Optimisation of Marine Boilers using Model-based Multivariable ...

6 1. INTRODUCTION
1.3.1 Boiler modelling
As we are interested in controlling the whole boiler system, models of both the boiler,
the burner and the feed water system are of interest. We are interested in deriving models
based on first principles rather than using system identification techniques to specify
a black box model based on e.g. linear parametric models, [Ljung, 1999]. This technique
is adopted as these models tend to be valid over a wider operating range. The goal
is to derive lumped parameter models that reflect the plant dynamics as well as possible
based on knowledge of the system behaviour and measurements. This approach is also
taken to achieve insight into the boiler system process. Further, detailed models like
these will be of great value as a simulation platform for controller designs.
Early work on lumped first principle dynamic models useful for advanced controller
design for the drum boiler can be found in [Chien et al., 1958]. More recent publications
are [Pellegrinetti and Bentsman, 1996] and the popular model by Åström and
Bell published in [Åström and Bell, 2000]. The main difficulty in modelling the boiler
dynamics is caused by the distribution of steam below the water surface. This steam
introduces a phenomenon called shrink-and-swell on the water level [Åström and Bell,
2000]. This is seen as a non-minimum phase zero in the response from steam flow, feed
water flow and fuel flow to the water level. Many proposals for a description of the
distribution of steam bubbles below the water surface have been documented – see e.g.
[Åström and Bell, 2000; Andersen and Jørgensen, 2007; Kim and Choi, 2005; Solberg
et al., 2005b; Sørensen et al., 2004]. Most of these are based on assumptions and all
end up including empirical constants to be estimated to fit the model to process data.
In [Kothare et al., 2000], an approach was taken to model the boiler as a collection of
linear models in which a non-minimum phase zero is easily inserted. A summary of
developments in modelling of boilers can be found in [Sørensen, 2004] where a model
of the WHR boiler is also presented.
The feed water system can be modelled using standard expressions for flow through
valves and pressure delivered by pumps – see e.g. [Eastop and McConkey, 1993].
Also, the standard pressure atomising burner does not cause any modelling difficulties.
However, we must also address a novel burner which instead of a conventional fan is
equipped with a gas turbine. The gas turbine is among other parts constructed of a
turbocharger. When constructing a model of this burner it is useful to look towards the
automotive industry where especially the turbocharger has received much modelling
attention – see e.g. [Amstutz and Guzzella, 1998; Jensen et al., 1991; Jung and Glover,
2003; Kolmanovsky and Moraal, 1999; Müller et al., 1998]. Also gas turbine theory is
described in [Saravanamuttoo et al., 2001], and a model for stationary gas turbines can
be found in [Sekhon et al., 2006]. In most works the flue gas is treated as an ideal gas
for which the general physics can be found in e.g. [Serway and Beichner, 2000].