стр. 48 
B
Reactor
Separator
E, C
E
Figure P519 Process for Problem 520.
product E and some unreactants, mainly A, referred to as liquid C. E and C
are separated and liquid C is recycled back to tank T104 to be fed back to the
reactor. The amount of B fed to the reactor depends on the amount of A and
on the amount of C fed to the reactor. That is, there must be some B to react
with the A fed, given by the ratio R1 = B/A, and some B to react with the C
fed, given by the ratio R2 = B/C. You may assume that all the п¬‚owmeters
provide a signal related to mass п¬‚ow. Design a control scheme to control the
total п¬‚ow T (lb/min) into the reactor.
Automated Continuous Process Control. Carlos A. Smith
Copyright 2002 John Wiley & Sons, Inc. ISBN: 0471215783
CHAPTER 6
BLOCK DIAGRAMS AND STABILITY
This chapter presents a discussion of block diagrams and control loop stability. It is
important to present the development of block diagrams because they are used in
the study of stability, in the design of feedforward controllers (Chapter 7), in under
standing the Smith predictor deadtime compensation (Chapter 8), and in under
standing multivariable control (Chapter 9). The presentation of stability is done
minimizing the mathematics and emphasizing the physical signiп¬Ѓcance.
61 BLOCK DIAGRAMS
Block diagrams show graphically how the process units and the instrumentation
interact to provide closedloop control. These diagrams are composed of three
elements.
1. Arrows: вЂ”вЂ”вЂ”вЂ”
The arrows indicate either variables or signals.
2. Blocks: I O
G
Every block has an input, I, and an output, O. Inside the box we write the
equation that describes how the input affects the output. In control work, this
equation is a transfer function. Remember: The transfer function tells us how
the input affects the output; that is,
how much the input affects the
output (K)
transfer function
how fast the input affects the
output (t, to)
127
128 BLOCK DIAGRAMS AND STABILITY
A C
+
3. Circles:

B
Circles have at least two inputs. They represent the algebraic summation of
the inputs, or C = A  B.
Let us now look at the development of block diagrams for two processes.
Example 61.1. Consider the heat exchanger control system shown in Fig. 61.1.
The author starts the block diagram by writing an arrow (Fig. 61.2) that represents
the controlled variable in engineering units, in this case the outlet temperature T.
Note that not only is the variable T written, but also, and very important, the units
are written. Recall that in Chapter 5 we always indicated the signiп¬Ѓcance of
every signal in a control diagram; the same should (must?) be done in block
diagrams.
Once the arrow is drawn, we continue by drawing the feedback loop until we
return to the variable just drawn. The п¬Ѓrst device of the loop is the sensor/trans
mitter (Fig. 61.3). Generally, the letter G is used to indicate transfer functions;
however, by convention, the letter H is used to represent the transfer function of
transmitters. Note that the letter c is used to represent the output signal from the
transmitter. This is to remind you that for the controller, this is the real вЂњcontrolled
Figure 61.1 Heat exchanger control system.
T, oF
Figure 61.2 Arrow representing the controlled variable in engineering units.
129
BLOCK DIAGRAMS
T, oF
c , % TO
H
Sensor/transmitter
Figure 61.3 Block diagram showing sensor/transmitter.
Controller
m
+ T, o F
set
e
c GC
% CO
% TO
% TO 
c , % TO
H
Sensor/transmitter
Figure 61.4 Block diagram with controller added.
variable,вЂќ as discussed in Chapters 2 and 3. We use the generic %TO as the units
of c.
We now continue moving around the feedback loop by drawing the controller
(Fig. 61.4). The controller is by convention drawn using a circle and a block. The
circle indicates that the п¬Ѓrst thing the controller does is to subtract the measure
ment, c, from the set point, cset, to look for an error, e; the controller equation then
acts on the error. Gc is the transfer function of the controller, given by Eq. (32.5),
(32.11), or (32.13), depending on the type of controller. Note that the letter m is
used to indicate the controller output and to remind you that for the controller, this
is the real вЂњmanipulated variable.вЂќ
From the controller we move to the п¬Ѓnal control element, a valve in this case
(Fig. 61.5). GV is the transfer function that describes how the controller output, in
%CO, affects the steam п¬‚ow, in lb/min.
Finally, we move to the process unit, the heat exchanger (Fig. 61.6). G1 is the
transfer function that describes how the steam п¬‚ow, in lb/min, affects the outlet tem
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