A suboptimal shifting based zero-pole placement method for systems with delays

Pekař, Libor; Matušů, Radek

dc.title	A suboptimal shifting based zero-pole placement method for systems with delays	en
dc.contributor.author	Pekař, Libor
dc.contributor.author	Matušů, Radek
dc.relation.ispartof	International Journal of Control, Automation and Systems
dc.identifier.issn	1598-6446 Scopus Sources, Sherpa/RoMEO, JCR
dc.date.issued	2018
utb.relation.volume	16
utb.relation.issue	2
dc.citation.spage	594
dc.citation.epage	608
dc.type	article
dc.language.iso	en
dc.publisher	Institute of Control, Robotics and Systems
dc.identifier.doi	10.1007/s12555-017-0074-6
dc.relation.uri	https://link.springer.com/article/10.1007/s12555-017-0074-6
dc.subject	Controller tuning	en
dc.subject	direct-search optimization algorithm	en
dc.subject	model matching	en
dc.subject	time delay system	en
dc.subject	zero-pole assignment	en
dc.description.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. © 2018, Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature.	en
utb.faculty	Faculty of Applied Informatics
dc.identifier.uri	http://hdl.handle.net/10563/1007892
utb.identifier.obdid	43878716
utb.identifier.scopus	2-s2.0-85042583159
utb.identifier.wok	000429572000018
utb.source	j-scopus
dc.date.accessioned	2018-05-18T15:12:04Z
dc.date.available	2018-05-18T15:12:04Z
dc.description.sponsorship	CZ.1.05/2.1.00/19.0376; FEDER, European Regional Development Fund
dc.description.sponsorship	European Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376]
utb.contributor.internalauthor	Pekař, Libor
utb.contributor.internalauthor	Matušů, Radek
utb.fulltext.affiliation	Libor Pekař* and Radek Matušů Libor Pekař and Radek Matušů are with the Faculty of Applied Informatics, Tomas Bata University in Zlín, Nad Stráněmi 4511, 76005 Zlín, Czech Republic (e-mails: {pekar, rmatusu}@fai.utb.cz). * Corresponding author.
utb.fulltext.dates	Manuscript received February 12, 2017 revised August 4, 2017 accepted August 28, 2017
utb.fulltext.references	[1] J. P. Richard, “Time-delay systems: An overview of some recent advances and open problems,” Automatica, vol. 39, no. 10, pp. 1667-1694, October 2003. [click] [2] J. J. Loiseau, W. Michiels, S.-I. Niculescu, and R. Sipahi, Topics in Time Delay Systems. Analysis, Algorithms and Control, Springer-Verlag, New York, 2009. [3] R. Sipahi, T. Vyhlídal, S.-I. Niculescu, and P. Pepe, Time Delay Systems: Methods, Applications and New Trends, Springer-Verlag, New York, 2012. [4] T. Vyhlídal, J. F. Lafay, and R. Sipahi, Delay Systems: From Theory to Numerics and Applications, SpringerVerlag, New York, 2014. [5] S. O. R. Moheimani and I. R. Petersen, “Optimal quadratic guaranteed cost control of a class of uncertain time-delay systems,” IEE Proc.: Control Theory and Applications, vol. 144, no. 2, pp. 183-188, March 1997. [click] [6] K. J. Aström and T. Hägglund, Advanced in PID Control, ISA, Research Triangle Park, 2006. [7] S. Srivastava and V. S. Pandit, “A PI/PID controller for time delay systems with desired closed loop time response and guaranteed gain and phase margins,” Journal of Process Control, vol. 37, pp. 70-77, January 2016. [click] [8] J. R. Partington, “Some frequency-domain approaches to the model reduction of delay systems,” Annual Reviews in Control, vol. 28, pp. 65-73, 2004. [click] [9] E. B. Lee and S. H. Zak, “On spectrum placement for linear time invariant delay systems,” IEEE Trans. on Automatic Control, vol. 27, no. 2, pp. 446-449, April 1982. [10] P. Zítek and T. Vyhlídal, “Dominant eigenvalue placement for time delay systems,” Proc. of the 5th Portuguese Conf. Automation and Control, pp. 605-610, September 2002. [11] Q. G. Wang, Z. Zhang, K. J. Åström, and L. S. Chek, “Guaranteed dominant pole placement with PID controllers,” Journal of Process Control, vol. 19, no. 2, pp. 349-352, February 2009. [12] M. Vítecková and A. Víteček, “2DOF PI and PID controllers tuning,” IFAC Proc. Volumes (9th IFAC Workshop