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

34 3. SUMMARY OF CONTRIBUTIONS
Note that the boiler pressure is assumed to be an unmeasured disturbance handled by
the feedback. The inverse mapping of g(zfw,ps) is a function mapping a reference
flow and a nominal boiler pressure to a valve stroke, g−1 : R2 ↦→ R.
1
zfw,ref =
log(R) log
�
�
˙mfw,ref
�
kf ∆pp,ref( ˙mfw,ref,kr) + pa − ps
+ 1 (3.5)
Note that here f(zfw) = 1
R Rzfw , where the term involving R0 has been omitted,
e −R0zfw = 0. The reason for this is that the gain of the system is very high at low valve
strokes and further the positioning of the valve stroke is not accurate enough to actively
operate at these small strokes. Instead, pulse width modulation is used for small valve
strokes, handling the control challenge Discontinuous input flows.
∆pp,ref is a function of ˙mfw,ref and was found as the solution to a quadratic equation:
∆pp,ref = −b1( ˙mfw,ref,kr) − � b1( ˙mfw,ref,kr) 2 − 4b2(kr)b0( ˙mfw,ref)
2b2(kr)
(3.6)
where b2, b1 and b0 can be found in [Solberg et al., 2008d]. In [Andersen and Jørgensen,
2007] the inverse (3.5) was approximated by the solution to a quadratic equation
in ˙mfw,ref , which proved to give satisfactory results in practice. Further, integrator
windup is handled in a tracking anti-windup scheme – see [Åström and Hägglund,
2006].
To sum up, a model of the feed water system has been derived, and a controller based
on gain scheduling and local feedback has been developed.
3.1.2 Burner
The contributions regarding burner control have mainly been concentrated on modelling
and control of a novel turbocharged burner unit. However, for completeness we will
shortly address the standard pressure atomising burner which we find on boilers that we
will discuss control strategies for later.
Pressure atomising burner
The conventional pressure atomising burner has been treated by pure feedforward. For
details – see [Andersen and Jørgensen, 2007; Solberg et al., 2008d]. The reason is
that the fuel flow is seldom measured on installed boilers of the capacity treated in this
project. The position of the damper controlling the air flow required to keep a clean
combustion is found through a pre-calculated function of the fuel valve stroke. This
function was found in [Andersen and Jørgensen, 2007]. This also means that there
is no feedback from the oxygen level in the exhaust gas. No details of the nozzlelance/atomiser
system have been found for which reason a first principle model for the
fuel system could not be derived. However, the gain from fuel valve stroke to fuel flow