Fall 2004
ICE Topics: Process Control by Design
10.492
Lecture Notes 2: Simulating the Shower Process
revised 2004 Dec 16
Dr. Barry S. Johnston, Copyright 2004.
1
the shower process is simple enough that we can simulate its operation
Over the past decade our tools for simulating processes have greatly improved.
In particular, we
can predict how the process will behave under dynamic conditions: startup, disturbance, and
shutdown.
Dynamic simulation can aid in specifying the control scheme and may catch potential
operating problems.
For the shower, we do not need a complex computer code – we can derive and solve a decent
equation set by hand.
We will do this simulation to illustrate
•
a simple control algorithm
•
how the process behavior was indicated by the RGA and DC tools
Simulation thus allows us to check the efficacy of our screening tools.
first we need to talk some more about process control
Recall how we defined feedback control: measurement of CV used to motivate a change in MV
to keep CV at set point.
To put this into practice, we must assert some control algorithm, that is,
a way to calculate how much to move MV.
We begin by defining error:
)
t
(
CV
SP
)
t
(
−
=
ε
(21)
Error is the difference between the desired value of CV, called the set point SP, and CV.
Of
course, CV might wander around with passing time, and so error would, as well.
If CV is at the
set point, the error is zero; should CV be disturbed, the error might be positive or negative. The
error is the input to the control algorithm.
the simple Proportional algorithm for a controller
An intuitively appealing algorithm is to make the response proportional to the error.
)
t
(
K
B
)
t
(
MV
C
C
ε
+
=
(22)
MV
the manipulated variable, which may vary in time
B
C
the value of MV when error is zero; known as the bias
K
C
adjustable controller gain (+ or )
we apply the proportional controller to our process
Start with flow control.
Call the set point F
sp
.
Then the error in the flow is
'
'
sp
r
r
sp
sp
F
F
F
F
F
F
F
F
F
−
=
+
−
−
=
−
=
ε
(23)
By introducing our reference value F
r
into the definition, we see that the error is also the
difference between two deviation variables.
In many cases, of course, we would take the set
point value F
sp
to be the same as our reference value, so that F
sp
′
is identically zero.
However,
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Fall 2004
ICE Topics: Process Control by Design
10.492
Lecture Notes 2: Simulating the Shower Process
revised 2004 Dec 16
2
distinguishing F
sp
from F
r
allows us to easily describe set point changes – that is, moving the
process from one condition to another under the supervision of the controller.
the error can be scaled
When we divide the error by the operating range for flow, we obtain a dimensionless error.
*'
*'
sp
F
*
F
F
F
F
−
=
∆
ε
=
ε
(24)
If we pair CV flow and MV hot water, the controller algorithm (22) is now written in these
dimensionless terms.
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 Spring '03
 RogerD.Kamm
 Orifice plate, RGA, ∆T Fr

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