/3-540-45470-5_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43865-6

  • Online ISBN: 978-3-540-45470-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics