Nonlinear Dynamics

, Volume 38, Issue 1, pp 305–321

Tuning of PID Controllers Based on Bode’s Ideal Transfer Function

  • Ramiro S. Barbosa
  • J. A. Tenreiro Machado
  • Isabel M. Ferreira
Article

DOI: 10.1007/s11071-004-3763-7

Cite this article as:
Barbosa, R., Machado, J. & Ferreira, I. Nonlinear Dyn (2004) 38: 305. doi:10.1007/s11071-004-3763-7

Abstract

This paper presents a new strategy for tuning PID controllers based on a fractional reference model. The model is represented as an ideal closed-loop system whose open-loop is given by the Bode’s ideal transfer function. The PID controller parameters are determined by the minimization of the integral square error (ISE) between the time responses of the desired fractional reference model and of the system with the PID controller. The resulting closed-loop system (with the PID controller) has the desirable feature of being robust to gain variations with step responses exhibiting an iso-damping property. Several examples are presented that demonstrate the effectiveness and validity of the proposed methodology.

Key words:

Bode’s ideal transfer functionfractional calculusfractional-order systemsISE optimizationPID tuning

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Ramiro S. Barbosa
    • 1
  • J. A. Tenreiro Machado
    • 1
  • Isabel M. Ferreira
    • 2
  1. 1.Department of Electrotechnical Engineering, Institute of Engineering of PortoRua Dr. António Bernardino de AlmeidaPortoPortugal
  2. 2.Department of Electrotechnical Engineering, Faculty of Engineering of PortoRua Dr. Roberto FriasPortoPortugal