Process Observers and Data Reconciliation Using Mass and Energy Balance Equations - Advanced Control and Supervision of Mineral Processing Plants - page 59

+

White
noise

+

G(Z -1 )

Stream junction

s

-

+

Internal disturbance generator

s kj

Flowrate mean
value

Zero-dynamics separator

+

+

Flowrate
variation

f

G(Z -1 )

Flowrate full value generator

Transfer function or feed
disturbance generator

Figure 2.14 Basic elements of an empirical model of a mineral separation plant

This empirical full model implicitly contains the mass conservation Equations
2.8, in the absence of component transformation as assumed in the operating condi-
tions defined by the previous selected basic units. Mass conversation for component
i is written

dm i
dt =

f i

M i B i z

M i f i = M i ( f i − )= ( t ) for i = 0to n + 1 (2.120)

since the constraint M i f i 0 is valid for the nominal state values. A representation

of the model for a single flotation cell is given in Figure 2.15. The same structure
can be used for all the stream components and for all the nodes of a complex plant.
The model requires, in addition to the steady-state values f , the knowledge of
the separation coefficients s kj , the transfer function coefficients, and the variance of
the driving white noise vector ξ including ξ i and ξ s . Both the empirical and the
phenomenological models contain numerous parameters to be calibrated. This is
why it is interesting to look at sub-models for dynamic data reconciliation.

=