Analog Computer Application Bulletin No. AB-856: Process Control Problems Yield to the Analog Computer
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Electronic Associates, inc.
Manufacturers of EIAICeE]) Precision Analog Computing Equipment
BULLETIN No. AB-856
Process-Control Problems
Yield to the Analog Computer
The analog computer has given systems engineering a big boost over the
older methods of design for process control systems in the chemical industry.
Interestingly, the answer is still “cut-and-try”, but the cut-and-try is now
done in minutes by turning computer knobs instead of in months by changing
actual control elements on the process. The savings in time and money are
obvious. This article shows, step by step, how a batch chemical process and
a control system proposed for it were set up and solved by simulation on an
analog computer. Though it did not happen in this case, the computer might
have shown the need for a change in the process itself to attain satisfactory
control with practical instruments.
C. W. WORLEY, Electronic Associates, Inc., and
R. W. E. FRANKS and J. F. PINK, E. I. du Pont de Nemours & Co., Inc.
Chemical processes often present control problems
that are unwieldy by the usual methods of solution.
Such a problem arose recently in a batch heating
operation, and it was decided that simulation of the
process and its control system on an analog computer
would produce an accurate answer in the quickest
and least-expensive way. ‘This article tells, step by
step, how this simulation was done. The process
described here is a good one to illustrate the method
because it includes several interesting simulation
problems and because its related batch operation is
common in the process industries.
Description of the physical system
Physically, the problem in-
volves only the batchholder (a
large kettle with a jacket into
which steam can be injected to
heat the batch), its instrumenta-
tion, and the control system.
Temperature is the unwieldly
parameter in this case because
of the strict process require-
ments that it follow as closely
as possible the ideal tempera-
ture-time curve of Figure 1.
Specifically, the batch enters the
kettle with its temperature somewhat below 150
deg F, is heated as quickly as possible to about 200
deg F, at which it is held for a fixed time, and then
is quickly cooled and sent on. A variation of only
1 deg F can cause off-standard product and losses.
The low temperature-overshoot required by the
process makes adequate reproduction of the curve
of Figure 1 impractical with manual controls. But
automatic control introduces other problems. For
one, the large thermal inertia of the batch controls
the rate at which batch temperature rises after steam
is admitted to the kettle jacket. For another, batch
size can vary, which means a variable heat transfer
lag. Also, the precise temperature to which the
batch is heated can be changed
according to process require-
ments, and steam and water sup-
ply pressures can fluctuate.
Several questions arise at this
point which are answered most
easily by an analog simulation.
For example:
PIs it possible to attain repro-
ducible start-up conditions for
every batch, with a maximum
transient overshoot of less than
4 deg F?
FIG. 1.- Desired temperature response
for batch process described.
Reprinted from CONTROL ENGINEERING
Copyright by McGraw-Hill Publishing Company, Inc.—All Rights Reserved
> Is a cascade-control system superior to a single-loop
control system? If so, by how much?
> What will be the optimum controller settings?
> How much will the system stability and reproduci-
bility be affected by changes in steam pressure, batch
size, ambient temperature, cooling water tempera-
ture, and batch reaction?
> Will controller drift be a serious problem in main-
taining system response within the required limits?
The simulated system
Simulation of the batch operation with a cascade-
control system will be described in detail in this
article. Simulation of the single-loop system will
not be described, since it is relatively simple.
In the cascade system, shown in Figure 2, the batch
temperature is recorded and transmitted by the pri-
mary controller to adjust the set-point of the second-
ary controller. ‘The secondary controller operates
“dualled” valves to supply cither cold water or steam
to the jacket of the kettle. A ratio relay in the out-
put of the primary controller limits the set-point
signal applied to the secondary controller. Without
this limit, the jacket wall would become excessively
hot during warm-up when a large error exists, and
thus would compromise product quality.
The primary measuring element in the batch is a
resistance-bulb thermometer, chosen for its accuracy
and reliability. It has a measured time constant of
4sec. Its output is converted to a pneumatic signal
and applied to the primary controller. This same
pneumatic signal actuates a pressure switch that is
preset to close when the holding temperature is
reached. The pressure switch starts the timer that
determines the holding period, and after this period
the set-point of the primary controller is dropped to
a lower temperature. This is done by a solenoid
valve and two variable set-point pressure supplies.
Jacket temperature is measured by a capillary-type
bulb placed within the jacket so as to measure an
FIG, 2. Batch process and
cascade-control systems,
average temperature. Both controllers are pneumatic
and have three adjustable modes—rate, automatic
reset, and gain. Whether valves have equal per-
centage or linear trim would be determined by the
analog study.
The computer solution
The usual reason for simulating a system by ana-
logs is that the analog system is relatively inexpen-
sive and quick to change, and obeys the same differ-
ential equations for its behavior in time as the
original system. The early mechanical analogs have
given way to the modern electronic analog computer
primarily because the electronic analog elements are
relatively noninteracting; i.e., they do not load one
another and thereby cause changed dynamic charac-
teristics. Electronic analogs also offer great flexi-
bility in circuit arrangement, and are relatively
inexpensive for high precisions. Although voltages
at various points in the computer simulate forces,
velocities, temperatures, etc., in the original system,
the circuits also represent its differential equation;
hence the term “computer”.
Returning to the batch heating operation, the
basic law of heat transfer by conduction can be
expressed in the form of the rate of heat transfer:
Hate = _ driving force
resistance
The driving force is the temperature drop across the
body, and the resistance is defined by Fourier’s law:
dQ) aT
"Sane © wD
where
a = Rate of heat flow in Btu/min
AT = Temperature differential in deg F
+ = Thermal resistance in deg F/Btu/min
The similarity between Fourier’s law and Ohm’s
a ee
—Hin
FIG. 3. Computer diagram for water-jacket section.
The rectangle attached to the triangular amplifier
symbol indicates that amplifier is connected as an
integrator (feedback via series capacitance). Plus
and minus signs indicate polarity of computer signal.
Note that input signs are opposite to Equation 3A,
because electronic integrator inverts signal.
Potentiometer
Amplification foctor
Amplifier
+Ty
law for electric current is immediately apparent, and
an analog simulation is applicable. This similarity
between heat flow and the flow of electricity (in a
noninductive circuit) leads next to a definition of
thermal capacity. ‘Thermal capacity signifies the
ability of a mass to store heat energy, and is deter-
mined by the specific heat of the substance. For
example, the specific heat of water at standard con-
ditions is unity; that is, if one pound of water is
raised in temperature by 1 deg F, 1 Btu will be
absorbed. ‘Therefore, by definition, the units of
thermal capacity for a specific mass are:
Cihermat = Btu/deg
The thermal capacities used in this analysis, C,,,
C;, and C;, are the heat capacities of the water
jacket, the jacket wall, and the batch product respec-
tively. To simplify these relations, the assumption
of one-dimensional heat flow was made.
To be theoretically correct, heat flow, like the
flow of electric current, must be represented by a
system having parameters distributed throughout the
body. Mathematical treatment of distributed para-
meter systems involves partial differential equations.
To simplify the analysis, the assumption of “lumped”
parameters was made by assuming uniform tempera-
ture distribution throughout each section of the
process.
For the simplifying assumption of uniform tem-
perature in the water jacket, the following heat bal-
ance equation can be written:
dT» Tw. — T;
Cw at Hin R
See Rennie ee eiereeee Soy
Heat Heat Heat
in out
This first-order differential equation is a simple
statement of the physical fact that the rate of change
of the water jacket temperature T,, is proportional
FIG. 4. Computer diagrams for entire jack-
eted kettle. Integrator outputs show scale
factor of parameter as well as polarity.
to the difference between the flow of heat entering
and leaving the jacket.
Transposing Equation 2 for the rate of change of
the water jacket temperature gives:
aT. Hu Teh (3)
di Ce RCw RCw
which can be set up directly on an analog computer
(Figure 3) by integrating both sides*.
Fer ise, - fen as f Re.
