Process Observers and Data Reconciliation Using Mass and Energy Balance Equations - Advanced Control and Supervision of Mineral Processing Plants - page 21

• concentrations of chemical species or minerals in particle size or density classes;

• pressures, temperatures.

Process variables may or may not be directly measured by sensors or analyti-
cal devices. For instance, ore flowrates may be obtained through the information
given by a slurry volume flowmeter, a density gauge, and ore specific gravity mea-
surement. Metal flowrates are other examples of process variables that are obtained
through a combination of measurements (flowrates and concentrations).
There is no unique way to select the set of variables X that characterize process
states. The structure of the models and constraints describing a process behavior
depends upon variable selection. This will have an impact on the observation or
data reconciliation method, although the resulting values of reconciled states should
not rest upon the problem formulation, if consistent information processing methods
are used. Similarly, the measured values Y of the Z process variables used as input
to the reconciliation procedure may or may not be raw measurements of the process
states X . Furthermore, they can be obtained by combining several sources of raw
measurements. The structure of the database Y and of its uncertainties may have
a significant impact on the reconciliation method and sometimes on the reconciled
results.
The variation of the process states X as a function of time depends on the intrinsic
dynamics of the process, on the variations of the operating conditions applied to the
process, and on the disturbance dynamics. The process operating regimes can be
classified into six types:

• the steady-state regime, when all the process input and state variables are con-

stant;

• the stationary regime, when the process dynamics are limited to random varia-

tions around a steady-state regime;

• the transient regime, where the process evolves from one steady-state to another

one;

• the quasi-stationary regime, which corresponds to stationary random variations

around persistent mean value changes;

• the cyclic regime, when the process operates cycles of production, such as in

the carbon-in-pulp process where the carbon transfer is cyclic, or in smelting
processes where the material is cyclically cast;

• the batch regime, when the states evolved according to a trajectory from an initial

state to a final state.

Figure 2.3 illustrates process state variations for four different operating regimes.
Local stochastic state variations are mainly due to input disturbances (ore grade vari-
ations for instance), while the trends are mainly the results of deterministic changes
of the manipulated variables. Since in real processes it is impossible to maintain
strictly constant conditions, the steady-state regime corresponds to virtual operating
conditions.
The statistical properties of any stationary process variable, a scalar or a vector
x (either input disturbances and/or process states and/or process outputs), can be