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ISA Effective Use of PID Controllers 3-7-2013
1. Effective Use of PID
Controllers
ISA New Orleans 3-7-2013
Standards
Certification
Education & Training
Publishing
Conferences & Exhibits
1
2. Presenter
– Greg is a retired Senior Fellow from Solutia/Monsanto and an ISA Fellow.
Greg was an adjunct professor in the Washington University Saint Louis
Chemical Engineering Department 2001-2004. Presently, Greg contracts as a
consultant in DeltaV R&D via CDI Process & Industrial and is a part time
employee of Experitec and MYNAH. Greg received the ISA “Kermit Fischer
Environmental” Award for pH control in 1991, the Control Magazine “Engineer
of the Year” Award for the Process Industry in 1994, was inducted into the
Control “Process Automation Hall of Fame” in 2001, was honored by InTech
Magazine in 2003 as one of the most influential innovators in automation, and
received the ISA Life Achievement Award in 2010. Greg is the author of 20
books on process control, his most recent being Advanced Temperature
Measurement and Control. Greg has been the monthly “Control Talk”
columnist for Control magazine since 2002 and has started a Control Talk
Blog. Greg’s expertise is available on the Control Global and Emerson
modeling and control web sites:
http://community.controlglobal.com/controltalkblog
http://modelingandcontrol.com/author/Greg-McMillan/
2
4. Top Ten Ways to Impress Management with Trends
• (10) Make large setpoint changes that zip past valve dead band and nonlinearities.
• (9) Change the setpoint to operate on the flat part of the titration curve.
• (8) Select the tray with minimum process sensitivity for column temperature control.
• (7) Pick periods when the unit was down.
• (6) Decrease the time span so that just a couple data points are trended.
• (5) Increase the reporting interval so that just a couple data points are trended.
• (4) Use really thick line sizes.
• (3) Add huge signal filters.
• (2) Increase the process variable scale span so it is at least 10x control region
• (1) Increase the historian's data compression so changes are screened out
4
5. Contribution of Each PID Mode
• Proportional (P mode) - increase in gain increases P mode contribution
– Provides an immediate reaction to magnitude of measurement change to minimize
peak error and integrated error for a disturbance
– Too much gain action causes fast oscillations (close to ultimate period) and can make
noise and interactions worse
– Provides an immediate reaction to magnitude of setpoint change for P action on Error
to minimize rise time (time to reach setpoint)
– Too much gain causes falter in approach to setpoint
• Integral (I mode) - increase in reset time decreases I mode contribution
– Provides a ramping reaction to error (SP-PV) to minimize integrated error if stable (since
error is hardly ever exactly zero, integral action is always ramping the controller output)
– Too much integral action causes slow oscillations (slower than ultimate period)
– Too much integral action causes an overshoot of setpoint (no sense of direction)
• Derivative (D mode) - increase in rate time increases D mode contribution
– Provides an immediate reaction to rate of change of measurement change to minimize
peak error and integrated error for a disturbance
– Too much rate action causes fast oscillations (faster than ultimate period) and can make
noise and interactions worse
– Provides an immediate reaction to rate of change of setpoint change for D action on
Error to minimize rise time (time to reach setpoint)
– Too much rate causes fast oscillation in approach to setpoint
6. Contribution of Each PID Mode
kick from filtered
derivative mode
Signal ∆%CO1
(%) step from
proportional ∆%CO2 = ∆%CO1
mode
repeat from
seconds/repeat Integral mode
∆%SP
PID structure with proportional, integral, and derivative action on error
Time
(seconds)
Contribution of Each PID Mode for a Step Change in the Set Point
Structure of PID on error (β=1 and γ=1)
7. Effect of Gain on P-Only Controller
Red is 150% of maximum, Green is 100% of maximum, Purple is 50% of maximum of Gain Setting
8. Effect of Reset Time on PI Controller
Red is 150% of maximum, Green is 100% of maximum, Purple is 50% of maximum Reset Time
9. Effect of Rate Time on PD Controller
Red is 200% of maximum, Green is 100% of maximum, Purple is 0% of maximum Rate Time
10. Proportional Mode Basics
Note that many analog controllers used proportional band instead of gain for the proportional mode tuning
setting. Proportional band is the % change in the process variable (∆%PV) needed to cause a 100% change
in controller output (∆%CO). A 100% proportional band means a 100% ∆%PV would cause a 100 % ∆%CO
(a gain of 1). It is critical that users know the units of their controller gain setting and convert accordingly.
Gain = 100 % / Proportional Band
• Proportional Mode Advantages
• Minimize dead time from stiction and backlash
• Minimize rise time
• Minimize peak error
• Minimize integrated error
• Proportional Mode Disadvantages
• Abrupt changes in output upset operators
• Abrupt changes in output upset other loops
• Amplification of noise
10
11. Integral Mode Basics
Note that many analog controllers used reset settings in repeats per minute instead of reset time
for the integral mode tuning setting. Repeats per minute indicate the number of repeats of the
proportional mode contribution in a minute. Today’s reset time settings are minutes per repeat or
seconds per repeat which gives the time to repeat the proportional mode contribution. Often the
“per repeat” term is dropped giving a reset time setting in minutes or seconds.
Seconds per repeat = 60 / repeats per minute
Integral Mode Advantages
• Eliminate offset
• Minimize integrated error
• Smooth movement of output
• Integral Mode Disadvantages
• Limit cycles
• Overshoot
• Runaway of open loop unstable reactors
11
12. Derivative Mode Basics
Nearly all derivative tuning settings are given as a rate time in seconds or minutes. The effective
rate time setting must never be greater than the effective reset time setting. The effective settings
are for an ISA Standard Form. The advantages and disadvantages of the derivative mode are
similar to that of the proportional mode except the relative advantages is less and the relative
disadvantages are greater for the derivative mode.
Seconds = 60 ∗ minutes
• Derivative Mode Advantages
• Minimize dead time from stiction and backlash
• Minimize rise time
• Minimize peak error
• Minimize integrated error
• Derivative Mode Disadvantages
• Abrupt changes in output upset operators
• Abrupt changes in output upset other loops
• Amplification of noise
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13. Reset Gives Operations What They Want
Should steam or water valve be open ?
TC-100
Reactor Temperature
CO PV SP
temperature
steam
valve
opens
SP
50% PV
water
valve
opens
? 48 52 time
14. Open Loop Time Constant (controller in manual)
Signal
(%)
%CO
Controller is in Manual
Open Loop
Error Eo (%)
%PV
0.63∗Eo %SP
0 θo τo Time
(seconds)
Dead Time Open Loop
(Time Delay) (process)
Time Constant
(Time Lag)
15. Closed Loop Time Constant (controller in auto)
Signal
(%)
%CO Controller is in Automatic
%SP
∆%SP
0.63∗∆%SP %PV
0 θo τc Time
(seconds)
Dead Time Closed Loop
(Time Delay) Time Constant
(Time Lag)
Lambda (λ)
16. Top Ten Signs Loops Need to be Tuned
• (10) Lots of trials and errors.
• (9) When asked what the controller gain setting is, the answer is given in %.
• (8) When asked what the controller reset time setting is, the answer is in repeats/min.
• (7) The data historian compression setting is 25%.
• (6) There is more recycle than product.
• (5) Valves are wearing out.
• (4) Tempers are wearing thin.
• (3) Operators are placing bets on what loop will cause the next shutdown.
• (2) The output limits are set to keep the valve from moving.
• (1) Preferred mode is manual.
