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To view the recording of Deminar #8, click on the above picture. If you want to just view the slides click on Deminar #8 - PID Control of Runaway Processes

Self-regulating processes are the easiest to control given similar dynamics (e.g. delays, lags, and gains), nonlinearities, and upsets. In manual, the process variable will eventually reach a steady state for a self-regulating process. Integrating processes are the next most difficult to control because in manual the process variable will always be ramping even if there are no disturbances. Runway processes are the most challenging and potentially the most dangerous because in manual the process variable is always moving and can accelerate in its divergence even if there are no disturbances. Runaway processes are termed "open loop unstable." The acceleration is characterized by a positive feedback time constant. Both integrating and runaway processes have a low gain limit that causes slow rolling oscillations and a divergence off-scale, respectively. Integrating processes are more sensitive to integral action and secondary lags than self-regulating processes and runaway processes are more sensitive to integral action and secondary lags than integrating processes. The most common problem with integrating and runway processes is too much integral action (too small of a reset time) and the omission of derivative action for secondary lags (rate time should be set equal to largest secondary lag). Some highly exothermic polymerization reactors have proportional plus derivative control to avoid the potentially unsafe situation of someone adding too much reset action. I have been in the control room when an exothermic reactor has reached a point of no return where the temperature acceleration was so high despite full cooling, the only thing the operators could do was prepare for the rupture discs to burst and the reactor contents blow over to the flare stack tank. Highly reactive chemicals lead to rapid and complete reactions but can also lead to an uncontrollable temperature rise since the reaction rate and hence heat release doubles for every 6 degree increase in temperature. Runaway processes can look like integrating processes unless the temperature controller is left in manual long enough for the temperature change to be large enough.

Deminar #8 shows the dramatic correction needed for the tuning settings. The factors used in the short cut tuning method for near-integrators in Deminar #6 and the classic Ziegler Nichols ultimate oscillation method are detailed and demoed. Equations are offered to predict the ultimate gain and ultimate period showing the dramatic effect of a secondary process or thermowell lag and loop deadtime. If a secondary lag or the loop deadtime approaches the positive feedback time constant, the window of allowable controller gains closes and the loop is unstable for all tuning settings. The virtual plant is where you want to learn about runaway processes. You can't experiment much or have the loop in manual for more than a few deadtimes with a true runaway process.

The PID enhancement for wireless (PIDPlus) offers an improvement wherever there is an update time in the loop. In the broadest sense, an update time can range from seconds (e.g. wireless updates and valve or measurement sensitivity limits) to hours (e.g. failures in communication, valve, or measurement). Some of the sources of update time are:

(1) Wireless measurement default update rate for periodic reporting (refresh time)
(2) Wireless measurement trigger level for exception reporting (sensitivity limit)
(3) Wireless communication failure
(4) Broken pH electrode glass or lead wires (failure point is about 7 pH)
(5) Large valve operating on upper part of installed characteristic (low sensitivity)
(6) Valve with backlash (deadband) and stick-slip (resolution and sensitivity limit)
(7) Valve with solids, high temperature, or sticky fluid that causes plugging or seizing
(8) Plugged impulse lines
(9) Analyzer sample processing delay and analysis or multiplex cycle time
(10) Analyzer resolution and sensitivity limit

The PIDPlus waits for an update in the measurement whereas a traditional PID continually ramps the output acting on old information. When there is an update, the PIDPlus considers the changes to have occurred over the elapsed time from the last update whereas the traditional PID thinks the entire change occurred in the PID module execution time. The result is a spike from derivative action by a traditional PID that is particularly large when a measurement recovers or a valve trim or solids break free.

The improvement in control by the PIDPlus 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 the 63% process response time that roughly corresponds to the 98% response time frequently cited in the literature, the controller gain can be set equal to the inverse of the process gain. This controller gain can provide an exact correction for changes in the measurement and setpoint.

The PIDPlus execution is kept fast so that the PID immediately responds to changes in setpoint, feedforward, mode, tuning, detail display parameters, and remote output. We have the interesting result that when the update is much larger than the 63% process response time so we can set the controller gain equal to the inverse of the process gain, the controller output goes immediately to the value needed to achieve the setpoint. An increase in update time to prolong battery life can actually translate to a faster setpoint response. However, if the process gain changes with time or operating point, the PID will require several updates to home in on the proper correction. An increase in update time will increase the settling time for unrecognized changes in the process gain. The use of an adaptive tuner such as DeltaV Insight that automatically identifies the process gain and schedules the tuning setting accordingly can sustain a fast setpoint response despite nonlinearities and a large update time.

The Emerson White Paper DeltaV-v11-PID-Enhancements-for-Wireless.pdf discusses these opportunities in more detail. Later this month, an entry on this site will show and discuss the trend plots that compare the enhanced PIDPlus with the traditional PID for the applications tested including valves with stick-slip and backlash.

It is important to distinguish between an update time and process deadtime. The update time is the time interval between successive updates by the final control element (initiated changes to the process input) and successive updates by the measurement (reported changes in the process output). The process deadtime is a continuous train of values delayed by the deadtime. The most common source of a pure process deadtime is a transportation delay of temperature and composition changes in a conveyor, extruder, dip tube, heat exchanger, pipeline, sheet line, or any volume where there is plug flow (no back mixing). Small time constants such as thermal lags, sensor lags, signal filter times, transmitter damping settings, effectively become additional deadtime in terms of a first order plus deadtime approximation (single time constant plus deadtime). The PIDPlus algorithm does not correct for process deadtime. As the process deadtime increases and approaches the update time, the opportunity to increase the PIDPlus gain decreases. For compensation of deadtime, a standard deadtime block can be inserted between the BKCAL_OUT of the AO block and the BKCAL_IN of the PID block if the DCS uses the positive feedback method for the integral mode (external reset) as reported in Advanced Application Note 3 "Compensation of Deadtime in PID Controllers".

In a future Deminar we will look in greater detail at the effect of updates time of discontinuous measurements and process deadtimes on the ultimate period and ultimate gain and if there is an improvement in loop performance offered by a combination of PIDPlus and deadtime compensation.

You can click on the above to view and hear the recording of the Deminar.

In Deminar #5 we first show that for a self-regulating process, the process variable will line out (reach a steady state) when the controller is in manual unless there are continual disturbances. The self-regulating response is most commonly encountered response because there are more flow loops than any other type of loop. Liquid pressure loops and temperature control loops in continuous operations have a self-regulating response. Level normally has an integrating response but in the Deminar we show test results for a conical tank level with self-regulating response due to gravity discharge flow. The flow across the discharge valve is proportional to the square root of the liquid head as the level increases, the discharge flow increases and vice versa. The self-regulating or steady state process gain increases with level as a result. The significant increase in cross sectional area with level due to the conical shape causes a dramatic increase in the process time constant that creates a stabilizing effect. The process response at high level is much slower enabling the use of more aggressive tuning settings. However, the test results show these settings at low level cause excessive oscillation. The adaptive level controller is able to keep the set point response smooth and consistent over the level range. For more details you can check out the Control magazine article "Adaptive Level Control"

Most of the Deminar focuses on how an auto tuner, adaptive tuner, and adaptive controller can be used to improve the response of liquid flow and liquid pressure loops. The principle nonlinearities are the control valve characteristic for the flow loop and pump curve for the pressure loop.

If you are interested in the auto tuning, identification of dynamics, and adaptive control of nonlinear processes checkout the Deminar #5 on June 9 at 10:00am.

To attend the event, go to http://bit.ly/JC-LiveMeeting
Use the information below to connect (if you're not using the available computer audio):
• Toll-free: +1 (877) 771-7176
• Toll: +1 (225) 383-1099
• Participant code: 264679

You can click on the above to view and hear the recording of the Deminar. In Deminar #3 we explored the confusing situations that can develop for slow control valves and slow secondary loops. The loop can look fine but suddenly burst into oscillations and later go back to smooth sailing. The normal thought is "what changed in the process or the loop?" Well it turns out that nothing changed except the size of the upset or setpoint change. For large errors, the primary controller output starts changing faster than secondary loop or valve can respond. You could slow down the primary loop, but we know this correspondingly reduces control system performance as clearly quantified on slide 1 of EffectsLoopTuning&Dynamics-KPI.pdf. The best solutions of course are to make the valve faster and make the secondary measurement and tuning faster, but the "Quick Fix" that also offers long term protection is to enable the "Dynamic Reset Limit" option in the PID. Even if there is not a problem now, just simply turning on this option to protect against unforeseen deterioration in measurements or valves. For example, someone might try to make a secondary flow or pressure loop look smoother by the overzealous addition of a signal filter or transmitter damping setting in the middle of the night. Even more dramatically the time lag of an electrode in a secondary static mixer pH loop might go from 3 seconds to 300 seconds due to coatings or high temperatures. The Control magazine article "The Power of External-Reset Feedback" offers an excellent explanation of power of the "Dynamic Reset Limit" option which uses the PV of secondary loop as the external reset signal in the positive feedback implementation of the integral mode.

In the future, the Deminars will take only 45 minutes to reduce time commitments and audio and video recording file size. The current range of 8 to 10 demos per Deminar will be reduced to 4 to 5 demos per Deminar. Also, a "Quick Fix" will be discussed near the beginning for viewers who are short on time. The start time in June will be moved up from 1:00 pm to 10:00 am CDT to encourage European participation. I have added subtitles noting the process control improvement (PCI) in parentheses to the Deminars. Also, note that I have changed the topics for Deminars 6 through 8.

In particular, checkout the next Deminar on Thursday May 27 that shows how you can dynamically explore your own case histories and scenarios by you using the free online process control labs.

To attend the event, go to http://bit.ly/JC-LiveMeeting
Use the information below to connect (if you're not using the available computer audio):
• Toll-free: +1 (877) 771-7176
• Toll: +1 (225) 383-1099
• Participant code: 264679

(1) PID Control of Sampled Measurements (How to Eliminate Oscillations from Analyzers and Wireless Measurements with a PID Enhancement) - April 7, Wed 1:00 pm CDT

(2) PID Control of Valve Sticktion and Backlash (How to Eliminate Continual Oscillations with the "Integral Deadband" PID option) - April 21, Wed 1:00 pm CDT

(3) PID Control of Slow Valves and Secondary Loops (How to Eliminate Bursts of Oscillations with the "Dynamic Reset Limit" PID option) - May 12, Wed 1:00 pm CDT

(4) Web Lab Access and Use Instructions (How to Use Free Online Process Control Labs for Fun and Profit and Become Famous by Friday or at Least Saturday) - May 27, Thurs* 1:00 pm CDT (* - Thursday date is to avoid conflict with the World Batch Forum)

(5) PID Tuning for Self-Regulating Processes (How to Compensate for Nonlinearities in Flow and Liquid Pressure Loops) - June 9, Wed 10:00 am CDT

(6) PID Tuning for Near-Integrating Processes (How to Reduce the Tuning Time for Column and Vessel Temperature and Pressure Loops by 90%) - June 23, 10:00 am CDT

(7) PID Control of True Integrating Processes (How to Reduce the Batch Cycle Time for Temperature and pH Loops by 25%) - July 14, 10:00 am CDT

(8) PID Control of Runaway Processes (How to Improve the Performance of Exothermic Reactor Temperature Loops) - July 21, Wed 10:00 am CDT

If you look at all the features and options of a PID controller that are sitting idle, you realize only a small fraction of the power of the PID is used even if you make the big assumption that the controller is tuned. How many loops use integral deadband, nonlinear gains, dynamic reset limits, setpoint velocity limits, or anything but the default PID structure?

The Deminar series started in April and continuing through July provides dynamic examples of how PID power can be used to reduce process variability and make batches and startups faster. In particular, the demanding and critical role of integrating processes is being revealed. We normally think of level as the primary integrating process and may dismiss the tightness of control as not important. Also statistics would say most of the loops are self-regulating. If you look closer you realize that the main reason for the large number of self-regulating loops is that the fact there are more flow loops than any other type of loop. Sure flow loops can be screwed up but auto tuners can find the right settings in matter of minutes and process control improvements can be quickly tested. What we often do not realize is that the really difficult and important loops have either a true integrating response (e.g. gas pressure and batch temperature and composition loops) or are so slow they are best treated as having a near integrating response (e.g. continuous temperature and composition loops). Furthermore, few realize that integrating processes are more sensitive to secondary lags, less than ideal valves, and have counter intuitive tuning rules. I would maintain that 90% of the loops with integrating processes are not tuned correctly and probably have too small of a reset time. The Deminar series and access to the web labs online should provide a source of exploring the opportunity to do better with these loops that matter the most. Check out the Deminar May 12 at 1:00 CDT to see how integrating loops suffer from slow valves and slow secondary loops.

To attend the event, go to http://bit.ly/JC-LiveMeeting
Use the information below to connect (if you're not using the available computer audio):
• Toll-free: +1 (877) 771-7176
• Toll: +1 (225) 383-1099
• Participant code: 264679

(1) PID Control of Sampled Measurements (How to Eliminate Oscillations from Analyzers and Wireless Measurements with a PID Enhancement) - April 7, Wed 1:00 pm CDT

(2) PID Control of Valve Sticktion and Backlash (How to Eliminate Continual Oscillations with the "Integral Deadband" PID option) - April 21, Wed 1:00 pm CDT

(3) PID Control of Slow Valves and Secondary Loops (How to Eliminate Bursts of Oscillations with the "Dynamic Reset Limit" PID option) - May 12, Wed 1:00 pm CDT

(4) Web Lab Access and Use Instructions (How to Use Free Online Process Control Labs for Fun and Profit and Become Famous by Friday or at Least Saturday) - May 27, Thurs* 1:00 pm CDT (* - Thursday date is to avoid conflict with the World Batch Forum)

(5) PID Tuning for Self-Regulating Processes (How to Compensate for Nonlinearities in Flow and Liquid Pressure Loops) - June 9, Wed 10:00 am CDT

(6) PID Tuning for Near-Integrating Processes (How to Reduce the Tuning Time for Column and Vessel Temperature and Pressure Loops by 90%) - June 23, 10:00 am CDT

(7) PID Control of True Integrating Processes (How to Reduce the Batch Cycle Time for Temperature and pH Loops by 25%) - July 14, 10:00 am CDT

(8) PID Control of Runaway Processes (How to Improve the Performance of Exothermic Reactor Temperature Loops) - July 21, Wed 10:00 am CDT

You can click on the above to view and hear the recording of the Deminar. The second Deminar answers two questions. The first question "Why? (Why do I write so much stuff and why I am I doing these Deminars and setting up free worldwide access to generic loop and unit operation labs?) is answered on slide 4. The virtual plant used in these Deminars that creates a non DCS specific control room type experience is the most exciting thing I have done in years. This is either a commentary on my sedate existence or is an indication of the possibilities for an interactive opportunity assessment that could provide the knowledge and justification for process control improvements.

The answer to the second question that is actually a list of questions on slide 8 about the source of oscillations that cannot be tuned out is, as you might expect, the subject of the Deminar.

I think there are 8 main concepts not widely known that one can take away from this Deminar to provide guidance for a wide variety of applications.

(1) Valve stick-slip will create a limit cycle in any control loop where there are one or more integrators. The integrators can be via the integral action in the PID controller(s) or in the process (an integrating process type such as level and batch temperature). Some of the implications are as follows:

a. For a self-regulating process, integral action in any PID controller in the control loop will cause a limit cycle from stick-slip. In order to eliminate the limit cycle all PID controllers must have their integral action turned off either by a I-deadband setting bigger than the limit cycle amplitude or by using a structure with no integral action (e.g. "P on error, D on PV, no I").

b. For an integrating process, the limit cycle from stick-slip cannot be eliminated even if the integral action is turned off in all PID controllers.

(2) The limit cycle amplitude from valve stick-slip is set by the process gain and hence cannot be altered by changing the controller gain. For nonlinear processes and nonlinear valve characteristics, the amplitude changes with operating point.

(3) The limit cycle period from valve stick-slip is proportional to integral time. Slowing down the reset time will make the period larger. Thus to increase the filtering effect of process time constants in the primary loop or downstream processes, a tuning strategy would be to decrease reset time and if peak error for load disturbances is not important to decrease the controller gain to allow a further decrease in reset time.

(4) Valve deadband will create a limit cycle in any control loop where there are two or more integrators. The integrators can be via the integral action in the PID controller(s) or in the process (an integrating process type such as level and batch temperature). Some of the implications are as follows:

a. For a self-regulating process, a single loop with integral action will not develop a limit cycle from valve deadband. A cascade loop with integral action in both controllers will develop a limit cycle from deadband.

b. For an integrating process, the limit cycle from valve deadband can be eliminated if integral action is turned off as seen in slide 1 in: NonSelfRegulatingProcessDeadbandLimitCycle.pdf

c. For a runaway process (exothermic reaction) I expect the behavior to be similar to an integrating process but to a greater extreme (larger amplitude for limit cycle and larger offset for no integral action in PID controller) as seen in slide 2 of NonSelfRegulatingProcessDeadbandLimitCycle. The lack of process self-regulating in both integrating and runaway processes causes similar problems for a non-ideal valve response.

(5) The limit cycle amplitude from valve deadband is inversely proportional to controller gain.

(6) The limit cycle period from valve deadband is proportional to the integral time and is inversely proportional to the square root of the controller gain.

(7) The limit cycle amplitude in the primary process variable or in downstream process variables is proportional to the period of the limit cycle of the secondary process. The ratio of the primary or downstream amplitude to the secondary limit cycle amplitude is determined by the filtering effect of the time constant in the primary or downstream processes. When the period is smaller than the primary or downstream process time constant, the attenuation of amplitude can be approximated by the equation in: LimitCycleAmplitudeAttenuation.pdf

(8) The offset created by the use of I-deadband or selecting a structure with no integral action is less disruptive to downstream processes because a constant load upset is readily corrected by downstream loops. Periodic disturbances are more disruptive and can be amplified if the period is close to the period of loops. An offset rather than an oscillation causes less interaction between loops. One of the ways to reduce interaction is to remove integral action and decrease the gain in the least important controller.

The PID I-deadband setting should be larger than the maximum amplitude allowing for measurement noise. Note that the valve stick-slip and deadband will vary with time and operating point. The stick-slip and deadband is generally greatest near the closed position and when process material coats or corrodes the closure element seal, seat, and stem. Any addition of I-deadband or change in PID structure should be carefully monitored. Of course, the best solution is to correct the root cause of the problem and select a control valve per the "Best Practices for Valve Performance" on slide 27 of Deminar 2.

The next Deminar on "PID Control of Slow Valves and Secondary Loops" is set for May 12 Wednesday 1:00 pm Central Daylight Time.

When I first started teaching process control to junior and senior chemical engineers at Washington University in Saint Louis after retiring from Solutia, the students were less than receptive to my introduction of stuff they actually needed to know on the job. Except for the couple of students who were summer interns at Anheuser-Busch, my attempts of adding relevance were viewed as just being disruptive to the traditional task of learning frequency response and state space matrices. When I introduced the virtual plant for a weekly lab of hands-on learning, the attitude shifted from annoyance to enthusiasm. The skill and interest in using new computer tools and the fact the process simulations and graphics made the experience all seem real resulted in the labs becoming the highlight of the week. Several students decided to go on to careers in process control. One former student I met at Interphex became the manager of an automation group of a major pharmaceutical company. Even if the students didn't become process control engineers, the labs helped develop skills needed in industry. The distributed control system (DCS) is the window into the process and the ability to use and get the most out of the powerful tools and industrial standards in the DCS is important to anyone working in the process industry. This excitement and feeling that I was doing something significant to help students on "Day 1" of their prospective job, led me to think what can I do for bridging the gap between the leading edge research at universities and the opportunities for process control improvement in industry? The virtual plant to me seemed to be the way for universities and industry to get on the same page. This concept is summarized in the ACC 2009 paper ACC2009-BridgingtheGap.pdf.

The next step was to make labs as a self-learning experience available over the web with the idea that an employee could spend a few hours a month at a convenient time (e.g. lunch and learn) trying out the latest in PID control capability for various process and automation system designs and objectives. These labs provide a chance to find process control improvements by setting up scenarios that are of particular interest. Since the user interface employ operator graphics, knowledge of the particular DCS is not required. The capture of the last and best scores in terms of key performance variables (KPI) should help promote recognition and competitiveness for finding the best solutions.

I think we have barely scratched the surface of the true capability of today's PID controller with all of its features (e.g. structures, integral deadband, dynamic reset limit, and nonlinear gain). This spring and summer I will focus on generic control loops. This fall I will move on to the control of unit operations such as crystallizers, evaporators, extruders, neutralizers, and reactors. We hope users will twitter their results. The potential for learning and sharing is enormous and may be a way of getting the next generation of engineers to not only benefit from past expertise but take process control to a whole new level (see January 2010 Control article "The Future is Now")

I will conduct live seminars and demos twice a month to show how to use the labs. The connection and the topics and dates for the first 4 months are:

Recorded Live Seminar and Demo Series

To attend the event, go to http://bit.ly/JC-LiveMeeting
Use the information below to connect (if you're not using the available computer audio):
• Toll-free: +1 (877) 771-7176
• Toll: +1 (225) 383-1099
• Participant code: 264679

(1) PID Control of Sampled Measurements (How to Eliminate Oscillations from Analyzers and Wireless Measurements with a PID Enhancement) - April 7, Wed 1:00 pm CDT

(2) PID Control of Valve Sticktion and Backlash (How to Eliminate Continual Oscillations with the "Integral Deadband" PID option) - April 21, Wed 1:00 pm CDT

(3) PID Control of Slow Valves and Secondary Loops (How to Eliminate Bursts of Oscillations with the "Dynamic Reset Limit" PID option) - May 12, Wed 1:00 pm CDT

(4) Web Lab Access and Use Instructions (How to Use Free Online Process Control Labs for Fun and Profit and Become Famous by Friday or at Least Saturday) - May 27, Thurs* 1:00 pm CDT (* - Thursday date is to avoid conflict with the World Batch Forum)

(5) PID Tuning for Self-Regulating Processes (How to Compensate for Nonlinearities in Flow and Liquid Pressure Loops) - June 9, Wed 10:00 am CDT

(6) PID Tuning for Near-Integrating Processes (How to Reduce the Tuning Time for Column and Vessel Temperature and Pressure Loops by 90%) - June 23, 10:00 am CDT

(7) PID Control of True Integrating Processes (How to Reduce the Batch Cycle Time for Temperature and pH Loops by 25%) - July 14, 10:00 am CDT

(8) PID Control of Runaway Processes (How to Improve the Performance of Exothermic Reactor Temperature Loops) - July 21, Wed 10:00 am CDT

Let's pull together this series on errors and conclude with a check list. The idea was prompted by perusing a popular book written on just the value of check lists. I didn't think you could write a book on just one concept but the result of saving lives for surgical procedures is impressive. I know as I have gotten older, check lists are essential to just remember what I am suppose to be doing. I have found checklists to be helpful for me from both a practical and psychological viewpoint when rushed or overwhelmed with details, tasks, and objectives.

In the following list, increases in on-stream time can increase efficiency besides capacity by eliminating the time and off-spec and waste associated with abnormal operations, startup, and shutdown. An increase in yield or decrease in recycle can be taken as a decrease in raw material costs (same production rate for lower feed rate) or an increase in production rate (higher production rate for the same feed rate). The order of the list is in order of things to check and somewhat in the order of priorities.

Check List to Improve Process On-stream Time, Production Rate, and Efficiency
(composition measurements include conductivity, dissolved oxygen, pH, and turbidity)

1. Use smart transmitters with the best sensor technology and integration of process and ambient conditions compensation.

a. Avoid older technologies particularly ones with mechanical elements

b. Seek sensor and transmitter with the best sensitivity and repeatability

2. Pick sensor location and installation method to provide the most representative measurement in process with no stagnation, best velocity, fastest response, and least noise.

a. For DP and pressure transmitters, avoid impulse lines (sensing lines) by direct mounting transmitters or using diaphragm seals and filled systems

b. For DP and vortex flow meters insure uniform velocity profile

c. For thermowells and electrodes increase velocity to reduce response time and coatings but not so high to cause abrasion, static charge, or vibration

d. For thermowells and electrodes pick location with good mixing, minimal transportation delay, and least bubbles, slime, and solids

3. Use real throttle valves with smart positioners.

a. Avoid on-off and isolation valves posing as throttling valves. Go to a control valve manufacturer instead of a piping valve manufacturer

b. Seek actuator, positioner, and valve type with best sensitivity of installed flow characteristic and signal response with least stick-slip and backlash

c. Verify positioner feedback measurement is representative of internal closure member (e.g. ball, disk, or plug) and not just actuator position

4. Tune control loop with on-demand auto tuner or adaptive controller to meet loop objectives. Tuning speed is chosen to:

a. Insure an exceptionally smooth PV and output response by decreasing transfer of variability from PV to output (increasing Lambda) for:

i. level loops on surge tanks to minimize feed upsets
ii. deadtime dominant loops (deadtime >> process time constant)
iii. interacting loops (e.g. headers)
iv. loops on piping or equipment with no back mixing (e.g. blenders, heat exchangers, extruders, static mixers, sheets, webs, and yarns)

b. Provide good load rejection of moderately fast disturbances by increasing transfer of variability from PV to output (decreasing Lambda) for:

i. Fed-batch and continuous agitated vessel and column composition, level, pressure, and temperature loops

c. Provide good load rejection of extremely fast disturbances by setting the gain and reset as a factor of deadtime rather than the time constant for:

i. Continuous agitated vessel and column composition, pressure, level, and temperature loops

d. Provide minimal overshoot of setpoints of slow lag dominant loops (process time constant >> loop deadtime and slower than 10 minutes) by tuning the loops as near-integrating processes for:

i. Fed-batch and continuous agitated vessels and column composition, pressure, and temperature loops (setpoint changes occur at startup or for changes in batch phase and product grade)

e. Provide minimal peak error by maximizing controller gain even if it requires increasing reset time to maintain robustness for:

i. Prevention of SIS activation
ii. Prevention of pressure relief
iii. Prevention of environmental violation
iv. Prevention of equipment damage

5. Add DCS signal filter or damping adjustment to keep loop output fluctuations from noise less than the valve deadband to prevent excessive valve packing wear and inflicting disturbances on loop. For wireless transmitters use damping adjustment to reduce keep transmitter output fluctuations from noise less than wireless deadband to eliminate unnecessary communication and extend battery life.

6. Eliminate on-off actions

a. Replace on-off control by switches with loops.

b. Eliminate manual actions by adding loops, keeping loops in highest design mode, adding feedforward, and automating and tuning loops to handle startup and abnormal operating conditions

c. Replace pure batch with fed-batch automation by replacing discrete sequential actions (e.g. stepping feeds) with loops (e.g. throttling feeds)

7. Tune loops that create feed disturbances (e.g. surge level loops) to provide a smooth slow transition in feed rate.

8. Add cascade control to compensate for nonlinearities and pressure disturbances (e.g. secondary flow loop and secondary coolant temperature loop).

9. Add feedforward control of measurable fast disturbances not compensated by secondary loop.

10. Optimize setpoints by operating closer to constraints for production rate or product quality spec.

a. Eliminate operating margin imposed by shift's perceived sweet spot or operating margin caused by process variability from not doing check list items 1-9

b. Find more efficient operating points based on R&D reports and virtual plant exploration - confirm with process tests

b. Add model predictive control to optimize setpoints as process conditions and market requirements change.

The tuning settings of many level loops aren't in the ball park. The result is persistent oscillations that spread throughout the process.

Level loops frequently manipulate feed flows to process operations. Variability in these feed flows causes variability in the temperature and composition in equipment whose process loops end up chasing continual changes in feed. Often the level loop creates slow rolling oscillations due to the product of level controller gain and reset time being too small. The solution of increasing the controller gain is counter intuitive and is rarely done correctly since the range of controller gains for level loops is exceptionally large and changes with the density of the fluid and the cross sectional area of the vessel.

Level loops make a good educational lab experiment in process control. To see how a DeltaV Insight adaptive controller automatically identified the tuning and compensated for nonlinearities for level control of a conical tank checkout the article "Adaptive Level Control". For more background on the dynamics and tuning of loops for integrating processes, see Appendix A referenced in this article and the September 2, 2009 entry on this website.

Simulation was such an integral part of my job it is difficult for me to visualize a process control career without models. I was asked to join Engineering Technology (ET) at Monsanto in 1976 because I had developed a dynamic compressor model as the lead Instrument and Electrical engineer for what was the largest Acrylonitrile plant in the world. I developed the model in order to understand more about the incredible surge phenomena where reversals of flow could occur in less than 0.01 seconds leading as a minimum to a loss in efficiency and in some cases to the damage of shafts and seals of large and expensive compressors from the extreme momentum swings and vibration. In most plants the ability to initiate and explore abnormal situations is severely limited or not allowed. A dynamic model allows you to readily and quickly try out "What if Scenarios" whose only limit is your imagination.

ET developed FLOWTRAN, a process simulator that was directed by the government to be sold to Aspen institute. Several key specialists left with the FLOWTRAN to develop the process modeling software that eventually was the state of the art process design modeling software by AspenTech. In the ET process control groups, we used FLOWTRAN to get the process gains and then used IBM's Continuous System Modeling Programs (CSMP) followed by Raytheon's Advanced Continuous Simulation Language (ACSL), and ultimately HYSYS Plant for dynamic simulations. After retirement from my career in ET, I focused on using the DCS as a Virtual Plant for simulation and control. The graphical configuration environment where function blocks are equipment and wires are streams (e.g. DeltaV Control Studio and MiMiC) allows the development of dynamic process models in the same familiar way as the configuration of control strategies.

My vision of a virtual plant has a simple first principle model that starts with one component (e.g. water and air) that is corrected by an experimental model automatically generated by a simple test that takes less 10 minutes to execute for most loops. The result is a plant wide simulator. As more information is available and desired, the process knowledge embedded in the model grows but the fundamental basis is the same. No re-write is required. The opportunities and associated fidelity needed are as follows:

1. Control system set point optimization - Fidelity 5

2. Control strategy analysis and R&D - Fidelity 4

3. Root cause analysis and data analytics R&D - Fidelity 4

4. Operator training for abnormal situation management - Fidelity 4

5. Controller tuning and PID structure and options analysis - Fidelity 3

6. Batch configuration checkout and operator training for system familiarization - Fidelity 2

7. Loop configuration checkout - Fidelity 1

Fidelity 1: loop process variables respond in the proper direction to their loop output

Fidelity 2: measurements respond in the proper direction when control and block valves open and close and prime movers (e.g. pumps, fans, and compressors) start and stop.

Fidelity 3: loop dynamics (e.g. process gain, time constant, and deadtime) are sufficiently accurate (e.g. 50%) to tune loops and see process interactions

Fidelity 4: measurement dynamics (response to valves, prime movers, and disturbances) are sufficiently accurate (e.g. 25%) to track down and analyze disturbances

Fidelity 5: process metrics (e.g. yield, raw material costs, energy costs, product quality, production rate, production revenue) are sufficiently accurate (e.g. 5%) to find optimums

In the ISA New Orleans section short course I am teaching on March 3 and 4 titled: "Exceptional Process Control Opportunities - An Interactive Exploration of Process Control Improvements", I will use a virtual plant suitable for process control research, development, and education. I will demonstrate how a user can perform a 10 minute test of a manipulated process flow to provide a fidelity level 3 and 4 model. The contact for the course is Robert Deeb (ISA New Orleans section education chairman).

In the InTech Jan-Feb 2010 Web Exclusive "Advances in Flow and Level Measurements Enable Dramatic Improvements in Process Knowledge and Control", the following perspective was offered on the importance of flows for many types of process models including the following:

• Projection to Latent Structure or Partial Least Squares (PLS)
• Model Predictive Control (MPC)
• PID Adaptive Controller Tuning
• Neural Network
• First Principle

Flows determine what is going on in a process. If you don't get the flows right, not much else matters. Because of valve backlash, stick-slip, nonlinearities, and variable pressure drop, all types of process models have suffered from the use of valve positions rather than flow measurements. PLS, MPC, and PID performance assumes dynamics that are linear and independent of direction and size, all bad assumptions when valve positions rather than flows are used as inputs. Additionally, the valve nonlinearity from the installed characteristic varies with pressures at the inlet and outlet of the valve.

Pioneering advances in dynamic modeling by Alex Muravyev offer a next generation of pressure-flow solvers that will be robust and flexible enough to provide flows from valve positions. The solver is expected to handle complex piping networks and the discontinuities from batch and startup sequences (AdvancedSimulationPressureFlowSolver.pdf). The ability to consistently and comprehensively compute flows for all streams will enable dynamic models to reach the highest levels of fidelity required for research, development, and design of automation systems for nearly all applications. Presently, models can only move up in fidelity when flow control loops are installed on the key streams so that feedback action removes the nonlinearity and unknowns of the valve and piping system. New pressure-flow solvers can eliminate this precondition. A side benefit will be the demonstration by these models of the improvement in process performance that can be gained from cascade, feedforward, and ratio control. The quantifiable benefits from demonstrable test cases can justify new flow devices to provide missing flow measurements or improve the accuracy of existing flow measurements.

There are a lot of ways of looking at rangeability. Nearly all of them lead to the wrong conclusion as to what type of valve is best for process control. Some of the absolute worse valves for control (e.g. on-off piping valves) have the highest stated rangeability.

Valve rangeability is particularly important for pH control, batch control, startup, and plant turndown (see Control Talk column "Downturn Turndown" in Control July 2009 issue)

From, a piping view point, a full bore ball valve might be thought to have the highest rangeability because when the valve wide open, the flow path is nearly an open unobstructed section of pipe. A conventional butterfly would not be far behind because the only obstruction is a disc that could be almost horizontal when wide open.

Another definition of valve rangeability I have heard is the maximum flow divided by the minimum flow where the actual flow characteristic deviates by some specified margin from the specified inherent flow characteristic. Based on this definition, a linear trim (linear inherent characteristic) is stated to have the best rangeability. This approach is bogus in that the installed characteristic will be different and the controller can compensate for a deviation in characteristic through reset action.

The largest controllable flow divided by the smallest controllable flow is the definition of valve rangeability from a control viewpoint. Just being able to pass a high flow for a given valve size or adherence to an inherent valve characteristic does not mean the valve has high rangeability for control. You need to look at the installed valve characteristic where the percent flow is plotted versus stroke. Note the plot uses percent flow so the magnitude of how much flow the valve passes is not the issue.