Using the same procedure, the heat-balance equa-
tion for the inner jacket wall can be written.
C; DT a le EF a gp RIED
Lag E R R
Heat “Heat Heat (4)
stored flow flow
in out
For the product batch
Ogee SE pe EEN 1 om
Cy er = R h(T, — To)
Heat Heat Heat ()
stored flow flow
in out
These equations can be set up in exactly the same
way as the one for the water jacket, but with different
coefficient potentiometer values. These circuits,
when connected as shown in Figure 4, yield the
complete computer diagram for the process.
Since the control valves are arranged to admit both
steam and cooling water to the water jacket, the heat
input into the simulated process is made up of two
components (shown in Figure 4). The coefficient
potentiometers labeled Ty,o/2, Tjo/2, and Tyo/2 estab-
lish initial process temperature at the start of the
computation. The signal shown at, the output of
* Electronic Analog Computers, Granino A. Korn and Theresa
M. Korn, McGraw-Hill Book Co., Inc., New York, 1952.
the amplifier identifies the process variable at that
point with its polarity and its scale factor.
Control valve simulation
The process temperature T, is controlled by modu-
lating the flow of steam or cooling water into the
water jacket according to the output of an industrial
pneumatic controller. This entrance of steam or
cold water displaces equivalent quantities of water
at temperature T;. ‘The control valves used to con-
trol these flows are diaphragm-operated and pneu-
FIG. 5. Action of control valves ys. controller output pressure.
matic, and are arranged to perform as in Figure 5.
For controller output pressures from 3 psi to 10.2
psi, the cooling-water valve moves from full open to
completely closed, while for pressures of 7.8 psi to
15 psi, the steam valve moves from full closed to
full open. Thus, the response of each valve overlaps
in the region of 9 psi.
The flow through a valve at a given opening is
a simple function of the maximum flow (W,,) that
can be delivered with the same pressure drop. This
function can be simulated on an analog computer
by using a servo multiplier, which is a servo-driven
series of potentiometers. The controller pressure,
represented as a machine voltage, drives a servo am-
plifier and motor to position the series of poten-
tiometers according to a signal fed back from a
reference voltage on one potentiometer. The volt-
age representing maximum flow is applied across
another potentiometer and the actual valve flow is
represented by the voltage fraction picked off by
the arm position. To simulate equal percentage
characteristics, the arm of the potentiometer is loaded
with a resistor whose value is approximately one-
tenth of the potentiometer resistance.
The computer circuit used to simulate the cold
water and steam valve is shown in Figures 6A and B.
In this case, P, has been chosen to have an excursion
of 75 volts, equivalent to 0—15 psi. From this in-
put is subtracted the 7.8-psi voltage equivalent for
the steam valve and the 3-psi voltage equivalent for
the cold water valve, so no valve operation occurs
when P, is below these values. The diodes on the
output of amplifier 31 limit its negative voltage
ae This effectively “cuts off” the action of the
ld water valve for P, greater than 10.2 psi (Figure
5). Servo-driven potentiometers 2B and 2A will
give the water flow and the heat flow respectively
when the correctly scaled voltages are applied. To
simulate the cold-water valve being fully closed for
control pressures of 10.2 psi and above, the negative
sides of potentiometers 2A and 2B are grounded.
A similar procedure applies for the steam valve.
Amplifier 32 is biased by diodes to limit its output
to 0 to minus 100 volts for controller output pres-
sures from 7.8 to 15 psi.
The calculation of the voltages to be applied to
the valve potentiometers can be illustrated with
the steam valve. The heat content of steam at 50
psi is 1,174 Btu = H, and at a maximum flow of
10 Ib per min for the valve wide open, gives a heat
flow of 11,740 Btu min. This steam condenses and
assumes the jacket-water temperature, the heat con-
tent of which is 10(T,,—32). Hence, heat liberated
by steam to the jacket water is:
11,740—10 (7,.—32) = 12,060 — 10.07,
Figure 6A shows the computer connections required
to simulate the heat flow through the valve. The
output voltage at the arm of potentiometer 4A con-
stitutes the heat flow into the process (Figure 4)
from the steam valve, divided by the scale factor
of 1 volt = 600 Btu min.