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17. Conversion of Signals for PID Algorithm
Final Control Element
% % %
SCLR SUB Control Process
PID SCLR AO
SP OUT Valve Equipment
% %CO MV
%PV (e.u.) (e.u.)
SCLR
PID
PV
(e.u.)
Smart Sensing
AI
Transmitter PV Element
PV - Primary Variable
SV - Second Variable* (e.u.)
TV - Third Variable*
DCS FV - Fourth Variable* Measurement
* - additional HART variables
The scaler block (SCLR) that convert between engineering units of application and % of scale
used in PID algorithm is embedded hidden part of the Proportional-Integral-Derivative block (PID)
To compute controller tuning settings, the process variable and controller output
must be converted to % of scale and time units of dead times and time constants
must be same as time units of reset time and rate time settings!
18. Series Form
Form in analog controllers and early DCS – available as a choice in most modern DCS
β Gain
∗ ∆ ∗ proportional
Inverse
%SP Reset All signals are % of scale in PID algorithm but
Time inputs and outputs are in engineering units
filter ∆ ∗ ∗ integral Σ %CO
Filter Time =
γ α ∗ Rate Time
Rate
Time
∗ ∆ ∗ ∗ filter derivative
%PV filter Σ
Switch position for no derivative action
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19. Parallel Form
Form in a few early DCS and PLC and in many control theory textbooks
Proportional
β Gain Setting
∗ ∆ ∗ proportional
%SP Integral
All signals are % of scale in PID algorithm but
Gain Setting
inputs and outputs are in engineering units
filter ∆ ∗ integral Σ %CO
γ
Derivative
Gain Setting
∗ ∆ ∗ derivative
%PV filter
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20. ISA Standard Form
Default Form in most modern DCS
β Gain
∗ ∆ ∗ proportional
Inverse
%SP Reset All signals are % of scale in PID algorithm but
Time inputs and outputs are in engineering units
filter ∆ ∗ ∗ integral Σ %CO
Filter Time =
γ Rate α ∗ Rate Time
Time
∗ ∆ ∗ ∗ filter derivative
%PV filter
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21. Positive Feedback Implementation of Integral
Form for Enhanced PID developed for wireless
Gain * Back out positive feedback of Feedforward (*FF) and ISA Standard Form of
Proportional (*P) and Derivative (*D) modes with β and γ factors
+ P = (β −1) ∗ Gain ∗ %SP
∗ ∆ ∗
−
All signals are % of scale in PID algorithm but
β inputs and outputs are in engineering units
%SP Feedforward
For zero error
For reverse action,
Out1 = 0 P FF
Error = %SP - %PV
+ Out1
filter ∆ ∗ Σ Σ Σ %CO
− Filter Time =
Positive Out2 D
Reset Time
Feedback
*P *FF
γ Switch position
Rate
filter ∆ ∆ for external
Time reset feedback
*D
+
∗ ∆ ∗ ∗ filter derivative
− E-R
Filter Time = E-R is external reset
%PV filter Reset Time (e.g. secondary %PVs)
Filter Time = Dynamic Reset Limit
α ∗ Rate Time
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22. Conversion of Series to ISA Form
To convert from Series to ISA Standard Form controller gain:
Ti ' + Td'
Kc = ∗ K c'
Ti ' Interaction factor
To convert from Series to ISA Standard Form reset (integral) time:
Ti ' + Td'
Ti = ∗ Ti ' = Ti ' + Td'
Ti '
To convert from Series to ISA Standard Form rate time:
Ti '
Td = ' ∗ Td'
Ti + Td'
Primed tuning settings are Series Form
Note that if the rate time is zero, the ISA Standard and Series Form settings are identical.
When using the ISA Standard Form, if the rate time is greater than ¼ the reset time the
response can become oscillatory. If the rate time exceeds the reset time, the response can
become unstable from a reversal of action form these modes. The Series Form inherently
prevents this instability by increasing the effective reset time as the rate time is increased.
22
23. Anti Reset Windup (ARW) and Output Limits
• For digital positioners and precise throttling valves
– ARW & Out Lo Lim = 0%, ARW & Out Hi Lim = 100%
• For pneumatic positioners & on-off heritage valves
– Lo Lim = -5%, Hi Lim = 105%
– ARW set inside output limits to get thru zone of ineffective valve
response (stick-slip, shaft windup, & poor sensitivity)
• For primary PID in cascade control, limits are set to match
secondary setpoint limits in engineering units
24. Checklist for PID Migration - 1
There are many features and parameters that vary with the DCS supplier. It is imperative the DCS
documentation and supplier expertise be fully utilized and all migrations tested by a real time
simulation for stability. Note the default of 0% low and 100% high output and ARW limits do not
change to match changes made in output scale or engineering units.
For cascade control did you set the output scale of the primary PID in engineering units of the PV
scale of the secondary loop?
For cascade control did you set the primary PID low and high output limits in engineering units to
match setpoint limits of secondary PID?
Did you set the anti-reset windup (ARW) limits to match the output limits using same units as
output limits unless there is some special need for ARW limits to be set otherwise?
Did you convert controller gain setting units (being especially aware of the inverse relationship
between proportional band and gain)?
Did you convert reset units setting (being especially aware of the inverse relationship between
repeats per minute and seconds per repeat)?
Did you convert rate units setting and make the alpha setting the same for the rate filter?
If rate time is not zero and ISA Standard Form is used, did you convert Series Form gain, reset,
and rate settings to corresponding ISA Standard Form settings?
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25. Checklist for PID Migration - 2
For override control if the positive feedback implementation of integral mode is used, did you
remove the filter on external reset signal used to prevent walk-off since this filter is already there?
For cascade control, id you turn on external reset feedback (dynamic reset limit) and use PV of
secondary loop for external reset feedback to automatically prevent burst of oscillations from violation
of cascade rule that secondary loop must be 5x faster than primary loop?
For slow or sticky valve, did you turn on external reset feedback (dynamic reset limit) and use a fast
PV readback for external reset feedback to automatically prevent burst of oscillations from violation of
cascade rule that positioner feedback loop must be 5x faster than primary loop and to prevent limit
cycles from stick-slip? Did you realize the PV readback must normally be faster than a secondary HART
variable update time?
For wireless control and at-line or on-line analyzer, did you use an enhanced PID developed for
wireless that suspends integral action between updates (PIDPlus option) and uses elapsed time in the
derivative action. The external-reset option should automatically be turned on?
Did you make sure the BKCAL signals are connected properly paying particular attention to the
propagation of the BKCAL settings for intervening blocks for split range, signal characterization, and
override control?
25
26. Top 10 Things You Shouldn't Say
When You Enter a Control Room
• (10) Does this hard hat make my butt look big?
• (9) At the last plant I was in we always did it this way.
• (8) I added alarms to each loop.
• (7) Does that flare out there always shoot up that high?
• (6) Ooooh! Did you mean to do that?
• (5) Can't somebody do something about all those alarms?
• (4) We just downloaded the version released yesterday
• (3) Here, I will show you how to operate this plant.
• (2) Are you ready to put all your loops in Remote Cascade?
• (1) We want a "lights out" plant!
26
27. Triple Cascade Loop Block Diagram
Process Primary Controller – Secondary Flow Controller – Digital Valve Controller
DCS Valve Positioner
Process Flow Drive Signal
SP SP CO Control Flow
PID PID AO PID* I/P Relay Process
External External Valve Meter
Reset Reset
BKCAL BKCAL Position (Valve Travel)
PV PV
Position Loop Feedback Process
AI AI Sensor
* most positioners use proportional only
Secondary (Inner) Loop Feedback
Primary (Outer) Loop Feedback
28. Effect of Slow Secondary Tuning (cascade control)
Secondary loop slowed down by a factor of 5
Secondary CO
Primary PV
Secondary SP
Secondary SP
Secondary CO
Primary PV
29. External Reset Feedback (Dynamic Reset Limit)
• Prevents PID output changing faster
than a valve, VFD, or secondary
loop can respond
– Secondary PID slow tuning
– Secondary PID SP Filter Time
– Secondary PID SP Rate Limit
– AO, DVC, VFD SP Rate Limit
– Slow Valve or VFD
– Use PV for BKCAL_OUT
– Position used as PV if valve is very
slow and readback is fast
– Enables Enhanced PID for Wireless
• Stops Limit cycles from deadband,
backlash, stiction, and threshold
sensitivity or resolution limits
• Key enabling feature that simplifies
tuning and creates more advanced
opportunities for PID control
30. PID Structure Options
(1) PID action on error (β = 1 and γ = 1)
(2) PI action on error, D action on PV (β = 1 and γ = 0)
(3) I action on error, PD action on PV (β = 0 and γ = 0)
(4) PD action on error, no I action (β = 1 and γ = 1)
(5) P action on error, D action on PV, no I action (β = 1 and γ = 0)
(6) ID action on error, no P action (γ = 1)
(7) I action on error, D action on PV, no P action (γ = 0)
(8) Two degrees of freedom controller (β and γ adjustable 0 to 1)
31. (1) PID action on error
• Fastest response to rapid (e.g. step) SP change by
– Step in output from proportional mode
– Spike in output from derivative mode can be made more like a kick by
decreasing gamma factor (γ <1)
– Zero dead time from deadband, resolution limit, & stiction
• Burst of flow may affect other uses of fluid
• Operations do not like sudden changes in output
• Fast approach to SP more likely to cause overshoot
• Setpoint filter & rate limits eliminate step & overshoot
32. (2) PI action on error, D action on PV
• Slightly slower SP response than structure (1)
– Still have step from proportional mode
– Spike or bump from derivative mode eliminated
• Decrease in SP response speed is negligible if
– Output hits output limit due to large SP change or PID gain
– Rate time is less than total loop dead time
– Alpha factor is increased (α > 0.125) (rate filter increased)
• Setpoint filter & rate limits eliminate step & overshoot
• Most popular structure choice
33. (3) I action on error, PD action on PV
• Provides gradual change in output for SP change
• Slows down SP response dramatically
• Eliminates overshoot for SP changes
• Used for bioreactor temperature and pH SP changes
(overshoot is much more important than cycle time)
• Used for temperature startup to warm up equipment
• Generally not recommended for secondary loops
34. (4 - 5) No Integral action
• Used if integral action adversely affects process
• Used if batch response is only in one direction
• Must set bias (output when PV = SP)
• Highly exothermic reactors use structure 4 because
integral action and overshoot can cause a runaway
– 10x reset time (Ti > 40x dead time) to prevent runaway
• Traditionally used on Total Dissolved Solids (TDS) drum
and surge tank level control because of slow integrating
response and permissibility of SP offset.
– Low controller gain (Kc) cause slow rolling oscillations due to
violation of inequality for integrating process. The inequality is
commonly violated since Ki (integrating process gain) is extremely
small on most vessels (Ki < 0.000001 %/sec/%).
Most common problem is use of too small of a reset time for vessel batch
composition and temperature, level, and gas pressure control causing
violation of following rule
2
K c * Ti >
Ki
35. (6 -7) No Proportional Action
• Predominantly used for valve position control (VPC)
– Parallel valve control (VPC SP & PV are small valve desired & actual
position, respectively, & VPC out positions large valve)
– Optimization (VPC SP & PV are limiting valve desired & actual
position, respectively, & VPC out optimizes process PID SP)
– VPC reset time > 10x residence time to reduce interaction
– VPC reset time > Kc∗Ti of process PID to reduce interaction
– VPC tuning is difficult & too slow for fast & large disturbances
• Better solution is external reset feedback & SP rate limits
36. Improvement in Batch Temperature by
Elimination of Integral action
Batch temperature response in a single ended temperature
control. Integral action causes overshoot.
Typical Batch Temperature
80
70
60
degrees C
50
40
30
20
10
0
1 51 101 151 201 251 301 351 401
Time (min)
Setpoint PV CO%
Batch temperature response in a single ended temperature
control. PD on error. No I action.
Batch Temperature (new tuning)
45.0
40.0
35.0
degrees C
30.0
25.0
20.0
15.0
10.0
5.0
0.0
1 51 101 151 201 251 301 351 401
Time (min)
Setpoint PV CO%
36
37. (8) Two Degrees of Freedom
• β and γ SP weighting factors are adjusted to balance fast
approach & minimal overshoot for SP response
• Alternative is using SP lead-lag with lag = reset time and lead =
20% of lag to achieve fast SP response with minimal overshoot
39. Top Ten Reasons to Use a DCS for Your BBQ
• (10) Automated recipes
• (9) Predicted BBQ times
• (8) Five-course meal no problem
• (7) Don't have to watch cooking shows
• (6) Feed-forward control
• (5) Process control comes home
• (4) Children want to become automation engineers
• (3) Spouse finally appreciates your expertise
• (2) Griller not grilled
• (1) More time to drink beer
39
40. Fed-Batch and Startup Time Reduction - 1
• PID on Error Structure
– Maximizes the step and kick of the controller output for a setpoint change.
– Overdrive (driving of output past resting point) is essential for getting slow loops, such
as vessel temperature and pH, to the optimum setpoint as fast as possible.
– The setpoint change must be made with the PID in Auto mode.
– “SP track PV” will generally maximize the setpoint change and hence the step and kick
(retaining SP from last batch or startup minimizes kick and bump)
• SP Feedforward
– For low controller gains (controller gain less than inverse of process gain), a setpoint
feedforward is particularly useful. For this case, the setpoint feedforward gain is the
inverse of the dimensionless process gain minus the controller gain.
– For slow self-regulating (e.g. continuous) processes and slow integrating (e.g. batch)
processes, even if the controller gain is high, the additional overdrive can be beneficial
for small setpoint changes that normally would not cause the PID output to hit a limit.
– If the setpoint and controller output are in engineering units the feedforward gain must
be adjusted accordingly.
– The feedforward action is the process action, which is the opposite of the control
action, taking into account valve action. In other words for a reverse control action, the
feedforward action is direct provided the valve action is increase-open or the analog
output block, I/P, or positioner reverses the signal for a increase-close.
41. Fed-Batch and Startup Time Reduction - 2
• Full Throttle (Bang-Bang Control) - The controller output is stepped to it output
limit to maximize the rate of approach to setpoint and when the projected PV
equals the setpoint less a bias, the controller output is repositioned to the final
resting value. The output is held at the resting value for one dead time. For more
details, check out the Control magazine article “Full Throttle Batch and Startup
Response.” http://www.controlglobal.com/articles/2006/096.html
– A dead time (DT) block must be used to compute the rate of change so that new values of
the PV are seen immediately as a change in the rate of approach.
– If the total loop dead time (θo) is used in the DT block, the projected PV is simply the current
PV minus the output of the DT block (∆PV) plus the current PV.
– If the PV rate of change (∆PV/∆t) is useful for other reasons (e.g. near integrator or true integrating
process tuning), then ∆PV/∆t = ∆PV/θo can be computed.
