El Duro

Controling a planar temperature grid
Andrés Julián Saavedra-Montes*, Liliana Fernández-Samacá**

Resumen
Este artículo presenta el diseño de controladores multivariables, uno distribuido y otro centralizado, para una rejilla plana de temperatura. El objetivo es mantener una superficie de temperatura constante en la rejilla. Aquí, presentamos el modelado del sistema a partir de pruebas escalón.También, presentamos el modelado del sistema con incertidumbres paramétricas en las constantes de tiempo. Para analizar el modelo del sistema, utilizamos la descomposición de valores singulares y el arreglo de ganancias relativas. Dos estrategias de control son aplicadas a el sistema, un controlador H∞ y un controlador multivariable PID. La rejilla de temperatura plana es útil para mostrar unsistema mal condicionado, el cual necesita análisis complejo. Palabras claves: Modelo de incertidumbres, control robusto, sistema mal condicionado, controladores multivariables.

Fecha de recepción: 22 de febrero de 2008 Fecha de aceptación: 30 de abril de 2008

Abstract
This paper presents the design of multivariable controllers, one distributed and another centralized, for a planar temperaturegrid. The objective is to keep a constant temperature surface on the grid. Herein, we present the modeling of the system by using step tests. Also, we present the modeling of the system with parametric uncertainties in time constants. To analyze the system model, we use the singular values decomposition and the relative gain array. Two control strategies are applied to the system, an H∞*Electrical Engineer, Master in Systems of Electrical Energy Generation and PhD student in Engineering, Universidad del Valle. Assistant professor in the School of Electrical and Mechanical Engineering at Universidad Nacional, Medellin. ajsaaved@unal.edu.co Address: Universidad del Valle, Ciudad Universitaria Meléndez, Edificio 353 Oficina 20-35. Cali, (Colombia). Telephone: (572)3391780- Ext 111. **Electronics Engineer, Universidad Pedagógica y Tecnológica de Colombia. Master in Industrial Automation, Universidad Nacional, Manizales. PhD student in Engineering at Universidad del Valle. Assistant professor in Universidad Pedagógica y Tecnológica de Colombia. lifersa@univalle. edu.co Grants and support: Saavedra Montes, A.J. acknowledges a fellowship for doctoral student from Colciencias(Instituto Colombiano para el Desarrollo de la Ciencia y la Tecnología Francisco José de Caldas), and a study commission from Universidad Nacional de Colombia. Fernández-Samacá, L. akcnowledges a study commisssion from Universidad Pedagógica y Tecnológica de Colombia. INGENIERÍA & DESARROLLO
Número 24 Julio-Diciembre, 2008 ISSN: 0122-3461

Andrés Julián Saavedra-Montes, Liliana Fernández-Samacácontroller and a multivariable PID. The planar temperature grid is useful for showing an ill-conditioned system, which needs complex analysis. Key words: Uncertainty model, robust control, ill-conditioned system, multivariable controllers.

INTRODUCTION

A planar temperature grid is an example of an ill-conditioned multivariable system useful for analyzing and designing multivariable controllers.This system is affected by disturbances like: environment temperature and wind currents, inter-zone effects, and self-induced wind currents [1]. The planar temperature grid had been used as a study case in resource allocation. Many works have applied bio-inspired solutions to achieve uniform temperature on the grid. In [2] a Honey Bee social foraging algorithm is used. An algorithm based on theBacteria Swarm foraging is presented in [3]. An Ant Colony system is also used, for example the work presented in [4] [5]. Two papers show how allocation strategy can achieve an Ideal Free Distribution (IFD) to achieve the maximum uniform temperature on grid under multivariable saturation constrains [6] [7]. [8] presents how the foraging theory is applied to track a desired temperature. In general,...