Copyright @ IF AC Advanced Control of Chemical Processes
Pisa, Italy, 2000 '
NONLlNEAR PROPORTIONAL INTEGRAL
CONTROLS ROBUSTLY STABILISE BIOLOGICAL
REACTORS
R. Antonelli and A. Astolfi
Centre for Process Systems Engineering,
Imperial College of Science, Technology and Medicine,
London SW7 2BY, UK
FAX:+44-171-5946606, E-mail:{ r.antonelli,a.astolfi}@ic.ac.uk
Abstract : Biological processes are often encountered in industrial applications. Nev-
ertheless several control problems are still unsolved, because of the intrinsic non-
linear behaviour, lack of measurements and large model uncertainties. In this work
Lyapunov-based methods are used to design nonlinear output feedback Proportional
Integral (PI) control laws yielding robust stability and guaranteed performance. It is
shown that the proposed control algorithm is able to cope with input constraints and
requires only a very limited knowledge of the process parameters . Applications to a
wastewater treatment reactor are described in detail and simulations are enclosed.
Copyright ©2000 IFA C
Keywords: Lyapunov Methods, Output Feedback, PI Control, Biological Reactors,
Wastewater Treatment Plant
1. INTRODUCTION
The selection of effective methodologies for the
supervision and control of complex processes is
essential for achieving optimal results. Feedback
stabilisation of biological reactors has become an
active area of research in recent years (Bastin
and Dochain, 1990; Daoutidis et al. , 1990; Hen-
son and Seborg, 1992; Bastin, 1992; Bastin and
Van Impe , 1995; Soroush, 1997). The classical
approach to the bioreactor control problem has
focused on biological modelling as a tool to appro-
priately describe the nonlinearities and to predict
their behaviour with time . Even though many
models with various degrees of complexity have
been proposed, it is well recognized that these
models are not easy to develop and often provide
solutions that are not satisfactory. The main diffi-
culty lies in the comparison between noisy experi-
mental data and nonlinear models with uncertain
parameters . Nowadays, continuous and fed-batch
biological reactors have been extensively studied
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mainly because of their prevalence in biological
wastewater treatment plants (WTPs) . Wastewa-
ter containing pollutants and organic materials
is generally treated in aerated tanks where it is
mixed with biological particles constituting the
biomass. After a sufficiently long contact time,
this mixture is discharged to a settler where the
suspended biomass is separated from the treated
water. A small amount of the biomass is purged
while the rest is recirculated into the tank . A
biological reactor, like any other process in which
living micro-organisms are involved, constitutes a
complex process which is difficult to control. The
main issues are the lack of detailed information of
the process; the variations of the reactor inflow,
both in quantity and in quality ; the variation of
the population of the catalytic bacteria in quan-
tity and in number of species; the unavailability of
reliable analyzers; the difficulty in the interpreta-
tion of the experimental data. Because of all these
factors control of biological reactors represents a
very interesting and challenging problem.