– If the process changes during the setpoint response (e.g. reaction or evaporation), the
resting value can be captured from the last batch or startup
– If the process changes are negligible during the setpoint response, the resting value can be
estimated as:
– the PID output just before the setpoint change for an integrating (e.g. batch) process
– the PID output just before the setpoint change plus the setpoint change divided by the process gain
for a self-regulating (e.g. continuous) process
– For self-regulating processes such as flow with the loop dead time (θo) approaching or
less than the largest process time constant (τp ), the logic is revised to step the PID
output immediately to the resting value. The PID output is held at the resting value for
the T98 process response time (T98 = θo + 4∗ τo ).
42. Fed-Batch and Startup Time Reduction - 3
• Output Lead-Lag
– A lead-lag on the controller output or in the digital positioner can kick the signal though
the valve deadband and stiction, get past split range points, and make faster
transitions from heating to cooling and vice versa.
– A lead-lag can potentially provide a faster setpoint response with less overshoot when
analyzers are used for closed loop control of integrating processes When combined
with the enhanced PID algorithm (PIDPlus) described in:
– Deminar #1 http://www.screencast.com/users/JimCahill/folders/Public/media/5acf2135-
38c9-422e-9eb9-33ee844825d3
– White paper http://www.modelingandcontrol.com/DeltaV-v11-PID-Enhancements-for-
Wireless.pdf
• Dead Time Compensation
– The simple addition of a delay block with the dead time set equal to the total loop dead
time to the external reset signal for the positive feedback implementation of integral
action described in Deminar #3 for the dynamic reset limit option
http://www.screencast.com/users/JimCahill/folders/Public/media/f093eca1-958f-4d9c-
96b7-9229e4a6b5ba .
– The controller reset time can be significantly reduced and the controller gain increased
if the delay block dead time is equal or slightly less than the process dead time as
studied in Advanced Application Note 3
http://www.modelingandcontrol.com/repository/AdvancedApplicationNote003.pdf
43. Fed-Batch and Startup Time Reduction - 4
• Feed Maximization
– Model Predictive Control described in Application Note 1
http://www.modelingandcontrol.com/repository/AdvancedApplicationNote001.pdf
– Override control is used to maximize feeds to limits of operating constraints via valve
position control (e.g. maximum vent, overhead condenser, or jacket valve position with
sufficient sensitivity per installed characteristic).
– Alternatively, the limiting valve can be set wide open and the feeds throttled for temperature
or pressure control. For pressure control of gaseous reactants, this strategy can be quite
effective.
– For temperature control of liquid reactants, the user needs to confirm that inverse response
from the addition of cold reactants to an exothermic reactor and the lag from the
concentration response does not cause temperature control problems.
– All of these methods require tuning and may not be particularly adept at dealing with fast
disturbances unless some feedforward is added. Fortunately the prevalent disturbance that
is a feed concentration change is often slow enough due to raw material storage volume to
be corrected by temperature feedback.
• Profile Control
– If you have a have batch measurement that should increase to a maximum at the batch end
point (e.g. maximum reaction temperature or product concentration), the slope of the batch
profile of this measurement can be maximized to reduce batch cycle time. For application
examples checkout “Direct Temperature Rate of Change Control Improves Reactor
Yield” in a Funny Thing Happened on the Way to the Control Room
http://www.modelingandcontrol.com/FunnyThing/ and the Control magazine article
“Unlocking the Secret Profiles of Batch Reactors”
http://www.controlglobal.com/articles/2008/230.html .
44. Dead Time Compensator Configuration
Must enable dynamic reset limit !
Insert
deadtime
block
45. Dead Time Myths Busted
• Dead time is eliminated from the loop. The smith predictor, which created a PV without
dead time, fools the controller into thinking there is no dead time. However, for an
unmeasured disturbance, the loop dead time still causes a delay in terms of when the loop
can see the disturbance and when the loop can enact a correction that arrives in the
process at the same point as the disturbance. The ultimate limit to the peak error and
integrated error for an unmeasured disturbance are still proportional to the dead time, and
dead time squared, respectively.
• Control is faster for existing tuning settings. The addition of dead time compensation
actually slows down the response for the existing tuning settings. Setpoint metrics, such as
rise time, and load response metrics, such as peak error, will be adversely affected.
Assuming the PID was tuned for a smooth stable response, the controller must be retuned
for a faster response. For a PID already tuned for maximum disturbance rejection, the gain
can be increased by 250%. For dead time dominant systems where the total loop dead
time is much greater than the largest loop time constant (hopefully the process time
constant), the reset time must also be decreased or there will be severe undershoot. If you
decrease the reset time to its optimum, undershoot and overshoot are about equal. For the
test case where the total loop dead time to primary process time constant ratio was 10:1,
you could decrease the reset time by a factor of 10. Further study is needed as to whether
the minimum reset time is a fraction of the underestimated dead time plus the PID module
execution time where the fraction depends upon the dead time to time constant ratio
For access to Deminar 10 ScreenCast Recording or SlideShare Presentation go to
http://www.modelingandcontrol.com/2010/10/review_of_deminar_10_-_deadtim.html
46. Dead Time Myths Busted
• Compensator works better for loops dominated by a large dead time. The reduction in
rise time is greatest and the sensitivity to per cent dead time modeling error particularly for
an overestimate of dead time is least for the loop that was dominated by the process time
constant. You could have a dead time estimate that was 100% high before you would see
a significant jagged response when the process time constant was much larger than the
process dead time. For a dead time estimate that was 50% too low, some rounded
oscillations developed for this loop. The loop simply degrades to the response that would
occur from the high PID gain as the compensator dead time is decreased to zero. While
the magnitude of the error in dead time seems small, you have to remember that for an
industrial temperature control application, the loop dead time and process time constant
would be often at least 100 times larger. For a 400 second dead time and 10,000 second
process time constant, a compensator dead time 200 seconds smaller or 400 seconds
larger than actual would start to cause a problem. In contrast, the dead time dominant loop
developed a jagged response for a dead time that was high or low by just 10%. I think this
requirement is unreasonable in industrial processes. A small filter of 1 second on the input
to the dead time block in the BKCAL path may have helped.
• An underestimate of the dead time leads to instability. In tuning calculations for a
conventional PID, a smaller than actual dead time can cause an excessively oscillatory
response. Contrary to the effect of dead time on tuning calculations, a compensator dead
time smaller than actual dead time will only cause instability if the controller is tuned
aggressively after the dead time compensator is added.
• An overestimate of the dead time leads to sluggish response and greater stability. In
tuning calculations for a conventional PID, a larger than actual dead time can cause an
excessively slow response. Contrary to the effect of dead time on tuning calculations, a
compensator dead time greater than actual dead time will cause jagged irregular
oscillations.
47. Top Ten Reasons Why Automation Engineers
Makes Great Spouses or at Least a Wedding Gifts
• (10) Reliable from day one
• (9) Always on the job
• (8) Low maintenance (minimal grooming, clothing, and entertainment costs
• (7) Many programmable features
• (6) Stable
• (5) Short settling time
• (4) No frills or extraneous features
• (3) Relies on feedback
• (2) Good response to commands and amenable to real time optimization
• (1) Readily tuned
48. General PID Checklist - 1
Does the measurement scale cover the entire operating range, including abnormal
conditions?
Is the valve action correct (increase-open for fail close and increase-close for fail open)?
Is the control action correct (direct for reverse process and reverse for direct process if the
valve action is set)?
Is the best “Form” selected (ISA standard form)?
Is the “obey setpoint limits in cascade and remote cascade mode” option selected?
Are the external reset feedback (BKCAL) signals correctly connected between blocks?
Is the PV for BKCAL selected in the secondary loop PID?
