Nonlinear Dynamics

, Volume 51, Issue 1, pp 329–343

Stabilization using fractional-order PI and PID controllers

Original Paper

DOI: 10.1007/s11071-007-9214-5

Cite this article as:
Hamamci, S.E. Nonlinear Dyn (2008) 51: 329. doi:10.1007/s11071-007-9214-5


This paper presents a solution to the problem of stabilizing a given fractional dynamic system using fractional-order PIλ and PIλDμ controllers. It is based on plotting the global stability region in the (kp, ki)-plane for the PIλ controller and in the (kp, ki, kd)-space for the PIλDμ controller. Analytical expressions are derived for the purpose of describing the stability domain boundaries which are described by real root boundary, infinite root boundary and complex root boundary. Thus, the complete set of stabilizing parameters of the fractional-order controller is obtained. The algorithm has a simple and reliable result which is illustrated by several examples, and hence is practically useful in the analysis and design of fractional-order control systems.


Fractional-order controlFractional-order PI controllerFractional-order PID controllerGlobal stability regionStabilization

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Electrical-Electronics Engineering Department, Engineering FacultyInonu UniversityMalatyaTurkey