Process Observers and Data Reconciliation Using Mass and Energy Balance Equations - Advanced Control and Supervision of Mineral Processing Plants - page 68

2.11 Instrumentation Strategy Design

If raw data delivered by sensors is to be updated by a reconciliation procedure,
which at the same time generates estimates of unmeasured variables, the sensors,
or more generally the variables to be measured, must be selected in a way to maxi-
mize the reconciliation procedure performance [51, 105-107]. The instrumentation
placement or measurement strategy design problem is defined as [64, 108-110]:

Knowing the state equation f ( X )= ε ,orCX = ε , and V ε (usually = 0

at the instrumentation design stage), find g ,orC,andV e in such a

way that the following properties of the data reconciliation procedure
are obtained, subject to the constraints that states X are observable:

(.)

o maximum accuracy of the estimated states and of the process perfor-

mance indices that are subsequently calculated with these estimates;

o Minimum instrumentation cost (capital investment, labor and mainte-

nance costs);

o maximum reliability of the process observer (maximum operating life

without loss of observability, in the presence of possible total failures
of sensors).

This is a multi-criterion discrete optimization problem since the properties of the
variables to be measured (type of sensor, accuracy of sensor, and sensor position in
the process network) have to be selected from a discrete set of available instrumen-
tation combinations. It is obvious that there is a necessary trade-off between the cost
of the sensors and the reliability and accuracy of the observer, since increasing the
number and accuracy of the sensors would improve both the observer accuracy and
reliability. The instrumentation design can be processed either as a multi-objective
problem or as a single-objective problem if the economical impact of improving the
process operation control by an accurate and reliable observer can be quantified in
the same units as the investment and maintenance costs. In the most general situ-
ation, there is no other available systematic method to find the best solution to the
design problem than to scan the set of possible combinations. However, for specific
cases such as the minimal cost combination or the minimal estimate variance for
the minimal number of sensors, the optimal design can be found analytically, or the
solution space scanned along paths minimizing the number of tested designs [67].
Table 2.7 illustrates the optimal instrumentation problem for the flotation plant
of Figure 2.7 [52], using two different criteria (the cost and the estimate accuracy)
and different allowed numbers of sensors for measuring the mineral flowrates.