Is the best “Structure” selected (PI action on error, D action on PV for most loops)?
Is the “setpoint track PV in manual” option selected to provide a faster initial setpoint
response unless the setpoint must be saved in PID?
48
49. General PID Checklist - 2
Are setpoint limits set to match process, equipment, and valve constraints?
Are output limits set to match process, equipment, and valve constraints?
Are anti-reset windup (ARW) limits set to match output limits?
Is the module scan rate (PID execution time) less than 10% of minimum reset time?
Is the signal filter time less than 10% of minimum reset time?
Is the PID tuned with a proven tuning method or by an auto-tuner or adaptive tuner?
Is the rate time less than ½ the dead time (the rate is typically zero except for temperature)
Is external-reset feedback (dynamic reset limit) enabled for cascade control, analog output
(AO) setpoint rate limits, and slow control valves or variable speed drives?
Are AO setpoint rate limits set for blending, valve position control, and surge valves?
Is integral deadband greater than limit cycle PV amplitude?
Can an enhanced PID be used for loops with wireless instruments or analyzers?
49
50. Feedforward Applications
• Feedforward is the most common advanced control technique used - often the
feedforward signal is a flow or speed for ratio control that is corrected by a feedback
process controller (Flow is the predominant process input that is manipulated to set
production rate and to control process outputs (e.g. temperature and composition))
– Blend composition control - additive/feed (flow/flow) ratio
– Column temperature control - distillate/feed, reflux/feed, stm/feed, and bttms/feed (flow/flow) ratio
– Combustion temperature control - air/fuel (flow/flow) ratio
– Drum level control - feedwater/steam (flow/flow) ratio
– Extruder quality control - extruder/mixer (power/power) ratio
– Heat exchanger temperature control - coolant/feed (flow/flow) ratio
– Neutralizer pH control - reagent/feed (flow/flow) ratio
– Reactor reaction rate control - catalyst/reactant (speed/flow) ratio
– Reactor composition control - reactant/reactant (flow/flow) ratio
– Sheet, web, and film line machine direction (MD) gage control - roller/pump (speed/speed) ratio
– Slaker conductivity control - lime/liquor (speed/flow) ratio
– Spin line fiber diameter gage control - winder/pump (speed/speed) ratio
• Feedforward is most effective if the loop deadtime is large, disturbance speed is fast
and size is large, feedforward gain is well known, feedforward measurement and
dynamic compensation are accurate
• Setpoint feedforward is most effective if the loop deadtime exceeds the process time
constant and the process gain is well known
For more discussion of Feedforward see May 2008 Control Talk
http://www.controlglobal.com/articles/2008/171.html
51. Feedforward Implementation - 1
• Feedforward gain can be computed from a material or energy balance ODE * &
explored for different setpoints and conditions from a plot of the controlled variable
(e.g. composition, conductivity, pH, temperature, or gage) vs. ratio of manipulated
variable to independent variable (e.g. feed) but is most often simply based on
operating experience
– * http://www.modelingandcontrol.com/repository/AdvancedApplicationNote004.pdf
– Plots are based on an assumed composition, pressure, temperature, and/or quality
– For concentration and pH control, the flow/flow ratio is valid if the changes in the composition
of both the manipulated and feed flow are negligible.
– For column and reactor temperature control, the flow/flow ratio is valid if the changes in the
composition and temperature of both the manipulated and feed flow are negligible.
– For reactor reaction rate control, the speed/flow is valid if changes in catalyst quality and void
fraction and reactant composition are negligible.
– For heat exchanger control, the flow/flow ratio is valid if changes in temperatures of coolant
and feed flow are negligible.
– For reactor temperature control, the flow/flow ratio is valid if changes in temperatures of
coolant and feed flow are negligible.
– For slaker conductivity (effective alkali) control, the speed/flow ratio is valid if changes in lime
quality and void fraction and liquor composition are negligible.
– For spin or sheet line gage control, the speed/speed ratio is valid only if changes in the pump
pressure and the polymer melt quality are negligible.
• Dynamic compensation is used to insure the feedforward signal arrives at same
point at same time in process as upset
– Compensation of a delay in the feedforward path > delay in upset path is not possible
52. Feedforward Implementation - 2
• Feedback correction is essential in industrial processes
– While technically, the correction should be a multiplier for a change in slope and a bias for a change
in the intercept in a plot of the manipulated variable versus independent variable (independent from
this loop but possibly set by another PID or MPC), a multiplier creates scaling problems for the user,
consequently the correction of most feedforward signal is done via a bias.
– The bias correction must have sufficient positive and negative range for worst case.
– Model predictive control (MPC) and PID loops get into a severe nonlinearity by creating a controlled
variable that is the ratio. It is important that the independent variable be multiplied by the ratio and
the result be corrected by a feedback loop with the process variable (composition, conductivity,
gage, temperature, or pH) as the controlled variable.
• Feedforward gain is a ratio for most load upsets.
• Feedforward gain is the inverse of the process gain for setpoint feedforward.
– Process gain is the open loop gain seen by the PID (product of manipulated variable, process
variable, and measurement variable gain) that is dimensionless.
• Feedforward action must be in the same direction as feedback action for upset.
• Feedforward action is the opposite of the control action for setpoint feedforward.
• Feedforward delay and lag adjusted to match any additional delay and lag,
respectively in path of upset so feedforward correction does not arrive too soon.
• Feedforward lead is adjusted to compensate for any additional lag in the path of the
manipulated variable so the feedforward correction does not arrive too late.
• The actual and desired feedforward ratio should be displayed along with the bias
correction by the process controller. This is often best done by the use of a ratio block
and a bias/gain block instead of the internal PID feedforward calculation.
53. Linear Reagent Demand Control
(PV is X axis of Titration Curve)
• Signal characterizer converts PV and SP from pH to % Reagent Demand
– PV is abscissa of the titration curve scaled 0 to 100% reagent demand
– Piecewise segment fit normally used to go from ordinate to abscissa of curve
– Fieldbus block offers 21 custom space X,Y pairs (X is pH and Y is % demand)
– Closer spacing of X,Y pairs in control region provides most needed compensation
– If neural network or polynomial fit used, beware of bumps and wild extrapolation
• Special configuration is needed to provide operations with interface to:
– See loop PV in pH and signal to final element
– Enter loop SP in pH
– Change mode to manual and change manual output
• Set point on steep part of curve shows biggest improvements from:
– Reduction in limit cycle amplitude seen from pH nonlinearity
– Decrease in limit cycle frequency from final element resolution (e.g. stick-slip)
– Decrease in crossing of split range point
– Reduced reaction to measurement noise
– Shorter startup time (loop sees real distance to set point and is not detuned)
– Simplified tuning (process gain no longer depends upon titration curve slope)
– Restored process time constant (slower pH excursion from disturbance)
53
54. Output Tracking for SP Response
• “Head-Start” logic for startup & batch SP changes:
– For SP change PID tracks best/last startup or batch final settling
value for best/last rise time less total loop deadtime
– Closed loop time constant is open loop time constant (λf =1)
– Not as fast as Bang-Bang (PID OUT is not at output limit)
• “Bang-Bang” logic for startup & batch SP changes:
– For SP change PID tracks output limit until the predicted PV one
deadtime into future gets within a deadband of setpoint, the output is
then set at best/last startup or batch final settling value for one
deadtime
– Implementation uses simple DT block (loop deadtime) to create an
old PV subtracted from the new PV to give a delta PV that is added to
old PV to create a PV one deadtime into future
– Works best on slow batch and integrating processes
55. Output Tracking for Protection - 1
• “Open Loop Backup” to prevent compressor surge:
– Once a compressor gets into surge, cycles are so fast & large that
feedback control can not get compressor out of surge
– When compressor flow drops below surge SP or a precipitous drop
occurs in flow, PID tracks an output that provides a flow large enough
to compensate for the loss in downstream flow for a time larger than
the loop dead time plus the surge period.
