Modeling and Control

Recent blogs appearing on http://www.EmersonProcessXperts.com and http://www.controlguru.com discussing the practical value of process models and various controller rules motivated me to write the following for my “Control Talk” column scheduled for the November issue of Control magazine.

I think most astute control people can devise a case where the literal use of their favorite tuning method is better than another method. In the book titled Handbook of PI and PID Controller Tuning Rules 2nd ed by Aidan O’Dwyer there are over 400 pages of tables of tuning rules. My rules are cited 6 times (incorrectly for dead time dominant processes). Obviously the authors of these rules all thought they had something better to offer.

To help put it all in perspective, I offer the following Top Ten List.

Top Ten Reasons to Devise Your Own Tuning Rule and Simulation Test

10. Opportunity to present papers at your favorite conference (whoops - not possible this year at ISA since there are no sessions on traditional process control)
9. Material to start a blog site
8. Competitive edge to start a consulting business
7. Listing in a book on tuning rules
6. Method named after you (sorry Ignatius Michael Coolman, the IMC acronym is taken)
5. Simulations tailored to prove your point
4. Linear processes without control valves
3. Speed since the time to steady state is just a matter of seconds in your simulation
2. Simplicity by ignoring the prevalence, size, speed, and entry point of unmeasured disturbances in real processes and non-stationary behavior
1. Chance to discount industrial online software for controller tuning as just hearsay

What prompted this impromptu column was the realization that diverse tuning rules have a common basis. For example, the equation for controller gain from the Ziegler Nichols ultimate oscillation, Lambda self-regulating and integrating process, and Internal Model Control tuning rules when set for maximum disturbance rejection reduce to the Ziegler Nichols reaction curve rule. For this discussion, we are focusing on loops dominated by a single time constant so that the dead time to time constant ratio is less than 0.5. It is important to remember that maximum disturbance rejection corresponds to maximum transfer of variability from the process control variable to the controller output, which may not be the entire objective. The following files show the basis and importance of this unification and simplification of tuning rules.

Nov 2006 Control Talk Details

Process Responses to Change in Controller Output

Tuning Rule Equations and Relationships

Scan Time Effect on Integrated Absolute Error (IAE)

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.

The tuning of a PID control loop should be based on an accurate knowledge of the control parameter response to a change in the associated manipulated process input. If the process response is determined using values communicated from a controller to a workstation, then these communications may impact the identified process response. For example, the control network may limit access by the workstations to 1 sec samples even thought the PID and its associated IO may be executing in the controller at a much faster rate e.g. 100 msec. Also, the timing associated with values seen at the workstation may vary or be delayed with communication loading i.e. communications jitter. The combined effect of communications sample rate, delay and jitter introduces a degree of uncertainty into the identification of the process response. For very slow processes, the error introduced in the identified process response may have little impact on the calculated tuning. However, for fast responding processes such as liquid pressure and flow loops such uncertainty can lead to unsatisfactory tuning. In general, to provide best tuning in a distributed environment it is necessary to capture the process response at the point of control.

The influence of communication sample rate, delay or jitter may be eliminated by capturing the process dynamic response as part of the function block execution. This approach also naturally allows the process response (control and manipulated parameter) to be collected at the block execution rate. Such functionality may be introduced into a control system as part of the PID block or as a modifier to the PID function block. The concept of a function block modifier is something that Dennis Stevenson and I developed and patented a few years ago. For controller based implementations, function block modifiers may be used to minimize controller memory requirements since the modifier is instantiate and exists only when the loop is being tuned.

When control is done in the field using fieldbus devices, then the sample limitations, communications delay and jitter from the controller to the workstation can be eliminated similar to controller based PID. This can be implemented by designing the autotune block modifier to work with the proxy that represents the field PID in the controller. However, to eliminate the delay and jitter introduced by communications between the field device and the controller, it is necessary to capture the process response at the field device. For example, the latest Emerson fieldbus devices provide this capability. Through the use of these techniques, it is possible to provide tuning support that is independent of where control is done.

If you would like to read more on this topic, then you may find it helpful to get a copy of the paper, Autotuning in Distributed Environment, Blevins, Wojsznis, Thiele, ISA TECN1999 conference. Copies of this paper can be downloaded through the ISA web site. Also, Aadditional information on how to minimize the impact of communications sampling, delay and jitter on PID tuning is contained in the following:

Minimizing Communications Delay/Jitter in PID Tuning

When replacing an existing control system, the startup of the new system can often be made much smoother by re-using the PID tuning that has been established over the years with the existing system. If you are lucky, the form of the PID and units of the tuning parameters of the old and new systems match and you can just re-enter the tuning values directly into the new control system. However, the form of the PID and the units of the PID tuning parameters often vary between manufacturers and thus it may be necessary to convert the tuning values before they can be used in the new control system. If you find the PID form and units of the tuning parameter for the old and new control systems do not match, then you will need to convert the tuning parameter values to obtain the same dynamic response in the new control system.

If the converted loops only use PI control i.e. derivative (rate) gain = 0, then whether the form of the PID is series or standard will have no impact on the tuning. The tuning of the standard and series PID (for the same dynamic response) vary only when derivative (rate) is used in control. When derivative action has been used in the older system, then it is always possible to convert series tuning to the equivalent tuning for the standard form of the PID.

The conversion of existing tuning should always take in account for the units of the tuning parameters. Examples of unit variations you may encounter in commercial products are:

Proportional Gain: %/% or Proportional Band
Integral (reset): repeats/min, repeats/sec, min/repeat, second/repeat
Derivation(rate): minute, second

Accounting for difference in gain units can be done independent of the form of the PID. Conversion between two commonly used units may be done as following:

Proportional Gain (%/%) = 100/Proportional Band

If the form of the PID in the old and new system is the same or derivative action is not used in the loop, then it is only necessary to consider the units of the tuning parameters. For example, if the reset unit used in the older system is repeats/min and the new system reset unit is min/repeat, then the reset value for the new system is just the reciprocal of the old reset value:

Reset (min/repeat) = 1/Reset (repeats/min)

Often you may find it will save time to create a spread sheet to do the calculations needed to convert tuning parameters. For example, the following spreadsheet was created to support conversion from series form with units of Gain(%/%), Reset (repeats/min), Rate(min) to either standard or series from where the units are Gain(%/%), Reset (second/repeat), Rate(sec)

Example Conversion of PID Tuning

Over the last few years the process industry has expressed a growing interest in the application of wireless technology for field measurements. The ISA-SP100 Committee was established in early 2005 to set standards and recommended practices for implementing wireless systems in the automation and control environment with a focus on the field level. Also, various industry consortiums have been established to promote the use of wireless technology. For example, the Hart Communication Foundation has adopted the use of IEEE 802.15.4 physical layer for the implementation of wireless HART. At the ISA2006 conference the HART Communication Foundation sponsored a booth in which wireless transmitters from multiple vendors were demonstrated. However, one of the technical challenges that manufacturers face in applying wireless technology to process measurements is how to reduce the power consumption to a level that can be supported for many years without the need for external power.

If the information from a wireless transmitter is only used to monitor slowly changing measurement values e.g. levels in a tank farm then the transmitter power requirements may be minimized by simply slowing down how often a measurement is made and communicated. However, if the measurement is used in control applications that respond in seconds rather than minutes, then simply slowing down how often a measurement is made and communicated will negatively impact control response. To provide best control, it is necessary to reduce the latency in control response to setpoint or load disturbances. In a traditional control system it is possible to minimize latency by over-sampling the control measurement used in control. However, such an approach is not an option if your objective is to minimize wireless transmitter power consumption.

One means of reducing the need for over-sample control measurements is to synchronize the measurement sample with control execution as is done in Foundation Fieldbus device. Using some of the proposed wireless protocols, such as Time Synchronized Mesh Protocol (TSMP), it is possible to synchronize a measurement sample and its associated communication with control execution done in another node. However, the traditional approach of executing control 4-10X faster than the process time constant still will create communication loads that are a barrier in applying wireless devices in faster process applications.

A few years ago we started looking at techniques that could be used to reduce wireless communication load without sacrificing control performance. It turns out that for many applications a 10X reduction in communications load can be achieved by following simple rules in communication and by restructuring the PID control to use non-periodic sample values. Much of this work is documented in a paper that we presented at ISA2005, Similarity-Based Traffic Reduction to Increase Battery Life in Wireless Process Control Network. An overview of this work is provided in the following:

Control Using Wireless Transmitters

If you would like to learn more about the wireless technology, then a good starting point is Protocols and Architectures for Wireless Sensor Networks (Hardcover) by Holzer Karl and Andreas Willig.

One of the phenomena’s that I have noted over the years is that plant startups inevitably run over into a holiday. This seems to be especially true of the Christmas holiday. Being onsite can be very demanding work but it is also very rewarding. Many of the problems that we must address in control design are best understood and remembered if you have struggled with the problem in the field. However, sending a person to the field who has no plant experience should be done with caution. One of the practices we like to follow is to match a person with no plant experience with one who has worked in industry for some time. In this way, the experience person can act as a guide for the inexperience person and help bring him or her up to speed by setting a good example.

When going onsite, I have found it is wise to always ask what clothing is appropriate. For example, in many plants there is a requirement for steel toe shoes. In most cases the plant will expect you to bring steel toed shoes with you. Often any other safety equipment, such as ear plug, hardhat, gas mask, eye protection will be supplied by the plant. If you will be entering an area of the plant that requires you to carry a gas mask, then the plant may have restrictions that require the face to be cleanly shaved i.e. no beard. In nearly all cases it will be necessary to go though plant safety training and to pass a safety test before being allowed to work in the plant.

Your contact at the plant will be responsible for guiding you into the process area(s) that are to be commissioned. He can also help establish and communicate the rule to follow when making a change that will impact plant operations. Normally all changes that impact the process will go through the operator since he is ultimately responsible for the process operation. In most cases I have found the operator to be extremely knowledgeable about the process. One of the biggest mistakes an onsite person can make is not to respect or work with the operator. The most successful startups are the result of a team effort that includes the operator.

When working at a plant site, you are the guest of the plant. As such there are rules that should be followed. Many of the things that should be considered when doing onsite work are discussed in the paper “A Guide For Doing Onsite Work”, Jean Gibbs, Steve Thorp, Bill Keels, Chemical Engineering, February, 1990. The authors of the paper have many years of plant experience. If you have no plant experience, then you may find this paper helpful in preparing for your first trip to the field.

While approaching an optimum something can sneak up that catches the loop off guard. Because of the deadly foe dead time, by the time the loop sees and reacts, it may be too late, particularly if it was blind sided.

The classic example is compressor anti-surge control. When moving to a lower discharge pressure or recycle flow (lower energy use), an inaccurate surge curve or untimely dip in feed can cause a precipitous drop to zero or negative flow in 0.03 seconds followed by huge reversals in flow from surge. Just a few of these surge cycles can damage the seals enough to reduce the efficiency of an axial compressor.

Another impressive case can occur for exothermic reactor control. During the approach to a higher reaction temperature and higher reaction rate (lower batch time) a higher than expected raw material concentration or catalyst activity can initiate a runaway acceleration of temperature and reaction rate.

Not quite as dramatic but still important in terms of environmental scrutiny occurs for an approach to a lower pH set point in a static mixer (lower base reagent use). A strong acid upset from a batch operation or level switch controlled sump can cause a low RCRA pH violation within seconds. Even if it lasts a few seconds and therefore has no measurable affect on any decent downstream volume, it can be a recordable environmental violation. In one particularly large application, an interlock diverted the feed from the plant waste treatment system if the control system could not do its job and a violation was eminent.The open loop backup successfully eliminated nearly all of these diversions.

A much slower but still important situation can occur for a bioreactor. During the approach to a lower substrate (glucose) concentration with less substrate inhibition (greater yield), non-ideal mixing and a drop in substrate feed can trigger starved biomass to eat their own product (ugh).

In each of these cases, there is a significant undesirable event that requires a slow approach to an optimum and a fast recovery from an inadvertent excursion into an extremely undesirable operating region. This is particularly true for the first three cases, which involve environmental and property protection. The last thing you want is to test the adequacy of your interlock system or have a recordable incident.

(1) Compressor Anti-Surge Control
(2) Exothermic Reactor Temperature Control
(3) Static Mixer RCRA pH Control
(4) Bioreactor Substrate Concentration Control

An open loop back up has been applied in the above applications to assist but not interfere with the PID controller trying to do its job. The calculation simply consists of incrementing the controller output from its last value via the ROUT mode every module execution when the process variable has exceeded a limit. The increment is stopped when the process variable has recovered beyond the trigger point plus some differential (e.g. noise band). It is normally only activated only when the controller is not in manual. There is a bumpless transition to PID action when the open loop backup is cleared.

For surge control, the clearing of the open loop back up has a time delay to insure the compressor is out of surge and the control system is not fooled by a flow reversal.

In each case, the need to get out of trouble as quick as possible overshadows any temporary loss in efficiency.

Another strategy is to use a fast opening but slow closing of the control valves for compressor vent or recycle flow, reactor coolant flow, pH reagent flow, and bioreactor substrate feed. This can be implemented by putting a rate (velocity) limit on a decreasing signal to the control valve. This can be implemented in the analog output block via the SP_RATE_DN parameter, which in this block is active on the set point even when the block is in the CAS mode. To insure the reset action in the PID block is not faster than the rate limiting in the AO block, the “Dynamic Reset Limit” option must be enabled in the PID and the “Use PV for BKCAL_OUT” option enabled in the AO block to use the working set point for the BKCAL_OUT. Any rate limit will affect tuning and must be implemented before running any tests to identify dynamics or tuning settings. The strategy also works on variable speed drives for reagent and substrate feeds to allow a fast increase but insure a slow decrease in speed.

The attached screen prints show a simple example of an open loop calculation and enabling of the above options. As with any new technique, the configuration should be thoroughly tested by a realistic simulation before used in an actual application.

Open Loop Backup and Slow Closing Valve Option

Another option is to schedule the controller reset action to be much faster (reset time much smaller) when the process variable approaches a risky region to promote a fast recovery. There may be some overshoot of the set point but a slow approach back should prevent a second crossing to the more eventful side of the set point. Scheduling a drastically higher controller gain may not be a good idea because it can cause a bounce back toward the undesirable region from proportional action before the process variable even gets near the set point. Some new DCS software, such as DeltaV Insight, can automatically identify process dynamics and schedule the corresponding tuning settings.

Sometimes the open loop back up is called a kicker. The following is an excerpt from the January 2005 Control Talk column in Control magazine that describes a kicker used by Terry Chmelyk to reduce the number of feed diversions required to prevent the violation of an environmental constraint. It is similar conceptually to the previously described RCRA limit application, but here the measurement was conductivity instead of pH.

Terry: In a multi-effect evaporator system, we used built-in and integrated model predictive control (MPC) and optimization to reduce variability in the product density from 2.8% to 0.3% and increase throughput by 6 to 8%. We also used innovative environmental constraint handling to increase the interval between diversions by an order of magnitude.

Greg: Environmental limits can come on suddenly and unexpectedly. My experience is that these involve unmeasured disturbances and scenarios you can not initiate to develop a model. There is nothing sadder than an advanced control engineer without a model. What did you do?

Terry: We added an external "kicker" algorithm around the MPC because of the highly non-linear characteristics of the constraint variables (in this case it was condensate conductivities). The environmental impact required us to take immediate and "substantial" action to eliminate the contamination in the condensates. In essence, we built a basic fuzzy algorithm that "kicked" the weak black liquor (WBL) feed to the evaporators during a significant upset.

The first slide in the attached file summarizes the achievements of the MPC/kicker application. The second slide shows how the "kicker" backed out the WBL flow on high condensate conductivity to prevent a diversion yet allowed the MPC to recover quite well from the disturbance.

Conductivity Kicker

Where have all the instrument and process control engineers gone? Are they in Florida enjoying golf and the weather, are they filling in part time for a contract engineering design job oblivious to the ice or snow storm, or are they like me venting into the blog sphere?

It is easy for plants to forget about people responsible for the tuning and performance of the loops. The few instrument engineers and process control engineers left are focused on buying transmitters and configuring the DCS, respectively. They do not have the time or training to recognize and analyze the tuning and performance of the loops and more importantly it is probably not in their goals. The manager can readily understand that a production unit needs hardware and configuration to make the plant run but to date the opportunity for better tuning and dynamics in the plant is ambiguous at best, which means it is not going to survive corporate downsizing. Studies that show 30% of the loops are poorly tuned and 30% suffer from poor dynamics (e.g. principally valve stick-slip and process transportation delays) are easy to dismiss if there is no onsite data.

Even when loop tuning and performance is on the radar screen, the number of loops assigned to the instrument or process control engineer in a large continuous plant has increased dramatically to hundreds and even a thousand or more. Batch processes have an order of magnitude fewer loops but the ones they have are generally more difficult because there is no steady state (another story).

Astute process engineers who are looking at the loops try to fill in for the missing control people. However, improving loops is probably not in their job description and they usually haven’t had the opportunity to learn about tuning methods, valve resolution and deadband, and even simple process dynamics. These things are not normally taught in a practical manner in chemical or systems engineering, where the focus is on Laplace and Z-transforms to prepare 1-2% of the students to go on to graduate school to major in control theory and become professors. There are exceptions (see my Feb 4 blog on Washington University and the article by Tom Edgar from the University of Texas in InTech last Fall).

A significant part of the value of recent breakthroughs in thinking and online tools is the recognition of the importance and understanding of how the automation system (e.g. valve and sensor) and process (e.g. piping, mixing, and vessel) affects the process dynamics per Advanced Application Note 4, how the dynamics affect the tuning settings, and in turn how the tuning settings affect the performance of the loop.

For those who are tired of reading or have email to do, the takeaway is:

(1) Plant design sets the minimum and maximums of the process dynamics and how these change with operating point of the process and valve, which in turn determines how the tuning should be scheduled
(2) Process dynamics slowly change with aging, fouling, and frosting
(3) Process dynamics rapidly change with throughput and load (most noticeable during startup and turndown) and show up as a change in the valve’s operating point
(4) Valve, pump speed, and sensor resolution limits create a variable dead time
(5) Process dynamics determine the ultimate possible performance
(6) Tuning settings determine the actual achievable performance
(7) All tuning methods end up with about same controller gain for maximum rejection of process load disturbances if there are no extenuating circumstances
(8) The reduction in error for a load disturbance can be simply estimated from tuning
(9) Online tools can identify valve stick-slip, deadband, and the valve characteristic
(10) Online tools can identify the process dynamics and schedule tuning settings

An article in Chemical Processing provides information on an online tool for the identification and monitoring of process dynamics and control valve resolution and deadband, and a corresponding calculation and scheduling of tuning settings. Changes in the process dynamics provide considerable insight but you need "Insight" to appreciate this insight.

The following slides show how to estimate the improvement in integrated error from less sluggish tuning for a load disturbance at the process input. The equations assume the aggressive tuning does not cause the loop to oscillate more than what it already does from valve resolution/deadband or measurement noise. Equation 2-2b is derived from Equation 2-2a, which was derived in Appendix C of New Directions in Bioprocess Modeling and Control. The equations are useful in terms of simplicity and recognition of cause and effect.

Load Disturbance IAE

More aggressive tuning increases the rate of change of the controller output and hence decreases the dead time from valve resolution/deadband. While it does not affect the amplitude, it increases the frequency of the limit cycle from valve resolution/deadband. This may or may not be a good thing. A faster cycle is more effectively filtered out downstream by a process volume but a faster cycle may be more disruptive to associated loops on the input to the process volume (e.g. loop interaction). More aggressive tuning setting (e.g. high controller gains) may also amplify measurement noise. Thus, there is a need to monitor the variability of all loops, which is an important feature in online software today.

This is not to say that all loops are tuned sluggishly. We have seen several loops that are oscillating nearly full scale (essentially on-off control) and the users have actually gotten use to this. The process runs moderately well because the average of the oscillations is OK. The oscillations are tough on valves and equipment and tough on the process engineer because he/she cannot see a discernable pattern in the controller output important for diagnosing changes in the process and loads.

Getting back to the more common case of sluggishly tuned controllers, how far off the mark is the controller gain for maximum disturbance rejection in some important loops? A Lambda factor of 2 to 4 is commonly used because this is what is appropriate for the flow, liquid pressure, pipeline, and heat exchanger loops frequently encountered, particularly in pulp and paper. However, for loops on biological or chemical reactors, evaporators, crystallizers, neutralizers, and distillation columns (unit operations distinguished by a high degree of back mixing from bubble flow and/or agitation), a Lambda factor of about 0.2 provides the best disturbance rejection with acceptable robustness because the dead time to time constant ratio is less than 0.2. Note that Lambda is the Lambda factor multiplied by the process time constant so setting the Lambda factor equal to the dead time to time constant ratio corresponds to setting Lambda equal to the dead time. Thus, current tuning practice gives a gain that is ten times too low and thus an integrated error for load disturbances that is ten times larger than achievable for highly back mixed volumes.

Many of these loops behave like they have integrating processes (like level) and may be best modeled as integrating (e.g. “near integrating”) even if they are not perfectly integrating. The integrating process gain is inversely proportional to the back mixed volume.

People are starting to understand this problem and plants may have some how arrived at the more aggressive settings on critical unit operations. It is important to note that to avoid problems with more aggressive tuning during startup and a turndown (lower throughput rates), the controller gain should be identified and scheduled online since the dead time is inversely proportional to the throughput rate and the valve gain (curve slope) changes with operating point on the installed valve characteristic. Also, it may be advisable to institute set point rate limits on primary loops to prevent big steps in the controller output from a set point change.