For liquid service, the ratio of the pressure drop of the valve wide open to the valve fully closed can be used to show the effect of pump and piping design on the installed characteristic. This valve drop ratio varies from 1.0 where the frictional loss from the piping is negligible (entire difference between pump discharge and destination pressure is available as a pressure drop across the valve) to a minimum of about 0.05 where the valve drop at wide open is about 5% of the system pressure drop for energy conservation (decreased pump head and hence size). Figures 7-47a through 7-47c in the attached ControlValveRangeability.pdf excerpt from the ISA book The Essentials of Modern Measurements and Final Elements - A Guide to Design, Configuration, Installation, and Maintenance show the effect of valve drop ratio on the installed characteristic for linear, equal percentage, and modified percentage inherent characteristic. These figures show that a linear trim distorts to an undesirable type of quick opening characteristic where there is a burst of flow near the closed position followed by a noticeably decreasing valve gain (valve sensitivity) above 30% open. Conversely, the equal percentage trim becomes more linear as the valve drop ratio decreases. The curves for the equal percentage trim shown in Figure 7- 47b are for a conservative rangeability parameter equal to 100 (R=100). Many valves designed for superior throttling service have a larger R that would lower all of the curves in Figure 7-47b near the closed position.

Some progress has been made in a more realistic assessment of valve rangeability based on changes in slope of the installed valve characteristic and hence changes in the valve gain (more commonly referred to as the process gain). The lowest controllable and highest controllable flow depends upon where the slope decreases to less than 1/4 of its maximum thereby putting a limit on the change in process gain of 4:1. Based on this criterion, a sliding stem valve has a better rangeability than a ball valve or the conventional disc butterfly as seen in Figures 7-48a through 7-48c in the excerpt.

Heat exchanger temperature and inline composition control loops often benefit from the increase in gain with stroke offered by an equal percentage characteristic because it helps compensate for the decrease in temperature or composition process gain as the flow through the valve increases. In fact there is theoretically an exact linearization possible for a valve drop ratio of 1.0, because the slope (valve gain) of the inherent equal percentage characteristic being proportional to flow exactly cancels out the process gain inversely proportional to flow.

For vessel level, pressure, and temperature control loops, the process gain is so small that the allowable controller gain is way above the controller gain used. Consequently, changes in valve gain have a negligible effect.

Flow loops have a linear process gain so the valve gain linearity affects tuning. The effect of this is minimized by the use of reset rather than gain action.

I have suggested for more than 20 years that a more absolute accounting of valve rangeability from a control perspective would be to take the stick-slip near the closed position and use this as the X coordinate and use the corresponding Y coordinate on the installed valve characteristic as the minimum controllable flow. You cannot control tighter than the limit cycle from the resolution limit near the closed position. Based on this criterion, valves with a minimum sticktion near the seat and a percentage type of characteristic would offer the best rangeability. Sliding stem valves with a percentage trim, a valve drop ratio of 0.25 or higher, low friction correctly tightened packing, diaphragm actuators, and digital positioners would have the best rangeability and the best dynamics. If the pressure drop allocated to the control valve is less than 10% of the system drop to save energy, the nonlinearity of the installed characteristic of most trims becomes potentially detrimental to loop tuning and performance.

I got on a roll listening to Bob Seger's "Roll."

Startups, grade transitions, and abnormal conditions are the most difficult, operator intensive, hazardous, and inefficient periods of plant operation. Operators often believe these conditions require operator evaluation and action. The conditions are thought to be too special and the response too situation dependent to automate. The operators are right in saying these periods of operation require the best in operator expertise. However, case histories show that the power of the PID can be used to automate the best operator responses and build on them to provide faster, safer, and more efficient plant operation during these difficult process conditions. For some specific examples dealing with compressors and reactors check out the two chapters "Wally and the Beave Automate Reactor Startups" and "Wally and the Beave Return to Automate Another Reactor Startup" in my E-book on this website A Funny Thing Happened on the Way to the Control Room. For impressive examples for chemical, mining, and pulp and paper operations, check out the Control Talk columns "Show Me the Money - Part 1" (November 2009) and "Show Me the Money - Part 2" (December 2009) in Control magazine.

An extensive interview of the operators and process engineers is necessary to capture the best responses for a preliminary functional description of the control system. There are often a lot of surprises hidden by the diversity of actions that are inevitable from human responses. Free will implies these decisions are basically unpredictable. The operator actions consistent with first principles and process knowledge offer a good starting point but not the final strategy. During the commissioning of the control system, the plant response must be carefully observed and the best operator actions verified and improved by the use of the many options built into a PID loop to deal with rampant problems as the plant goes from zero to full rate, or vice versa. For example, output tracking, dynamic reset limiting, set point ramping, PID structure, gain scheduling, adaptive control, and override control can be used to deal with the problems at low rates such as noisy or inaccurate flow signals, excessive valve stick-slip near the closed position, larger transportation delays, and unrepresentative measurements. One of the common solutions is to head start (initialize) the controller output via output tracking to the best valve position for startup, transition, or abnormal situation. The initial position can be a "Full Throttle" position for fastest set point response. When the set point approaches the set point, the controller output can be momentarily set to a resting value based on experience or average position captured from a representative operating point from the last run. For fast loops such as flow and pressure, the resting value can be used as the "head start". One of the common mistakes is for process engineers to get carried away with trying to sequence the PID controller output too much or hold the controller output in the track mode for too long. For shutdown, the output must normally be held but otherwise the PID controller should be returned to automatic as soon as possible to deal with disturbances, unknown process effects, raw material variability, and nonlinearities. The process is not known or measured well enough to sequence flows without feedback control. It is particularly important to return pressure loops to automatic as fast as possible. Smart techniques for startup, transitions, and abnormal situations that take full advantage of the flexibility of the PID controller have been the source of the most impressive benefits in process control improvement. In general, these were also "quick hits" in that they were implemented in a matter of a couple of weeks by just configuration changes and controller tuning.

After all is said and done, articles and books have been the main method of advancing and sharing the technology for industrial process control.

I don't know of an undergraduate degree in process automation. Chemical, electrical, mechanical, and systems engineering programs offer an undergraduate course or two on process control. However, the typical university control course needs to spend most of the time on Laplace transforms, frequency response, and state-space to provide a theoretical understanding and groundwork for graduate courses. Outside of chemical engineering the focus is more on set point response and signal noise for servo mechanism and aerospace control. Consequently, the student doesn't learn about the critical characteristics of control for the process industry where nonlinearities, deadtime, valve stick-slip, unmeasured load disturbances, and incredibly long time frames are the cause of most tuning and control loop performance problems. Throw into the mix the unknown features of proprietary PID algorithms, and you have a script for islands of expertise. I personally like tropical islands so maybe this is OK. I could retire to one and conduct web based courses instead of doing cross word puzzles.

Courses may not be the whole answer considering that more than 80% of the details presented are forgotten. The PowerPoint slides often don't tell the real story. In my days, professors used the chalk board with only passing references to a book so my only record of knowledge is in notes long gone. Maybe the best way to make courses have a greater long term value is by providing labs for hands-on learning and refresher exercises, key memorable concepts, and resources for reference and further investigation. Audio should be combined with the presentation as exemplified by the slidecast of my Boston ISA presentation Exceptional Process Control Opportunities.

Considering that people don't have time to read books maybe courses and seminars and the structure of books themselves could provide better direction to areas of specific interest to solve problems. This is an argument for electronic books with interactive queries and demos.

For process automation, the articles and books written by practitioners are our best way of capturing and advancing the technology. Unfortunately users are not given the time or priority to write and most companies are reluctant to disclose information that could be considered to provide a competitive advantage for manufacturing. Consequently, suppliers of automation systems and services write most of the magazine articles and books on the practical application of process control. University professors write most of the journal articles and technical conference papers on the theoretical advancements in process control. The two groups don't talk much to each other. The use of industrial control systems for labs is one glimmering area of hope for the meeting of minds from universities and industry (see my last entry on "Exceptional Opportunities in Process Control - Expertise Development" and the June 1, 2009 entry "What I have Learned? - Bridging the Gap between Universities and Industry").

For me writing books was a way of organizing and expanding knowledge gained on the job. I found it allowed me to put technologies to bed (at least temporarily) so I could clear my head for the next area of expertise. My serious technical books in order of oldest to most recent publication date are: Axial and Centrifugal Compressor Control, Biochemical Measurement and Control, Continuous Control Techniques for Distributed Control Systems, Tuning and Control Loop Performance, Advanced Temperature Measurement and Control, Process/Industrial Instruments and Controls Handbook, Good Tuning - A Pocket Guide, Advanced pH Measurement and Control, Advanced Control Unleashed, Models Unleashed, New Directions in Bioprocess Modeling and Control, and The Essentials of Modern Measurements and Final Elements. My favorite book, which is a mostly serious collection of case histories written in a humorous way, is A Funny Thing Happened on the Way to the Control Room. My mostly humorous books in order of oldest to most recent publication date are: How to Become an Instrument Engineer - The Making of a Prima Donna, Logical Thoughts at 4:00 am, How to Become an Instrument Engineer - Part 1.523, Dispersing Heat Through Conviction, The Life and Times of an Automation Professional - an Illustrated Guide, and The Funnier Side of Retirement for Engineers and People of the Technical Persuasion. The last two books were written solely for comic relief.

While I had to largely write the books on my own time (except for the last serious one), the companies I worked for were supportive in terms of approval and recognition. In the end I expect books helped me along with my heroes Shinskey and Liptak to be the first group of inductees into Control magazine's Process Control Hall of Fame.

I think the following message titled "Why Books" from Ted Stillwell who is of the same vintage as me concisely offers "memories of the way we were."

Because I learned process control on the job books provided the only formal learning environment. Starting with the first treatment plant, with a control panel that would not fit through the door, I began my knowledge quest about instruments and process control. Chemical Engineering published Process Automation a 14-Part Series. My first book purchase was Liptaks' Instrument Engineers' Handbook that I read commuting back and forth to the office. The process control companies offered a great training ground for young engineers. Highly experienced application specialists at these companies wrote most of the articles and books on process control. I have five books by Shinskey, the most recent being Feedback Controllers for the Process Industries (McGraw-Hill 1994).

The opportunity afforded by online metrics is worth summarizing in this series even though it has been discussed in several entries on this website.

The need to cut costs has translated to an increased emphasis on process efficiency and the ability to justify software, hardware, and personnel. Increasingly these need to be hard benefits (e.g. reduction in raw material, downtime, and energy costs).

When I worked in process control improvement (PCI) in the technology department of a large chemical company, we had to show new benefits each year that were at least twice our salary to justify our job. By the end of the five year process control improvement effort we had 75 million dollars per year in savings documented. The PCI core group had 5 modeling and control specialists working with 20 or more process control engineers at key plants. The benefits reported depended upon the skills of particularly one person Glenn Mertz) who was extremely proficient in cost sheet analysis and working with operations and process technology.

Some companies are fortunate enough to have PCI as part of their culture as seen in the Control Talk Columns "Going, Going, Gone - Part 2" (September) and Part 3 (October) for examples. For many companies, benefits need to be reported in order for PCI and our profession to move forward or even exist. See the December 1 and 5, 2008 entries on this website "Past, Present, and Future of Automation - Part 5 (Benchmarking and Opportunity Assessment)" and Part 6 (Operator Interface) and the December 28, 2007 entry "Biggest Opportunities in Process Control Improvement - The Operator (Online Metrics) for more discussion of the aspects and importance of identifying and showing PCI benefits.

There are a lot of initiatives in the plant to improve plant operation by better operating procedures, equipment, and maintenance. All of these people take great pride in their work and are naturally eager to attribute better process operation to their efforts. Process technology often has the last say. The best way for PCI to get credit for improvement in plant operation is for the improvement and change to be visible in the data historian. A visible change in capacity, efficiency, or quality after a change in the process control system provides the documentation needed. If the PCI could be turned on and off, the correlation would be irrefutable but this is usually not practical. If no other events occurred when the PCI went online, a beginning of improved plant operation coinciding with the completion of the PCI, and a good explanation of cause and effect, will normally suffice for PCI to get credit. To help guide management and operations, comments should be entered in the historian and event makers for PCI provided.

PCI metrics for continuous process capacity are generally available from product flow measurements, downtime due to trips, and the time to startup or make a product grade transitions. PCI metrics for batch process capability can be generated from batch size, end point concentration, batch cycle time, and time in between batches. Quick and dramatic improvements in batch capacity have been achieved be the elimination of operator attention requests, manual actions, trips, and wait times for resource allocation (e.g. utility or charge systems), lab results, and reaction completion. Model predictive control and override control applications have been very successful for fed-batch processes. Reductions of 25% or more in batch cycle time are common for PCI. For a summary of some of the many possible batch control opportunities see BatchCycleTimeReduction.pdf from my PCI days.

PCI metrics for process efficiency are best expressed as a ratio of kilogram (pound) of input used (e.g. feed, fuel, reagent, and utility) per kilogram (pound) of product produced. For fuels, the numerator in the ratio may be expressed in thermal units, such as kilojoules (BTUs). For batch processes, the totalized input flow is divided by the batch size multiplied by the fractional product end point concentration. For continuous processes the instantaneous input flows are divided by intermediate or final product flow multiplied by the fractional product concentration. Synchronization of input flows to output flows can be done by the addition of a time constant equal to residence time and a time delay equal to the transportation delay. The flows can be totalized to compare shifts and periods of operation. Online process efficiency measurements require online or at-line analyzers or inferential measurements from first principle, neural network, polynomial, or statistical (e.g. PLS) models. These models in turn require flow measurements because nonlinear valve characteristics, backlash, and stick-slip make the use of controller outputs directly as model inputs ineffective and misleading. While reactant and fuel flows are typically measured, utility and reagent flows are often not. This short sightedness by plant projects (figuratively and literally), severely limits the ability to make improvements in the efficiency of use of these process inputs. I would wager a 10% reduction in the use of these inputs would more than pay for the flow meters. The old saying, you cannot control what you don't measure holds true for process efficiency. If I was a project manager, I would have a flowmeter on any input flow whose usage cost per year exceeded twice the installed cost of the flowmeter. I would at least provide the process connections for inserting a mobile wireless flowmeter. Where energy heat transfer rate calculations (e.g. heat removal rate as an inference of reaction rate) would be useful, I would install wireless RTD temperature transmitters on the streams entering and exiting the coils, exchangers, and jackets. Wireless transmitters allow the user to find during actual process operation the applications with the maximum benefit.

I hesitated at first to include sample time as one of the exceptional opportunities in process control because in most loops it is not issue. Then I realized I should give my perspective on the effect of sample time for the following reasons:

(1) Since we live in a digital world, sampled data is the norm. Just from the volume of applications, the opportunity is large

(2) There are no clear guidelines for various types of process control applications

(3) In some applications conventional sample times can cause severe safety and performance issues

(4) In most cases the tuning of the controller dictates that sample times could be significantly slower. If DCS module execution times and wireless communication time intervals could be increased, controller loading is reduced and wireless battery life is prolonged, respectively

(5) If we want more at-line analyzers to provide measurements of stream compositions that tell us what is really going on in the process and offer the opportunity for a more advanced level of control, we need to understand and address sample processing and analyzer cycle times

(6) If we want to move to more wireless measurement that give us the flexibility and intelligence for process control improvement, we need to understand and address wireless communication intervals

I am considering sample time as the time between updates in sampled data in the broadest sense. The following discussion should be useful for determining whether DCS scan or module execution times, wireless communication time intervals, model predictive control execution time, and at-line analyzer cycle time will affect control system performance.

If you are pressed for time you can skip the discussion below and just check out ProcessControlSampleTimes.pdf

There is considerable confusion as to when sample times affect the ability of a control system to compensate for unmeasured disturbances. The following is my quick attempt to provide some concepts to sort out fact from fiction and provide some guidance.

The performance of a control loop depends upon the tuning. Specifically, the peak and integrated errors are inversely proportional to the controller gain. The peak error is not affected much by the integral time setting. However the integrated error is proportional to the integral time. Thus, a loop with good dynamics can be made to perform as poorly as a process with bad dynamics by sluggish tuning. The effect of slow sample times is hidden by large integral times or small controller gains. Thus, it is critical for any comparison, that tuning criteria be specified. In fact there is an implied deadtime as a result of the tuning of the loop as derived and discussed in Advanced Application Note 5. The tuning of the controller puts a practical limit on how fast the sample time must be for the effect to be negligible.

If a controller is tuned for maximum performance, the peak error is proportional to the loop deadtime to process time constant ratio. The integrated error is proportional to the deadtime squared. These statements are strictly true only when the process time constant is large compared to the loop deadtime. The loop dead is the sum of final element deadtime (e.g. valve pre-stroke time delay, deadband, and sticktion), process deadtime (e.g. mixing, thermal, and transportation), automation deadtime (e.g. sensor lag, transmitter damping, and sample times), and small process time constants. All of the time constants smaller than the largest time constant become effectively deadtime in the first order plus deadtime approximation used in industry. Process and automation system dynamics places an ultimate limit on loop performance. There is a corresponding ultimate limit on the sample time.

The relationships between process dynamics (e.g. total loop deadtime), controller tuning, and loop performance is detailed in the Theory section in Chapter 2 of Advanced Control Unleashed, and Appendix C in New Directions in Bioprocess Modeling and Control. All of my books and many of my articles take advantage of the fundamental understanding gained from these relationships.

The effect of sample times can be accessed in terms of practical and ultimate limits on performance. Critical loops where peak errors can cause destruction or environmental releases such as compressor surge control, furnace pressure control, exothermic reactor temperature control, and RCRA pH control, the tuning is necessarily aggressive. As a result the practical limit is much closer to the ultimate limit. For a discussion of cases where exceptionally fast sample times are needed, checkout the April 2, 2007 entry "Analog Control Holdouts."