on Time Delay Systems), vol. 43, no. 2, pp. 343-348, June 2010. [13] J. Liu, H. Wang, and Y. Zhang, “New result on PID controller design of LTI systems via dominant eigenvalue assignment,” Automatica, vol. 62, pp. 93-97, December 2015. [click] [14] W. Michiels, K. Engelborghs, P. Vansevant, and D. Roose, “Continuous pole placement for delay equations,” Automatica, vol. 38, no. 5, pp. 747-761, May 2002. [click] [15] W. Michiels and T. Vyhlídal, “An eigenvalue based approach for the stabilization of linear time-delay systems of neutral type,” Automatica, vol. 41, no. 6, pp. 991-998, June 2005. [click] [16] T. Vanbiervliet, K. Verheyden, W. Michiels, and S. Vandewalle, “A nonsmooth optimization approach for the stabilization of time-delay systems,” ESAIM Control Optimisation and Calculus of Variations, vol. 14, no. 3, pp. 478-493, July 2008. [click] [17] W. Michiels and S. Gumussoy, “Eigenvalue-based algorithms and software for the design of fixed-order stabilizing controllers for interconnected systems with timedelays,” T. Vyhlídal, J. F. Lafay, and R. Sipahi (eds.), Delay Systems: From Theory to Numerics and Applications, Springer-Verlag, New York, pp. 243-256, 2014. [18] P. Zítek, J. Fišer, and T. Vyhlídal, “IAE optimization of PID control loop with delay in pole assignment space,” IFAC-PapersOnLine (13th IFAC Workshop on Time Delay Systems), vol. 49, no. 10, pp. 177-181, June 2016. [click] [19] A. F. Ergenc, “A matrix technique for dominant pole placement of discrete-time time-delayed systems,” IFAC Proc. Volumes (10th IFAC Workshop on Time Delay Systems), vol. 45, no. 14, pp. 167-172, June 2012. [20] W. Michiels, T. Vyhlídal, and P. Zítek, “Control design for time-delay systems based on quasi-direct pole placement,” Journal of Process Control, vol. 20, no. 3, pp. 337-343, March 2010. [click] [21] T. Vyhlídal and M. Hromčík, “Parameterization of input shapers with delays of various distribution,” Automatica, vol. 59, pp. 256-263, September 2015. [click] [22] J. A. Nelder and R. Mead, “A simplex method for function minimization,” The Computer Journal, vol. 7, no. 4, pp. 308–313, January 1965. [23] J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993. [24] T. Vyhlídal and P. Zítek, “QPmR - Quasi-polynomial root-finder: algorithm update and examples,” T. Vyhlídal, J. F. Lafay, and R. Sipahi (eds.), Delay Systems: From Theory to Numerics and Applications, Springer-Verlag, New York, pp. 299-312, 2014. [25] W. Michiels and S.-I. Niculescu, Stability, Control, and Computation for Time-Delay Systems: An EigenvalueBased Approach, SIAM, Philadelphia, 2014. [26] C. Bonnet, A. R Fioravanti, and J. R. Partington, “Stability of neutral systems with commensurate delays and poles asymptotic to the imaginary axis,” SIAM Journal on Control and Optimization, vol. 49, no. 2, pp. 498-516, April 2011. [click] [27] A. S. Lewis and M. L. Overton, “Nonsmooth optimization via quasi-Newton methods,” Mathematical Programming, vol. 141, no. 1, pp. 135-163, October 2013. [click] [28] H. E. Erol and A. Iftar, “Decentralized controller design by continuous pole placement for incommensurate-timedelay systems,” IFAC-PapersOnLine (12th IFAC Workshop on Time Delay Systems), vol. 48, no. 12, pp. 462–467, June 2015. [29] P. Zítek, V. Kučera, and T. Vyhlídal, “Meromorphic observer-based pole assignment in time delay systems,” Kybernetika, vol. 44, no. 5, pp. 633-648, October 2008. [30] L. Pekař and R. Prokop, “The revision and extension of the RMS ring for time delay systems,” Bulletin of Polish Academy of Sciences – Technical Sciences, vol. 65, no. 3, June 2017.
utb.fulltext.sponsorship	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.
utb.wos.affiliation	[Pekar, Libor; Matusu, Radek] Tomas Bata Univ Zlin, Fac Appl Informat, Stranemi 4511, Zlin 76005, Czech Republic
utb.scopus.affiliation	Faculty of Applied Informatics, Tomas Bata University in Zlín, Nad Stráněmi 4511, Zlín, Czech Republic
utb.fulltext.projects	CZ.1.05/2.1.00/19.0376