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

38 3. SUMMARY OF CONTRIBUTIONS
f1(x)
rxO 2 ,fn
1
τ1s+1
r ˙mfu r ˙mfu1
f2(x)
/
α
- r ˙mfu2
xfn,O2
−k2τ2s+1
τ2s+1
m
i
n
-
PI
Figure 3.6: Control structure for the burner unit. A nonlinear feedforward is combined with some dynamic
compensation to take into account the dynamics of the process. A feedback around the oxygen is closed to
handle disturbances and model uncertainty.
Note that this controller consists of a feedback and a feedforward path. The feedforward
from the total fuel flow reference, r ˙mfu , is functions calculating optimal steady state
values for the fuel distribution, r ˙mfu1 = f2(r ˙mfu ), r ˙mfu2 = r ˙mfu − r ˙mfu1 , and the
corresponding oxygen level, rxfn,O = f1(r ˙mfu ). Note that no feedforward compen-
2
sation is made for disturbances. The feedforward functions are calculated by inverting
the steady state version of the model. The functions can be approximated by piecewise
quadratic functions consisting of three pieces. The dynamic lag filter, k2τ2s+1
τ2s+1 , introduced
after the nonlinear feedforward function for r ˙mfu2 is introduced to accommodate
the non-minimum phase behaviour to xfn,O2 when changing ˙mfu1. The “min” block
1
ensures that air lack never occurs. The other filter τ1s+1 has a time constant close to
that of the closed loop oxygen response. The feedback, a PI controller, adjusts the ratio,
α = ˙mfu1
, between the two fuel flows to correct the oxygen level if the feedforward
˙mfu2
compensation is not accurate due to disturbances or model uncertainty. Anti-windup
compensation, not shown, is made for the PI controller. The input saturation configuration
to the right in the diagram ensures that the reference can be achieved even though
˙mfu2 has saturated.
Simulation results gathered from the nonlinear model are presented in Figure 3.7 and
Figure 3.8.
From the simulation results it can be seen that the designed controller is robust against
disturbances and capable of tracking the fuel flow reference. Further, the number of
constraint violations (xfn,O2 < 3%) is small. Note that the functions used in the nonlinear
feedforward are easy to identify during burner commissioning.
Thus regarding burner control, focus was on a new turbocharged burner for which a first
principle model was derived and a control strategy based on a nonlinear feedforward
and a feedback oxygen controller was suggested.
α
1+α
1
1+α
-
˙mfu1
˙mfu2