For excellent final elements, clean sensors, and transmitter damping settings of 0.2 sec, we can suggest practical and ultimate sample times for different types of processes with typical dynamics. The ultimate limit (fastest conceivable sample time requirement) is set to be less than 1/10th of the sum of the minimum loop deadtime and minimum process time constant with some consideration as to maximum practical controller gains to reduce valve cycling and noise amplification. For any loop with a a large control valve, the minimum loop deadtime is about 1 second for an unmeasured disturbance (unless volume boosters have been added to the output of the positioner) so the ultimate limit on sample time is about 0.1 second. The practical limit reflects current tuning practices (much slower tuning to insure a smooth gradual response despite unknowns and nonlinearities). For integrating processes, the process time constant shown is the inverse of the integrating process gain (denoted by single exclamation point). The double exclamation point denotes a runaway (positive feedback) process time constant. Consultants says it is impossible to generalize but I think some guidance is helpful to the user with the realization there are always exceptions and the actual process dynamic and tuning should be identified by automated online tuners and adaptive controllers (e.g. DeltaV Insight). I didn't consider ultimate sample times slower than 60 sec. Note that slower sample times will affect the deadtime identified. A Rough Guide to DCS and Measurement (e.g. Wireless) Sample Times is offered in ProcessControlSampleTimes.pdf

For many digital devices the update is available near the beginning of the sample time (latency is negligible), which means the average deadtime from the sample time is about half the sample period. For at-line analyzers (field analyzers with automated sample systems), the result is not available until the end of the sample processing and analyzer cycle time, which translates to an average effective deadtime that is about 1.5 times the time interval between updates in the analyzer output signal. Theses deadtimes determine the minimum peak error for an unmeasured step disturbance at the input to the process.

The detrimental effect of sample time is greater than deadtime in that for continuous sources of dead time such as process transportation and mixing time delays and small process time constants, there is a continuous train of updates. For sampled data there are no intervening values. Consequently, the effects can be worse. For example, there is aliasing of oscillations where the indicated amplitude is smaller and the period is larger than actual. There can be jitter due to variations in latency and lack of synchronization of digital data that introduce variable time delays and noise for rapidly changing signals.

The PIDPLUS modification of the traditional PID developed for wireless applications helps the PID deal with the sample time from digital devices and communication, and at-line analyzers. The improvement is most dramatic for self-regulating processes but is also significant for integrating processes as seen in the tests documented in ControlStudiesPIDPLUS1.pdf. The PID-Plus algorithm also breaks the limit cycle from the resolution limit from the deadband setting for exception reporting of wireless devices because integral action is only done when there is a measurement update.

As I reflected on my career, I reaffirmed that what drives me is gaining a deeper understanding and sharing what I have learned, hopefully with a few laughs along the way. Throughout my career I sought with an open mind the knowledge and insights of the leaders in process modeling and control. I then used simulations to rapidly explore process relationships and to prototype control improvements that incorporate process understanding. The knowledge prepared me to solve tough plant control problems.

During my career at Monsanto I wrote a bunch of articles in the 1980s for InTech on my time in the plants with some humor introduced to help make the material more accessible and memorable. These articles were compiled and published in the book A Funny Thing Happened on the Way to the Control Room available for viewing as an E-book in the April 3, 2009 list of my books on this website. This is my favorite book, I didn't write much in the way of articles or books in the 1990s. I was on the road most of the time.

When I retired from Monsanto-Solutia in 2001 (sans package), I taught at Washington University. The students were great but after the course and lab was developed, it became routine. Also, I felt isolated.

I tell people I flunked retirement. I moved to Austin in September 2004 and started a second career as a part time consultant at Emerson Process Management. This gave me a chance to keep up to date with the latest new tools besides continue my exploration of process control opportunities. Plus it felt like home since Monsanto and Fisher Controls were one for most of my career.

I have been blessed with access to the best minds. In Monsanto's Engineering Technology I got to work with the leaders in process modeling and control. Some went on to distinguished chairs at prestigious universities, several were inducted into the Process Control Hall of Fame, some served as presidents of ISA and AIChE, and others left to become the principal technical resources for leading simulation companies. Here in Austin in Applied Research I get to work with the brains behind DeltaV. Plus my second career is more balanced. Except for the spike in work this year, I take a total of 4 months off each year to travel to see relatives, friends, and neat places and to write books.

Key points of my articles written in my post retirement years provide a quick overview of what I have been doing. The entries on this website in July will focus on the dozen articles I have written since retiring from my full time job. Here are the articles from 2003-2004.

"Has Your Valve Responded Lately", Control, May, 2003
"What is Your Flow Control Valve Telling You", Control Design, May 2004

Putman publications decided to do an encore publication in a second magazine. Some nomenclature typos were corrected in the reissue of the article in Control Design.

1. Deadband originates from backlash in the linkage and connections between the actuator and the plug, disc, or ball. Stick-slip comes from friction in stem packing and seals around the sealing of the plug, disc, or ball for process isolation

2. Deadband from linkage and connection backlash and stick-slip from trim and packing friction create deadtime for slowly changing controller outputs

3. Deadband will create a limit cycle in any control system where there are two integrators in series, such as a PI controller on an integrating process (e.g. level)

4. For deadband, the limit cycle amplitude is the ratio of deadband to controller gain

5. For stick-slip, the limit cycle amplitude is the product of the open loop gain and the stick-slip

6. For both deadband and stick-slip, the limit cycle period is proportional to the controller integral time and inversely related to the controller gain

7. Large actuators can have a large stroking time for a large change in signal

8. The size of the changes signal typically used to checkout control valves will not reveal the deadband or stick-slip and make all but the largest valves look good

9. A volume booster can reduce the stroking time of big actuators but has a large deadband. The booster should be put on the positioner output to quickly drive through this deadband. The booster bypass must be opened enough to prevent fast cycling from the positioner output looking into the booster's small inlet volume

10. Unstable oscillations can break out for large disturbances when the integral action in process loop becomes faster than the valve response. The integral time must be greater than the product of the valve slewing rate, disturbance size, and controller gain. (Not mentioned in the article but frequently discussed on the this website is that position read back from digital positioners and the PID dynamic reset limit option can automatically prevent the controller output from outrunning the valve)

11. Limit cycles are attenuated (filtered or washed out) by vessels or columns. The ratio of the attenuated to original amplitude is proportional to the period of the oscillation and inversely proportional to the residence time (volume/flow)

12. The control valve with the best response is a sliding stem valve with a digital positioner. If one must use a rotary valve, avoid tight shutoff and high friction packing and use a diaphragm actuator with a short shaft and splined connections between the actuator shaft and the stem of ball, disc, or plug. Make sure the stem is cast with the ball, disc, or plug to avoid another connection with backlash

Postscript: Rotary valves designed by piping manufacturers have a lot of deadband and stick-slip as discussed in the July 2009 Control Talk column "Downturn Turndown" in Control magazine.

"The Next Generation - Adaptive Control Takes a leap Forward", Chemical Processing, September, 2004

1. Nearly all controllers are detuned (backed off from maximum performance) to some degree to provide a smooth response and to deal with the inevitable changes in the process dynamics

2. Older technology adaptive controllers had these undesirable features
a. The process had to be disturbed or oscillated (e.g. patter recognition)
b. The dynamics were embedded in tuning settings
c. No real insight as to where the process has been or where it is going
d. Tuning method was fixed
e. Always playing catch up even if same situation was seen a thousand times

3. The next generation adaptive controller can
a. Normal changes in a controller's set point or manual output are used
b. The process dynamics are displayed and historized
c. From changes in the process dynamics, plant problems can be diagnosed
d. Several tuning methods are available
e. Tuning settings identified can be scheduled for preemptive action

4. "The information on changes in the process model may be directly used to monitor loop performance and to provide more intelligent diagnostics. The models can provide the dynamics for simulations and identify candidates for feedforward control and advanced control techniques. For example, loops dominated by a dead time or exhibiting disturbance models for multiple variables, are prime candidates for model predictive control. The dynamic process models in general can be used to create or adapt real time simulations for prototyping new control strategies, exploring "what if" scenarios, and training operators. Process gains that decrease or time constants that increase with feed totals are ripe for real time optimization of the run time between defrosting or cleaning and catalyst reactivation or replacement. The beauty of this route is the models and tuning settings are available from the adaptive controller for a higher level of control by a better knowledge of the topology"

"Advanced Control Smorgasbord - A Lot of Tasty Choices", Control, May, 2004

The online version is missing the following introductory sentences at the beginning of the first paragraph.

"By the time I was assigned to my first electronic control room project, some very smart engineers had already developed most of the techniques to exploit PID controllers.
Relative gain arrays and simple decoupling of the controller output were used to analyze and deal with interaction on a steady state gain basis. The outputs from PID controllers, whose process variable was a constraint variable, were sent to a signal selector to form an override control scheme to maximize or minimize a manipulated variable."

1. Previously, advanced process control (APC) required software packages at $100K a clip, separate computers, special interfaces, and consultants to do the studies and implementation. The total bill could easily approach or exceed a million dollars for a medium project, the biggest chunk being the consultant's time charges. Even a greater consideration was that the process knowledge to exploit or to just maintain the system disappeared when the consultants left the site

2. At the turn of the century, APC technologies were integrated into the basic process control system. License fees were minimal and whole cost of implementation decreased by a factor of twenty or more by the automation of the configuration, displays, testing, simulation, and tuning

3. In the time it takes to read this article, a model predictive controller or neural network could have been configured

4. Perhaps the biggest opportunity for driving the application of APC is the development of online process performance indicators

5. The key variable for process performance monitoring is the ratio of the manipulated flow to the feed flow

6. The controlled variable is best expressed and plotted as a function of the flow ratio (e.g. pH versus reagent to feed ratio, column temperature versus reflux to feed ratio, exchanger temperature versus coolant to feed ratio, and stack oxygen is versus air to fuel ratio)

7. The process efficiency is seen in difference between the actual and optimum ratio rather than in the gap between the actual and optimum controlled variable

8. A novel method has been developed to use model predictive control (MPC) to simultaneously adapt multiple first principle process model parameters

9. For closed loop process control, consider
a. PID for tight control of integrating or runaway processes
b. MPC for multivariable control, interactions, and optimization

10. For online property estimators for continuous processes, consider
a. ANN for highly nonlinear predictions with uncorrelated inputs
b. LDE for lag dominated linear predictions with uncorrelated inputs
c. PLS for steady state predictions from large number of correlated inputs

ANN is an artificial neural network, LDE is a linear dynamic estimator, and PLS is a projection to latent structures or partial least squares prediction discussed in Chapter 8 of Advanced Control Unleashed

Sometimes it seems universities and industry reside on planets that are light years apart. Too bad we don't have Star Ships with warp drive. Universities have leading edge research. Industry has "state of the art implementation."

Why are universities and industry "worlds apart?"

Engineers in industry don't seem to understand how to apply the research from universities. Professors don't appear to really know what is needed in industry. The tools are quite different. Engineers in chemical, pharmaceutical, and pulp & paper plants configure their control strategies in a distributed control system (DCS). Professors typically have their graduate students program their algorithms and test cases in Matlab.

One way to get industry and universities on the same page is to provide a DCS to the university with all the tools needed for research, such as a Matlab interface. In many cases the Matlab code can end up being configured in the DCS as part of the maturation of the innovation. The use of the DCS minimizes the reinvention of the wheel, such as the PID algorithm with all of its evolutionary enhancements. The setup facilitates the transfer of knowledge between the universities and industry. Being able to explore, prototype, and demo university innovations in a DCS makes it more real to industry and leads to rapid deployment and sharing of actual plant results.

If there is a unit operations lab, process control lab, or pilot plant, the DCS can be used to control the equipment used in the experiments. Students gain valuable experience in learning how to work with a toolset that is designed to meet industrial standards. Just learning the nomenclature and working with a DCS gives the student practical skills and confidence when as a new employee the student enters the control room. The window to see and affect the process is the DCS. Whether the student is going into automation or process design & technology, the student needs to be able to understand how to access and review modes, limits, options, and variables that determine how well a process runs. For example, the student gets to work in a university DCS on PID features commonly used in industry:

(1) PID limits (e.g. output, set point, and anti-reset windup limits)
(2) PID options (e.g. set point tracking of the process variable in manual, dynamic reset limiting, and nonlinear gain modification)
(3) PID form (series and standard)
(4) PID structure to determine whether each PID mode (proportional, integral and derivative) works on the process variable or the error (difference between the set point and the process variable)
.
The first semester I taught the Chemical Engineering course "Introduction to Process Dynamics and Control" at Washington University in Saint Louis as an adjunct professor, the students could not relate to my attempt to introduce practical plant applications and considerations in the normal course of Laplace transforms and bode plots. The second semester I added a virtual plant that consisted of a DeltaV DCS running in the Simulate mode integrated with HYSYS dynamic process simulations for each student. I later configured most of the process simulations directly in control studio. I was amazed how fast the students learned how to work in the graphical configuration environment and operator interface. All they needed was a few screen prints on navigation to get them started. Several of the students subsequently got intern or permanent positions doing configuration at the local DCS industry center. I had these students with experience in the automation industry come back to speak to the next class. The result was a dramatic turnaround in appreciation and understanding of what they would face in industry. The students decided on their own to go online to find and buy tee-shirts with Duncan, the DCS mascot, windsurfing. I ended up buying tee-shirts too and we all posed for a group photo by one of the students.

The main obstacle to the use of the DCS in the university is the initial installation and training. This is addressed by the support of industries with the same DCS who have a working relationship with the university and the local business partners of the DCS supplier. This method has enabled over 100 DeltaV DCS installations at educational institutions.

At the Automatic Control Conference in Saint Louis on June 11, I am co-chairing a session with Professor Tom Edgar from the University of Texas on "Bridging the Gap between Universities and Industry." The presentations are:

(1) "Bridging the Gap Between Universities and Industry"
(2) "Digital Process Control Lab at Washington University"
(3) "The Bioprocess Laboratory at Washington University"
(4) "Rose-Hulman Institute of Technology Unit Operations Laboratory"
(5) "Engineering Research Center for Structured Organic Particulate Synthesis (Rutgers, Purdue, New Jersey Institute of Technology, University of Puerto Rico at Mayaguez)"
(6) "Using a Distributed Control System (DCS) for Distillation Column Control in an Undergraduate Unit Operations Laboratory (University of Texas)"

My next blog will be June 22. In the mean time enjoy summertime.

So the question on the minds of automation engineers for process control and even the members of congress for the banks and the economy is how do you fix your model? Will feedback correction be enough? Will the correction arrive too late? How do you deal with a response that is not self-regulating but is integrating or a possibly a runaway?

If you want the bottom line and don't have time for technical jibber-jabber: "The most universal but not well known solution for feedback correction of the flow feedforward model for ratio control uses a Ratio block in tandem with a Bias/Gain block as shown in slide 7 of RatioControl.pdf. The Ratio block operates in the AUTO mode and has its local setpoint adjusted by the operator. The Bias/Gain block runs in the CAS mode and has its CAS setpoint (bias) connected to the output of the process controller used for rapid feedback correction." Of course, you need to checkout and test this solution like any other.

Ratio control is basically a very simple flow feedforward model that involves a simple bias and gain applied to independent flow to compute the dependent flow. On a plot of dependent flow (Y-axis) versus independent flow (X-axis), the gain is the slope and the bias is the intercept. The feedforward multiplier and summer in a process controller for feedback correction of the ratio control would change the slope and bias, respectively. The slope is the ratio factor (delta dependent flow/ delta independent flow).

Nearly all PID blocks have internal feedforward functionality. Some PID blocks have feedforward multipliers besides feedforward summers but the internal structure is fixed and often difficult to understand and maintain. For ratio control, the feedback correction by multiplication or summation is best done outside of the PID block. The use of the Ratio block and Bias/Gain block provide the flexibility and visibility needed through its BKCAL and built-in features and options such as bumpless transfer to the existing ratio. In either case, the independent flow is the IN_1 input and the dependent flow is the IN input to the Ratio (RTO) block as shown in Slide 7 of RatioControl.pdf. The setpoint of the RTO block is the desired flow ratio and the PV is the actual flow ratio.

For a feedback correction by multiplication, the output of the process controller manipulates the ratio factor used in the multiplication of the independent flow. The RTO block is put in the CAS mode and the output of process feedback PID is connected to the CAS_IN of the RTO block. The output of the RTO block becomes the CAS_IN setpoint of the dependent flow loop.

For a feedback correction by summation, the output of the process controller directly manipulates a bias after the multiplication of the independent flow by an operator set ratio factor. The RTO block is put in the AUTO mode and the operator adjusts the local setpoint (SP). The output of the RTO block becomes the input (IN) and the process feedback controller becomes the setpoint (SP) of a Bias/Gain (BG) block. The output of the BG block becomes the CAS_IN setpoint of the dependent flow loop.

A straightforward feedforward explanation can be found on pages 73-83 of the E-book posted on this site on April 3 titled Continuous Control Techniques for Distributed Control Systems. Just ignore the antiquated Figures 5-1a and 5-1b that offered a solution to the missing adjustable filter and time delay blocks back in the early days of the DCS. For more on the nuances of feedforward, check out the May 2008 Control Talk Column "Feeding on Feedforward:" http://www.controlglobal.com/articles/2008/171.html

To visualize and quantify the correction you can use Excel to plot on the Y axis the dependent flow and on the X axis the independent flow for various operating conditions (e.g. compositions and temperatures) so you have a family of lines. If the lines all intercept close to zero, then the slope or ratio factor is mostly changing and a feedforward multiplier would be the apparent choice as shown in Figure 5-2a on page 77 for a ratio of reagent to feed flow. This relationship holds for most blend, composition, pH, % solids, and temperature control systems in continuous (self-regulating) processes. In other words, if the feed flow goes to zero, the reagent, reactant, blend, or coolant flow should go to zero.

