
 
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
581