Process Control
Reprinted with permission from CEP (Chemical Engineering Progress), June 2008. Copyright © 2008 American Institute of Chemical Engineers (AIChE).
Improve Control of Liquid Level Loops Use this tuning recipe for the classic integrating process control challenge.
Robert Rice Douglas J. Cooper Control Station, Inc.
B
ecause most processes are self-regulating, it can sometimes be challenging to tune a controller for an integrating process. The principal characteristic of a self-regulating process is that it naturally seeks a steadystate operating level if the controller output and disturbance variables are held constant for a sufficient period of time. For example, a car’s cruise control is self-regulat self-regulating. ing. By holding the fuel flow to the engine constant (assuming the car is traveling on flat ground on a windless day), the car is maintained at a constant speed. If the fuel flowrate
V P
Self-Regulating
PV tracks up and down with CO
O C
V P
Integrating (non-self-regulating) behavior in manual mode
IntegratingBehavior
PV at new value when CO returns O C
Time
Figure 1. Integrating processes are characterized by the process variable moving to a new value when the controller output returns to its starting value. In an ideal self-regulating process, the process variable returns to its original value when the controller output is stepped back down. ■
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is increased by a fixed amount, the car will accelerate and then settle at a different constant speed. The temperature of a process stream exiting a heat exchanger is also self-regulating. If the shellside cooling fluid flowrate is held constant and there are no significant external disruptions, the tubeside exit stream temperature will settle at a constant value. If the cooling flowrate is increased, allowed to settle, and then returned it to its original value, the tubeside exit stream temperature will move to a new operating level during the increased flowrate and then return to its original steady-state. Tanks that have a regulated exit flow stream do not naturally settle at a steady-state operating level. This is a common example of what process control practitioners refer to as a non-self-regulating (or integrating) process. Integrating processes can be remarkably challenging to control. This article explores their distinctive behaviors. Armed with this knowledge, you may come to realize that some of your facility’s more-difficult-to-control level, temperature, pressure and other loops have such character.
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The top plot of Figure 1 shows the open-loop (manual mode) behavior of a self-regulating process. In this idealized response, the controller output (CO) signal and measured process variable (PV) are initially at steady state. The CO is stepped up from this steady state and then back down. As shown, the PV responds to the step, and ultimately returns to its original operating level. The bottom plot of Figure 1 shows the open-loop response of an ideal integrating process. The distinctive behavior occurs when the CO returns to its original value and the PV settles at a new operating level.
Level control in a surge tank for a single-valve kegging (SVK) system
S
urge tanks are designed to counteract fluctuations in flow characteristics that would otherwise disrupt upstream or downstream systems. Surge tanks are often installed between two process systems with incompatible flow patterns to provide flow smoothing. The “wild stream” has flow control requirements that are difficult to influence, and the controller then adjusts the controlled stream to maintain the liquid level in the tank. The primary objective of a surge tank is to absorb the fluctuations of the wild stream without significantly impacting the controlled stream. To best achieve this result, the level in a surge tank should be allowed to swing between an upper and a lower level limit. The more the tank is allowed to swing, the larger the surge capacity of the tank. Often, however, these swinging tanks are viewed as poor performers and are then tuned for tight performance, counteracting the intended design objective. A major beer brewer uses an SVK system to fill several lanes of kegs (top). Because the kegfilling lanes are operated in an on/off fashion, the wild stream flowrates requested by the SVK system can quickly vary from 0 to 180 gal/min depending on the number of kegs being filled at any point in time. As shown in the figure on the bottom, adjusting the flow of beer pumped from the large storage tanks controls the level in the surge tank. Due to the sensitive nature of beer and of the analytical instrumentation involved, a surge tank is installed to dampen the large demand fluctuations required by the keg-filling system. By allowing the surge tank to swing more freely between its constraints, the control changes sent to the large storage tank are reduced.
Single Valve Kegging System
Draft Beer Storage Beer Pump FT02 CT01
FLOW
CO2 FT01
FC
FLOW
TT01 TEMP
Beer Surge Tank
LIC LIC
PT01
AT01
PT02
CT02
PR ES
B ALL
PSI
O2
CT04 O2 T T02
AT 02
PT 03
TEMP
pH
PRES
CT03 BALL
Beer Valve Racker Pump Surge Tank Performance
70
% , P 60 S / V P l 50 e v e L
Upper Constraint
Lower Constraint
40
A gg re ssi ve ly Tu ne d P I Co nt ro ll er
C on se rv at iv ely Tu ne d P I C on tr ol le r
% 40 , O 20 C n 140 i m a / m120 l 100 e r t a g S - , 80 d l i w o 60 l W F 40 20 0
0
5
10
15
20
25
30
Time, h
Tuning a control system for a beer-keg filling line (top) to allow the surge tank to fluctuate more between its constraints (bottom) reduces the control changes sent to the storage tank. ■
The integrating behavior plot is somewhat misleading, as it implies that for such processes, a steady controller output will produce a steady process variable. While this is possible with idealized simulations like that used to generate the plot, such “balance point” behavior is rarely found in integrating processes in industrial operations. More realistically, if left uncontrolled, the lack of a balance point means that the process variable of an integrating process will naturally tend to drift up or down, possibly to extreme and even dangerous levels. Consequently, integrating processes are rarely operated in manual mode for long.
P-only control behavior is different To appreciate the difference in controlled behavior for integrating processes, first consider the proportional, or P-only, control of an ideal self-regulating simulation. As
shown in Figure 2 (p. 56), when the setpoint (SP) is initially at the design level of operation (DLO) in the first moments of operation, then PV equals SP (the DLO is where the setpoint and process variable are expected to be during normal operation when the major disturbances are at their normal or typical values). The setpoint is then stepped up from the DLO on the left side of the plot. The simple P-only controller is unable to track the changing SP, and a steady error, called offset, results. The offset grows as each step moves the SP farther away from the DLO. Midway through the process, a disturbance occurs, as shown in the middle of the plot. (Its size was predetermined for this simulation to eliminate the offset.) When the SP is then stepped back down (on the right) the offset shifts, but again grows in a similar and predictable pattern. CEP
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Process Control
% , P65 S60 d55 n a50 V P60 %55 , O50 C45 %65 , D
3) … shifting the offset
1) Offset grows …
2) … then disturbance load changes …
50 100
200
300
400
500
600
Time
Figure 2. P-only control of an ideal self-regulating process shifts the offset caused by disturbances. ■
%65 , P60 S d55 n50 a V P
Controller output behavior is telling
1) No offset …
The CO plots in Figures 2 and 3 demonstrate an interesting feature that distinguishes self-regulating from integrating process behavior. In the self-regulating process plot, the average CO value tracks up and then down as the SP steps up and then down. In the integrating process plot, the CO spikes with each SP step, but then in a most unintuitive fashion, returns to the same steady value. It is only the change in the disturbance flow that causes the average CO to shift midway through the plot, where it then remains centered around the new value for the remainder of the SP steps.
3) … producing sustained offset
60
% , 50 O C40
2) ...then disturbance load changes …
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%52 , D50
40
80
120
160
PI control behavior is different
Time
Figure 3. Unlike an ideal self-regulating process, P-only control for an ideal integrating process shifts the baseline operation of the process, producing a sustained offset even as the setpoint returns to its original value. ■
%56 , P54 S d52 n a50 V48 P 60
With this as background, consider an ideal integrating process simulation under P-only control. Even under simple P-only control, as shown on the left of Figure 3, the process variable is able to track the setpoint steps with no offset. This behavior can be quite confusing, as it does not fit the expected behavior of the more-common self-regulating process. This happens because integrating processes have a natural accumulating character (and is, in fact, why “integrating process” is used as a descriptor for non-self-regulating processes). Since the process integrates, it appears that the controller does not need to. Yet the setpoint steps in the right of Figure 3 show this is not completely correct. Once a disturbance shifts the baseline or balance-point operation of the process (shown roughly at the midpoint in the plot), an offset develops and remains constant even as SP returns to its original design value.
= 0.3 No oscillation K c
= 0.3 Modest oscillation K c
= 1.2 PV oscillates K c
The dependent, ideal form of a proportional-integral (PI) controller (1) is one of numerous algorithms that are widely employed in industrial practice: CO = CObias + K ce(t ) +
%57 , P54 S d 51 n a 48 V P45
%80 , O60 C40
45
20 300
450
600
(1)
K c =
4 K c = 8 Overshoot but PV oscillates no oscillation
150
225
300
Time
Figure 4. Increasing controller gain (K c ) for the PI control of an ideal self-regulating process causes the process variable response to move from a sluggish to an oscillatory response behavior. June 2008
1 PV oscillates
75
■
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K c =
∫ e(t )dt
750
Time
56
T i
100
%55 , O C50
150
K c
CEP
Figure 5. For PI control of an integrating process, oscillatory response behavior can occur both when the controller gain (K c ) of a PI controller is too small and when it is too large. ■
Figure 4 shows an ideal self-regulating process simulation that is controlled using this PI algorithm. Reset time, T i, is held constant throughout the simulation while controller gain, K c, is doubled and then doubled again. As K c increases, the controller becomes more active, and, as expected, this increases the tendency of the PV to display oscillating (underdamped) behavior. For comparison, consider PI control of an ideal integrating process simulation as shown in Figure 5. T i, is again held constant while K c, is increased. A counter-intuitive result is that as K c becomes small and as it becomes large, the PV begins displaying an underdamped (oscillating) response behavior. While the frequency of the oscillations is clearly different between a small and large K c, when seen together in a single plot, it is not always obvious in what direction the controller gain needs to be adjusted to settle the process, in particular, when seeing such unacceptable performance on a control room display.
A tuning recipe provides benefit One of the biggest challenges for practitioners is recognizing that a particular process shows integrating behavior prior to starting a controller design and tuning project. This, like most things, comes with training, experience and practice. Once in automatic mode, closed-loop behavior of an integrating process can be unintuitive, and even confounding. Trial-and-error tuning methods can lead one in circles trying to understand what is causing the unacceptable control performance. A formal controller design and tuning procedure for integrating processes helps overcome these issues in an orderly and reliable fashion. Best practice is to follow a formal recipe when designing and tuning any PID controller. A recipebased approach causes less disruption to the production schedule, wastes less raw material and utilities, requires less personnel time, and generates less off-specification product. The controller design and tuning recipe for integrating processes contains four steps, as follows (2): 1. Establish the design level of operation (the normal or expected values for the setpoint and major disturbances). 2. Bump the process, and collect dynamic process data of the process variable response to changes in controller output. 3. Approximate the process data behavior with a firstorder-plus-dead-time integrating (FOPDT integrating) dynamic model. 4. Use the model parameters generated in step 3 and the correlations in Table 1 to complete the controller tuning. It is important to recognize that real processes are more complex than the simple FOPDT integrating model. In spite of this, the model does provide an approximation of process behavior that is sufficiently rich in dynamic
Table 1. Use tuning correlations for PI and PID controllers for integrating processes
.
Kc
1
PI
Ti
2T c + θ p
2T c + θ p
K p* (T c + θ p )2
PID
1
T d
2T c + θ p
2T c + θ p
K p* (T c + 0.5θ p )2
0.25θ p 2 + T cθ p 2T c + θ p
information to yield reliable and predictable control performance when used with the rules and correlations in Step 4 of the recipe.
The FOPDT integrating model The FOPDT dynamic model commonly used to approximate self-regulating dynamic process behavior has the form: dPV (t ) T p + PV (t ) = K p CO(t − θ p ) dt
(2)
where K p is the steady-state process gain, T p is the overall process time constant, and θ p is the process dead time. Yet this model cannot describe the kind of integrating process behaviors explored above. These dynamic behaviors are better described with the FOPDT integrating model form: dPV(t ) dt
= K p*CO (t − θ p )
(3)
It is interesting to note when comparing these two models that individual values for the familiar process gain, K p, and process time constant, T p, are not separately identified for the FOPDT integrating model. Instead, an integrator gain, K p*, is defined that has units of the ratio of the process gain to the process time constant, or: K p* [=]
K p T p
or
K p* [=]
PV
(4)
CO × time
Tuning correlations for integrating processes The FOPDT integrating model parameters K p* and θ p can be computed using a graphical analysis of plot data, or in an industrial setting by automated analysis using a commercial software package. Once the model parameters are known, the tuning values for the dependent, ideal PI form, Eq. 1, as well as the popular PID algorithm form, can be calculated: CO = CObias + K ce(t ) +
K c
e(t )dt − K cTd T i ∫
dPV dt
(5)
For integrating processes there is no identifiable process time constant in the FOPDT integrating model. Thus, dead time, θ p, is used as the baseline marker of time CEP
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Process Control
Brine Feed Flow, L/min
Disturbance Flow, L/min
15.3
2.5
D
4
m , 2 l e v e L 0
SP
PV
80
70
4.0
LC
4.01
20
CO Controller Output, % 70.0
Discharge Flow, L/min 17.8
Figure 6. Simulated pumped-tank level control in automatic mode uses a throttling valve to adjust the process variable, the liquid level in the tank. ■
for tuning. Specifically, θ p is used as the basis for computing the closed-loop time constant, T c. Building on the popular internal model control (IMC) approach to controller tuning, the closed-loop time constant is computed as T c = 3θ p (3). The controller tuning correlations for integrating processes use this T c, as well as the K p* and θ p from the FOPDT integrating model fit, in the correlations of Table 1.
A simulated example — the pumped-tank A pumped-tank simulation illustrates the design and tuning of a controller for an integrating process. As shown in Figure 6, the process has two liquid streams feeding the top of the tank and a single exit stream pumped out of the bottom. The measured process variable (PV) is the liquid level in the tank. To maintain the liquid level, the controller output (CO) signal adjusts a throttling valve at the discharge of a constant-pressure pump to manipulate the flowrate out of the bottom of the tank. This approximates the behavior of a centrifugal pump operating at relatively low throughput. Note that a pump strictly regulates the discharge flowrate out of the tank. As a consequence, the physics do not naturally work to balance the system when any of the stream flowrates change. This lack of a natural balancing behavior is why the pumped tank is classified as an integrating process. If the total flow into the tank is more than the flow pumped out, the liquid level will rise and continue to rise until the tank fills or a stream flow changes. If 58
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Exit flow increases …
% , O75 C
Setpoint, m
Tank Level, m
… and tank drains
CEP
25
30
35
40
45
Time, min
Figure 7. With the simulated level control in manual mode, the liquid level falls as the controller increases the flowrate out of the bottom of the tank. ■
the total flow into the tank is less than the flow pumped out, the liquid level will fall and continue to fall. Figure 7 is a plot of the pumped-tank behavior with the controller in manual mode (open-loop). The CO signal is stepped up, increasing the discharge flowrate out of the bottom of the tank. The flow out becomes larger than the total feed into the top of the tank and, as shown, the liquid level begins to fall. As the situation persists, the liquid level continues to fall until the tank is drained. The sawtoothed pattern occurs when the tank is empty because the pump briefly surges every time enough liquid accumulates for it to regain suction. Figure 7 does not show that if the controller output were to be decreased enough to cause the flowrate out to be less than the flowrate in, the liquid level would rise until the tank was full. If this were a real process, the tank would overflow and spill, creating safety and profitability issues.
Graphical modeling of integrating process data The graphical method of fitting an FOPDT integrating model to process data requires a data set that includes at least two constant values of controller output, CO1 and CO2. As shown in Figure 8 for the pumped tank, both must be held constant long enough that a slope trend in the PV response (tank liquid level) can be visually identified. An important difference between the traditional process reaction curve graphical technique for self-regulating processes and integrating processes is that integrating processes need not start from a steady-state value before a bump is made to the CO. The graphical technique discussed here is only concerned with the slopes (or rates of change) in PV and the constant controller output signal that caused each PV slope. The FOPDT integrating model describes the PV behavior at each value of constant controller output, CO1 and CO2, as:
Slope 2
5.2
m4.8 , l e4.4 v e L4.0
m4.8 , l e4.4 v e L4.0
Slope1
75
CO1 CO2
CO1 = 65
CO2 = 75
65
20
25
30
35
40
20
Time, min
Figure 8. To perform a manual-mode bump test of the pumped-tank process, the controller outputs must be held constant long enough to show the slope trend in the PV response.
dPV
= K p* CO2 (t − θ p )
*
(6))
m4.8 , l e4.4 v e L4.0
θP =
2
Subtracting and solving for K p* yields: dt
2
CO2 − CO1
1
=
Slope2 − Slope1 CO2 − C O1
1 min
75
% , O70 C
dPV dt
40
5.2
and
−
35
Figure 9. The slopes are calculated from bump test data to compute the integrator gain, K p .
1
dPV
30
■
= K p* C O1 (t − θ p )
dPV
25
Time, min
■
K p* =
(36, 4.6) (24, 4.8)
% , O70 C
65
dt
(31, 5.2)
75
% , O70 C
dt
(27, 5.2)
5.2
(7)
65 20
25
Graphical modeling of pumped-tank data Computing integrator gain. The values of the open-loop data from the pumped-tank simulation in Figure 8 are displayed in Figure 9. The CO is stepped from 71% down to 65%, causing the liquid level (the PV) to rise. The controller output is then stepped from 65% up to 75%, causing a downward slope in the liquid level. The slope of each segment is calculated as the change in tank liquid level divided by the change in time. From the plot data, Slope1 is calculated to be 0.13 m/min and Slope 2 as –0.12 m/min. Using the slopes with their respective CO values yields the integrator gain, K p* = –0.025 m/%-min. Computing dead time. The dead time, θ p, is calculated as the difference in time from when the CO signal was stepped and when the measured PV starts to exhibit a clear response to that change. From the plot in Figure 10, the pumped-tank dead time is estimated be θ p = 1.0 min.
PI control study Now the controller design and tuning recipe for integrating processes can be used to design and test a PI controller. Determining bias value, CObias. A commercial controller
30
35
40
Time, min
Figure 10. The difference in time from when the CO signal is stepped and when the measured PV starts to show a clear response to that change provides an estimate of the dead time from the bump test data. ■
is normally put into practice using bumpless transfer — that is, when switching to automatic control, SP is initialized to the current value of PV and CO bias to the current value of CO. By choosing the current operation as the design state at switchover, the controller needs no corrective actions and it can smoothly engage. Controller gain, K c, and reset time, T i. The first step in using the IMC correlations listed in Table 1 is to compute T c, the closed-loop time constant. T c describes how active the controller should be in responding to a setpoint change or in rejecting a disturbance. For integrating processes, the design and tuning recipe suggests: T c = 3θ p = 3 × 1.0 min = 3 min
The PI controller gain, K c, and reset time, T i, are computed as: CEP
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Process Control
Level control in a distillation column reflux drum
A
t the top of a petroleum-refinery distillation column (below, top), vapor enters a condenser and flows as liquid into a reflux drum. The liquid then exits the drum and either returns to the column as reflux or exits the unit as distillate. The control strategy design for the column is to maintain a fixed distillate flow and adjust the level of the reflux drum through manipulation of the reflux flowrate returning to the top of the column. Distillation columns are very sensitive unit operations with very slow response times (long time constants). If the level controller is tuned aggressively for tight setpoint tracking, large and rapid reflux flow changes could dramatically impact column efficiency and stability. Thus, the reflux drum needs to be tuned for conservative control actions while maintaining the level constraints. Using the tuning procedure outlined in this article, the reflux drum level not only tracks closer to setpoint — it does so with 95% less controller output movement.
% , 5.0 P 4.8 S d 4.6 n 4.4 a V P
Accept some PV overshoot …
… to get disturbance rejection
80
%70 , O 60 C % , D
inlet flow disturbance
4 3 2 1 10
20
30
40
50
60
70
80
Time Sample Time, T = 1 s
Figure 11. A PI controller provides setpoint tracking and disturbance rejection. ■
K c =
1
⋅
2T c + θ p
K p* (T c + θ p )2
Ti = 2T c + θ p
(8)
Substituting the K p*, θp and T c identified above into these tuning correlations, we compute: Condenser Reflux Drum
LIC
Distillation Column
Kc =
FIC L
FIC D
Reflux Valve
Distillate Valve
Reflux Drum Level Performance % , 60 Upper Constraint P S / V 50 P l e v e L 40
1
2(3) + 1
–0.025 (3 + 1)2
= –18 m/%
T i = 2(3) + 1 = 7 miin
Recall that the P-only control of an integrating process (Figure 3) can provide a rapid setpoint response with no overshoot until a disturbance changes the balance point of the process. As labeled in Figure 11, the PI control setpoint response now includes some overshoot. The benefit of integral action is that when a disturbance occurs, a PI controller can reject the upset and return the process variable to its setpoint. This is because the constant summing of integral action continues to move the controller output until the controller error is driven to zero. Thus, PI control requires accepting some overshoot during setpoint tracking in exchange for the ability to reject disturbances. In many industrial applications, this is CEP considered a fair trade.
Lower Constraint
30 90
Aggressively Tuned PI Controller
Conservatively Tuned PI Controller
Literature Cited
% 80 , w 70 o l 60 F x 50 u l f e 40 R
1.
30 20 0
4
8
12
16
20
24
28
Time, h
Using the tuning recipe for reflux drum (top) level control improves the performance (bottom) with 95% less controller output movement. ■
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Cooper, D. J., ed., “Practical Process Control,” www.controlguru.com (2008). 2. Rice, R., and D. J. Cooper, “A Rule-Based Design Methodology for the Control of Non-Self-Regulating Processes,” Proc. ISA Expo 2004, ISA CD Vol. 454, TP04ISA076 (2004). 3. Arbogast, J. E., and D. J. Cooper, “Extension of IMC Tuning Correlations for Non-Self-Regulating (Integrating) Processes,” ISA Transactions, 46, pp. 303 (2007).
Glossary and Nomenclature CO CObias DLO e(t) FOPDT IMC K c K p* PV SP SVK T T c T i T p
θ p
= controller output signal = controller bias or null value = design level of operation = current controller error, defined as SP – PV = first-order-plus-dead-time model = internal model control = controller gain, a tuning parameter = integrator gain = measured process variable = setpoint = single-valve kegging = sample time = closed-loop time constant = reset time, a tuning parameter = overall process time constant = process dead time
ROBERT RICE, PhD, is director of solutions engineering at Control Station, Inc., a
provider of process control solutions (One Technology Dr., Tolland, CT 06084; Phone: (860) 872-2920 x101; E-mail:
[email protected]; Website: www.controlstation.com). He has extensive field experience in both regulatory and advanced controls and has published papers on a wide array of topics associated with automatic process control, including multi-variable process control and model predictive control. He has led the development and support of LOOP-PRO Product Suite, a PID diagnostic and optimization toolkit, and is a trainer for the company’s portfolio of practical process control training workshops. Prior to joining Control Station, he was an engineer with PPG Industries. He received his BS in chemical engineering from Virginia Polytechnic Institute and State Univ. and both his MS and PhD in chemical engineering from the Univ. of Connecticut. DOUGLAS J. COOPER, PhD, is founder and chief technology officer of Control
Station, Inc. (Phone: (860) 872-2920; E-mail:
[email protected]) and a professor of chemical, materials and biomolecular engineering at the Univ. of Connecticut. He is also the author and editor of controlguru.com, an e-book of industry best practices for improving process control. He is a recognized specialist in the fields of advanced process modeling, monitoring and control; intelligent technologies and adaptive process control; and software tools for process control system analysis, tuning and training. Prior to forming Control Station, he held research positions with Arthur D. Little and Chevron. He received his BS in chemical engineering from the Univ. of Massachusetts, Amherst, MS in chemical engineering from the Univ. of Michigan, and PhD in chemical engineering from the Univ. of Colorado.
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