A similar procedure is involved in scaling the heat
carried away by the cold water. For this case the
scale factor is 1 volt = 4,000 Btu min. This output
is introduced to the process of Figure 4 through an
attenuator.
Simulation of temperature transmitter
Tests have shown that the dynamic characteristics
of the resistance bulb, instrument, and transmission
can be approximated by two first-order lags with
4sec time constants. The transfer function is:
1
(48+1) (4s+1)
The performance of the temperature transmitter as
described by this equation is easily simulated on
the analog computer.
One of the advantages of analog computation is
the ability to transform the time scale of a particular
problem. In this process, transients up to 30 min
are involved and a time-scale change of 60 to 1 has
been made.
With the time scale change factor B=1/60, this
transmitter transfer function becomes:
Pe. (a) = 1
T» ~ (4B,+1) (4B,+1)
The computer circuit which is employed to simu-
P.
Ba es
late the temperature transmitter is shown in Figure 7.
The batch-temperature-transmitter output of 3-15
psi is the equivalent of 15-75 volts in the com-
puter. The first amplifier is biased so that its output
range is plus 42.5 to minus 40 volts for the entire
range of T,. The diode rectifier limits its output
to 0 to minus 40 volts. Amplifiers 4 and 5 are con-
nected as first-order lags with time constants of
Br=1/15-sec computer time. The last summing
amplifier multiplies the 40 volts by 1.5 and adds a
constant 15 volts (3 psi) to give the equivalent
output pressure in volts.
Jacket-water temperature
The jacket-water temperature transmitter trans-
mits a 3-to-15-psi pneumatic pressure proportional
to the water temperature. The range of this instru-
ment is 0-250 deg F. Its dynamic characteristics
can be represented by two first-order lags. How-
ever, the time constant varies with the amount of
water turbulence, being approximately 4 sec for high
turbulence and 6 sec with no turbulence.
The computer circuit used to simulate these con-
ditions is similar to the circuit for the batch-tem-
perature transmitter and is shown in Figure 8. In
this case, however, instead of being set at a fixed
value, the potentiometers are made to vary auto-
matically as a function of turbulence. This is done
by using the servo-driven potentiometers of a servo
multiplier whose input is a function of a selected
=
1 { 3000)-——* +100v
Wy
Btu/min) 3000
000 2000,
>Output
—* -0.5]y
Btu/min
600 2) We
300
Hs Ws + 32 Ws
33 600
FIG. 6. A—Computer simulation of control
valve flow rates; B—simulation of valve turbu-
lence factor for input of water jacket tempera-
ture transmitter, Figure 8. Connections for posi-
tive and negative ends of servo-feedback pots are
indicated on servo symbol. Points marked B on
diodes are connected to input grid, placing diode
across amplifier as a limiter.
FIG. 7. Computer circuit for batch temperature transmitter. The
r indicates that the computer is not operating in real time—i.e.,
that time has been scaled. In this case time has been speeded up
by a factor of 60.
FIG, 8. Circuit for jacket-water temperature transmitter. Tem-
perature input is via a scaling pot varied by valve turbulence. Tur-
bulence servo-feedback pot arm is loaded to proper nonlinearity.
turbulence factor. This factor is found by adding
the effects of steam and water flow into the jacket,
assuming that 20-percent steam flow alone produces
maximum turbulence (giving a thermo-well time
constant of 4 sec).
Controllers
The primary and secondary loop controllers used
to control the process temperature are pneumatic
stack-type industrial controllers. Two-mode pneu-
matic controllers provide an output proportional to
the difference between the set-point and the meas-
ured variable (the error), and proportional to the
time integral of the error. In equation form, the
output can be written as a function of time:
P,() = Kye + f eit (7)
Where
P, = controller output
K, = controller gain
e« =error difference between desired and actual output
Tt = reset time constant
In Laplace notation:
K.
