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feeders.
Basically, the flow control implemented in the
car dumpers is a closed loop control, where the
process variable is the estimated flow of the material
at the output of the feeders and the control variables
are the rotational speeds of these feeders. The
estimated flow of material is calculated from the
velocities and currents of the feeders and corrected
with the readings of the existing physical flow scale
at another point in the discharge line. The logic
diagram of the flow control is shown in Figure 2.
Figure 2: Logical diagram of the flow control.
This article demonstrates the theories used to carry
out the implementation of this flow controller and
the results obtained with this implementation.
2 FLOW ESTIMATOR
2.1 Mathematical Modelling
Due to the distance between the car dumper and the
flow scale located at the discharge line, and its
consequent time delay, which would hinder the
implementation of a flow control, it was necessary to
develop a mathematical model that would represent
the flow at the discharge line (estimated flow).
Using the estimated flow as the process variable
(PV) eliminates the effects of the time delay, also
known as dead time (Smith, 1957; Astrom et. Al,
1994; Hagglund, 1992; Astrom et. Al, 1995),
allowing the implementation of the flow control
logic.
For the development of the estimated flow it was
first necessary to perform the data acquisition of the
actual flow (through the flow scale in the discharge
line), current and speed of the feeders. After the
acquisition of the data, a mathematical model
relating the data acquired was created in order to
obtain the estimated flow. In order to
mathematically represent the estimated flow, the
ARX linear model (Aguirre, 2007), was used
together with the Extended Least Squares Method
(Aguirre, 2000) to estimate the parameters. To
determine the order of the model we used the
Method of Analysis of Eigenvalues for linear models
(Lopes et al., 2010).
The mathematical model for the car dumper 01
(VV01), obtained using the least squares estimator is
shown below.
y (t) = (-3.445 * u1 (t)) + (80.31 * v1 (t)) -
(0.5513 * u2 (t)) + (89.11 * v2 (t))
Where: y= Estimated flow, u1= Current of the
motor powering feeder 01, v1 = speed of the feeder
01, u2 = Current of the motor powering feeder 02
and v2= Speed of the feeder 02.
The model was implemented in a PLC
(Programmable logic controller) controlling the car
dumper VV01 and Figure 3 shows, through actual
data extracted from the PIMS (Process Information
Management System), a comparison between the
estimated flow (Green) and the real flow (Pink). The
analysis of the graphic shows that the estimated flow
is a good representation of the actual flow.
Figure 3: Comparison between estimated and actual flow.
2.2 Reinforcement Learning
To ensure that the estimated flow is corrected over
time, a new technique of reinforcement learning was
implemented. This technique consists of comparing
the results of the estimated flow with the actual flow
to create a correction factor. This correction factor is
then applied to the estimated flow. The
reinforcement learning logic was implemented in the
car dumpers supervisory system.
As shown in Figure 4, each car dumper may
operate on four of the discharge lines and a
discharge line may be used by more than one car
dumper.
The reinforcement learning technique was based
on the following information:
Knowledge of the discharge line being used by
the car dumper;
Use of Flow Control on Car Dumpers - A Case of Success at Vale
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