• “Open Loop Backup” to prevent RCRA violation:
– An excursion < 2 pH or > 12 pH for even a few sec can be a
recordable RCRA violation regardless of downstream volume
– When an inline pH system PV approaches the RCRA pH limit the PID
tracks an incremental output (e.g. 0.25% per sec) opening the
reagent valve until the pH sufficiently backs away
• “Open Loop Backup” for evaporator conductivity
56. Open Loop Backup Configuration - 2
SP_Rate_DN and SP_RATE_UP used to insure fast getaway and slow approach
Open Loop Backup Configuration
Open loop backup used for prevention of
compressor surge and RCRA pH violation
59. RCRA pH Kicker
Optimization of pH filter and kicker increment saved $50K in reagent costs
MPC-1
MPC-2
Waste
middle selector
RCAS RCAS
Kicker
ROUT
AC-1 AC-2 AY AY
splitter splitter AT AT AT
AY AY AY
middle selector middle selector Filter
FT FT
AY AY Attenuation
Tank
Stage 1 AT AT AT Stage 2 AT AT AT
Mixer Mixer FT
61. Setpoint Filter
• PID SP filter reduces overshoot enabling fast tuning
– Setpoint filter time set equal reset time
• PID SP filter coordinates timing of flow ratio control
– Simultaneous changes in feeds for blending and reactions
– Consistent closed loop response for model predictive control
• PID SP filter sets closed loop time constant
• PID SP filter in secondary loop slows down cascade control
system rejection of primary loop disturbances
– Secondary loop must be > 4x faster than primary loop
• Primary PID must have dynamic reset limit enabled
• Setpoint Lead-Lag minimizes overshoot and rise time
– Lag time = reset time
– Lead time = 20% lag time
62. Setpoint Rate Limits
• AO & PID SP rate limits minimize disruption while protecting
equipment and optimizing processes
– Offers directional moves suppression
– Enables fast opening and slow closing surge valve
– VPC fast recovery for upset and slow approach to optimum
• AO SP rate limits minimize interaction between loops
– Less important loops are made 10x slower than critical loops
• PID driving AO SP or secondary PID SP rate limit must have
dynamic reset limit enabled so no retuning is needed
• PID faceplate should display PV of AO to show rate limiting
63. Top Ten Reasons to do APC from your Home
• (10) Can immediately implement an inspiration.
• (9) Can watch the ball game on one of your screens.
• (8) Get to wear shorts and sandals.
• (7) Get to listen to music rather than alarms.
• (6) Lose weight from not eating doughnuts.
• (5) Can BBQ while solving control problem.
• (4) No more lonely nights and meals.
• (3) Your kids start to recognize you.
• (2) Your kids want to become automation engineers.
• (1) Your spouse starts to offer you advanced process control.
63
64. Enhanced PID for Wireless Features
• Positive feedback implementation of reset with external-reset
feedback (dynamic reset limit)
• Immediate response to a setpoint change or feedforward signal or
mode change
• Suspension of integral action until change in PV
• Integral action is the exponential response of the positive feedback
filter to the change in controller output in elapsed time (the time
interval since last update)
• Derivative action is the PV or error change divided by elapsed time
rather than PID execution
71. Stop Limit Cycles
Traditional PID Enhanced PID
PID PV
PID Output
Limit Cycles from Valve Stick-Slip
72. Benefits Extend Beyond Wireless - 1
• The PID enhancement for wireless offers an improvement wherever
there is an update time in the loop. In the broadest sense, an update
time can range from seconds (wireless updates and valve or
measurement sensitivity limits) to hours (failures in communication,
valve, or measurement). Some of the sources of update time are:
– Wireless update time for periodic reporting (default update rate)
– Wireless measurement trigger level for exception reporting (trigger level)
– Wireless communication failure
– Broken pH electrode glass or lead wires (failure point is about 7 pH)
– Valve with backlash (deadband) and stick-slip (resolution)
– Operating at split range point (no response & abrupt response discontinuity)
– Valve with solids, high temperature, or sticky fluid (plugging and seizing)
– Plugged impulse lines
– Analyzer sample, analysis cycle, and multiplex time
– Analyzer resolution and threshold sensitivity limit
To completely stop a valve limit cycle from backlash or stick-slip,
measurement updates must not occur due to noise
73. Benefits Extend Beyond Wireless - 2
• Enhanced PID executes for a change in setpoint, feedforward, or
remote output to provide an immediate reaction based on PID structure
• The improvement in control by the enhanced PID is most noticeable as
the update time becomes much larger than the 63% process response
time (defined in the white paper as the sum of the process deadtime
and time constant). When the update time becomes 4 times larger than
this 63% process response time ( 98% response time frequently cited in
the literature), the feedforward and controller gains can be set to
provide a complete correction for changes in the measurement and
setpoint.
– Helps ignore inverse response and errors in feedforward timing
– Helps ignore discontinuity (e.g. steam shock) at split range point
– Helps extend packing life by reducing oscillations and hence valve travel
• Since enhanced PID can be set to execute only upon a significant
change in user valve position, this PID as a valve position controller
offers less interaction and cycling for optimization of unit operations by
increasing reactor feed, column feed or increasing refrigeration unit
temperature, or decreasing compressor pressure till feed, vent,
coolant, and/or steam, valves are at maximum good throttle position.
Website entries on Enhanced PID Benefits
http://www.modelingandcontrol.com/2010/08/wireless_pid_benefits_extend_t.html
http://www.modelingandcontrol.com/2010/10/enhanced_pid_for_wireless_elim.html
http://www.modelingandcontrol.com/2010/11/a_delay_of_any_sorts.html
74. Why over 100 PID Tuning Rules?
• Aidan O’Dwyer’s Handbook of PI and PID Controller Tuning
Rules - 2nd Edition has over 500 pages of rules
• The originators all think their rules are best due to
– Gamesmanship
– Diverse sources of change
– Diverse objectives
– Diverse dynamics
– Diverse metrics
75. Convergence of Tuning Rules
• The most popular PID rules converge to the same equations
for 99% of temperature, composition, level, and gas pressure
loops despite diversity of metrics, dynamics, objectives, and
sources of change if the following is used:
– Tuning to minimize the effect of unmeasured disturbances
– Tuning to maximize absorption of variability (e.g. surge tank level)
– Dead time block in identification of process dynamics
– Primary PID Setpoint Lag = reset time and Lead = 20% of Lag
– Analog output setpoint rate limit and PID external-reset feedback
– Enhanced PID developed for wireless with threshold sensitivity
• For the remaining cases:
– For drastic deceleration from dead time dominance decrease gain,
reset time, and rate time
– For severe acceleration from runaway reaction, increase gain,
reset time, and rate time
76. Diverse Sources of Change
• Raw material and recycle composition and impurities
• Weather (temperature, humidity, snow, rain)
• Utility temperature and pressure
• Operators (production rate changes and manual actions)
• Interactions and Optimization
• Batch sequences and on-off control
• Startups, transitions, and shutdowns
• Measurement and process noise
• Limit cycles
77. Diverse Process Objectives
• Maximize safety
– Prevent activation of relief devices and Safety Instrumented
Systems (SIS)
• Maximize equipment, environmental, & process protection
• Minimize product variability
– Minimize limit cycles
– Minimize oscillatory loop response
– Minimize interaction between loops
– Maximize coordination between loops
• Maximize process capacity and efficiency
– Increase production rate and decrease raw material and utility use
79. Diverse Process Objectives
Maximize Protection
• Eliminate temperature shock and water hammer
– Slow action of control valve in direction of causing shock
• Eliminate compressor surge
– Slow closing of surge valves and downstream user valves
– Fast opening of surge valves
• Eliminate flare stack emissions
– Fast opening of runaway reactor coolant valves
• Eliminate RCRA pH Violations
– Fast opening of base reagent valve when approaching 2 pH
– Fast opening of acid reagent valve when approaching 12 pH
80. Diverse Process Objectives
Minimize Product Variability
• Minimize cycling from valve discontinuities
– Suspension of integral action when valve is not moving or for an
impending unnecessary crossing of the split range point
• Minimize oscillatory response
– Slow approach to setpoint and suspension of integral action between
updates from analyzers and wireless transmitters
• Minimize interaction between loops
– Slow and fast action of less and more critical loop, respectively
• Maximize coordination of loops
– Identical ratioed rates of change of feeds particularly for plug flow
reactors, and inline systems, such as blenders and static mixers
81. Diverse Process Objectives
Maximize Efficiency and Capacity
• Use PID for valve position control (VPC) to increase feed or
reduce raw material or energy use for valve constraint.
