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NONLINEAR CONSTRAINED PREDICTIVE CONTROL OF
EXOTHERMIC REACTOR
Joanna Ziętkiewicz
Institute of Control and Information Engineering, Poznan University of Technology, Piotrowo 3A, Poznan, Poland
Keywords: Predictive Control, Feedback Linearization, LQ Control.
Abstract: Predictive method which allows applying constraints in the process of designing control system has wide
practical significance. The method developed in the article consists of feedback linearization and linear
quadratic control applied to obtained linear system. Employment of interpolation method introduces
constraints of variables into control system design. The control algorithm was designed for a model of
exothermic reactor, results illustrate its operation in comparison with PI control.
1 INTRODUCTION
The predictive algorithms have a wide industrial
applications because of the simplicity of its
operation and good features of regulation. One of
important advantages of the predictive control is the
possibility to impose the signal constraints in the
process of designing the control law. In the practical
applications it is convenient to use the linear models
for the theory of them is well known.
First examples of the industrial use of the MPC
applications had place in 1970’s, but the idea was
known earlier (Lee, Markus, 1967). One of the most
important algorithms was the Dynamic Matrix
Control (Cutler, Ramaker,1980) and Quadratic DMC
(Garcia et al.,1989) with linear models. There
appeared a number of articles with nonlinear models
with the exact and suboptimal algorithms. The use of
nonlinear models cause additional problems with
finding global minimum and can have an effect on
calculation time (Tatjewski, 2002). Adaptation of a
controller with linearization around the working
point may result in system instability (Dimitar et al.,
1991), changes of variables have to be limited.
The aim of the work was to design an application
used for control of an exothermic reactor with
constraints, to propose use of feedback linearization
for this nonlinear plant, present predictive control
method solving problem of constraints(Poulsen et
al., 2001) and its modification (Ziętkiewicz 2008)
for changed reference signal.
2 EXOTHERMIC REACTOR
2.1 CSTR Model
The plant to be controlled is the Continuous Stirred
Tank Reactor (CSTR). The structure of reactor is
presented on figure 1. It contains tank, cooling
jacket, inflow and outflow of both elements. It is
assumed that, because of perfect mixing, there are
no spatial gradients of parameters in the tank area.
The work of reactor is described by 3 differential
equations. First equation (1) illustrates the mass
balance,
),()(
)(
tVRtCC
dt
tdC
V
i
(1)
where C(t) is the concentration of product measured
in [kmol/m
3
]. The second and the third equations
(2,3) represent the balance of energy in the reactor,
T,C
T
i
,C
i
T,C
T,C
Φ
j
,T
j0
T
j
Φ
Figure 1: Model of exothermic reactor.
),()()()(
)(
tVRtQtTTc
dt
tdT
cV
iipp
(2)
208
Zi˛etkiewicz J. (2010).
NONLINEAR CONSTRAINED PREDICTIVE CONTROL OF EXOTHERMIC REACTOR.
In Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics, pages 208-212
DOI: 10.5220/0002954202080212
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SciTePress