Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 105143, 20 pages
Research Article

The Design of QFT Robust Compensators with Magnitude and Phase Specifications

1Departamento de Lenguajes y Computación, Escuela Politécnica Superior, Universidad de Almeria, 04120 Almeria, Spain
2Departamento de Informática y Sistemas, Facultad de Informática, Universidad de Murcia, 30100 Murcia, Spain

Received 27 April 2010; Revised 29 October 2010; Accepted 27 December 2010

Academic Editor: Jerzy Warminski

Copyright © 2010 José Carlos Moreno et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The frequency response is an important tool for practical and efficient design of control systems. Control techniques based on frequency response are of special interest to dealing with important subjects such as the bandwidth and the cost of feedback. Furthermore, these techniques are easily adapted to deal with the uncertainty of the process to control. Quantitative feedback theory (QFT) is an engineering design technique of uncertain feedback systems that uses frequency domain specifications. This paper analyzes the phase specifications problem in frequency domain using QFT. This type of specification is not commonly taken into account due to the fundamental limitations of the linear control given by Bode's integral. An algorithm is proposed aimed at achieving prespecified closed-loop transfer function phase and magnitude variations, taking into account the plant uncertainty. A two-degrees-of-freedom feedback control structure is used and a new type of boundary is defined to satisfy these objectives. As the control effort heavily depends on a good estimation of these boundaries, the proposed algorithm allows avoiding overdesign.