A final point, if you don’t tune the temperature loop on a highly exothermic reactor aggressively, a runaway can occur due to positive feedback (higher temperature causes a higher reaction rate through Arrhenius equation). Customers have learned the hard way to use a more aggressive controller gain to keep the relief system from blowing. For these reactors there is a lower controller gain limit besides the normal upper limit for stability. There is also a window of allowable controller gains for integrating processes when the controller has integral action (PI or PID), but this is getting too deep.

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.

For a constant flow and set of process operating conditions, is the observed total loop deadtime relatively constant? We know from last week’s blog, the deadtime also depends upon the sensor time constant and hence it’s fouling. Less recognized is that it depends upon whether a step change is made in the controller output versus its setpoint.

The closed loop deadtime (e.g. deadtime in automatic mode) is generally greater than the open loop deadtime (e.g. deadtime in manual mode).

The deadtime from control valve stick-slip and backlash is the valve resolution and deadband, respectively divided by the rate of change of the controller output. For small step changes (particularly for pneumatic positioners), the response time also gets incredibly slow. For a large step change in controller output, the dead time from stick-slip and backlash is zero and the response time is minimal (except for large actuators). Next week, we will discuss some other ramifications of step size.

For a step change in controller setpoint, there is a kick from proportional action (for a PID structure with proportional action on error) and a ramp from reset action. If the kick is not enough to get the valve to move then the loop has to wait on reset action and the chosen closed loop time constant. Thus the deadtime identified for a setpoint change depends upon the controller tuning. Equations 2-47 through 2-50 in the book Advanced Control Unleashed show the development of an equation to estimate the increase in the deadtime from a control valve based on the open loop deadtime. While, these equations are for deadband, they can be used for stick-slip if you consider that half of a deadband is roughly equal to a resolution limit, which is often the case for the best throttle valves (e.g. sliding stem valves with diaphragm actuators). Note the presence of a detuning factor Kx that is approximately the inverse of the Lambda factor (the ratio of closed loop to open loop time constant).

For adaptive controllers or on-demand tuning software that rely upon setpoint changes, very sluggish initial tuning or an unnecessarily large closed loop time constant specified will lead to a larger identified deadtime and overly conservative settings that tends to keep the loop deadtime larger and hence the controller detuned.

Dead time is bad news because the controller has no effect on the process during this time interval. The minimum peak error for a disturbance is basically how far the process is driven away from set point during the total loop deadtime by the process upset. The minimum peak error from a load upset can be estimated as the average rate of change of the process variable multiplied by the dead time. The minimum integrated error is proportional to the deadtime squared. These relationships for peak and integrated error are developed in Equations 2-38 through 2-44 of Advanced Control Unleashed. If this is not enough to get you to rush out and buy a copy, I am offering for a limited time a $0.25 rebate (generous considering the royalties are donated to a university). Just send me your receipt in a self-addressed and with enough postage to get to my secret island hideaway.

What steps can be taken to make the real loop deadtime step forward? Last week we found that a step made in the controller setpoint rather than its output for a controller gain less than one increases the deadtime because of the time it takes for the controller output to work through the valve deadband and resolution. Slower tuning makes the deadtime larger. Subsequent increases in Lambda factors for additional robustness can get the user into a downward spiral in terms of loop performance (slower tuning -> larger deadtime -> slower tuning -> larger deadtime).

Additionally, small steps in the signal to control valves, particularly those with pneumatic positioners, have a dramatic effect on valve response time and hence loop deadtime. The following tests show that the response time of positioner can increase from 1 second to 100 seconds when the step size is decreased from 10% to 0.2%. While you may not be making such a small change in controller output, consider that a 1% change in setpoint to a controller with a 0.2 gain translates to a 0.2% step in the signal to the valve.

Effect of Step Size on Positioner Response

For slow loops like tank level and temperature, the time it takes for a change in the process variable to work through the resolution limit or noise band of the measurement creates another increase in deadtime. For a 1980s vintage DCS with 12 bit A/D (one sign bit) wide range thermocouple cards, the resolution limit of about 0.25 degrees adds significant deadtime besides loop A/D noise. The additional deadtime can be estimated as the measurement resolution divided by the rate of change of the process variable. For a temperature loop changing 0.05 degrees per minute from a step change in controller output, a resolution limit of 0.25 degrees can add 5 minutes of loop deadtime.