On the other hand, if the intercept varies and the slope is relatively constant, then a feedforward summer is the first choice as shown in Figure 5-2b on page 78 for a ratio of feed water flow to steam flow where the blow down flow shifts the operating line.

The steady state process gain for continuous processes is best seen on a plot of the controlled variable (temperature, composition, % solids, blend, and pH) on the Y-axis versus the ratio of manipulated flow (coolant, reactant, dilution, blend, and reagent flow) to the feed flow. These plots can be generated from the first principle equations in the Advanced Application Note 3 posted April 3 on this website or by simulation programs that use first principle equations. The result is a steady state process gain that is inversely proportional to the feed flow. By using a feedforward multiplier, you are effectively multiplying the controller output by the feed flow which cancels out the steady state gain.

So why are feed forward summers mostly used in industrial applications? The short answer is that they work well enough and are easy to implement and understand. You can do an awful lot with a bias correction. The feedback correction of nearly all advanced control tools such as model predictive control, neural network estimators, and partial least squares estimators use a simple bias that is a fraction of the error between the predicted value and the measured value.

There are also good technical reasons to use a summer if you dig deeper. The bias corrects for offset and drift, which is the largest error in most flow measurements. You don't need to nail the ratio factor range for scaling the controller output. You can simply use a + and - % correction to the flow feedforward. In some older versions of the DCS you had to implement a bias of 50% so that we could get a "+ and - 50% correction. If the controller output was 50%, the flow feedforward was perfect. The deviation from 50% was a measure of the flow feedforward error. An integral only valve position controller (VPC) whose setpoint (SP) is 50% and whose process variable (PV) is the feedback controller output can then trim the ratio factor (RTO setpoint). If the VPC IDEADBAND option is employed so you get no integral action if the PV is within 10% of the SP, you get a gradual slope correction only if the fast bias correction is insufficient.

For well mixed vessels and distillation columns, the process time constant is inversely proportional to the feed flow. Since the maximum controller gain for load rejection is proportional to the process time constant divided by the process gain which itself is inversely proportional to flow, the net effect of feed flow on controller gain is cancelled out. The use of a feedforward multiplier now creates a nonlinearity where the controller tuned for low flow will tend to oscillate at a higher flow. This is often aggravated by an equal percentage flow characteristic whose slope (valve gain) is proportional to flow.

If you have an integrating process response, you need an overcorrection to get you back to set point. The correction is most readily visualized as a bias. The easiest to understand example of an integrating response is the level loop where the correct ratio of manipulated discharge flow to the feed flow is one. If the level is too high, keeping the discharge flow equal to the feed flow will not bring the level down. Batch temperature, pH, and composition control tend to have integrating responses. Continuous processes where the process output flow comes from vapor phase tend to have an integrating response in liquid phase. Conductivity (total dissolved solids) control of a boiler drum is an example because the only way to get solids out of the liquid is by blowdown. The ratio of blowdown flow to feedwater flow shifts based on the amount of unbalance in the integrated response. If the total dissolved solids is below the set point, the correct ratio of blowdown to feedwater flow is zero. Similarly, impurity concentration builds up in reactors with a vapor phase product or a significant recycle stream. Here the ratio of purge rate to fresh feed rate shifts due to the integrating response. The overcorrect requirements for a runaway response are even greater because the process is accelerating away from the setpoint. For some reactors, there is a point of no return where the best you can do is to implement the emergency and evacuation procedures. Let's hope that is not the case for the economy. Mars doesn't look terribly inviting and the Martians in the movies have bad attitudes

The main scope of applications where a feedforward multiplier provides a desirable compensation for a nonlinearity is when the feedback controller output goes to a linear installed characteristic or flow controller for blend, composition, % solids, and pH control at the outlet of a static mixer or for temperature control at the outlet of an exchanger because this process equipment has essentially plug flow (with very little backmixing) and hence a negligible process time constant.

This leaves us with the final question, why do oxygen controllers on a boiler stack correct the air flow rather than the ratio of air to fuel flow? Why go to the confusion of a calculated versus a real air flow? The main reason is to actively use the cross limits or lead-lag systems employed in a combustion control system to insure the air flow leads the fuel flow on an increase in firing demand and air lags fuel on a decrease in firing demand.

Regardless of whether a feedforward multiplier or summer is used, the desired ratio before feedback correction and the actual ratio after feedback correction should be displayed, historized, and trended along with the controller output and independent flow.

We conclude with a ten step implementation procedure for helping you get the most out of your cascade control system.

(1) Pick a fast secondary measurement with enough rangeability to correct for nonlinearities and disturbances. Flow is the most popular secondary measurement because it is relatively fast and can compensate for nonlinear valve characteristics and pressure upsets. However differential head meters may lack sufficient rangeability for some applications. A common triple cascade loop is vessel temperature to jacket temperature to makeup coolant flow, which makes the primary loop linear and corrects for coolant makeup temperature and pressure upsets and non-ideal control valve behavior. If you have a positioner on the coolant valve (highly recommended), you have a quadruple cascade. If you have a digital valve controller (DVC) as your positioner with an inner loop of actuator pressure, you have graduated to a quintuple cascade control system.

(2) If you have a positive feedback network for the integral mode in your secondary PID and have fast reliable feedback of the variable that the secondary loop is manipulating, enable external feedback ("Dynamic Reset Limit") in the secondary PID and provide the manipulated variable for external reset feedback. Fieldbus read back is fast enough for any valve with a pneumatic actuator whereas HART read back is fast enough for very large pneumatic actuators. Some variable speed drives (VSD) have tachometer feedback creating an inner speed loop. The use of speed for external reset feedback is particularly useful for dealing with overly conservative maximum ramp rate settings in the VSD.

(3) Remove set point filtering on the secondary loop.

(4) Tune the secondary (inner) loop first for a fast response to set point changes. Consider set point feedforward in the secondary loop for a low secondary PID controller gain (< 0.5) to make the secondary response to setpoint changes faster.

(5) If you a positive feedback network for the integral mode, enable external feedback ("Dynamic Reset Limit") in the primary PID and provide the secondary loop PV for external reset feedback.

(6) Put the secondary loop in the remote setpoint cascade (RCAS) mode.

(7) Make sure the output limits of the primary PID match up with the setpoint limits of the secondary PID.

(8) Add a PV noise filter to the primary loop just large enough keep from unnecessarily moving the secondary loop set point.

(9) Tune the primary (outer) loop for a smooth response. The primary closed loop time constant must be at least five times larger than the secondary closed loop time constant to eliminate any interaction between the primary and secondary loops. If the secondary loop time constant cannot be made faster, you must slow down the primary loop time constant by decreasing the primary controller gain.

(10) Add feedforward signals as necessary to the primary controller output to improve its response to measured disturbances. Add a PV noise filter to the feedforward signal just large enough to prevent unnecessary movement of the secondary loop set point. Add dynamic compensation (delay and/or lead/lag) to the feedforward signal so that the correction by the secondary loop doesn't arrive too soon or too late relative to the disturbance at the same point in the process.

A cascade control system has a secondary (inner or slave)) loop that gets a remote set point that is the output of a primary (outer or master) loop. The set point of the secondary loop is driven to meet the needs of the primary loop. Most of the benefits stem from the secondary loop correcting for disturbances, nonlinearities, and non-self-regulation before they affect the primary loop. A more obscure benefit is the speeding up of the primary loop by decreasing its natural frequency, particularly when there is a secondary process lag. All of these benefits depend upon the cascade rule that the secondary loop be sufficiently faster than the primary loop. The trend plot SlowSecondaryLoopOscillations.pdf shows how oscillations break out when the secondary loop is slowed down by a factor of five.

Where do you cascade control systems and how many do you already have in service?

How many control valves do you have? Would you believe you should have as many cascade control systems as you have control valves?

Every control valve connected to a digital control system should have a digital valve controller (DVC). The DVC is a high gain fast secondary loop that takes care of most of the non ideal stuff that can occur with valve position due to backlash, friction, and actuator response plus give you diagnostics on the valve's health and dynamic capability, and feedback (readback) of the actual valve position. In the old days, with analog loops, putting a pneumatic positioner on a fast loop was stated to be a "no-no"! The solution (the use of a booster instead of a positioner) was worse than the problem as discussed in the chapter "Compressor Surge Control - Traveling in the Fast Lane" in the E-book A Funny Thing Happened on the Way to the Control Room and in the Chapter "Instrument Requirements" in the E-book Centrifugal and Axial Compressor Control. In reality, even in the old days, the analog flow loop was usually tuned so slow, the cascade rule was not really an issue. Of course, some positioners were poorly designed, particularly the spool type single stage positioners slapped onto on-off valves posing as throttle valves. Every now and then I see the question still asked; when should you use a valve positioner on a control valve? Academics and people stuck in the mindset of the days of analog controllers will say "important slow loops." The right answer in my book is "every loop" if you are talking about an electronic high performance positioner (e.g. DVC) unless you really don't care what the valve is doing.

The next most common secondary loop is the flow loop, which corrects for pressure upsets and valve characteristic nonlinearities before they affect the primary loop. Most of the common primary loops (e.g. composition, pressure, level, and temperature loops) can benefit from cascade control. If you are going to do flow ratio or flow feedforward control, secondary flow loops are almost essential. Most secondary flow loops should have secondary valve position loop forming a triple cascade control system.

There are exceptions as to when a secondary flow loop is useful. If the flow measurement has significantly less rangeability than the control valve or excessive noise or failure rate, a secondary flow loop can do more harm than good. In 3 element boiler drum level control, the level controller output switches from cascade control of a secondary flow loop to direct manipulation of boiler feed water valve at low loads because of the insufficient rangeability of the differential head flow meter on the feed water.

Liquid or polymer and some gas pressure loops are too fast to have a secondary flow or valve position loop. In general, the controller output of these extremely fast pressure loops should go directly to a variable speed pump via a high resolution input card with a suitably designed variable speed drive with minimal velocity limiting and no deadband. In some cases, the pressure loop should use an analog electronic controller or a DCS with special fast scan and execution time.

Inline (e.g. pipeline or static mixer) pH loops have a response almost as fast as the flow loop. The pH loop must consequently be detuned to be slowed down enough to satisfy the cascade rule. Also, the flow loop often lacks the rangeability needed for pH control and flow ratio control is inexact at best due to the extreme effect of immeasurable changes in feed concentration. Most inline pH loops perform better if their output goes directly to a final element with good resolution and minimal deadband. The exception is when there are Coriolis feed and reagent flow meters, a relatively constant feed composition, and the pH set point is on the relatively flat part of the titration curve making mass flow ratio control more sensitive than pH. If there is no flow feedforward, a "head start" to momentarily preposition the valve or the use of signal characterization helps the pH loop deal with startup and large load disturbances.

In some cases, the process gain of an equal percentage valve characteristic, which is proportional to throttle flow rate, compensates for a process gain that is inversely proportional to load (e.g. feed rate). The most common cases are inline concentration and pH control and heat exchanger temperature control. The use of a secondary flow loop removes this compensation of the process gain making the primary loop more nonlinear.

In part 2 we look in greater detail at the cascade rule, the use of reset in the secondary loop, and how dynamic reset limiting with external reset is a powerful tool for cascade control. In part 3 we conclude with the "Rules of Thumb" summary for cascade control.

If the pressure set point is a fraction of an inch of water column, you have a high integrating process gain. The response is often a high speed ramp in the control region. For a waste incinerator and a phosphorous furnace I worked on decades ago, the pressure could ramp off scale in 0.2 and 5 seconds, respectively. Trying to control the incinerator and furnace pressure was reported to be like trying to control an explosion when there was a shutdown or a slag slide, respectively, and a corresponding burst of vapors and gases. Needless to say these pressure loops could never go to manual and open loop tuning methods were down right dangerous. In the old days I used a modified ultimate oscillation method and a high speed recorder. As with runaway reactors, the reset time (e.g. sec/repeat) was increased by 100x to make reset action negligible and the controller gain was increased until there was the start of an oscillation. The reset time was set equal to the period of the damped oscillation and the controller gain was halved. A set point change was then made and if the response was more oscillatory than dictated by valve limit cycles from stick-slip or deadband, the controller gain was decreased. If damped oscillations persisted and got worse or slower, then the reset time was increased until the oscillations period and decay rate were faster. This test was repeated and the gain decreased or the reset time increased until the response was sufficiently smooth.

Before we go further, one should realize that the original ultimate oscillation method asked the user to increase the controller gain until there were equal amplitude oscillations. This was too exciting and gave controller tuning settings that were too oscillatory especially if there was an increase in the loop dead time or process gain or a decrease in the process time constant. The damped oscillations mentioned here are rapidly decaying where each succeeding peak is less than ¼ the previous peak.

The damped oscillation period is larger than the ultimate oscillation period and the damped oscillation controller gain is smaller than the ultimate oscillation gain and the factors of 1.0 for period and 0.5 for controller gain are not per the textbook definitions of the Ziegler-Nichols ultimate oscillation method. Using the text version of the closed loop (ultimate oscillation) or open loop (reaction curve) Ziegler-Nichols tuning method and thinking that tuning settings with more than one significant digit are practical, is a great way to reject the pioneering work of Ziegler and Nichols and to glorify new tuning methods. What I found early in my career is a simple change of using damped oscillations instead of ultimate oscillations and using easy to remember rounded off factors, gave me the proportional mode action needed for these loops that lack self-regulation and can be headed for a trip point. I also quickly realized that the nonlinear and non-stationary nature of chemical processes and valve stick-slip and backlash meant that the long term tuning setting accuracy of better than 50% was wishful thinking.

Today, integrated online adaptive tuning tools that look at set point changes, such as DeltaV Insight, should be able to automatically identify tuning settings of most fast integrating processes. However, some pressures can be so fast (e.g. the cited incinerator) digital delays must be eliminated and tuning tools that directly connect to the I/O, such as those used by EnTech, are needed. It is important that the module execution time, the tuning tool, and the trend chart update time not cause aliasing or an extra observed dead time. The controller, final element, and pressure sensor must also be extremely fast. Finally, it is particularly critical to test and observe new tuning settings for these and other types of loops that require aggressive feedback control.

If you want to get more details on the importance of making the loop fast enough, check out the chapter "Pressure Control: Without Deadtime I Might be Out of a Job" in the free E-book A Funny Thing Happened on the Way to the Control Room on pages 31-41: http://www.modelingandcontrol.com/FunnyThing/.

My head is spinning with myths. The examples seem endless.

(11) The process dynamics can be identified with the controller in auto without any perturbation - a loop startup or shutdown, change in set point, or an injection of a pulse or step in the controller output is needed to sort out the process dynamics from the controller dynamics. Bob Otto (Monsanto Fellow) alerted me to this dilemma 20 years ago. Cecil Smith published an article about 5 years ago making the same point. Now if you have inside knowledge of the process gain, it may be possible to find the process time constant from estimates of the dead time. However, even sophisticated process simulations have difficulty in providing an accurate process gain. So why not face up to the situation and benefit from perturbations? Batch processes often have plenty of perturbations because there is a loop startup for each batch and changes in the loop set point and output by the batch sequence. New closed loop process identification tools such as DeltaV Insight can do a good job of taking advantage of these batch opportunities. Continuous processes time often run at the same set point long periods of time and require a periodic injection of a pulse into the output. Fortunately, the size and duration of the pulse can be rather innocuous in most cases.

(12) Model predictive control is not suitable for batch operations - the reason frequently given is that the process is too nonlinear but that's old news. The world of industrial process control is nonlinear. The real issue is more the one direction integrating response for bioreactors and some chemical reactors. If you make a translation of the controlled variable from composition to slope of the composition profile, an MPC can control a trajectory of a key component over a key portion of the batch. While the MPC applications in continuous processes dominate the literature, there have been successes in batch temperature and composition control with far greater benefits (e.g. 25% increase in capacity by 25% reduction in cycle time).

(13) Rate is more trouble than it is worth - don't try controlling a severely exothermic reactor without rate unless you like exercising the plant relief system and alarm system. In general, for temperature control, rate should be set equal to 1/5 the process time constant or thermowell lag, whichever is largest.

(14) You need to start and end at a steady state to tune a loop in manual - there is no steady state for integrating and runaway processes. Even self-regulating processes may be moving with the controller in manual from frequent upsets. The short cut tuning method in my Good Tuning - Pocket Guide works well for these less than ideal conditions.

(15) Process dynamics are in the process - the most common loops are flow and pressure and for these loops most of the dynamics are in the automation system (valve, transmitter/sensor, and the PID execution and signal filtering). The process delay and nonlinearity is negligible compared to that of a control valve and the process lag is negligible compared to measurement filters. The term "process dynamics" is a misnomer. A better term would be "open loop dynamics" so people would better realize the dynamics are often in the automation system. The reality is I can't get people despite 20 years of publications to think "open loop gain" instead of "process gain" and "open loop time constant" instead of "process time constant" , and "total loop dead time" instead of "process dead time." Maybe I need some catchy phrases like "don't blame it all on the process" or "the only loop with only process dynamics is in your college textbook."

Before I leave to enjoy a crawfish boil and Cajun music, here are some more myths.

(6) Loop oscillations can always be decreased by reducing the controller gain - too low of a controller gain can cause nearly sustained slow rolling oscillations in an integrating process (e.g. level or gas pressure) and instability in a runaway process (e.g. exothermic reactor temperature). Decreasing the gain makes the problem worse for these cases. There are also limit cycles that persist regardless of controller gain.

(7) Limit cycles can always be stopped by eliminating valve stick-slip - limit cycles can also be caused by output limits, IO card resolution limits, deadband in integrating processes and cascade loops, and extreme nonlinearities, such as the pH titration curve.

