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