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Mathematical Problems in Engineering
Volume 2015, Article ID 271216, 6 pages
Research Article

A New Application of the Hill Repressor Function: Automatic Control of a Conic Tank Level and Local Stability Analysis

1Departamento de Ingeniería Química y Bioprocesos, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, 7820436 Santiago, Chile
2Escuela de Ingeniería Eléctrica, Pontificia Universidad Católica De Valparaíso, Avenida Brasil 2950, 2340000 Valparaíso, Chile
3Departamento de Tecnologías Industriales, Universidad de Talca, Camino a Los Niches km 1, 3440000 Curicó, Chile

Received 12 March 2015; Accepted 27 April 2015

Academic Editor: Sergio Preidikman

Copyright © 2015 José Ricardo Pérez-Correa 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 Hill function is commonly used as a building block to model different dynamic patterns found in the response of genetic regulatory circuits within microorganisms and cells. These circuits are characterized by fast response and robustness against unmeasured disturbances. Therefore, microorganisms and cells can survive even if they are subjected to strong changes in their environment. However, as far as we know, the Hill function has not been used before to design process control systems. In this work, the repressor Hill function is applied to control the level of a conic tank. To eliminate the offset, we added integrative action. A local analysis was applied to define stability limits for the control parameters. A cost function that includes the error and the control effort was used to compare the performance of the Hill control against a standard PI and a PID-Dahlin controller.