Predictive control of nonlinear systems in the process
industry
Project members: H.H.J. Bloemen, T.J.J. van den Boom, J.M.A. Scherpen,
M. Verhaegen, V. Verdult, H. Oku, H.B. Verbruggen
Sponsored by:
STW
The project aims at the development of methods that enable to
transfer the high investment return of currently used Modelbased
Predictive Controller (MPC) schemes for linear systems to
important classes of nonlinear systems in the process industry.
 The first class contains systems which can, from an inputoutput
point of view, accurately be described by a linear dynamical model
when the operating range of the system is limited. Though, the
present generation of MPCs are designed for this limited operating
range, the tendency to produce more client oriented, will cause the
processes to frequently make a transition from one limited operating
range to the next. Using existing MPC technology these transient
effects are not taken into account, possibly leading to nonsmooth
transitions and therefore economical losses.
 The second class contains processes that even for a limited
operating range demonstrate a nonlinear behavior. An example is a
high purity distillation column which for a particular operating
range can accurately be described by a series connection of a linear
timeinvariant (LTI) dynamic model followed by a static output
nonlinearity (NL), a socalled Wiener model (see Figure
6).
Figure 6:
Block diagram of a Wiener model.

The special way in which the nonlinearity enters the Wiener model
can be exploited by transforming it into uncertainty. The result
will be an uncertain linear model, which enables to use robust
linear MPC techniques. A similar approach can be applied for
Hammerstein systems, in which case a linear dynamic block is
preceded by a static input nonlinearity. This HammersteinWiener
MPC algorithm [8] extends the linear MPC algorithm described in
[10]. A case study, concerning the distillation column benchmark,
has demonstrated the effectiveness of the proposed Wiener MPC
algorithm and is presented in [7].
Also discretetime bilinear models may be useful for blackbox
identification of nonlinear processes. In bilinear models the
nonlinearity enters the dynamic part of the model, i.e. the state
equation contains a product term between the current state and the
current input. This property can be exploited for solving a
''classical'' finite horizon MPC problem [9]. An application of
bilinear MPC to a polymerization reactor is presented in [12].
Extensions to an infinitehorizon bilinear MPC algorithm can be
found in [5,11]. Extensions to bilinear MPC algorithms that
aim at a low computational demand for the online computations are
reported in [6,5].
This project is part of STW project DEL
55.3891.
This project is done in cooperation with the Control group of the
University of Oxford, UK.
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