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Mathematical Problems in Engineering
Volume 2006 (2006), Article ID 51874, 15 pages

Constrained regulator problem for linear uncertain systems: Control of a pH process

1Constrained and Robust Regulation Research Unit, Physics Department, Faculty of Sciences, Cadi Ayyad University, B.P. 2390, Marrakesh, Morocco
2Departamento de Ingeniería de Sistemas y Automática, Universidad de Valladolid, Valladolid 47005, Spain

Received 8 November 2005; Accepted 14 February 2006

Copyright © 2006 Fouad Mesquine 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 regulator problem for linear uncertain continuous-time systems having control constraints is considered. Necessary and sufficient conditions of positive invariance of polyhedral domains are extended to the case of continuous-time uncertain systems. Robust constrained regulators are then derived. An application to the control of pH in a stirred tank is then presented. First, the uncertainty in the pH process is evaluated from first-principle models, then the design of a robust constrained regulator is presented. Simulation results show that this control law is easy to implement and that robust asymptotic stability and control admissibility are guaranteed.