close

Вход

Забыли?

вход по аккаунту

?

Патент USA US3088673

код для вставки
May 7, 1963
M. W. OGLESBY, JR., ET AL
3,088,664
METHOD OF AND APPARATUS FOR PROCESS DEAD TIME SIMULATION
Filed March 15, 1961
‘an
I
v
u!
w
E
ISL,
_’
gm %M4/7"M
ATZORNEVS
Jnited States Patent O?hce
3,088,664
Patented May 7, 1963
1
2
3,088,664
time. Further, we have discovered a method of and
apparatus for simulating a long dead time in a process
METHOD OF AND APPARATUS FOR PROCES§
DEAD TIME SIMULATION
Minor W. Oglesby, Jr., and Roy T. Brashear, Bartlesville,
Okla, assignors to Phillips Petroleum Company, a cor
poration of Delaware
Filed Mar. 13, 1961, Ser. No. 95,089
6 Claims. (Cl. 235-61)
control system with said simulated dead time responding
as a pure dead time at higher frequencies.
FIGURE 1 is a diagrammatic representation of the
inventive pneumatic circuit for a simulated dead time of
a second order approximation.
FIGURE 2 is a portion of the diagrammatic pneumatic
circuit of FIGURE 1.
FIGURE 3 is another portion of the diagrammatic cir
This invention relates to a method of and apparatus 10
cuit of FIGURE 1.
for simulating process dead time. In one speci?c aspect,
Referring to FIGURE 1, there is illustrated a conduit
this invention relates to a method of and apparatus for
pneumatically simulating process dead time.
Dead time in a process can be de?ned as the time
means 10 for transmitting a pressure P1 to a conventional
pneumatic force balance computing relay 11, such as a
elapsing between the initiation of a change in the process 15 Foxboro M58-1 computing relay illustrated in bulletin
13-19 distributed by Foxboro. The relay employed must
and the detection of the effect of the change upon the
be capable of solving the equation,
process.
In some instances, a process or a part of a process can
X (Output) =g (A-C)
be characterized dynamically as a pure dead time. A
where
A
and
C
are
variables and g is the adjustable gain
pure dead time process is one which will pass all input
of the relay. A conduit means 12 transmits a pressure
P2 from computing relay 11 to a ?ow restriction means
an amount equal to the dead time. Pure dead time
13 having a resistance R1. Conduit means 14 transmits
processes or processes with long dead times as compared
a reduced pressure from restriction means 13 to a capac
with their largest time constants are difficult to control
with the conventional three~mode controller. In order 25 itor 15 having a capacitance C1. A restriction means and
a capacitor connected as illustrated produces a ?rst order
for a process control loop containing dead time to be
lag. A conduit means 16 transmits a pneumatic pres
stable, the controller gain and reset action must be de
sure from capacitor 15 to a conventional 1:1 repeating
creased from those values that could be used if the dead
relay
17. As hereinafter noted, under speci?ed condi
time was not present. This results in large deviations
tions repeating relay 17 can be removed from the pneu
of the control variable from the set point and longer
signals unattenuated in amplitude but delayed in time by
recovery time.
Procedures exist for compensating for dead time in
process control, but to employ these procedures it is
matic circuit.
A conduit means 18 transmits a pneu
matic pressure P3 from repeating relay 17 to a restriction
means 19 having a resistance R2. Measuring the pres
necessary to simulate the dead time in the process. The
sure drop across restriction means 13 and 19, and divid
time models, a device dynamically equivalent to the con
trol system which is being analyzed, are not available for
through each said restriction means is the method where
di?iculty with this approach is that good reliable dead 35 ing each said pressure drop by the quantity of ?ow
plant operations.
by values for R1 and R2 are obtained. A pnuematic
pressure P3 is transmitted from repeating relay 17 via
conduit means 18 and 25 to a conventional force balance
When all variations or frequencies of a controlling
variable are relayed, merely delaying the passage of said 40 computing relay 23.
A reduced value of penumatic pressure P3 is trans
frequencies, said delay then is identi?ed as pure dead
mitted from restriction means 19 via conduit means 20
time. With the unavailability of reliable and inexpen
to a capacitor 21 having a capacitance C2. Conduit
sive dead time models, it is necessary to obtain an eifec
means 22 transmits a pneumatic pressure R, from capac
tive approximation of pure dead time for use in process
45 itor 21 to a conventional pneumatic force balance com—
control.
puting relay 23 such as a Foxboro M58~1 computing re
The prior art discloses several methods of obtaining a
lay. The computing relay employed must be capable of
perfect dead time model such as employing an electro
magnetic delay, a magnetic tape, magnetic drums or
solving the equation X (Output) =g (A—-C)+B, where
A, B, and C are variables and g is the adjustable gain
discs, punch tape, etc. However, these are all very eX
pensive and are not commercially available or adaptable 50 of the relay. A conduit means 24 transmits an output
to plant operation.
pressure F5 from computing relay 23. A pneumatic pres
Accordingly, an object of this invention is to provide
an improved method and apparatus for simulating proc
sure P4 is transmitted via conduits 22 and 27 from capac
itor 21 to said conventional force balance computing re
lay 11. A pneumatic pressure P1 is transmitted via con
Another object of this invention is to provide an im 55 duit means 26 to said conventional force balance com
ess dead time.