(8) The installed valve resolution and deadband meet catalog specifications - often tests by manufacturers are for hand tight packing at positions remote from the seating friction. Also, temperature and fouling can make the installed performance worse.

(9) The most accurate type of pH sensors are used most often - the most popular sensors are the ones that require the least amount of maintenance, such as references with solid electrolytes, even though these may require more time to equilibrate and have a more variable junction potential. The flowing liquid junction reference for the right materials of construction and electrolyte is generally the most accurate but the least used type of pH electrode in industry because of the need to pressurize and refill the reservoir.

(10) Thermocouples are faster than RTDs - while this would be true for a bare element, nearly all the installations in the chemical industry I have seen use thermowells. The fit, design, and materials of construction of the thermowell have a far greater effect than the sensor on the speed of response of the temperature measurement.

(1) A compressor shuts down
(a) The first out sequence indicates the compressor tripped on high speed
(b) A precipitous drop in suction flow followed by a rapid 1-2 second oscillation in suction flow preceded the speed deceleration from compressor shutdown
(c) The readback of actual surge butterfly position indicates the valve closed before the initial drop in flow.
(d) The surge set point flow controller set point was constant.
(e) The butterfly disc closed despite a controller output asking it to be open.
(f) The control valve is fail-open (inc-close) so a loss in signal or activation of the solenoid valve is not the cause
(g) Conclusion - the volume booster sensitivity and actuator size and type caused a butterfly disk instability at high flow

(2) A thermal oxidizer shuts down
(a) The first out sequence indicates the oxidizer tripped on high temperature
(b) A spike in natural gas flow occurred before the trip
(c) The natural gas set point was constant
(d) A readback of actual gas valve position indicates the gas valve position was relatively constant before the spike and started to closed after the spike
(e) The pressure transmitter upstream of the gas valve spiked high about the same time as the flow spike
(f) Conclusion - the natural gas pressure regulator upstream went open

(3) A pH tank has sustained nearly equal amplitude oscillations
(a) The pH oscillation amplitude stayed the same when the controller gain was increased or decreased*
(b) The pH amplitude changed for a different pH set point*
(c) A readback of actual valve position indicates the minimum change in valve position is 0.5% or alternately indicates a step in an actual valve position change always precedes the pH change.
(d) Conclusion - the oscillation is caused by the resolution limit (stick-lip) of the control valve which multiplied by the process gain is the amplitude of the pH limit cycle (a change in pH set point changes the process gain from the operating point nonlinearity associated with the titration curve)

(4) A column sump level has very slowly decaying oscillations
(a) The amplitude of the oscillation takes a day to decay
(b) Feed, steam, and reflux flows are relatively constant
(c) The oscillation is more persistent (decay and period slower) when the level controller gain is decreased
(d) Actual readback of level valve position matches the controller output within 0.05% a couple of seconds
(e) Conclusion - the controller gain is below the low gain limit (controller gain multiplied by controller reset time must be greater than 4 divided by the integrating process gain) A controller gain that is too high causes faster oscillations that would die out if the controller gain is decreased**

* - these controller tuning or set point changes provide affirmation but are not required to diagnose the problem

** - valve diagnostics confirm it is not a valve problem

Who is living with the process every minute? Who changes the feed rates or charges? Who changes the modes and set points of the control system? Who starts or stops batches or unit operations? In most plants, it is the operator, yet the displays and education of the operator haven't changed much in the last 20 years. We still have faceplates, trend charts, and digital values of process variables, and changing or flashing colors or shades. We still have minimal operator training based more on tiebacks and interface familiarization than on first principles and process understanding.

If the operator knew the yield and cost per pound of product for the last eight hours of each shift, the operator could be more recognizant and probably more competitive. This could be achieved by flows that are synchronized, shift totalized, and ratioed with dollar amounts assigned for each flow. Consider a reactor and an 8 hour shift. Here the total flow of each reactant and utility for the last 8 hours would be ratioed to the total product flow for the last 8 hours for each shift. Each flow total would be multiplied by the cost of the stream ($/lb) to provide cost to product ratios for the last eight hours. The reactant and utility flows could be delayed to match them up time wise with the product flow. The use of totals for the last 8 hours reduces the accuracy requirement of this synchronization besides decreasing noise. The use of ratios decreases the effect of production rate on metrics. Also, changes in ratios offer keys to tracking down disturbances and changes in concentrations of feeds (e.g. raw materials, intermediate, or recycle streams). Both totals and ratios for each shift could be indicated. Shift metrics could be treated similar to batch metrics where each shift is like a different piece of equipment running the same batch process. The shift metrics could be plotted similar to batch metrics.

For waste pH systems, it would simply be the total reagent flow ratioed to the total effluent flow ratio for the last eight hours. I developed a real time virtual plant in DeltaV using this concept a couple of years ago to show the value of adaptive controller tuning for pH control. If you want a copy, contact your rep.

The concept could be expanded to use totals to cover the last week or month or the last "n" number of batches for each shift and all shifts.

If the operator could plot these ratios versus changes in operating points, what insight could be gained on process nonlinearity and for process optimization? What if the operator had XY plots, worm plots, and 3-D plots built into the operator graphics for all historized variables like what engineers generate in Excel and statistical packages?

When comparing the performance of similar plants in the USA and Belgium, it was found that the Belgium plants had consistently better yields. The Belgium operators lead the design of experiments and guided the process improvements. Could better online performance metrics and process training be the key for operators to perform roles of the increasingly scarce process and process control engineers?

One of the simplest and easiest techniques to evaluate and implement is set point feed forward. The maximum feedforward gain is the inverse of the process gain. You just need to make sure the process gain is converted to the same units used for the feedforward gain and only a fraction of the maximum is used as the actual feedforward gain to allow for nonlinearities, errors, and PID action. New adaptive controllers such as DeltaV Insight can find and schedule the process gains and hence the set point feedforward.

If the controller gain is large (> 1.0) and the controller structure has proportional action on error, set point feed forward has little value because there is already a sizeable step in controller output from a set point change. However, large dead times can cause low controller gains. Here, set point feedforward can get you to a set point much faster, which can be useful for loop set points driven by batch, cascade, or advanced control.

The "Two Degrees of Freedom" structure functionally can give you the smooth transition online between 4 choices of PID structure. The user can adjust the set point weights for proportional action and derivative action between zero and one.

If the set point weights are zero. there is no step or bump from a set point change for proportional (gain) and derivative (rate) action, respectively. Zero weights slow down the response to a set point change because you are relying on integral action. For processes with small time constants (e.g. flow, liquid pressure, liquid blending, inline temperature and composition, and sheet thickness), the response is smoother and the likelihood of an overshoot is reduced. However, for large process time constants (e.g. continuous vessel temperature and composition), the time to get to set point can be too long. For an integrating processes (e.g. batch vessel temperature and composition), the controller output must drive past the final settling value and is best achieved by proportional action on the set point change. The set point weights can be increased from zero to give an effect similar to a set point filter to work a compromise between a smooth and fast response.

For cascade loops, do we want to tune the secondary the loop for a set point response?

As you have probably surmised by now from previous blogs the answer to my question is unexpected. The typically desired set point response (smooth, gradual, with no overshoot) when applied to the secondary loop is not generally best for the purposes of the primary loop. A set point filter or weight on the secondary loop is counter productive. For cascade control, the secondary loop should respond immediately to the requests of the primary loop. In fact, a zero set point weight on proportional action makes the cascade response worse than if the cascade was eliminated. This assessment does not take into account the beneficial compensation of nonlinearities and feedforward offered by a secondary loop.

While the ability of a primary loop to reject load upsets is affected by a set point weight or filter on a secondary loop, this is not the case for the primary loop or a single loop assuming these loop set points are constant during the load change.

In my December 18 blog "Linear in a Nonlinear World" we discussed the use of signal characterization to compensate for the installed characteristic of the control valve where the valve gain depends upon the operating point on the control valve characteristic. In part II we are looking at the use of signal characterization to compensate for a nonlinear process gain by translation of the original nonlinear process variable to a new linear one to enable adaptive controllers to better focus on other nonlinearities such as feed flow. Here in part II the process gain depends upon the operating point of the process variable. Examples of this translation to a new controlled variable are:

(1) Conductivity to % acid, base, or salt concentration
(2) Column top temperature to % reflux demand
(3) pH to % reagent demand

For conductivity, there is a peak in a plot of conductivity versus the acid, base, or salt concentration. The new process variable scale must be on one side or other of the peak. There is uncertainty in the exact location of the peak. If the operating point were to cross the peak, the process gain would go to zero and then change sign, which is disastrous to a control loop. The operating point must steer well clear of the peak.

For all of these examples, concentrations of other components in the feed can shift or change the shape of the curve but often the translation is better than no compensation at all for the process nonlinearity. For conductivity and pH, the effect of process temperature based on lab samples should be part of the calculation. For temperature, the effect of column pressure should be included (e.g. shift in boiling point with pressure).

The implementation involves first plotting the original versus the new process variable. For the examples noted this would be conductivity versus ion concentration for various temperatures, column temperature versus % reflux to feed ratio for various pressures, and pH versus % reagent to feed ratio for various temperatures. Since you are getting the X axis from the Y axis (the opposite of what is being done by the process), the data points for signal characterization are entered as Y,X pairs with a nonlinear bias to Y from a fit to the shift in the family of curves. Since the Fieldbus signal characterizer allows variable space of data points, closer points are used in the area of greatest curvature near the set point. This translation must be done for both the set point and the process variable. The original and new set points and process variables must be displayed and historized.

The benefits are most noticeable in pH loops because of their extreme sensitivity nonlinearity, and rangeability where changes in process gain of 100:1 and of reagent demand of 1000:1 are routine. Signal characterization has been shown to make dramatic reductions in startup time by the loop's recognition that the acid or base reagent flow is really decades away from set point. It also prevents pH from zipping right through the neutral point (e.g. 7 pH) and banging between the flat portions of the titration curve, offering a settling time where there was none. The characterization restores the process time constant by slowing down the excursion rate and helps a continuous pH loop look more self-regulating by removing the acceleration from movement to steeper slopes on the titration curve. Thus, you see and realize the benefit from an investment in a well mixed vessel where the residence time is a process time constant that slows down concentration disturbances as discussed in blogs from the past few weeks.

There are some issues besides inaccurate curves and confusion in the operator interface. If your set point is always on a flat portion of the curve and the control system can keep the operating point close to the set point for the largest disturbance, the benefit from linearization is minimal. Additionally, if an excursion to the steep portion of the curve represents an extremely undesirable situation for equipment or environmental protection, then the elimination of the overreaction of the loop by removal of the acceleration through linearization may be the wrong thing to do even though it reduces overshoot and wasted reagent when returning the pH to its set point.

While you increase the dead time from valve dead band and resolution limits when the set point is on the steep part of the curve because you are slowing down the rate of change of the process variable and the overreaction of the controller output, this normally is much less important then the suppression of oscillations. The increase in dead band for operating points on the steep portions of the valve characteristic can be a concern for control valves because there is usually no stability issue from the much less severe nonlinearity of a valve.

These and other considerations and an application for pH control are shown in the attached file on "Linear Reagent Demand Control" which is an excerpt from my ISA pH Web Seminar at 2:00 EDT on May 16.

Linear Reagent Demand Control

I conclude with a top ten list that will appear in a future "Control Talk" column.

Top Ten Reasons Not to Use Linear Reagent Demand Control

(10) How do you know it is a pH loop if it is not oscillating
(9) You can better see if the pH sensor is still alive
(8) You can better tell if the operator is still alive
(7) You like bang-bang control
(6) Gives you chance to try out the manual mode
(5) The titration curve from the lab shows a straight line through the set point
(4) You like seeing the full effect of valve stick-slip
(3) Retuning loops is job security
(2) You can eat more doughnuts while waiting for a loop to startup and settle out
(1) Linear loops are for wimps

I just completed today a World Batch Forum (WBF) Webcast on Process Analytical Technology (PAT). The Webcast was fun and I can see where it opens up a whole new avenue of education even though the technology is not quite as far along as I expected. The Webcast went well thanks to the help of Deb Franke and Ed Guinn at Emerson Process Management and Mike McEnery (committee chairman for the WBF Webcast & Education Committee). I would encourage anyone doing this for the first time to do a pretest and trial run with the same equipment and in the same room used for the Webcast with two PCs and the help of audio and Web people. One PC is in the normal view to see the Q&A pane and provide faster navigation between slides. The other PC is in the full screen presentation mode. It is also important to realize that custom animation is not yet consistently feasible for a webcast due to variations in internet connection speeds and there are compatibility issues between Internet Explorer 7.0 and "Live Meeting."

This WBF PAT Webcast was based on the book New Directions in Bioprocess Modeling and Control. You can check out a review of the book by Control magazine editor Walt Boyes in his March 13 blog http://waltboyes.livejournal.com/207809.html

The following questions and answers may be instructive:

What are some examples of "near" and true integrators for batch operation?

The classic true integrator is level where the rate of liquid mass accumulation in a batch (level ramp rate) is proportional to the feed rates.

Gas pressure in the head space is a "near" integrator when the change in drop across the vent valve from a change in head space pressure is small compared to the normal pressure drop. Also, since the process constant is much larger than the process dead time, the open loop response looks like a ramp in the control region. If the drop across the vent valve becomes critical, the gas pressure becomes a true integrator because a change in pressure does not cause a change in vent flow.

For liquid temperature and composition, there is no discharge flow during the part of the batch of interest. Consequently, there is a loss of self-regulation inherent in continuous processes. For a change in temperature, there is change in temperature drop across the heat transfer surfaces (e.g. jacket), but this is small compared to the normal drop. Like the gas pressure loop, the process constant is much larger than the process dead time for the temperature loop. Finally, the magnitude besides the relative size of the process time constant is very large making any steady state beyond the time frame of interest.

For pH and substrate control, as the reagent or substrate is consumed (e.g. ammonia and glucose), the response is a "near" integrator from its large process time constant although the nonlinearity of the titration curve may cause the response to accelerate or decelerate for increases and decreases in pH, respectively.

Normally there is a peak in the plot of biomass growth rate or product formation rate versus pH, substrate, or temperature. Deviations from the optimum operating conditions can alter the metabolic rates enough to change the reagent demand and cause a delayed and very slow secondary effect in the same or opposite direction of the initial change.

How much wireless communication delay can I have before I see degradation in fermenter control?

Let's assume there are no aliasing or jitter issues communication delay so we can focus on the effect of an increase in lop dead time on loop performance.

Dead time dominant loops do not have as much leeway as loops where the process time constant is greater than the dead time but a communication delay that is less than 20% of the existing dead time is normally within the variation already seen from the many sources dead time so this is a reasonable rule of thumb. This allowable additional dead time is quite small for secondary flow and speed loops and depends heavily upon the module execution time and final element resolution.

For "near' or true integrators you can introduce an interval up to 50% of the existing dead time for a controller that has a Lambda factor of one (Lambda equal to the process time constant). This permissible additional delay is quite large for the slow primary fermenter loops.

When should a batch MPC for production rate optimization be turned on?

The MPC should be turned on when the concentration and rate of change of the concentration becomes significant. In the example given, the MPC was turned at about the peak in the product formation rate so the set point track PV feature could capture the best rate for the batch and try to hold it until the end point was reached. There could be a separate MPC to first maximize biomass growth and then to maximize product formation rate.

What are some other examples of MPC used for bioreactors?

Amgen at the 2004 Emerson Exchange and Rutgers in the Control magazine August 2004 issue showed the use of MPC for pH and DO. In this blog site we discussed the setup of an MPC to eliminate split ranged controller outputs and the associated limit cycling around the split range point. The MPC is documented in the Advanced Application Note 002 titled "MPC Implementation Methods for the Optimization of the Responses of Control Valves" http://www.modelingandcontrol.com/repository/AdvancedApplicationNote002.pdf

How can I get enough batch data for batch analytics?

Best bet is to run bench top trials that have an industrial DCS and data historian with automated lab entry. Match up the virtual plant to these profiles and then use the virtual plant to generate more data.

How can I predict batch end points?

You could run a virtual plant faster than real time out to completion of the batch. If you have MPC helping to maintain the slope of the batch profile, after the peak in the product formation rate you can multiply the slope by the remaining batch time and add it to the product concentration from the last sample. You can keep updating this prediction after each lab sample. If the slope is variable, you could do the prediction piece wise based on a reference profile. If none of this is possible, you could simply bias the predicted batch profile by the difference between it and the current profile much like the simple feedback correction of the future process trajectory for MPC. A prediction is generally not viable until the concentration and rate of change of the concentration are both significant.

New adaptive controllers are coming soon to your control room to individually schedule the tuning as a function of any variable. So given all the choices, what process variable generally works best taking into account what we have recently learned about mixing and process dynamics?

The short answer is controller output for continuous processes and level for batch processes. Of course this is just a best guess and doesn't replace the need to test any variable or calculation used to set controller tuning.

If you are curious as to how I arrived at the above conclusions, read on.

Let's consider first the flow loop. Nothing complicated here, we just need to remember that the controller gain is inversely proportional to the product of the valve gain, process gain, and measurement gain for a control loop. The valve gain is generally nonlinear since it is the slope of the installed characteristic of the valve. For flow, the process gain is one (how lucky can one be). Just like for other loops, the measurement gain is simply 100% divided by the scale span of the PID. So the only nonlinearity in a flow loop (barring a missing square root extractor for a head meter) is the valve. A good choice for the controller gain would be to schedule it as a function of controller output (position on the installed characteristic of the valve). The reset time is set equal to the largest time constant in the loop. For liquid flow, the process time constant is only 50 to 100 milliseconds, which is generally smaller than the effective time constant associated with the valve, measurement or DCS. Thus, the reset time depends upon on the slowest part of the automation system. If a signal filter in the DCS becomes the largest time constant in the loop, the reset time is approximately the filter time setting. For aggressively tuned flow loops or big valves, it is a good idea to enable the Dynamic Reset Limit and use the read back of actual valve position as the external reset to prevent the PID reset action from outrunning the speed of the valve.

