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

12 1. INTRODUCTION
there are methods such as the autocovariance least-squares method for estimating noise
covariances [Odelson et al., 2006a,b]. Another method which we will use on the marine
boiler example is the loop transfer recovery (LTR) method (the LQG/LTR approach).
Notes on LTR can be found in e.g. [Doyle and Stein, 1981; Maciejowski, 1985, 2001,
1989; Saberi et al., 1993]. This approach is for linear controllers, however, for an
example of application to MPC, see [Rowe and Maciejowski, 1999].
Robustness and nonlinearity Work has also been carried out in the area of robust
model predictive control. However, this direction is still in the development phase and
not yet suited for industrial applications. Two sources of uncertainty are dealt with
in the robust predictive control framework: model uncertainty and uncertainty with
respect to disturbances – see e.g. [Chisci et al., 2001; Gaulart and Kerrigan, 2006;
Kothare et al., 1996; Smith, 2006].
As mentioned earlier this thesis deals with MPC using linear models. However, such
schemes only work well when the nonlinear system to be controlled is working around
an operating point. When the operating point is changed from the nominal situation,
the controller might not perform well due to model mismatch. One way of tackling this
by still using linear models is to switch among a set of these according to the current
plant state. Examples of this can be found in e.g. [Kothare et al., 2000; Pedret et al.,
2000] where the latter refers to this method as model-varying predictive control. This
method has not been used in this thesis but might become relevant in the future.
There exists a number of tools to assist the engineer in performing design, analysis and
development of his MPC controller. The ones that have been used in this thesis, apart
from the authors own algorithms, are the multi-parametric toolbox (MPT-toolbox),
[Kvasnica et al., 2004] and the MPC-toolbox from the The MathWorks , [Bemporad
et al., 2006], which are both software packages for MATLAB � .
Hybrid/switching control
In many industrial processes, e.g. the thermodynamical and chemical processes a mixture
of on/off valves and heating elements might be present. When describing such
systems they fall into the class of hybrid systems. The marine boiler is such a system as
both the burner and feed water valve can be operated continuously down to some minimum
level whereafter the output from these systems must be switched off to reduce
the load further. This means that when operated at low load some switching control
must take place. Traditional methods for controlling such systems are hysteresis control
and pulse width modulation (PWM). However, both these methods have a number
of shortcomings discussed in [Solberg et al., 2008a]. For the feed water system these
shortcomings are not crucial and here we shall use PWM. However, for the burner system
things are more complicated, and in this thesis we will investigate how to optimally
control processes which require switching control.
A special property of the systems with discrete inputs is that in some cases the optimal