František GazdošIntroducing a New Tool for Studying Unstable Systems. International Journal of Automation and Computing, vol. 11, no. 6, pp. 580-587, 2014.
Citation: František GazdošIntroducing a New Tool for Studying Unstable Systems. International Journal of Automation and Computing, vol. 11, no. 6, pp. 580-587, 2014.

Introducing a New Tool for Studying Unstable Systems

doi: 10.1007/s11633-014-0844-z
  • Received Date: 2013-08-05
  • Rev Recd Date: 2013-10-11
  • Publish Date: 2014-12-20
  • This paper presents the starting project of a web site focussed on unstable systems. It is a web-based database in a bilingual version (English/Czech), which can be used as an information database for models of unstable processes. The web site contains the mathematical models of such systems, including their simulation files together with basic information about the stability of dynamic systems. The paper outlines the motivation for the development of this database, presents its basic structure, and discusses several models from the site. The areas of prospective usage are also suggested together with the possible directions of further development of this project. The contribution ends with a case study using the database for control system analysis and design of the Amira inverted pendulum. The systematic polynomial approach is fruitfully utilised for the task together with some useful tools from the robust control theory.


  • loading
  • [1]
    M. Chidambaram. Control of unstable systems: A review. Journal of Energy, Heat and Mass Transfer, vol. 19, pp. 49-57, 1997.
    R. Padma Sree, M. Chidambaram. Control of Unstable Systems, Oxford: Alpha Science Int. Ltd., 2006.
    G. Stein. Respect the unstable. IEEE Control System Magazine, vol. 23, no. 4, pp. 12-25, 2003.
    R. H. Middleton. Trade-offs in linear control system design. Automatica, vol. 27, no. 2, pp. 281-292, 1991.
    S. Skogestad, K. Havre, T. Larsson. Control limitations for unstable plants. In Proceedings of the 15th Triennial World Congress, IFAC, Barcelona, Spain, pp. 328, 2002.
    J. L. Willems. Stability Theory of Dynamical Systems, New York: Wiley, 1970.
    S. Skogestad, I. Postlethwaite. Multivariable Feedback Control: Analysis and Design, Chichester: Wiley, 2005.
    P. C. Parks. A. M. Lyapunov's stability theory-100 years on. IMA Journal of Mathematical Control and Information, vol. 9, no. 4, pp. 275-303, 1992.
    K. J. Åström, R. M. Murray. Feedback Systems: An Introduction for Scientist and Engineers, Princeton: Princeton University Press, 2008.
    J. C. Doyle, B. A. Francis, A. R. Tannenbaum. Feedback Control Theory, Mineola, New York: Dover Publications, 2009.
    J. H. Park, S. W. Sung, I. B. Lee. An enhanced PID control strategy for unstable processes. Automatica, vol. 34, no. 6, pp. 751-756, 1998.
    G. Marchetti, C. Scali, D. R. Lewin. Identification and control of open-loop unstable processes by relay methods. Automatica, vol. 37, no. 12, pp. 2049-2055, 2001.
    R. Lozano, P. Castillo, P. Garcia, A. Dzul. Robust prediction-based control for unstable delay systems: Application to the yaw control of a mini-helicopter. Automatica, vol. 40, no. 4, pp. 603-612, 2004.
    P. García, P. Albertos, T. Hägglund. Control of unstable non-minimum-phase delayed systems. Journal of Process Control, vol. 16, no. 10, pp. 1099-1111, 2006.
    P. Dostál, F. Gazdoš, V. Bobál. Design of controllers for time delay systems, Part II: Integrating and unstable systems. Journal of Electrical Engineering, vol. 59, no. 1, pp. 3-8, 2008.
    X. K. Zhang, X. L. Jia. Solving robust controller of unstable process using mirror-injection method. Systems Engineering and Electronics, vol. 22, no. 4, pp. 10-12, 2000.
    B. R. Barmish. New Tools for Robustness of Linear Systems, New York: Macmillan, 1994.
    S. P. Bhattacharyya, H. Chapellat, L. H. Keel. Robust Control: The Parametric Approach, New Jersey: Prentice-Hall, 1995.
    C. T. Liou, Y. S. Chien. The effect of nonideal mixing on input multiplicity in a CSTR. Chemical Engineering Science, vol. 46, no. 8, pp. 2113-2116, 1991.
    J. H. Blakelock. Automatic Control of Aircraft and Missiles, New York: John Wiley, 1991.
    W. L. Rogers, D. J. Collins. X-29 H controller synthesis. Journal of Guidance, Control, and Dynamics, vol. 15, no. 4, pp. 962-967, 1992.
    R. Clarke, J. J. Burken, J. T. Bosworth, J. E. Bauer. X-29 flight control system: Lessons learned. International Journal of Control, vol. 59, no. 1, pp. 199-219, 1994.
    AMIRA. PS600 Laboratory Experiment Inverted Pendulum, Amira GmbH, Duisburg, Germany, 2000.
    P. Chalupa, V. Bobál. Modelling and predictive control of inverted pendulum. In Proceedings of the 22nd European Conference on Modelling and Simulation, EDMS, Nicosia, Cyprus, pp. 531-537, 2008.
    J. Marholt, F. Gazdoš, P. Dostál. Control of the unstable system of the inverted pendulum using the polynomial approach. Cybernetic Letters, 2011.
    J. Kolařík. Web-based Database of Unstable Systems, Bachelor Dissertation, Faculty of Applied Informatics, Tomas Bata University in Zlín, Czech Republic, 2012. (in Czech)
    J. Marriott, E. Waring. The Official Joomla! Book, 2nd ed., Boston: Addison-Wesley Professional, 2013.
    V. Kučera. Diophantine equations in control-a survey. Automatica, vol. 29, no. 6, pp. 1361-1375, 1993.
    K. J. Hunt. Polynomial Methods in Optimal Control and Filtering, London: Peter Peregrinus Ltd., 1993.
    B. D. O. Anderson. From Youla-Kucera to identification, adaptive and nonlinear control. Automatica, vol. 34, no. 12, pp. 1485-1506, 1998.
    M. J. Grimble. Robust Industrial Control: Optimal Design Approach for Polynomial Systems, London: Prentice Hall, 1994.
    F. Gazdoš, J. Marholt, J. Kolařík. Unstable systems database: A new tool for students, teachers and scientists. In Proceedings of Nostradamus 2013: Prediction, Modeling & Analysis of Complex Systems, Springer, Ostrava, Czech Republic, pp. 275-284, 2013.
  • 加载中


    通讯作者: 陈斌,
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索



    Article Metrics

    Article views (4950) PDF downloads(1846) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint