ENGINEERING, DESIGN, AND PROCESS DEVELOPMENT
ALLAN R. CATHERON AND BRUCE D. HAINSWORTH The Foxboro Co., Foxboro, Mass.
HIS report is the culmination of a long study of the characteristics of a liquid flow system and the devices commonly used industrially t o control the rate of flow of liquids. The study brought to light-or a t least put a spotlight on-some aspects of the nature of the flow control problem. Each component part of the flow control loop has been studied with a view t o improving the quality of control by improving dynamic response. Figure 1 shows a common liquid flow control system. The difference between upstream and downstream pressures a t the orifice is a measure of the rate of flon of the process liquid. The differential pressure is measured a t the orifice, and the measurement is transmitted to the controller. The controller compares the measured value with the desired value (set point). If there is any difference (deviation), the controller modifies the signal t o the motor-operated control valve so as t o bring the measured value of rate of flow back to the desired set point.
PRIMARY ELEEEF
PROCESS
VALVE
PROCESS F L U ID
I
~t---------t-'
9
VALVE MOTOR
TRANSMITTER
__c
TRANSMISSION
Figure 1.
CONTROLLER
-
TRANSMISSION
Typical flow control system
A representative flow line-140 feet of 2-inch pipe-was set up for these studies. Provision is made for easily changing the differential pressure-measuring instrument, changing the length of transmission lines, and changing the control valve. Experimental Flow Line The test equipment was planned with the intent of setting up a liquid flow line which JTould be reasonably representative of industrial practice and experience and, a t the same time, permit constant conditions to be maintained and measured. K a t e r was selected as the liquid. The line is made of 2-inch pipe, and the n*ater supply is sufficient for flows up to 100 gallons per minute (making velocities up to 10 feet per second). The line is level throughout, except a t the discharge point. The length can he reduced if desired, and the arrangement also permits variation of the spacing and order of primary element and valve. The line, together with the supply system and the instrumentation used, is shown in Figure 2. T o provide a uniform, readily adjustable head for driving the mater through the system, a tank is attached to the input end of the line. A pressure controller admits or vents air above the water in the tank t o provide the desired static head, At the other end of the line, the water is discharged into a sump, from which
1042
it is picked up b y a centrifugal pump and returned to the driver tank a t the head of the line. h liquid level control on the sump operates through a valve on t,he pump discharge to maintain the sump level 71-ithin an inch or t.ir.0. Results of early experimentation indicated that it ITas desirable t o use a submerged discharge into the sump, with a nozzle a t that point to maintain positive pressure in all parts of the line. The system was instrumented to obtain t'he following information: in the driver and sump, records of driver pressure (head), water temperature, and sump level. Indicating gages permit a check of the pressure a t the pump output and the driver pressure. A ribbon indicator shows driver level. I n the flow line, the major part of the instrumentation is a t the primary element,. Whether orifice, nozzle, or Venturi, two independent sets of differential taps are provided. One pair is connected to an electronic differential pressure cell TThich may be used to provide a picture of x h a t is actually happening a t the element. The other set of taps is connected to a pneumatic differential transmitter. The output of this transmitter goes to a strip chart recorder, and it is also connected to a recorder-controller. These connections are made through a n air switch that permits the insertion of a pneumatic transmission line, if one is t o be used. This is the basic controller of the system, and the one on which adjustments are made. The recorder provides a record of the measured variable as the cont,roller sees it,, after transmission lines, damping restrictions, etc. A record of the valve motor pressure is made by the controller. The output' pressure signal from the controller is run to the valve through another air switch for the insert'ion of transmission line. Another indication of the actual flow in the line is afforded by a magnetic flowmeter, the pickup being located a few feet downstream of the primary element. This inst'rument is connected t,o a second strip chart' recorder. For the measurement of flow process characteristics, the meter head was connected directly t o an a.c. amplifier, TThich was followed by a phase det'ector, and a small filter bo reduce residual 60-cycle signals before entering the d.c. amplifier. fThe 60-cycle signal was not entirely removedthis to ensure that the response of the recording system remained adequately high.) At t,he valve, which may, of course, be equipped with positioning devices, booster relays, etc., a strain bar spring coupled to the valve stem may be connected t o a third strip chart recorder to give a record of actual valve position. It, can readily be seen that this reading niay not always correspond to the valve motor pressure, especially under dynamic conditions. For added indication or records, if t,hey may be required, the flow line is equipped with static pressure taps a t a number of points, particularly in the valve flanges so t h a t valve drops may be determined.
Dynamics of Liquid Flow Line Flow control problems are somelvhat different from other process control problems. Perhaps the most significant difference is that the liquid flon- process has almost no capacity €or the storage of energy. This almost total lack of energy-storage capacity means that the rate of flow is a direct function of valve stem
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 48, No. 6
PROCESS CONTROL
-
PNEUMATIC FLOW RECORDER
RANSMITTER FLOW RECORDER
LEVEL CONTROLLER\
t l
F DIFFERENTIAL TRANSMITTER
Figure 2.
Laboratory flow process with instrumentation
position a t any frequency (or correspondingly steep wave front) below about 1 cycle per second. I n temperature or pressure control, there is always some storage of energy in the process. The measured temperature or pressure is then a time integral of the valve position. A fast flowmeter mill sense a short-duration, sharp upset and transmit a signal calling for corrective action by t h e controller. Largely because of the integrating action of the process, a thermometer may hardly sense a n equally sharp short upset and therefore will not call for corrective action. The short, sharp (high frequency) measurement signals are seldom even considered in temperature control; most industrial temperature sensors are too slow to respond t o a fast momentary upset. But these high frequency upsets pose a very real problem in flow control. Some of the high frequency fluctuations in signal may be caused by actual variation of the rate of flow, b u t a large part are spurious signals or “noise”-e.g., pressure variation a t either one of the orifice pressure taps. The objective must be to pass all the signals which represent actual variations of flow and to reject as many as possible of the spurious signals-in the language of the communications engineer, t o achieve a high signal-to-noise ratio, Analysis of literally miles of high speed charts led to the conclusion t h a t most of the objectionable noise is at frequencies above 3 cycles per second. True signals, denoting actual changes in the rate of flow, may come through a t frequencies above this, but tests showed t h a t controller performance was not seriously impaired by losing all frequencies above 3 cycles per second. Again using the vocabulary of the communications engineer, the signal can be filtered without harmful distortion. This filtering action is ordinarily achieved in the valve actuating device, but some very fast systems require additional smoothing which must be supplied in another component. This June 1956
smoothing is a result, for example, of the system of flow control using wide proportioning band and fast reset. It has lately been possible t o obtain improved high speed recordings of the response of the flow in the test system t o step changes in valve position. The flow was measured with a magnetic flowmeter, which has a linear scale and which also eliminates “noise” caused by local pressure variations. One of the records obtained in this way is shown in Figure 3. The flow change is about 15% of the 100-gallon/minute scale, with the average level of operation at 55 gallons/minute. T h e small 60-cycle signal appearing in the flow record was left unfiltered purposely, as a check on the response of the measuring system.
Figure 3.
Response of liquid flow line to step disturbance of va Ive
These records indicate the very considerable speed of response of such a process in comparison t o that of conventional control equipments. Specifically, the flow record of Figure 3, when approximated as a dead time followed by a single capacity response, reads 0.06-second dead time and 0.22-second time constant.
INDUSTRIAL AND ENGINEERING CHEMISTRY
1043
ENGINEERING. DESIGN. AND PROCESS DEVELOPMENT This over-all response of less than a third of a second remains the smallest time unit in a commercial pneumatic flow control system, although the speeds of the newer type components are approaching this value. This step test was confirmed by frequency response tests. The points are taken from both runs, and a single curve is drawn. This curve follows closely in both gain and phase the one for a single capacity with the added phase lag for 0.06-second dead time. The time constant of the actual run seems t o be about 0.19 second as contrasted to 0.22 second from the step tests. However, the attenuation of the frequency response test is not carried to the level where a firm determination of slope can be made. This was not possible a t the noise level existing in our system.
Flowmeter Dynamics The objective of the first of these flow control studies w a ~ simply to find out more about the nature of flow processes. The catalyst for these tests was a revolution in flow measurement in 1947, when the dry differential pressure transmitter began t o replace the mercury manometer, the old stand-by for flow measurement in the process industries. The response of the mercury flowmeter is so slow in comparison with the other components of the flow control loop that, when the mercury manometer is used to measure the differential pressure across the orifice, the dynamic response of the whole flow control loop is, for all practical purposes, the response of the mercury flowmeter.
7
S'L IC
I
Figure 4. Mercury meter (leff) and d r y differential transmitter (right) on same orifice a i same time
When a mercury flowmeter i, replaced Tvith a dry differential pressure transmitter, the nature of the control problem is entirely changed, because the measuring element is no longer the slowest component of the control loop. The difference in measurement is shown in Figure 4. Contrast the even, filtered record from the mercury Ron-meter transmitter with the "live" response of a dry differential pressure t,ransmitter on the same orifice. Filtering can be carried too far! This change in the characteristics of the signal reaching the controller meant that the controller could now maintain the actual flow much closer to the recorded value. When load upsets were applied t o a flow process controlled from a mercury meter signal, a dry differential pressure transmitter connected to the same orifice showed that the flow disturbances were act>uallymuch larger than the deviations recorded by the mercury meter. (Figure 4 shows upset with control from dry differential transmitter signal.) 1044
The dry differential pressure transmitter shows that flow rate may change very rapidly indeed. Therefore, a reconsideration of the contributions of the various parts of the flow control system to the total of lags was in order.
Valve Operator Dynamics Measurements were made of the dynamics of control valve operators ( 3 ) with various lengths of pneumatic transmission linea. The figures show the relative effect of each of the system components, based on t,he recovery from a 10% load upset, and a bar chart of the sunimation of the time constants of each of the system components. The first test (Figure 5A) was madewith 100 feet of 0.188-inchi.d. metaI transmission line from the differential pressure transmitter to the controller and 100 feet of transmission line from the controller directly to the 150-cubic inch valve motor. Figure 5B shows the improvement of control and the increase in speed of response afforded by eliminating the transmission line. Xote that the dominant response lag is in the valve motor. It is apparent, that the transmission line by itself does not contribute too much lag, because the response lag of a similar line from the transmit't'er to t,he controller is only a small fraction of the lag of the valve motor and i t s transmission line, Oversimplifying: A signal (information) passe? through tlie line with much less delay than does the volume of air required to drive the motor, chiefly because of the frictional resistance of t>he line to the large volume of air. Now the next step was t'o mount a volume booster, essentially a volume relay, on the valve motor. T h e output signal of the eontroller (3 to 15 pounds/square inch) is transmitted t o t,he snlall volume (1.6 cubic inches) of the booster; the booster, with an airhandling capacity of about 14 cubic fcet/minute, supplies the valve motor with poxer. Figures 5C and 5D show the response of the systems of Figurea 5A and 5B when the volume booster is installed at' the valve. The same lOy0load upset is med. There is a marked improvement in control performanee and a marked dewease in the lag attribut,able to the valve motor (and its transmission line). Comparison of Figures 513 and 5C shon-s that tlie system with the volume booster and 100 feet of transmission line gives very nearly the same performance as the conventional controller mounted directly a t the valve. This again hears out the fact. that it is the large volume on the end of the transmission line that is most harmful--not the line itself. I t simplifies t,he problem for t'he controller to have one la.rge time constant dominant in the system (as in Figure 5A). This Pituation permits a narrow proportioning band, which is soniet imes considered "better" control. But is it, reilly better control? Processes are not set up for the benefit of t'he controller, and now they seldom need be, because modern controllers have such a wide range of adjustment. A device like the booster relay, which takes a load off the valve transmiFsion line, cut,? the long time constanh doxn to size. This results in a theoretically more compler process, but a process that permit,s truly better control, as sho1v-n in Figure 5C. Transmission lines from mcasuring elemenl to controller have alm,ys been less of a dynamic prohlem than l x v e valve lines. The data transmission line from measuring eiexncnt to controller transmits only information and transmits t o a uniform and small volume load. The valve line transmits not only information but also enough air to pon-er the valve motor. Trammitting this power to the very conPiderable volurce of the valve motor of course introduces additional transmiwion lag. Transmitting the controller output air pressure t o the volume booster instead of directly to the valve motor improves dynamic response, then, because only information, and not power, i:? transmitted to t'he valve.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 48, No. 6
PROCESS CONTROL N O T R A N S M I S S I O N LINE RECORD OF DIFFERENTIAL
T R A N S M I S S I O N LINE, I 0 0 FT.
RECORD OF DIFFERENTIAL
.