proved method of and apparatus for pneumatically simu
puting relay 23.
lating a second order dead time approximation.
It is well known in the art that the transfer function
Other objects, advantages, and features of our inven
for a second order dead time approximation is of the
tion will be readily apparent to those skilled in the art
form:
60
from the above description and the appended claims.
A process control system based on approximate dead
time is limited in the frequencies it can relay without
alteration. The phase shift of an approximate dead
where T is the dead time and S is the Laplace operator.
time operation will be the same as for a pure dead time
A second order dead time will perform as a pure dead
operation up to a maximum frequency and then will be 65 time up to a frequency where:
gin to deviate. By increasing the order of the approxi
W:1.7/T
mation, the maximum frequency at which the phase shift
of an approximate dead time operation and a pure dead
W is radians per minute and T is the dead time in min
time operation will be the same is increased.
Broadly, we have discovered a method of and ap 70 utes.
In the derivation of the transfer function of the pneu~
paratus for simulating a second order dead time approxi
matic circuit of FIGURE 1, it is noted that the general
mation for a process control system having a long dead
3,088,664
35
form of the equation expressing the second order dead
time approximation is:
where T is the dead time being simulated. For any
desired value of dead time, T1, one of the four parameters
(T1, T2, g1 or g2), can be assumed. The other three
parameters can then be determined by the above equation.
Input _(T»S')2+6TS+l2
By dividing the numerator by the denominator the follow
ing equation is obtained:
7
Output__
Input * __E!:
T
2
S
6_S
By employing the disclosed inventive pnuematic circuit
simulating a second order dead time approximation in
series with a ?rst order pneumatic dead time approxima
1_2
tion circuit and/or other pneumatic second order dead
time approximation circuits, higher order dead time ap~
Referring to FIGURE 2, there is illustrated a portion
of FIGURE 1.
The equation that relay 11 solves can
proximations can be simulated.
be written as:
An advantage of the inventive pneumatic circuit em
15 ployed to simulate a second order dead time over an
electronic circuit employed to simulate a second order
where the subscript (S) denotes the Laplace form and
dead time is the simplicity and low cost of the pneumatic
P2(s>=g1(P1<s)—P/.(s))
g1 is the gain in relay 11. The 121 relay 17 is used for
isolation purposes only. Having relay 17 in this circuit
circuit. Electronic circuits employed to simulate second
and higher order dead time lags are extremely complex.
prevents the loading of one penumatic RC by another.
Relay 17 can be removed from the pneumatic circuit in
Also, electronic circuits are not as compatible with pres
ent plant control systems as the pneumatic circuit, since
those special instances where the capacitance C1 is rel
atively large when compared to the Capacitance C2. In
most plant control systems are pneumatic. As a result,
an electronic circuit requires a power supply and EMF
to pneumatic transducers in addition to the ‘basic circuit.
this manner, the loading e?ect previously noted can be
prevented.
25 This increases the complexity and cost of the electronic
From FIGURE 2 it can be seen that:
dead time approximation and reduces its reliability.
Although an electronic circuit can be employed to
simulate a second order dead time approximation, it is
not economically feasible to utilize the electronic circuit
30 to simulate a relatively long dead time. For example, the
capacitance of the electronic circuit is very limited for
practical purposes while the capacitance of the pneumatic
circuit can be readily expanded. As previously noted,
where S is the Laplace operator, time constant T1 equals
RlCl, and time constant T2 equals RZCZ.
the results ‘obtained when an electronic circuit is em
Substituting the values for P2, P3 and P4, obtained 35 ployed to simulate a relatively long dead time approxima
tion are not as reliable and the equipment required is far
above in the equation for relay 11, there is obtained:
more expensive when compared to a penumatic circuit.
As will be evident to those skilled in the art, various
modifications of this invention can be made, or followed,
40 in the light of the foregoing disclosure and discussion
without departing from the spirit or scope thereof.
We claim:
1. A method of pneumatically simulating a second
order dead time approximation which comprises passing
Referring to FIGURE 3, the equation that relay 23
a ?rst pneumatic pressure P1 representative of a meas
solves can be written as:
ured condition toa ?rst pneumatic computing zone and
a second computing zone, passing a second pneumatic
pressure P2 hereinafter ‘described to said ?rst computing
zone, said ?rst computing zone solving the equation
Pats)=92(P4<s)—Pa(s>)-l-P1<s)
where g2 is the gain of relay 23. Substituting previously
obtained values of P3 and P4 into the above equation,
there is obtained the overall transfer function P5/P1 of
the pneumatic circuit of FIGURE 1.
where g1 is the adjustable gain of said ?rst computing
zone, passing a third pneumatic pressure P3 from said
?rst computing zone and through a ?rst pressure reduc~
55 ing zone having a resistance R1 to a ?rst storage zone
having a capacitance C1, passing a pressure P4 from said
?rst storage zone to a second pressure reducing zone hav
ing a resistance R2 and to said second pneumatic com
