Environmental Engineering Reference
In-Depth Information
u (collector)
f 2 ; c 2
f 1 ; c 1
f 1 ; c 1
f 3 ; c 3 = y
f 2 ; c 2 ; f 3
On-line
data
recon-
ciliation
Flotation
Controller
u
Plant
-
y sp
y
Set-point
Net revenue
maximization
Figure 2.26 Real-time optimization of a flotation plant ( f j =oreflowrate; c i = ore grade)
covered but the chapter explores techniques that could be helpful to practitioners
as well as to researchers willing to deepen the concepts. The following issues arise
from this limited presentation:
1. Measurement error sources are many and their variances are additives. There is
a complex intricacy between the true measurement errors and the true dynamic
variations of the process variables. It is most important to clarify these concepts
at the beginning of a reconciliation procedure, to properly define the pursued
reconciliation objectives.
2. The reconciliation objectives vary from the estimation of the underlying process
steady-state operating regime to the fast tracking of its real instantaneous dy-
namic state. The method to be used for reconciliation must be adapted to the
subsequent utilization of the reconciled data, which are mainly monitoring, mod-
eling, control, and optimization;.
3. Assumptions that process variables variations and measurement errors are Gaus-
sian and unbiased are frequently made. This is obviously not exactly true. This
is why it is so important to make a prior detection of abnormal data or process
behavior and a posterior analysis of the reconciliation residuals.
4. The reconciliation criterion may contain different types of residuals and weight-
ing factors. Its formulation is essential to adequately match the reconciliation
objectives, as well as the structure of data statistical properties. It must be rig-
orously designed, avoiding as much as possible users subjectivity or empirical
tunings.
5. The reconciliation feasibility must be carefully investigated, by looking at redun-
dancy of data and constraint information content.
 
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