292
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Controller design for delay systems via eigenvalue assignment – on a new result in the distribution of quasi-polynomial roots

, , &
Pages 2457-2476 | Received 30 May 2014, Accepted 01 May 2015, Published online: 04 Jun 2015

References

  • Asl, F.M., & Ulsoy, A.G. (2003). Analysis of a system of linear delay differential equations. Journal of Dynamic Systems, Measurement, and Control, 125(2), 215–223.
  • Åström, K., & Hägglund, T. (2006). Advanced PID control. Research Triangle Park, NC: Instrumentation, Systems, and Automation Society.
  • Bellman, R., & Cooke, K.L. (1963). Differential-difference equations. London: Academic Press.
  • Bozorg, M., & Termeh, F. (2011). Domains of PID controller coefficients which guarantee stability and performance for LTI time-delay systems. Automatica, 47(9), 2122–2125.
  • Corless, R.M., Gonnet, G.H., Hare, D.E.G., Jeffrey, D.J., & Knuth, D.E. (1996). On the Lambert W function. Advances in Computational Mathematics, 5(1), 329–359.
  • Engelborghs, K., Luzyanina, T., & Roose, D. (2002). Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL. ACM Transactions on Mathematical Software, 28, 1–21.
  • Fliess, M., Marquez, R., & Mounier, H. (2002). An extension of predictive control, PID regulators and Smith predictors to some linear delay systems. International Journal of Control, 75(10), 728–743.
  • Franke, M. (2014). Eigenvalue assignment by static output feedback-on a new solvability condition and the computation of low gain feedback matrices. International Journal of Control, 87(1), 64–75.
  • Górecki, H., Fuksa, S., Grabowski, P., & Korytowaki, A. (1989). Analysis and synthesis of time delay systems. Warszawa: Polish Scientific Publishers.
  • Gu, K., Kharitonov, V.L., & Chen, J. (2003). Stability of time-delay systems. Boston, MA: Birkhäuser.
  • Hale, J.K., & Verduyn Lunel, S.M. (1993). Introduction to functional differential equations. Applied Mathematical Sciences (Vol. 99). New York, NY: Springer.
  • Hale, J.K., & Verduyn Lunel, S.M. (2002). Strong stabilization of neutral functional differential equations. IMA Journal of Mathematical Control and Information, 19(1–2), 5–23.
  • He, S.-A., & Fong, I. (2012). PID controllers for a class of unstable linear time-delay systems: An eigenvalue-loci approach. Journal of Process Control, 22, 1722–1731.
  • Hohenbichler, N. (2009). All stabilizing PID controllers for time delay systems. Automatica, 45(11), 2678–2684.
  • Iyer, A., & Saeks, R. (1984). Feedback system design: The pole placement problem. International Journal of Control, 39(3), 455–472.
  • Kharitonov, V.L., & Zhabko, A.P. (1994). Robust stability of time-delay systems. IEEE Transactions on Automatic Control, 39(12), 2388–2397.
  • Leventides, J., Rosenthal, J., & Wang, X.A. (1999). The pole placement problem via PI feedback controllers. International Journal of Control, 72(12), 1065–1077.
  • Méndez-Barrios, C.-F., Niculescu, S.-I., Chen, J., & Maya-Méndez, M. (2013). Output feedback stabilisation of single-input single-output linear systems with I/O network-induced delays. An eigenvalue-based approach. International Journal of Control, 287(2), 346–362.
  • Michiels, W., Engelborghs, K., Vansevenant, P., & Roose, D. (2002). Continuous pole placement method for delay equations. Automatica, 38(5), 747–761.
  • Michiels, W., & Gumussoy, S. (2014). Eigenvalue based algorithms and software for the design of fixed-order stabilizing controllers for interconnected systems with time-delays. In T. Vyhlídal, J.-F. Lafay, R. Sipahi (Eds.), Lecture notes in delays and dynamics (pp. 243–256). New York, NY: Springer.
  • Michiels, W., & Niculescu, S.-I. (2007). Stability and stabilization of time-delay systems: An Eigenvalue-based approach. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM).
  • Michiels, W., & Vyhlídal, T. (2005). An eigenvalue based approach for the stabilization of linear time-delay systems of neutral type. Automatica, 41, 991–998.
  • Michiels, W., Vyhlídal, T., & Zítek, P. (2010). Control design for time-delay systems based on quasi-direct pole placement. Journal of Process Control, 20, 337–343.
  • Michiels, W., Vyhlídal, T., Zítek, P., Nijmeijer, H., & Henrion, D. (2009). Strong stability of neutral equations with an arbitrary delay dependency structure. SIAM Journal on Control and Optimization, 48(2), 763–786.