puting zone, passing a pressure from said second pressure
reducing zone to a second storage zone having a capaci
tance C2, passing said second pneumatic pressure P2 from
82+
T1112
T1 T2
said second storage zone to said ?rst and second com
1
puting zones, said second computing zone solving the
equation
Comparing the above equation with the conventional
equation written for a second order dead time approxi
P5=g2(P2-P4) +131
mation establishes that the two equations are of the same
form. If T1, T2, g1, g2 are adjusted so that the following
where g2 is the adjustable gain of said second computing
zone, and passing a ?fth output pneumatic pressure P5
equalities are satis?ed, then the pneumatic circuit shown
from said second computing zone in response to said
in FIGURE 1 will provide a second order dead time ap
proximation
?rst input pressure P1 representative of said ?rst pressure
70 P1 with a dead time of the second order.
2. The method of claim 1 wherein the pneumatic cir
cuit is adjusted so that
9192
75
R101
3,088,664.
5
6
fecting an adjustable ?rst order lag, a third conduit means
communicating between said ?rst means of pneumatical
ly effecting a ?rst order lag and a second means of pneu
matically effecting an adjustable ?rst order lag, a fourth
conduit means communicating between said second
means of pneumatically effecting a ?rst order lag and a
where T is the dead time being simulated.
second pneumatic computing means, said second pneu
matic computing means capable of solving the equation
3. A method of pneumatically simulating a second
order dead time approximation which comprises passing
a ?rst pneumatic pressure P1 representative of a meas
10
ured condition to a ?rst pneumatic computing zone and
where A, B and C are variables and g2 is the adjustable
a second computing zone, passing a second pneumatic
gain of said second pneumatic computing means, a ?fth
pressure P2 hereinafter described to said ?rst computing
conduit means communicating between said third con
zone, said ?rst computing zone solving the equation
duit means and said second pneumatic computing means,
15 a sixth conduit means communicating between said
fourth conduit means and said ?rst pneumatic comput
Where g1 is the adjustable gain of said ?rst computing
ing means, a seventh conduit means communicating be
zone, passing a third pneumatic pressure P3 from said
tween said ?rst conduit means and said second pneumatic
?rst computing zone and through a ?rst pressure reduc
computing means, and an eighth conduit outlet means
ing zone having a resistance R1 to a ?rst storage zone
communicating with said second pneumatic computing
having a capacitance C1, passing a pressure R, from said 20
?rst storage zone and through a lz'l relay zone to a sec
sure from said second pressure reducing zone to a second
storage zone having a capacitance C2, passing said sec
ond pneumatic pressure P2 from said second storage zone
means.
6. Apparatus comprising a ?rst conduit means com
ond pressure reducing zone having a resistance R2 and
to said second pneumatic computing zone, passing a pres
municating with a ?rst pneumatic computing means, said
?rst pneumatic computing means capable of solving the
25
equation
where A and C are variables and g1 is the adjustable
gain of said ?rst pneumatic computing means, a second
conduit means communicating between said ?rst pneu
30
matic computing means and a ?rst means of pneumati
where g2 is the adjustable gain of said second computing
cally effecting an adjustable ?rst order lag, a third con
zone, and passing an output pneumatic pressure P5 from
duit means communicating between said ?rst means of
said second computing zone in response to said input ?rst
pneumatically effecting an adjustable ?rst order lag and
pressure P1 representative of said ?rst pressure P1 with
a pneumatic 1:1 relay means, a fourth conduit means
to said ?rst and second computing zone, said second com
puting zone solving the equation
35
a dead time of the second order.
communicating between said pneumatic 1:1 relay means
4. The method of claim 3 wherein the pneumatic cir
and a second means of pneumatically effecting an ad
cuit is adjusted so that
justable ?rst order lag, a ?fth conduit means communi
cating between said second means of pneumatically ef
fecting an adjustable ?rst order lag and a second pneu
matic computing means, said second pneumatic comput
ing means capable of solving the equation
g1+1
_1_2
(R1C1)(RzC2)_T2
where T is the dead time being simulated.
5. Apparatus comprising a ?rst conduit means com
municating with a ?rst pneumatic computing means, said
45 where A, B and C are variables and g2 is the adjustable
gain of said second pneumatic computing means, a sixth
conduit means communicating between said fourth con
duit means and said second pneumatic computing means,
a seventh conduit means communicating between said
?fth conduit means and said ?rst pneumatic computing
?rst pneumatic computing means capable of solving the 50 means, an eighth conduit means communicating between
equation
X(Output) =g1(A-.C)
said ?rst conduit means and said second pneumatic com
puting means, and a ninth outlet conduit means com
municating with said second pneumatic computing
where A and C are variables and g1 is the adjustable gain
of said ?rst pneumatic computing means, a second con 55 means.
duit means communicating between said ?rst pneumatic
computing means and a ?rst means of pneumatically ef
No references cited.
Документ
Категория
Без категории
Просмотров
0
Размер файла
462 Кб
Теги
1/--страниц
Пожаловаться на содержимое документа