Copyright @ IFAC Control Applications of Optimization, St. Petersburg, Russia, 2000 UNCERTAIN OPTIMIZATION IN MPC: A CASE STUDY Jose Alberto Bandoni Jose Luis Figueroa ' Planta Piloto de /ngenieria Quimica - UNS - CON/CET Camino La Carrindanga Km . 7. - 8000 - Bahia Blanca - ARGENTINA Te/. (054) 2914861700 Fax (054) 2914861600 e-mail: cofiguer@criba.edu.ar Abstract: A significant number of model predictive control algorithms solve on-line appropriate optimization problem and do so at every sample time. The major attraction of such algorithms lies in the fact that they can handle hard constraints on variables of the system. The presence of such constraints results in an on-line optimization problem that produces a nonlinear controller. The problem became more complex if we want to control uncertain processes. In this paper, an algorithm to solve the problem of control of a uncertain linear process with hard constraints is applied to a Steam Generating Unit. Copyright ©2000 /FAC Keywords: Model Based Control, Dynamic Programming, Mathematical Programming, Uncertain Dynamic Systems, Constraints, Steam Generators. 1. INTRODUCTION Linear approximations of real and normally highly non-linear industrial problems, is a common practice in process control theory and applications. Such procedure makes use of an idealized view of the real word, despite the linear models are normally substantiated by measurements made in the real plants. But the measurements themselves have a variable degree of uncertainty because systematic and random inherent errors of the instruments used. As a result, the coefficients in the linear models are uncertain to a significant extent. This uncertainty, in turn, affects the validity of the conclusions reached with these models, such as the optimality and feasibility of the problems. To face these real world complications, many different mathematical procedures have been presented in the literature to I Also in Dpto. de Ing. Electrica - UNS - Avda. Alem 1253 - (8000) Bahia Blanca - ARGENTINA. 41 deal with the uncertainty in engineering problems (Halemane and Grossman, 1983; Swaney and Grossman, 1985 ; Grossman et ai, 1983). Friedman and Reklaitis (1975) presented a method to solve a Linear Programming (LP) problem under uncertainty; in their approach the uncertain parameters are the coefficients of the variables in the linear model, and they are considered as independent uncertain parameters. Bandoni and Romagnoli (1989) extended this procedure to the case in which the variables coefficients and the independent terms of the linear equations are not uncertain on their own, but their uncertainty stems from their functional dependence of some parameters which, in turn, are subject to uncertainty. Other practical problems exist in almost every chemical processes. For example, the existence of actuator's saturation even when the process dynamics can be assumed linear; safety and performance