– Slow approach by VPC to optimum to avoid upsetting loops
– Fast getaway by VPC for upset to avoid running out of valve
– Suspension of integral action in VPC for valve that is not moving or
whose movements are inconsequential
82. Key PID Features for VPC
Feature Function Advantage 1 Advantage 2
Direction Velocity Limit VPC Action Prevent Running Out Minimize Disruption
Limits Speed Based on of Valve to Process
Direction
Dynamic Reset Limit VPC Action Direction Velocity Prevent Burst of
Limit Speed to Process Limits Oscillations
Response
Adaptive Tuning Automatically Identify Eliminate Manual Compensation of
and Schedule Tuning Tuning Nonlinearity
Feedforward Preemptively Set VPC Prevent Running Out Minimize Disruption
Out for Upset of Valve
Enhanced PID Suspend Integral Eliminate Limit Cycles Minimize Oscillations
(PIDPlus) Action until PV Update from Stiction & from Interaction & PV
Backlash Update Delay
83. Examples of Optimization by VPC
Optimization VPC PID PV VPC PID SP VPC PID Out
Minimize Prime Reactor Feed Max Throttle Position Compressor or Pump
Mover Energy Flow PID Out Pressure SP
Minimize Boiler Steam Flow PID Out Max Throttle Position Boiler
Fuel Cost Pressure SP
Minimize Boiler Equipment Max Throttle Position Boiler
Fuel Cost Temperature PID Out Pressure SP
Minimize Chiller Equipment Max Throttle Position Chiller or CTW
or CTW Energy Temperature PID Out Temperature SP
Minimize Purchased Purchased Reagent or Min Throttle Position Waste Reagent
Reagent or Fuel Cost Fuel Flow PID Out Or Fuel Flow SP
Minimize Total Final Neutralization Min Throttle Position First Neutralization
Reagent Use Stage pH PID Out Stage pH PID SP
Maximize Reactor Reactor or Condenser Max Throttle Position Feed Flow or Reaction
Production Rate Temperature PID Out Temperature SP
Maximize Reactor Reactor Vent Max Throttle Position Feed Flow or Reaction
Production Rate Pressure PID Out Temperature SP
Maximize Column Reboiler or Condenser Max Throttle Position Feed Flow or Column
Production Rate Flow PID Out Pressure SP
Maximize Ratio or Process Feedback 50% Flow Ratio or
Feedforward Accuracy Correction PID Out (Zero Correction) Feedforward Gain
84. Liquid Reactants (Jacket CTW)
Liquid Product Optimization
ratio ZC1-4 ZC1-4 is an enhanced PID VPC
FC CAS LC
calc OUT
1-1 1-8
PT PC FC 1-1 ZC
FY CAS
1-6 1-5 1-5 1-4
reactant A FT FT vent
1-1 1-5
LY residence
1-8 time calc LT TT TC
1-8 1-3 1-3
CAS FC
1-2
TT TC
reactant B FT 1-4 1-4
1-2
return
Valve position controller (VPC) setpoint
is the maximum throttle position. The
VPC should turn off integral action to
prevent interaction and limit cycles. The AT AC
correction for a valve position less than 1-6 1-6
setpoint should be slow to provide a slow
approach to optimum. The correction for
a valve position greater than setpoint must
be fast to provide a fast getaway from the makeup
point of loss of control. Directional velocity CTW
limits in AO with dynamic reset limit in an FC
enhanced PID that tempers integral action 1-7
can achieve these optimization objectives.
FT product
1-7
84
85. Liquid Reactants (Jacket CTW)
Gas & Liquid Products Optimization
ratio ZY1-1
FC PT PC ZC
calc OUT
1-1 1-5 1-5 1-5
FY CAS LC TT FT product
1-6 1-8 1-10 1-5
TC
reactant A FT 1-10
ZY-1
W
1-1 IN1
LY residence
1-8 time calc TT TC ZC
LT 1-10
CAS FC 1-3 1-3
1-8
1-2
ZY-1
TT TC
IN2
reactant B FT 1-4 1-4
1-2
return
ZC-5
OUT
ZC
low signal 1-4
selector AT AC
FC1-1 ZC-10 1-6 1-6
ZY
CAS 1-1 OUT
ZY-1
IN3
makeup
ZC-4
OUT CTW
CAS FC
1-7
ZC1-4, ZC-5, & ZC-10 are enhanced PID VPC FT product
1-7
85
86. Innovative PID System to Optimize
Ethanol Yield and Carbon Footprint
Corn
Production Rate
Average Fermentation Time
Enhanced PID
Enhanced PID
setpoint Slurry Solids
AC SC AT XC Enhanced PID
1- 4 1-4 NIR-T
1- 4 1- 4 Feedforward
DX DC RCAS
2- 4 2- 4
Fermentable Starch
AY XY Correction
1- 4 1- 4
FC
1- 5
Dilution Water FT
1- 5
FC
1- 6
DT
Backset Recycle FT 2- 4 Coriolis
1- 6 Meter
Slurry Slurry
Tank 1 Tank 2
Lag and Delay
DY Predicted Fermentable Starch
2- 4
86
87. Loop Block Diagram
(First Order Approximation)
Delay Lag Gain
θd τL Kd
∆DV Delay <=> Dead Time
Load Upset Lag <=>Time Constant
Secondary Secondary Primary Primary
Delay Lag Gain Delay Lag Delay Lag Gain
θv τv Kv θs τs θp τp Kp
∆Fv
Valve Process ∆PV
τo is the largest lag in the loop (hopefully τp)
Kv = slope of installed
flow characteristic For self-regulating processes: Ko = Kv ∗ Kp ∗ Km
For near integrating processes: Ki = Kv ∗ (Kp / τp) ∗ Km
Local
% ∆%CO Km = 100% / span
Set Point
%SP
PID Kc Ti Td
%
½ of Wireless Default Update Rate
% ∆%PV
Delay Lag Gain Lag Delay Lag
τc2 θc τc1 Km τm2 θm2 τm1 θm1
Lag Delay
Controller Measurement
First Order Approximation: θο ≅ θv + θs + θp + θm1 + θm2 + θc + Y∗τv + Y∗τs + Y∗τm1 + Y∗τm2 + Y∗τc1 + Y∗τc2
(set by automation system design for flow, pressure, level, speed, surge, and static mixer pH control) 87
88. Open Loop Response of
Self-Regulating Process
Response to change in controller output with controller in manual
%PV
% Controller Output (%CO) Ko = ∆%PV / ∆%CO
% Process Variable (%PV)
Self-regulating process gain (%/%)
%CO
or
Maximum speed ∆%PV
in 4 dead times
is critical speed
0.63∗∆%PV
∆%CO
Noise Band
observed
θo τo ideally τp Time (seconds)
total loop
dead time Self-regulating process open loop
negative feedback time constant
88
89. Open Loop Response of
Integrating Process
Response to change in controller output with controller in manual
%PV
Ki = { [ %PV2 / ∆t2 ] − [ %PV1 / ∆t1 ] } / ∆%CO
% Controller Output (%CO)
% Process Variable (%PV)
Integrating process gain (%/sec/%)
%CO
or
Maximum ramp rate
in 4 dead times is used
to estimate integrating
process gain
∆%CO
ramp rate is ramp rate is
∆%PV1 / ∆t1 ∆%PV2 / ∆t2
Time (seconds)
observed θo
total loop
dead time
89
90. Open Loop Response of
Runaway Process
Response to change in controller output with controller in manual
Ko = ∆%PV / ∆%CO
Runaway process gain (%/%) Acceleration
% Controller Output (%CO)
% Process Variable (%PV)
