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A Suboptimal Shifting Based Zero-pole Placement Method for Systems with Delays

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  • Control Theory and Applications
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Abstract

An appropriate setting of eventual controller parameters for a derived controller structure represents an integral part of many control design approaches for dynamical systems. This contribution is aimed at a practically applicable and uncomplicated controller tuning method for linear time-invariant time delay systems (LTI-TDSs). It is based on placing the dominant poles as well as zeros of the given infinite-dimensional feedback control system by matching them with the desired ones given by known dynamical properties of a simple fixed finite-dimensional model. The desired placing is done successively by applying the Quasi-Continuous Shifting Algorithm (QCSA) first such that poles and zeros are forced to be as close as possible to those of the model. Concurrently, rests of both system spectra are shifted to the left as far as possible to minimize the spectral abscissa. The obtained results are then enhanced by a non-convex optimization technique applied to a selected objective function reflecting the distance of desired model roots from the eventual system ones and the spectral abscissae. Retarded LTI-TDS are primarily considered; however, systems with neutral delays are touched as well. The efficiency of the proposed method is proved via numerical examples in Matlab/Simulink environment. Some drawbacks and possible improvements or extensions of the algorithm for the future research are also concisely suggested to the reader.

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Authors and Affiliations

  1. Faculty of Applied Informatics, Tomas Bata University in Zlín, Nad Stráněmi 4511, 76005, Zlín, Czech Republic

    Libor Pekař & Radek Matušů

Authors
  1. Libor Pekař
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  2. Radek Matušů
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Corresponding author

Correspondence to Libor Pekař.

Additional information

Recommended by Associate Editor Hongyi Li under the direction of Editor PooGyeon Park. This work was supported by the European Regional Development Fund under the project CEBIA-Tech Instrumentation No. CZ.1.05/2.1.00/19.0376.

Libor Pekař received his B.S. degree in Automation and Informatics from Tomas Bata University in Zlín, Czech Republic, in 2002, an M.S. degree in Automation and Control Engineering in Consumption Industry in 2005 and a Ph.D. degree in Technical Cybernetics from the same institution in 2013. From 2006 to 2013, he was working as a junior lecturer at the Faculty of Applied Informatics, Tomas Bata University in Zlín, Czech Republic. He is currently with the same institution as a senior lecturer. His research interests include analysis, modelling, identification and control of time-delay systems, algebraic control methods, autotuning and optimization techniques.

Radek Matušů received his M.S. degree in Automation and Control Engineering in Consumption Industry from Tomas Bata University in Zlín, Czech Republic, in 2002, and his Ph.D. degree in Technical Cybernetics from the same institution in 2007. He worked as a junior lecturer at the Faculty of Applied Informatics, Tomas Bata University in Zlín, Czech Republic, from 2004 to 2006. Since 2006 he has been working here as a junior researcher and a project manager. His research interests include robust control, uncertain systems and algebraic methods in control design.

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Pekař, L., Matušů, R. A Suboptimal Shifting Based Zero-pole Placement Method for Systems with Delays. Int. J. Control Autom. Syst. 16, 594–608 (2018). https://doi.org/10.1007/s12555-017-0074-6

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  • DOI: https://doi.org/10.1007/s12555-017-0074-6

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