Root-Locus Analysis of Delayed First and Second Order Systems

  • Moisés Ríos Flores Instituto Politécnico Nacional
  • J.F. Marquez-Rubio Instituto Politécnico Nacional
  • B. del Muro-Cuellar Instituto Politécnico Nacional
  • E. Aranda-Bricaire CINVESTAV IPN
Keywords: time-delay, root locus diagram, feedback control, poles, zeros


For finite dimensional linear system the root-locus method is well established however for the case of delayed systems the method has some problems due to the transcendental term involved. This work intends to illustrate the problems that arises when a root-locus diagram is performed as well as to develop a Matlab function that provides the root-locus diagram for delayed low order systems. In this way, some comments about the problems that should be tackled to obtain a generalization of the computational method for delayed systems with real m poles and n zeros


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Banker, G. (2011). PID tuning of plants with time delay using root locus. Master's Theses. San Jose State University.
Gouaisbaut, F. a. (2006). Stability of time delay sistems with non-small delay. In Proccedings of the 45th IEEE Conf. on Deciion and Control, 840-845. San Diego, CA, USA.
Munz, U. E. (2009). Stability analysis of time-delay systems with incommensurate delay using positive polynomials. IEEE Transactions on Automatic Control, 54(5), 1019-1024.
Silva, G., & Bhattacharyya, S. (2005). PID controllers for time-delay system. Birkhuser, Boston.
Suh, I., & Bien, Z. (1982). A root-locus technique for linear systems with delay. IEEE Transactions on Automatic Control. 27-1, 205-108.
Wang, Z., & Hu, H. (2008). Calculation if the rightmost characteristic root of retarded time-delay systems via lambert w function. Journal of Sound and Vibration, 318, 757-767.
How to Cite
Ríos Flores, M., Marquez-Rubio, J., del Muro-Cuellar, B., & Aranda-Bricaire, E. (2018). Root-Locus Analysis of Delayed First and Second Order Systems. Enfoque UTE, 9(4), pp. 69 - 76.
Automation and Control, Mechatronics, Electromechanics, Automotive