For safety reasons, tests are
terminated within 4 dead times
before noticeable acceleration 1.72∗∆%PV
or
∆%PV
∆%CO
Noise Band
observed
θo τ’
o must be τ’
p
Time (seconds)
total loop
dead time runaway process open loop
positive feedback time constant
90
91. Diverse Loop Metrics
• Peak and integrated errors for load disturbances
• Rise time for setpoint change (time to reach setpoint)
• Overshoot for setpoint change
• Settling time for setpoint change
• Standard deviation of oscillations
92. Diverse Metrics
Peak and Integrated Error
The use of a setpoint lead-lag with the lag equal to the reset time and the lead
20% of the lag will provide a fast setpoint response with minimal overshoot
despite tuning for maximum load rejection
93. Ultimate Limit to Loop Performance
Peak error is proportional to the ratio of loop dead time to 63% response time
(Important to prevent SIS trips, relief device activation, surge prevention, and RCRA pH violations)
Total loop deadtime
that is often set by
automation design
θo
Ex = ∗ Eo
(θ o + τ o )
Largest lag in loop
that is ideally set by
large process volume
Integrated error is proportional to the ratio of loop dead time squared to 63% response time
(Important to minimize quantity of product off-spec and total energy and raw material use)
θ o2
Ei = ∗ Eo
(θ o + τ o )
For a sensor lag (e.g. electrode or thermowell lag) or signal filter that is much larger
than the process time constant, the unfiltered actual process variable error can be
found from the equation for attenuation
94. Effect of Disturbance Lag on Integrating Process
Periodic load disturbance time constant
increased by factor of 10
Adaptive loop
Baseline loop
Adaptive loop
Baseline loop
Primary reason why bioreactor control loop tuning
and performance for load upsets is a non issue!
95. Practical Limit to Loop Performance
Peak error decreases as the controller gain increases but is essentially the
open loop error for systems when total dead time >> process time constant
Open loop error for
fastest and largest
1
Ex = ∗ Eo
load disturbance
(1 + K o ∗ K c )
Integrated error decreases as the controller gain increases and reset time decreases
but is essentially the open loop error multiplied by the reset time plus signal
delays and lags for systems when total dead time >> process time constant
Ti + ∆t x + τ f
Ei = ∗ Eo
Ko ∗ Kc
Peak and integrated errors cannot be better than ultimate limit - The errors predicted
by these equations for the PIDPlus and deadtime compensators cannot be better
than the ultimate limit set by the loop deadtime and process time constant
96. Implied Dead Time from Slow Tuning
Slow tuning (large Lambda) creates an implied dead time where the loop performs
about the same as a loop with fast tuning and an actual dead time equal to the
implied dead time (θi)
θ i = 0.5 ∗ (λ + θo )
For most aggressive tuning Lambda is set equal to observed dead time
(implied dead time is equal to observed dead time)
Money spent on improving measurement and process dynamics
(e.g. reducing measurement delays and process dead times)
will be wasted if the controller is not tuned faster to take
advantage of the faster dynamics
You can prove most any point you want to make in a comparison
of control system performance, by how you tune the PID.
Inventors of special algorithms as alternatives to the PID
naturally tend to tune the PID to prove their case. For example Ziegler-Nichols
tuning is often used to show excessive oscillations that could have be
eliminated by cutting gain in half
97. Disturbance Speed
Effect of load disturbance lag (τL) on peak error can be estimated by replacing the
open loop error with the exponential response of the disturbance during the loop dead time
For Ei (integrated error), use closed loop time constant instead of dead time
E L = (1 − e −θo /τ L ) ∗ Eo
For a load disturbance lag much larger than the dead time, the load error in one dead time
Is very small, allowing a very large implied dead time from slow tuning. In other words,
tuning and control loop dynamics are not important in terms of disturbance rejection. The focus
is then on the effect of tuning and dynamics on rise time (time to reach a new setpoint)
98. Setpoint Response Rise Time
Rise time (time to reach a new setpoint) is inversely proportional to controller gain
∆% SP
Tr = + θo
K i ∗ min ( | %∆COmax |, ( K c + K ff ) ∗ ∆% SP )
Rise time can be decreased by setpoint feedforward and bang-bang logic that
sets and holds an output change at maximum (∆%COmax) for one dead time until
future PV value is projected to reach setpoint. The fastest possible rise time is:
∆% SP
Tr = + θo
K i ∗ | %∆COmax |
99. Basic Lambda Tuning (Self-Regulating Processes)
Self-Regulation Process Gain:
∆% PV
Ko =
∆%CO
Controller Gain
Ti
Kc =
K o ∗ (λ + θ o )
Lambda (Closed Loop Time Constant for Setpoint Response)
λ = λ f ∗τ o
Controller Integral Time
Ti =τ o
Lambda tuning excels at coordinating loops for blending,
fixing lower loop dynamics for model predictive control,
and reducing loop interaction and resonance
100. Fastest Lambda Tuning (Self-Regulating Process)
For max load rejection set lambda equal to dead time
λ = θo
τo
K c = 0.5 ∗
Ko ∗ θo
Ti =τ o
101. Basic Lambda Tuning Integrating Processes
Lambda (closed loop arrest time in load response)
λ = λ f / Ki
Integrating Process Gain:
∆% PV2 / ∆t 2 − ∆% PV1 / ∆t1
Ki =
∆%CO
Controller Gain:
Ti
Kc =
K i ∗ [ λ + θ o ]2
Controller Integral (Reset) Time:
Ti = 2 ∗ λ + θ o
Controller Derivative (Rate) Time:
Td = τ s secondary lag
102. Fastest Lambda Tuning Integrating Processes
For max load rejection set lambda equal to dead time
λ = θo
Controller Gain:
3
Kc =
Ki ∗ 4 ∗ θo
Controller Integral (Reset) Time:
Ti = 3 ∗ θ o
Controller Derivative (Rate) Time:
Td = τ s secondary lag
Check for prevention of slow rolling oscillations:
2.25
K c * Ti =
Ki
103. Often Violated Criteria for Integrating Processes
To prevent slow rolling oscillations:
2
K c * Ti >
Ki
103