Let's further consider that we put this flow loop to good use as a secondary controller for cascade control where the primary loop is level, temperature, or concentration. A secondary flow loop removes the control valve nonlinearity from the primary loop and makes the primary loop ready, willing, and able to use flow feedforward (e.g. a flow ratio corrected by the output of the primary loop).

Finally, let's focus on volumes with different types of mixing. The two major types are inline (e.g. pipeline) volumes that have only some radial mixing from bafflis or pipe fittings and vessel (tank) volumes that have axial mixing as the result of an agitator, eductor, and/or sparger. The inline systems have a uniform composition and temperature in a cross section but not along the length of the pipeline. The process dead time is much larger than the process time constant. These inline volumes provide little to no smoothing with respect to time and are called "plug flow." Well mixed vessel volumes have a uniform composition and temperature throughout the vessel volume. The process dead time is much smaller than the process time constant. These vessel volumes provide maximum smoothing with respect to time and are called "back mixed." For batch operations, these "back mixed" volumes have an integrating response. The following figures show the self-regulating response for "plug flow" and "back mixed" volumes for continuous processes and the integrating response for batch operations.

Mixing Effect on Open Loop Responses

For plug flow volumes, the residence time (volume/flow) becomes a process dead time making the dead time inversely proportional to flow. The process gain is also inversely proportional to flow. As a result, the primary controller gain for composition control is proportional to flow and flow squared, if the Lambda is set equal to a factor of the integral time and dead time, respectively. Since most applications set Lambda equal to multiple of the integral time, controller output would be a good choice again for gain scheduling. Examples of plug flow systems are pipelines, static mixers, desuperheaters, sheet lines, web lines, extruders, and sheet lines. The process dead time is larger than the process time constant in these primary composition loops. Like the secondary flow loop, the integral time depends upon the valve, measurement, or filter time lag.

One word of caution, these primary loops may not be much faster than the flow loop, so the primary loop may have to be tuned to be slower than expected to avoid violating the cascade rule (primary loop should be at least 4 times slower than the secondary loop). Using gain scheduling in the flow loop helps makes make the flow loop faster, which reduces the need to make the primary loop slower.

For back mixed volumes, the residence time (volume/flow) almost entirely becomes a process time constant for composition control. If the primary loop's integral time is set to be a factor of the time constant, it is then inversely proportional to flow. This assumes the injection delay associated with the dip tube or pipeline feed is small (not a good assumption for small additive or reagent flows). The process gain is also inversely proportional to flow. The process dead time is the turn over time and is relatively fixed for a constant agitator speed. Good gosh, controller output is again a good choice for scheduling tuning settings. Examples of back mixed volumes are agitated reactors and fermentors (except mammalian cell). Most agitated blend tanks, crystallizers, and evaporators behave more like a stirred reactor than a pipeline. The dynamics can be approximated by splitting the total volume into a small plug flow volume combined with a large back mixed volume.

For pH, I would use signal characterization to translate the controlled variable from pH to reagent demand based on the titration curve. This makes it just a reagent concentration loop whose process gain like other composition loops is inversely proportional to flow, which means I can again schedule the controller gain as a function of controller output.

Hmm, I wonder what the default variable will be for scheduling controller tuning for these self-regulating loops. Could it be controller output?

Composition loops of large back mixed volumes and batches have a "near" and true integrating response, respectively. The process gain is inversely proportional to liquid volume. For liquid temperature, the change in heat transfer surface area covered by liquid may cancel this effect out. For gas pressure, the process gain increases as the liquid level decreases. So for integrating loops, the variable for scheduling tuning is often level.

Most of the literature makes valve nonlinearity seem bad or just plain ugly. However, if you take into account process dynamics and valve stick-slip, you might actually consider valve nonlinearity as good in some applications. So before we continue on to a discussion of the implications of mixing on tuning next week, let's consider the role played by the valve.

If we consult the last page of Advanced Application Note 4, we see the controller gain is proportional to the process time constant and inversely proportional to the open loop gain and dead time for maximum disturbance rejection. If we further consider that this same note shows that the open loop gain is the product of the valve gain, process gain, and measurement gain, we have the principles to be more intelligent in our valve trim choices and gain scheduling. Most people call the "open loop gain" a "process gain" even though it depends upon the valve flow characteristic and measurement scale besides the process.

The equal percentage trim has an inherent flow characteristic whose valve gain (curve slope) is proportional to flow. A lot has been published on how bad this is for controller tuning. For flow loops, this is true, but for temperature and composition (including pH) control in pipelines, static mixers, and heat exchangers (plug flow), this valve gain helps cancel out the process gain that is inversely proportional to flow. If you further consider the dead time is inversely proportional to flow, this valve nonlinearity is good.

How about well mixed vessels? Well the valve nonlinearity does the same thing so far as canceling the effect of flow on the process gain. However, since the residence time becomes a time constant rather than a dead time for a back mixed volume as discussed last week, the numerator for the controller gain is inversely proportional to flow so the benefit of canceling it out of the denominator is not such a good deal. Now the dead time from mixing is set by the turnover time and is only a weak function of feed flow. If there is a pipeline or dip tube with a significant transportation delay or poor mixing, then we are back to the case of the dead time being inversely proportional to flow. So for vessels, an equal percentage characteristic may be good or bad from a controller gain view point. There are other considerations that make this trim choice the right choice.

While a linear trim supposedly has the greatest rangeability based on best conformity of the flow coefficient to a designated curve, if you consider the effect of stick-slip which is greatest near the seat, the equal percentage trim has the best turndown (smallest controllable flow), which is more important to me than conformity of the trim characteristic. If you also consider that this trim can deal with the diminishing valve pressure drop caused by higher piping system pressure drops at higher flows and can thus prevent the installed characteristic from flattening out at large lifts, you have clues as to why an equal percentage trim is so popular.

In my book, quick opening trim is mostly ugly because the valve gain is so high near the seat it accentuates stick-slip and the process gain nonlinearity for temperature and composition control. This trim also hastens the premature flattening of the installed characteristic from a diminishing valve drop. However, for liquid pressure control, the process gain is proportional to flow so you can make a case a quick open trim is good for this loop. In fact pressure regulators tend to have this characteristic. Also, for anti-surge control and pressure relief, quick opening trim is used to establish a vent flow as quickly as possible.

Finally, I have to admit quick opening trim can help flush solids out of the seat. However, I would rather preprogram some kicker action in the DCS configuration to provide this burst so I can have a good flow characteristic to work with. I can also switch to pulse duration control for small controller outputs to prevent small flow areas that would plug.

If you ever wondered if you are agitated enough, then this blog may help stir up some thoughts. Specifically, how does the relative type and degree of mixing in the plant design affect your job as an automation professional? If the process engineer tells you the project is installing a radial instead of an axial agitator, do you shudder with profound disappointment or just utter a sigh? What if the agitated vessel is replaced with a static mixer? Do you turn the project over to the intern and take early retirement?

I will first continue my role in life as a pH stalker but then move on to other processes and more general considerations.

I became sensitized to mixing because of the extreme sensitivity of pH loops to plant design. I have talked before about how pH processes are the best known indicators of valve stick-slip, particularly near the neutral point, A control valve resolution of 0.1% (exceptional by any standards) can cause a pH swing that is more than noticeable.

Similarly, pH processes are the best known indicators of the uniformity of mixing. Concentration fluctuations in hydrogen ion concentration as small as 0.0000001 normality can cause noise with a 1 pH amplitude at the neutral point. The only study I have seen on the mixing required for pH was a cop out because it was done at 4 pH where the sensitivity (slope of the titration curve) was 1000 times less.

Additionally, the consequences of mixing delays are most severely felt in pH processes. An increase in loop dead time increases the excursion in pH for a given load upset, which increases the nonlinearity seen by the control loop. The operating point nonlinearity for pH can be extreme. The process gain is proportional to the slope of the titration curve and inversely proportional to the total flow and can change by a factor of ten for each pH unit deviation from the neutral point in a strong acid and base system.

The game in a pH loop more than any other loop is to minimize noise and dead time.

For other processes, the required degree of mixing is a lot less, but whether you are talking about temperature or concentration control, poor mixing still shows up as more noise and more dead time. The percent nonuniformity from mixing multiplied by the conversion factors to get to percent of the measurement scale gives you the noise amplitude seen by the controller algorithm. The dead time from mixing in a well designed agitated vessel is roughly the turnover time, which in turn can be approximated as the liquid volume divided by the sum of the feed flow, recirculation flow, and agitator pumping rate. The average dead time is ideally more like ½ of the turnover time whereas the maximum dead time is the turnover time. This helps explain why you see ½ to 1 times the turnover time in the literature as the mixing delay. Since we are generally short on our dead time estimates because there are so many sources of process dead time, I don't like to skimp on the mixing delay. See my Nov 20 2006 blog "Without Dead Time and Disturbances I Would Be Out of a Job" in the Plant Design category for a list of sources.

Unfortunately, the above assumes the liquid height is about the same as the vessel diameter (unless there a multiple levels of impellers), baffles every 90 degrees to prevent swirling, and an axial agitator to pull down liquid (not air) from the surface. If a camera shows the surface not being broken or swirling, or there is foaming, you can say "Houston we have a problem", particularly if the vessel vendor or design firm is in Houston. In processes that cannot withstand high agitation because crystals or cells may be broken by the blades, there may be an opportunity to increase the recirculation flow and use a jet or eductor to amplify the effect of the flow (e.g. jet fermentors).

Bob Heider, adjunct Washington University professor, wisely pointed out that baffles cannot be used for biomass, crystals and particles when the baffles cause the solids to dam up or break up. Bob also provided the following memory dump on agitation.

Agitation Info

A bigger potential source of dead time is the injection delay from dip tubes for small manipulated flow (e.g. nutrient, reagent, reactant, or additive). The normal design practice is to have a robust sized dip tube go about halfway down the liquid to the impeller. Unfortunately, this creates a dead time when the manipulated flow is shutoff for a prolonged period of time that is the submerged dip tube volume divided by the flow. For example, just a gallon volume will cause a dead time of 1 hour for a 1 gph flow when the control valve reopens. There can be an even larger dead time because to see the final effect of stopping the flow, you have to wait till the concentration inside the dip tube drains and migrates into the mixture in the vessel. Various method of reducing injection and mixing delays are discussed in the ISA book Advanced pH Measurement and Control, 3rd edition, 2005.

This brings us to one grand generalization. For concentration changes, the residence time (volume divided by flow) becomes a process dead time for a pipe but becomes a process time constant for a well mixed vessel. Check out next week's blog for the effect on tuning and loop performance. In the mean time, stay agitated.

My favorite "Far Side" cartoon has Einstein at a chalk board full of derived equations ending up with the ultimate equation "time=money." In my mind, the negative free time of the process control engineer places some doubt as to whether this endangered species still exists. There have been sightings but the uncertainty principal says we can only ascertain their location or function but not both.

Experimental models do a good job of minimizing the time and expertise required of process control engineers by not relying upon process knowledge. Since these models are identified from test data, they are consistent with the ultimate goal of matching reality even if process understanding lags behind. Each technique excels at addressing a particular aspect. For example, Neural Networks (NN), Projections to Latent Structure (PLS), and Model Predictive Control (MPC), excel at identifying the nonlinear, interdependent, and dynamic, respectively, nature of process inputs. The strong point of one method is often the weak point of others and in the end somebody with some sort of process understanding should check to make sure the models make physical sense. There are several watch outs. For example, avoid extrapolation by a NN outside of its training data range because nonlinear relationships can take off exponentially. Since PLS and MPC assume linearity, you have to be careful about deviating too far from an operating point to the point where turndown and startup may require the identification and switching of different models. NN and PLS don't try to model the process time constant or integrating process gain, so there is a model mismatch for well mixed volumes where the residence time translates to a process time constant or a "near" or "real" integrating process gain. Also, NN and PLS are often sold based on just throwing existing historical data at them ignoring the transfer of variability by closed control loops and not perturbing process inputs. The richness of the dynamics, the rangeability, and the identification of cause and effect suffers. What has been so important to the success of MPC, seems to have been lost

What about all the other types of models?

Tiebacks are very attractive because they initially require hardly any effort. They can be automatically generated from the configuration. These are great for control system familiarization and interface improvements (e.g. operator training and critiquing of graphics) and I/O checkout. They can be used to mimic the process response by the heuristic customization of ramp rates triggered by piping path logic to test out the configuration, particularly important for complex continuous and batch control systems.

Finally, there are the models based on chemistry and physics (not necessarily popular subjects). Very sophisticated software has been developed to provide a graphical flow sheet simulation of processes. Unfortunately, these generally require a sophisticated budget and user. Most of the big players focus on continuous steady state operation, the traditional realm of chemical engineering programs. Separate special purpose packages are typically required for batch. My experience with "state of the art " process modeling software is that they do a good job of process design but are not as good as you might expect in showing the process dynamics especially considering they carry the label "high fidelity". The process gain is off because the installed characteristic of the control valve and measurement scale are not included, the process dead time is too small because transportation and mixing delays are missing, and the process time constant is too small because thermal lags and jackets/coils are missing. To top it off, the trends are way too smooth because there is no mixing or sensor noise and no limit cycles from control valve stick-slip or backlash. For more enlightenment on the issues with dynamic process simulators see the Control magazine August 2005 article titled "The Light at the End of the Tunnel is a Train (Virtual Plant Reality)".

When you sit back (something I am getting better at being partly retired) and look at the whole picture, it seems fractured.

Why aren't there basic generic first principal models that focus on the process dynamics without getting bogged down in the complexity needed for process design? Why aren't there hybrid models that take advantage of the best of what each method has to offer? What would we call these models that provide the type of fidelity needed for process control? Are we stuck in a rut because each expert thinks their particular method is best? Are there people with broad enough skills and attitude to pull it off?

Control systems assume linearity. Unfortunately the world is basically nonlinear. For the next few weeks we are going to explore how gains, process time constant, and dead times change with plant design and operating condition. This week we start out looking at valve gains.

A plot of the flow versus valve position (installed characteristic) of most control valves is nonlinear. Here the slope is the valve gain. If we were to plot a process variable versus this flow, such as temperature or composition, it would also be nonlinear. Here the slope is the process gain. These are called operating point nonlinearities. If the process variable stays close to its set point, the slope doesn't change much. Thus, for a constant set point, minimal dead time, and good tuning, the process nonlinearity is not much of an issue. On the other hand, the control valve may have to move a lot to achieve tight control. The loop is more likely to see the nonlinearity of the control valve. Generally the slope of the installed characteristic gets too flat at low and high positions. Entech published a gain specification that the % flow divided by % signal should be between 0.5 and 2.0 (a gain change of 4:1). The following examples of installed characteristics show that the throttle range is shortest for a butterfly valve and longest for a sliding stem valve. For a detailed discussion of these figures see Chapter 2 of Advanced Control Unleashed.

Valve Gains

The rangeability statements by valve manufacturers are defined in terms the uniformity of the inherent characteristic. These statements do not take into account a gain specification, an installed characteristic, or the increased stick-slip at low valve positions from friction of the seating and sealing surfaces, particularly for tight shutoff valves.

A signal characterizer block can be inserted between the controller output and analog output block to compensate for the nonlinearity of the control valve gain. The characterizer is set up to calculate the % flow from % position (the Y axis from the X axis of the installed characteristic). The input signal to the control valve is now % desired flow rather than % desired position. This can confuse operations and maintenance if not adequately documented and displayed. The accuracy of this gain compensation depends upon the knowledge of the system pressures and friction losses that affect the pressures at the inlet and outlet of the control valve. Software can predict the installed characteristic but this is done typically offline with manual entry of data. There is an opportunity for pressure measurements upstream and downstream to provide better compensation of the valve nonlinearity besides facilitate the monitoring and trouble shooting of disturbances. Many times I wished more pressure transmitters were installed to figure out why a loop just got clobbered, but this is another story.

Another practical issue relates to valve stick-slip and backlash, whose effect and compensation we alerted readers to in our Dec 4 and 11 blogs. For operation on the steeper portion of the installed characteristic, the characterizer makes the change in signal to the control valve smaller. Thus it takes longer for the signal to work its way through the resolution limit and dead band. However, for operation on the flatter portion of the installed characteristic, the change in the control valve signal is larger reducing the dead time from the resolution limit and dead band. If you ever waited for the controller output to work its way along the upper flat portion of a butterfly valve characteristic for a process unit operating at or beyond its design limit, you can appreciate the acceleration offered by the signal characterizer. Of course, at some point you just run out of valve and need to take a look at the pump and piping system design besides the valve size.

How can we get rid of dead time in our loops so we can be rich and famous by Friday? PID controllers with dead time compensation are reported to eliminate dead time in terms of a controller seeing the effect of changes in its controller output. For set point changes where all the controller needs to be concerned with is how its output responds to a new set point, the results are impressive for an exact knowledge of the process dead time. However, for unmeasured load disturbances at the process input, the only way to eliminate dead time other than an improvement in the plant or control system design is to accelerate the control system to the speed of light. So unless you have Scotty and Warp Drive on the Starship Enterprise, you are stuck with the dead time from the process equipment, piping, control valves, instrumentation, and digital devices. A dead time compensator can offer some improvement in load rejection by facilitating more aggressive tuning of the PID but with a considerable risk of oscillations from an inaccurate dead time.