TS
The computer circuit is easily obtained by summing
the two terms as shown in Figure 9.
PAs) ae Kee +
€ (8)
FIG. 9. Circuit for simulating theoretical two-mode controller.
FIG. 10. Circuit for compensated derivative controller.
By definition, the transfer function of the com-
pensated derivative mode of control is:
P; " tras +1
P; (s) = ara +1 (9)
Where
P, = output pressure of derivative controller
P; = measured process variable
tq = derivative time constant
@ = compensating gain — 1/15
Solving this equation for the output pressure gives:
P, (s) = Po : x[ Pare]
& atd
The computer circuit for solving this equation is
shown in Figure 10. In order to prevent the voltage
simulation from exceeding the maximum output of
the controllers, diodes are added.
Ratio relay
Neglecting the dynamic characteristics of the ratio
relay, this device is simulated merely as an attenuator
with a value of 0.65. Thus, the set-point for the
secondary controller is held at a maximum desirable
temperature during start-up and maximum output
from the primary controller.
Computer operation
The computation procedure consists of combining
all computer diagrams into a complete circuit by
connecting related variables. From this diagram the
computer pre-patched panel is prepared by making
patchcord connections between the various ampli-
fiers, multipliers, and attenuators. The patch panel
is then inserted into the computer console patch-
bay, and the reference voltage is turned on. The
values of the various coefficient potentiometers are
then set with the aid of the digital voltmeter. By
placing the programmed patch panel in the patch-
bay before the potentiometers are adjusted, any pos-
sible error due to imperfect loading can be avoided.
The first step in the computation usually is to
check the operation of the various components in
the system. For instance, a known flow rate of steam
is introduced into the circuit and the resultant
process temperature is monitored to check this part
of the circuit. The circuits for the valves and con-
trollers are also isolated and checked both dynami-
cally and statically for ranges and accuracy. Once
all components have been checked individually, the
system can be reconnected and the computation
can begin.
It is best to establish the validity of the simu-
lation by making a series of check solutions. A check
solution establishes the fact that the simulation
operates similarly to the existing system or else agrees
closely with steady-state calculations. Once this is
established, the investigation of the system-design
changes for satisfactory performance can be made
with complete confidence.
LINEAR
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FIG. 11. Instability due to nonoptimum
controller settings at first indicated linear
valve trim was better than equal percentage
trim; this was later disproved. Note that in all
recorder charts time increases from right to
left.
THE RESULTS
During this simulation several runs were
made, varying many of the parameters. The
output of the computer was recorded and a
record kept of each change. Changes which
would have taken months in the field were
completed in seconds with the computer. In
addition, data were obtained in a form which
was readily understood without any compro-
mise in conditions such as can occur in field
tests.
The results of the computation are shown
in Figures 11 to 16. Note particularly that the
curves advance from right to left with increas-
ing time. Channels 5 and 6 show the move-
ment of the valves. Channels 1 and 2 show
the batch temperature—that in channel 2 being
expanded in scale. Channel 3 shows the jacket
temperature T,,.
By using the computer for this problem, at
least one man-month of an engineer's time was
saved. In addition, much equipment that
otherwise would have been purchased was not
required. The best control system for the
process was derived and a better knowledge
of the influence of varying parameters and the
areas of critical adjustments was obtained.
EMER.
brisk tight iar
if et
FIG, 13. Sudden 25-percent increase in steam pressure had no FIG. 14. A 400- nt increase in steam flow also shows
effect on cascade temperature control. Single-loop system showed favorable results. Single-loop system showed 5-deg-F overshoot
a disturbance of more than 1 deg F. and considerable valve cycling.
TAL beter
AHA EE
i
FIG. 15. Rate adjustment on primary controller proved critical. Existing
controllers do not provide the precision of rate adjustment needed for this
control application. Controller rate action would have to be stabilized
epee a FIG. 16. Best response for any setting of single-
loop controller was relatively poor. Single-loop
system tied primary controller directly to valves,
bypassing ratio relay and secondary controller.
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