  • Olgac, N., Vyhlídal, T., & Sipahi, R. (2008). A new perspective in the stability assessment of neutral systems with multiple and cross-talking delays. SIAM Journal on Control and Optimization, 47(1), 327–344.
  • Oliveira, V.A., Cossi, L.V., Teixeira, M.C.M., & Silva, A.M.F. (2009). Synthesis of PID controllers for a class of time delay systems. Automatica, 45(7), 1778–1782.
  • Oliveira, V.A., Teixeira, M., & Cossi, L. (2003). Stabilizing a class of time delay systems using the Hermite–Biehler theorem. Linear Algebra and Its Applications, 369, 203–216.
  • Ou, L., Zhang, W., & Gu, D. (2006). Sets of stabilising PID controllers for second-order integrating processes with time delay. IEE Proceedings – Control Theory and Applications, 153(5), 607–614.
  • Ou, L., Zhang, W., & Yu, L. (2009). Low-order stabilization of LTI systems with time delay. IEEE Transactions on Automatic Control, 54(4), 774–787.
  • Padula, F., & Visioli, A. (2012). On the stabilizing PID controllers for integral processes. IEEE Transactions on Automatic Control, 57(2), 494–499.
  • Richard, J.-P. (2003). Time-delay systems: An overview of some recent advances and open problems. Automatica, 39(10), 1667–1694.
  • Silva, G.J., Datta, A., & Bhattacharyya, S.P. (2001). PI stabilization of first-order systems with time delay. Automatica, 37(12), 2025–2031.
  • Silva, G.J., Datta, A., & Bhattacharyya, S.P. (2002). New results on the synthesis of PID controllers. IEEE Transactions on Automatic Control, 47(2), 241–252.
  • Silva, G.J., Datta, A., & Bhattacharyya, S.P. (2005). PID controllers for time-delay systems. Boston, MA: Birkhäuser.
  • Sipahi, R., Niculescu, S.-I., Abdallah, T., Michiels, W., & Gu, K. (2011). Stability and stabilization of systems with time delay. IEEE Control Systems Magazine, 31(1), 38–65.
  • Vanbiervliet, J., Verheyden, K., Michiels, W., & Vandewalle, S. (2008). A nonsmooth optimisation approach for the stabilisation of time-delay systems. ESAIM Control, Optimisation and Calculus of Variations, 14(3), 478–493.
  • Vyhlídal, T., Michiels, W., Zítek, P., & McGahan, P. (2009). Stability impact of small delays in proportional-derivative state feedback. Control Engineering Practice, 17(3), 382–393.
  • Vyhlídal, T., & Zítek, P. (2009). Mapping based algorithm for large-scale computation of quasi-polynomial zeros. IEEE Transactions on Automatic Control, 54(1), 171–177.
  • Wang, D.J. (2007a). Further results on the synthesis of PID controllers. IEEE Transactions on Automatic Control, 52(6), 1127–1132.
  • Wang, D.J. (2007b). Stabilising regions of PID controllers for nth-order all pole plants with dead-time. IET Control Theory and Applications, 1(4), 1068–1074.
  • Wang, H., Liu, J., Yang, F., & Zhang, Y. (2014). New result on low-order controller design for first-order delay processes via eigenvalue assignment. 19th IFAC world congress, August 24–29, 2014, Cape Town, South Africa
  • Wang, Q.G., Zhang, Z., Astrom, K.J., & Chek, L.S. (2009). Guaranteed dominant pole placement with PID controllers. Journal of Process Control, 19(2), 349–352.
  • Wang, X., Martin, C.F., Gilliam, D., & Byrnes, C.I. (1992). Decentralized-feedback pole placement of linear systems. International Journal of Control, 55(2), 511–518.
  • Yi, S., Nelson, P.W., & Ulsoy, A.G. (2010a). Eigenvalue assignment via the Lambert W function for control of time-delay systems. Journal of Vibration and Control, 16(7–8), 961–982.
  • Yi, S., Nelson, P.W., & Ulsoy, A.G. (2010b). Time-delay systems: Analysis and control using the Lambert W function. Singapore: World Scientific.
  • Yi, S., Nelson, P.W., & Ulsoy, A.G. (2013). Proportional-integral control of first-order time-delay systems via eigenvalue assignment. IEEE Transactions on Control Systems Technology, 21(5), 1586–1594.
  • Zítek, P. (1997). Frequency-domain synthesis of hereditary control systems via anisochronic state space. International Journal of Control, 66(4), 539–556.
  • Zítek, P., Fis̆er, J., & Vyhlídal, T. (2013). Dimensional analysis approach to dominant three-pole placement in delayed PID control loops. Journal of Process Control, 23(8), 1063–1074.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.