If you don't have time for the details or just want to cut to the chase, here are the recommendations

(1) First improve the PID controller tuning before even considering dead time compensation. Setting Lambda equal to the maximum dead time (Lambda factor equal to the maximum dead time to time constant ratio) is effective for load disturbances at the process input if there are no extenuating circumstances.

(2) Add feedforward control whenever it is possible to measure or infer load disturbances at the process input.

(3) If there is economic justification for further improvement and the dead time can be updated within 25% accuracy for varying operating conditions, trial test and closely monitor a PID with delayed external reset for low dead time to time constant ratios.

(4) For loops with high dead time to time constant ratios, multiple manipulated variables, interactions, or constraints, consider model predictive control.

The ultimate performance achievable in terms of load disturbance rejection depends upon the dead time. In the "Theory" section of Chapter 2 of Advanced Control Unleashed equations are developed that show the minimum peak error is proportional to the dead time and the minimum integrated error is proportional to the dead time squared for unmeasured load upsets. How close the actual performance of a control loop comes to this ultimate performance depends upon PID structure, tuning, and enhancements. This blog focuses on the effect of variations in dead time on the performance and robustness of dead time compensation as an enhancement and Lambda as a tuning rule for disturbance rejection. The two predominant methods of dead time compensation studied here are the Smith Predictor PID and the PID with a delayed external reset.

The Smith Predictor was extensively documented in the 1970s. It provides a new controlled variable that is the response of the process variable to its controller output without dead time. It requires entry of three parameters commonly known as process gain, dead time, and time constant. The Smith Predictor uses these parameters to create models of the process from the controller output. In its most documented form, the Smith predictor subtracts a model of the process with dead time from a model of the process without dead time and adds the net result to the measured process variable to create a new controlled variable. If the model is perfect, the new controlled variable has zero dead time in terms of the controller seeing the effect of its own controller output. Since the maximum allowable controller gain is inversely proportional to dead time, the controller gain can theoretically be increased without limit for a perfect model provided you ignore extenuating circumstances, such as loop interaction, measurement noise, and final element dead band and resolution. One of the practical issues with the Smith Predictor is that the new controlled variable of the PID is no longer the actual process variable. The original process variable must be restored for the operator interface to the PID. Also, performance monitoring or trending must look at the original process variable rather than the new controlled variable used by the PID. Terry Blevins proposed in the 1979 ISA paper "Modifying the Smith Predictor for an Application Software Package" a multiplicative and additive correction of the process variable to deal with changes in the slope (gain) and intercept (bias), respectively in the process model.

The PID with a delayed external reset was informally presented in the 1980s and published in the early 1990s. It simply consists of putting a dead time (DT) block in the external reset. This method only requires that a single parameter commonly known as process dead time be entered as the dead time in the DT block. Terry Blevins documented in the early 1990s how the Smith Predictor for a particular Lambda tuning reduces to this PID with a delayed external reset.

The results presented here show that for a perfect model and the same controller tuning the PID with a delayed external reset performed better for processes with a small dead time to time constant ratio (time constant dominant), whereas the Smith Predictor performed better for processes with a large dead time to time constant ratio (dead time dominant). The Smith Predictor did not do as well for small dead time to time constant ratios because the control error seen in the controlled variable by the PID is much smaller than the actual control error in the process variable. In both cases, the improvement was not as impressive as the improvement gained from setting Lambda equal to the dead time rather than the time constant. Surprisingly the improvement in load disturbance rejection from dead time compensation was greater for processes with small dead time to time constant ratios. This goes against the conventional wisdom that the best opportunity for dead time compensation is for dead time dominant loops. The results can be explained in terms of the ultimate limit for performance of dead time dominant loops being lower. The reduction in the peak excursion from more aggressive tuning settings is negligible for dead time dominant processes because the peak error is essentially the open loop error.

Another startling result was how quickly a Smith Predictor erupted into rapidly growing oscillations in the controller output when the model dead time was more than twice the actual process dead time. The fast full scale oscillations in the controller output resembled on-off control. While it is relatively well known that dead time compensators are sensitive to model mismatch, the effect was expected to be gradual and thought to be more in terms of a model dead time being too small. The concern for rapid deterioration for a model dead time being too large was raised in Good Tuning - a Pocket Guide and was documented for model predictive control in Models Unleashed. While a PID with delayed external reset is also adversely affected by a dead time mismatch in both directions, this PID develops a small amplitude high frequency dither rather than a full scale oscillation in controller output for an excessively high model dead time. The consequence is less severe and may be adequately handled by the addition of a small dither filter inserted in the PID controller output, but this was not tested.

PID controller tuning for self-regulating processes without extenuating circumstances can develop oscillations when the identified (model) process dead time is too small. PID controllers with dead time compensation and model predictive controllers can develop oscillations when the identified (model) dead time is too large as well as too small.

In order to get the performance benefit from dead time compensation, the PID must be tuned more aggressively. In other words, a PID with dead time compensation will perform the same as a PID without dead time compensation if they are tuned the same. While the improvement in integrated absolute error (IAE) for load upsets from more aggressive tuning (higher controller gain and lower reset time) can be accurately estimated for a regular PID, the equation does not work well for a dead time compensator. Furthermore, a dead time compensator soon reaches a point of diminishing returns. For example, the improvement in load rejection of a Smith Predictor from a controller gain that is quadrupled may not be noticeable whereas for a regular PID, it normally results in a four fold reduction in IAE. It is important to remember there is a tradeoff between performance and robustness for any feedback controller in that as you make controller tuning more aggressive to improve load rejection you make the controller more sensitive to changes in the process gain, dead time, or time constant.

A nonlinear gain from the installed characteristic of a control valve has been widely discussed. However, the nonlinearity of the process gain of the temperature or composition response is the inverse and consequently the combined effect is less than documented when these loops directly manipulate a control valve. The variability of dead time is often larger than the variability of the process gain or time constant because the dead time is inversely proportional to a rate (e.g. flow rate or pumping rate or rate of change of a signal) and has many different sources (e.g. valve deadband or resolution, piping transportation delay, mixing delay, process lags in series, sensor lags, signal filters, and discrete communication or scan intervals). Thus, it is problematic to compute the dead time accurately enough to get the benefit of a dead time compensator.

In all of the following test results AC1 is always an uncompensated PID with Lambda equal to the process time constant (lag), which is equivalent to a Lambda factor of one.

The first set of test results illustrates the effect of different tuning. Here AC2 is an uncompensated PID with Lambda equal to the process dead time (delay), which is equivalent to a Lambda factor set equal to the dead time to time constant ratio.

Tuning Rule Test 1

The second set of test results shows how well a Smith Predictor can do. Here AC2 is a Smith Predictor PID with the gain doubled and the reset time halved after Lambda has again been set equal to the process dead time. In other words, this AC2 has twice the proportional and integral action of the uncompensated AC2 in the first set of test results.

Smith Predictor Test 2

The third set of test results shows how well a PID with a delayed external reset can do. Here AC2 is a PID with delayed external reset with the gain doubled and the reset time halved after Lambda has again been set equal to the process dead time. In other words, this AC2 has twice the proportional and integral action of the uncompensated AC2 in the first set of test results.

Delay Comp Test 3

For discussion of the test results and configuration, request from me a copy of the Advanced Application Note 003 titled "Compensation of Dead Time in PID Controllers."

If the total loop dead time was zero, you could set the controller gain as large and the reset time as small as desired. If there were no disturbances, you could simply sequence the controller outputs for startup, transitions, and shutdown. Process dynamics, controller tuning, and loop performance would be a non issue.

I once had a loop with zero dead time. I was studying the performance of my new algorithm for adaptive pH control in an Advanced Control Simulation Language (ACSL) program for my Master's Thesis. The larger I set the controller gain, the tighter the control I got. I was ecstatic. I was going to become "way famous". Then the let down - I had inadvertently turned off the dead time function. All I had left for process dynamics was a single time constant. The operating point nonlinearity of pH had no effect because I could stay incredibly close to set point. Since then I have seen tuning studies for a single time constant that beat to death a scenario where all the normal concerns are non existent. I decided to become sensitive to dead time especially since I could reduce my time on a pH startup by reducing dead time.

Control textbooks and studies tend to focus on set point responses ignoring unmeasured disturbances at the process input (e.g. load upsets). Special algorithms can be designed and tuned to prove a point. This may work well in simulations, aerospace, and hydraulic systems where dead time is either negligible or predicted/compensated and the servo response rules, but the real world of industrial process control isn't so kind.

The variety and variability of the sources of dead time and disturbances in process control is quite impressive. The following lists are just some major sources that come to mind.

Sources of Disturbances

1) Limit cycles (split ranged point discontinuity, resolution, and cascade dead band)
2) Interaction between loops
3) Slow secondary loops (cascade control)
4) Design limits (equipment operating limits)
5) Low residence times (e.g. undersized feed, recycle, surge, and waste tanks)
6) Manual procedures and manual valves
7) Field switches (e.g. on-off level control)
8) Activity (catalytic and metabolic)
9) Ambient conditions
10) Interlocks and sequences
11) Raw materials
12) Recycle streams
13) Startups, shutdowns, and product transitions
14) Fouling (e.g. process coatings) and frosting (e.g. crystal accumulations)
15) Parallel trains
16) Undersized cooling towers
17) Bored board operators
18) Shift change
19) Initiatives
20) Goal reviews

My worst experiences have been with undersized recycle, surge, and waste tanks. The residence time (volume divided by throughput rate), which is the process time constant, is so low there is not enough filtering of the changes in stream composition. Also, the level control on these tanks is forced to jockey the feeds to downstream operations to keep the tank from overflowing or running dry. Plants tend to avoid putting in the bigger tank to save money and reduce inventories when they need to debottleneck or push a process.

Sources of Dead Time

1) Discrete execution and communication interval
2) Analyzer cycle time (e.g. chromatograph)
3) Transportation delay (e.g. sample line)
4) Mixing delay (e.g. agitator, eductor, and sparger)
5) Injection delay (e.g. back filled dip tube)
6) Resolution limit (e.g. VSD, control valve)
7) Dead band (e.g. VSD, control valve)
8) Instrument time constants in series (e.g. sensor and signal filter lag)
9) Process time constants in series (e.g. thermal lags and residence times)
10) Lab samples (e.g. sample hold, processing, and analysis time)

Dead time is often inversely proportional to a rate and therefore a function of test conditions. The dead time from transportation delays, sample lines, sensor lags, and residence times in series is inversely proportional to flow rate. Mixing dead time is inversely proportional to agitator pumping rate or eductor flow rate. The dead time from dead band and resolution limits is inversely proportional to the rate of change of the signal (e.g. rate of change of process variable for measurement resolution limits and rate of change of controller output for valve dead band and stick-slip). The time it takes a measurement to get out of its resolution limit or noise band can be significant for level or temperature and depends upon how fast the process is driven to change and hence the step size in the controller output or set point. The dead time for control valves becomes just the summation of the pre-stroke dead time, discrete processing, and communication interval (all usually small) if the step in controller output is larger than the valve dead band or resolution limit. The dead time effect of dead band and resolution limits unfortunately does show up for unmeasured load upsets at the process input.

My intention is now to avoid any further dead time or disturbances to an evaluation of dead time compensators and model predictive control so check here next week for more fun than control engineers should be allowed to have with advanced control.

Last week we discussed the effect of disturbance timing on performance. This week we turn our attention to the location and speed of the upset and the Delay/Lag (dead time to time constant) ratio of the process.

Most control text books and papers show a step disturbance on the process output, which is the process measurement. This is the worst case scenario in that the disturbance fully hits the controller before the controller can take any corrective action. The abrupt change in the process measurement can cause a large step and bump in the controller output from gain and rate action, respectively. In some respects, this disturbance location is similar to noise. Conventional Lambda factors (>1.0) do well in helping a controller to not overreact to this disturbance.

Most control literature also tends to focus on a process where the delay (dead time) is comparable in size or larger than the lag (time constant). In these cases, conventional Lambda factors again give good performance and robustness.

I have often heard professors and operators say that a loop is terrible because it has a huge lag (process time constant). This is true for disturbances downstream of the process entering directly into the measurement. For a load upset (e.g. feed, utility, or ambient upset) into the process, the large process time constant (Delay/Lag < < 1.0) can provide incredibly tight control if a much smaller Lambda factor is used (<<1.0).

Most of the important loops I have worked on in the chemical industry (column or vessel composition, pressure, and temperature control), have disturbances on the process input and a Delay/Lag ratio much less than one. The book New Directions in Bioprocess Modeling and Control discusses how the interactive process temperature time constants cause the Delay/Lag ratio to be about 0.2 and how batch composition responses have a Delay/Lag ratio so small they look like they have an integrating process response.

Static mixers used for neutralization have a Delay/Lag ratio about one but the addition of the electrode time constant or signal filter makes the Delay/Lag ratio less than one. Poor reagent piping, injection, and mixing design and a large control valve dead band or resolution limit, can cause the delay to sky rocket. Large Delay/Lag ratios are often a symptom of poor plant/system design for chemical processes. On the other hand, there are processes, such as sheet or web thickness, and analyzers with large cycle times and transportation delays that make the loop very dead time dominant (Delay/Lag >> 1.0).

Feed composition, catalyst activity, metabolic pathway, and ambient temperature disturbances are generally very slow (upset lag of hours). Cooling water and steam disturbances can be faster depending upon system design (upset lag of minutes). Feed flow disturbances are much faster and generally reflect the response from reset action (upset lag of seconds). Step flow changes occur when pumps are turned-on and on-off (isolation valves) are opened.

As the upset slows down (upset lag increases), the peak error (maximum deviation) and integrated absolute error (total error) decreases but the fractional improvement in IAE from more aggressive tuning stays the same for loops with a large process time constant (Delay/Lag < 1.0) or increases for dead time dominant loops (Delay/Lag > 1.0). In a way, the upset lag performs a similar task to the process time constant in terms of slowing down the excursion rate of the process variable.

If there were no upsets, you wouldn't need a controller. You could just set the control valve to a predetermined position.

The following screen prints and excel file compares the performance of different types of tuning for various Delay/Lag ratios for load upsets that enter as process inputs. Lambda tuning does well for dead time dominant processes and can made to do as well as the Simplified Internal Model Control (SIMC) for lag dominated processes by the use of a Lambda equal to the dead time (Lambda factor equal to the Delay/Lag ratio). See our first blog on the Unification of Tuning Methods for more info.

Delay/Lag Ratio Test

Tuning Rules Results

Not discussed here is interaction and noise and how it reduces the desired degree of transfer of variability from the controlled variable (controller PV) to the manipulated variable (controller output). Also, not addressed is what change in the loop gain, delay, and lag (nonlinearity) can occur and does this change in dynamics make the loop too oscillatory. In general there is a trade off between performance and robustness whenever you are tuning a controller. Larger Lambda factors reduce the transfer of variability and improve the robustness of the controller. In summary, to evaluate a control strategy, algorithm, or tuning one should consider:

(1) Desired degree of transfer of variability from controller PV to controller output
(2) Amount of nonlinearity and its affect on variability
(3) Timing of disturbance
(4) Location of disturbance
(5) Speed of disturbance
(6) Delay/Lag ratio

How upsetting is this to dead compensators and model predictive controllers? For answers to this and more, stay tuned.

Terry described an innovative technique of using the PID block for combining split ranged control and valve position control (see Terry's Oct 16 entry). This technique eliminates the limit cycle at the split range point caused by the increase in nonlinearities and the decrease in resolution imposed by backlash, backfilled pipes and dip tubes, rangeability limits, and friction particularly associated with starting a flow from zero. This technique also eliminates the conceptual and tuning problems with valve position control. People tend to confuse valve position control with valve positioners or digital valve controllers. The tuning of the integral-only controller for valve position control is much more critical than most people realize to prevent interaction but provide a fast enough response to reject large load upsets. The best quantitative analysis I have seen on the severity of the tuning issues with "valve position control" is the article by Cheng-Ching Yu and William L. Luyben titled "Analysis of Valve-Position Control for Dual-Input Processes" (Ind. Eng. Chem. Fundam. Vol. 25, No. 3, 1986 pp 344-349).

Instead of a special network for PID control, a standard Model Predictive Control (MPC) block can be configured to eliminate the need for split ranged control and valve position control. The MPC is simply set up for two manipulated variables (MV), one controlled variable, and one optimization variable. The optimization variable is the manipulated variable that provides the finest control (e.g. set point of the fastest and most precise control valve or variable speed drive). The optimization objective is to gradually return the "fine" MV to a mid range (e.g. 50%) after helping the "coarse" MV reject a load upset or minimize overshoot of a new set point. To insure the optimization takes a back set to tight regulation and set point response of the controlled variable, the "penalty on error" (PE) of the optimization variable is decreased (e.g. optimization variable PE=0.1).

When the MV have different process dynamics, the advantage of MPC is greater. By the automatic identification and incorporation of the MV dynamics in MPC, better feedback, feedforward, and constraint control is possible. The longer term view of the MPC also makes it less sensitive to resolution limits. Additionally, the "maximum MV rate" parameter can be written to zero when the controlled variable is close enough to set point to eliminate the limit cycle from the "coarse" MV. The following white paper discusses in more detail this use of a MPC to eliminate split ranged control and valve position control. The article titled "A Fine Time to Break Away from Old Valve Problems", in the November 2005 issue of Control magazine provides more background and a perspective.

White Paper on Dual MV MPC