Abstract
During the development of algebraic controller design in a special ring for time delay systems (TDSs) a problem of a suitable free controller parameters setting appeared. The first author of this contribution recently suggested a natural idea of placing the dominant characteristic numbers (poles) and zeros of the infinite-dimensional feedback control system on the basis of the desired overshoot for a simple finite-dimensional matching model and shifting of the rest of the spectrum. However, the original procedure called the Pole-Placement Shifting based controller tuning Algorithm (PPSA) was not developed and described entirely well. The aim of this paper is to revise the idea of the PPSA and suggest a possible ways how to improve or extend the algorithm. A concise illustrative example is attached to clarify the procedure for the reader as well.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Hale, J.K., Verduyn Lunel S.M.: Introduction to functional differential equations. Appl. Math. Sci. 99, (1993)
Kolmanovskii, V.B., Myshkis, A.: Introduction to the theory and applications of functional differential equations. Cluwer Academy, Dordrecht (1999)
Niculescu S.I.: Delay effects on stability. Lecture Notes in Control and Information Sciences, vol. 269. Springer, Berlin (2001)
Richard, J.P.: Time-delay systems: An overview of some recent advances and open problems. Automatica 39, 1667–1694 (2003)
Zítek, P., Kučera, V.: Algebraic design of anisochronic controllers for time delay systems. Int J Control 76, 1654–1665 (2003)
Pekař, L.: A ring for description and control of time-delay systems. In: WSEAS Transaction on Systems 11. Special Issue on Modelling, Identification, Stability, Control and Applications, pp. 571–585 (2012)
Michiels, W., Engelborghs, K., Vansevevant, P., Roose, D.: Continuous pole placement for delay equations. Automatica 38, 747–761 (2002)
Michiels, W., Vyhlídal, T.: An eigenvalue based approach for the stabilization of linear time-delay systems of neutral type. Automatica 41, 991–998 (2005)
Michiels, W., Vyhlídal, T., Zítek, P.: Control design for time-delay systems based on quasi-direct pole placement. J Process Control 20, 337–343 (2010)
Pekař, L.: On a controller parameterization for infinite-dimensional feedback systems based on the desired overshoot. WSEAS Trans. Syst. 12, 325–335 (2013)
Zelinka, I.: SOMA-self organizing migrating algorithm. In: Onwobolu, G.C., Babu, B.V. (eds.) New optimization techniques in engineering, pp. 167–217. Springer, Berlin (2004)
Vanbiervliet, T., Verheyden, K., Michiels, W., Vandewalle, S.: A nonsmooth optimization approach for the stabilization of time-delay systems. ESIAM: Control Optim. Calc. Var. 14, 478–493 (2008)
Nelder, J.A., Mead, R.: A simplex method for function minimization. Comput. J. 7, 308–313 (1965)
Vyhlídal, T.: analysis and synthesis of time delay system spectrum. Ph.D. thesis. Faculty of Mechanical Engineering, Czech Technical University in Prague, Prague (2003)
Zítek, P., Kučera, V., Vyhlídal, T.: Meromorphic observer-based pole assignment in time delay systems. Kybernetika 44, 633–648 (2008)
Pekař, L., Prokop, R.: Algebraic optimal control in RMS ring: a case study. Int. J. Math. Comput. Simul. 7, 59–68 (2013)
Acknowledgements
The authors kindly appreciate the financial support which was provided by the European Regional Development Fund under the project CEBIA-Tech No. CZ.1.05/2.1.00/03.0089.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Pekař, L., Navrátil, P. (2014). PPSA: A Tool for Suboptimal Control of Time Delay Systems: Revision and Open Tasks. In: Silhavy, R., Senkerik, R., Oplatkova, Z., Silhavy, P., Prokopova, Z. (eds) Modern Trends and Techniques in Computer Science. Advances in Intelligent Systems and Computing, vol 285. Springer, Cham. https://doi.org/10.1007/978-3-319-06740-7_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-06740-7_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06739-1
Online ISBN: 978-3-319-06740-7
eBook Packages: EngineeringEngineering (R0)