IO
5
0 -
0
10
SECONDS
SECONDS
TIME CONSTANTS
TIME CONSTANTS SECONDS
n
-P
I
'
-3 looh
SECONDS
8
s
IO
11
OF LINE GLUS VALVE'MOTOR
'
'
'
4
5
6
7
12 - O
I
Z
3
4
S
6
yT;:zRF PROCESS Figures 5A and
5B.
Dynamic performance of flow control systems-medium
valve motor without booster
e
Figure 5C also shows that the response of the transmission system now has a relatively greater effect, although not great in terms of time, on the dynamic response of the system. An effort was made, therefore, to develop a means of minimizing the effect of transmission line lag.
Reducing Transmission Line Lag
A theoretically possible means of minimizing transmission line lag is shown in Figure 6. The output pressure of the controller or transmitter (input to the transmission line) is continuously compared with the output of the transmission line by means of an "instantaneous" feed-back line. Any difference between the pressure applied to the transmitter and the pressure a t the far end of t,he transmission line is amplified, and the amplified signal modifies the input pressure to the line in order t o reduce the difference. (Note the close analogy t o the operation of a conventional controller on a process.) This device is impractical, but the use of an analog of the transmission line solves the problem neatly. Analysis based on the transmission line study ( 8 ) preceding this work showed that a two-capacity R-C network adequately approximates the dynamic characteristics of the line. This analog has the further advantage that the resistances are easily adjusted t o represent
T R A N S M I S S I O N LINE, 100 FT.
different line lengths. The analog can be contained directly in the transmitter, where its output is readily compared t o the input signal t o the line. This construetion is shown in Figure 7 . Such devices (line-shrinkers) were built, tested, and duccesefully operated (6). Dynamic performance was markedly improved, particularly for the longer transniission lines. Effectively, the device halves the length of the line. That is, a 500foot line with a line-shrinker has about the same dynamic characteristics as a 250-foot line without a line-shrinker.
Control Valve The control valve was the subject of a study ( 4 ) , although it was not a device t h a t was modified. The plant gain and the valve characteristic are closely related: Plant gain is the change in the measured variable produced by a given change in valve stem position; valve characteristic is the relation between rnte of flow and the valve stem position. Even if the best valve is selected for a process, the plant gain may vary widely from the top of the scale to the bottom. Therefore, really optimum controller settings cannot be used, because a controller adjusted for optimum response a t one point on the scale may be either unstable or unresponsive a t some other point.
NO T R A N S M i S S l Q N LINE
RECORD OF DIFFERENTIAL RECORD
OF
DIFFERENTIAL
0
5
TIME CONSTANTS SECONDS
0
1
2
.-
SEeowos
SECONDS
TIME CONSTANTS
3
SECONDS
VALVE MOTOR RANSMITTER
-TRANSMITTER PROCESS
\ Figures
June 1956
5C
and 5D.
Dynamic performance of flow control systems-medium
valve motor with booster
INDUSTRIAL AND ENGINEERING CHEMISTRY
1045
ENGINEERING, DESIGN, A N D PROCESS DEVELOPMENT Flow measurement inferred from the square root of a differential pressure aggravates this condition. The magnetic fiom meter, which has a linear scale of flow response, shows a considerable improvement in uniformity of cont(ro1response and permits the use of more nearly optimum controller adjustments.
Flow Controller Performance K h e n the change was made from the mercury meter transmitter to the dry differential type. the resulting shift in process characteristic called for a noticeable change in controller adjustments. The optimum proportioning band changed from about 20 to over 150%. The optimum reset times changed from about one half minute to perhaps one second. Control was much faster, yet equally stable.
AMPLIFIER
INSTANTANEOUS FEEDBACK
Figure 6.
Reduction of transmission line lag LINE COMPENSATOR r------y
SIGNAL
AMPLIFIER
TO LINE
ANALOG OF i------J
Figure 7.
I
Line-shrinker
Under examination, this change is reasonable. The proportioning band (gain) of a controller must be set appropriate to the dynamic gzin of the process to be controlled by it. The dynamic gain, of course, varies irith the static gain, which in turn depends on such things as the adequacy of supply of the process fluid and speed of response of the various system elements. The system 17-ill be unstable if the "open loop" gain equals or exceeds 1.0 a t the frequency at, which the phase lag is 180". The mercury meter is sloxvy--that is, it has poor dynamic response--and it attenuates high frequency signals so much that high controller gain can be used nithout approaching an open loop gain of 1.0 at' t,he critical phase lag of 180". The fast dry differential pressure transmitter permits high gain to reach the cont,roller a t higher frequencies (where the cont'roller is contributing to phase lag) so that the controller gain must be reduced accordingly. For much the same reason, long settings oi" reset time were nec~ s s a r ywith the s l o mercury ~ meter system, because reset contributes phase lag as well as gain on slow disturbances. With the fast transmitter, hoTrever, especially with short transmission lines and a fast acting valve operator, the fast reset times, as given, become appropriate. T o describe the operation in a different way, in the mercury meter system a, large part of the correction for a load change is made through the proportioning action with the reset supplving the final trim. With the fast differential transmitter, the proport'ioning action does little more than suggest a correction, while the ma,jor work is done by the reset action. A reset control is sometimes thought of as a relatively slox-acting control, but this reset, is so fast in action t h a t recovery time is materially reduced in comparison to that of the former system. Illustrative of the new concepts permitted by fast fiom control action is the idea of relying on the process itself for an indicat'ion
1046
of valve position. Feed-back information as to valve position, via the process, is so rapid and precise that no valve positioner is needed.
A N e w Flow Controller What had been learned about the characteristics of the fiow process now led to a soniervhat revolutionary approach to the design of a flow controller. Modern industrial controllers are provided with as many a6 three mode adjustments-proportional band. reset, and derivative The function of these adjustments is to enable the operator to match the dynamic response of the controller to the process loop to be controlled. Study of the flow control piocess had shown that the response of the flox line was so much faster than the response of other components of the loop that the response of the flow line itseli makes almost no contribution to the open loop response curve. This immediately suggested that inode adjustments are unnecessary for a controller on a liquid flow process. The response of the controller should be matched to the response of the rest of the control loop, but on a liquid flow process the response of the loop is the r e s p h s e of the auxiliary equipment in the looptransmitter, transmission lines, valve operator. All these components are or can be furnished by the maker of control equipment, and as such are under his control and readily available for detailed analysis. This thorough dynamic analysis has been made, and only a limited range of variation n a s observed, indicating that i t n a s possible to select one set of controller adjustments that would function satisfactorily over the entiie range. This meant t h a t a controller without adjustments-one with fixed mode values-was practicable. Such a controller was indeed devised ( I ) , tested, and placed on the market. Experience has shown t h a t it works successfully on liquid flow processes (for which i t was designed) and on a wide variety of gas flow lines as well.
Perspective A study has been made of the dynamic response of commercially available equipment for process Aorv control-the differential pressure transmitter, the pneumatic transmission lines, the controller, the pneumatic valve motor. I n addition to adding t o knowledge of the flow control loop, this st'udy has led t,o a dry diflerential pressure transmitter Tvitli a deliberately limited dynamic response, a device for reducing the time lags introduced by pneumatic trammission lines, a "universal" liquid flow controller, and a measurement of the iinprovement in control afforded by the use of volume relays to minimize the time lag introduced by the valve motor. Thus, speed of response of the process control loop has already been pushed to the point where considerations of safety set a limit on rates of closing of valves in large, high velocity flow lines. Knowledge of the real character of flow measurement is still limited, and work continues on identifying and clarifying the mass of data made available by such things as high speed pressure pickups and the magnetic flowmeter. The final determination of a boundary in frequency bet\!-een useful data and noise and the factors that locate this boundary, the nature and cause of the noise itself, and the efYect of noise on control-these are questions that remain for the future.
biteratasre Cite (1) Bowditch, H. L.. "Development of a Cnivereal Controller for Liquid Flow," Instrument Society of America, paper N o . 52-
15-3, annual conference, Cleveland, Ohio. Sept. 8-12, 1952. (2) Biadnor, M e n d , Instruments 22, 818-25 (1949). (3) Catheron, A. R., I b i d . , 24, 705-10 (1951). (4) hiilham, F., Catheron, A. R., I b i d . , 25, 596-8 (1952). (5) Vannah, 1' . E., Catheron, A. R., 25, Ibid., 1733-7 (1952). RECEIVED for review January 21, 1956.
INDUSTRIAL AND ENGINEERING CHEMISTRY
ACCEPTEDApril 6, 1956.
Vol. 48, No. 6