I remember trying to use an auto tuner on level loops on large tanks and waiting what seemed like forever for the measurement to get out of the noiseband. I quickly realized that I needed to take larger steps to drive the level faster before the auto tuner or my brain timed out.

Where tight control is needed for slow level and temperature loops, the controller is normally tuned with a controller gain much larger than one. This is a tip that the step changes in the controller output should be large so you are not waiting till the cows come home to see the process variable stir. For more Texas talk, see my Control Talk Column “Puzzler Roundup” in the July issue of Control magazine.

If a control loop is oscillating, would it be best to increase or decrease the controller gain?

The standard answer of decreasing the controller gain is right for a decaying or growing oscillation in a relatively fast self-regulating loop (loop whose PV quickly goes to a steady value when in manual and disturbances have dissipated). If the oscillation is banging between set point limits of a secondary loop or output limits of any loop, then you could end up with an equal amplitude oscillation for an unstable loop and the best thing to do is to first decrease the controller gain until it settles down.

If the oscillation amplitude does not decay but is relatively constant and the loop is staying well within its set point and output limits, the oscillation is probably a limit cycle caused by stick-slip, or a resolution limit in the control valve. Decreasing the controller gain will not reduce the oscillation amplitude but will make its period longer. Over a narrow time range, this may make the trend appear smoother but the longer oscillation period is less filtered out by downstream volumes and is consequently more likely to appear in the product. Here a well mixed downstream volume divided by the throughput flow acts like a filter time constant.

If you have an integrating loop (a loop whose PV ramps away from the set point when in manual) or a runaway loop (a loop whose PV accelerates away from the set point when in manual), decreasing the controller gain can make the oscillation worse if you were below the low controller gain limit. Note that the oscillations are extremely slow and may not be noticeable over a trend for a single shift. The minimum controller gain for an integrating loop is approximately 4 divided by the product of the reset time and integrating process gain. The minimum controller gain for a runaway loop is approximately the inverse of the process gain.

For integrating loops, if you are near the limit, the controller gain should be increased if the reset time is decreased to prevent an oscillation, which is counter intuitive. With real processes, the dynamics can change so any tuning should be thoroughly tested and the user must be well below the high gain limit that causes instability. Lambda tuning prevents violating the low gain limit for integrating processes. To avoid getting too close to the high gain limit, Lambda must be larger than the largest possible total loop dead time.

There are many important types of loops that have an integrating response besides level, such as batch chemical and fermenter dissolved oxygen, pH, overhead pressure, and temperature. Extremely exothermic batch and continuous reactors (e.g. polymerization reactors) can have a runaway response.

There are 8 different choices for controller structures in a modern DCS. Which one is the best for your application and does it take a download to change it?

One choice is for integral only controller (no proportional or derivative action). The most common I-only control is a valve position controller (VPC) which is trying to slowly optimize the position of a valve to save energy or to provide better resolution and rangeability. For example, the furthest open air feed valve position for trains of reactors becomes the PV of a VPC whose set point is the maximum useable throttle position (e.g. 60% for a rotary valve) and whose output sets the air compressor speed or guide vanes. Then there is the classic big and small valve setup where the VPC keeps the small valve in its mid throttle range for fine adjustments by making coarse adjustments to the big valve. Slow I-only tuning is used to minimize the interaction between the VPC and the existing process loops. The VPC is difficult tune and the problem is better solved with model predictive control (see my Advanced Application Note 2).

Proportional-derivative controllers are sometimes used on highly exothermic reactors with a runaway response or for batch temperature or batch pH control where the response in integrating and in only one direction. For example, when heating up a batch with no vaporization or heat loss, the temperature will only rise and cannot drop. Similarly, when adding a base to a batch with no reagent consumption or escape, the pH will only rise and cannot drop. Here integral action causes overshoot from which there is no recovery. Pulse width modulation of a proportional only pH controller output has been successfully used to mimic titration in a batch vessel which can be thought of as very large beaker.

You can get proportional-integral control by simply setting the rate to zero. This still leaves many choices as to structure most of which involve whether you want proportional or derivative action on error.

Since a change in structure require a download, once you have decided you want both proportional and integral action, by choosing the “two degrees of freedom controller” you can tune or write to the set point weights online. Furthermore the transition of the weights can be smooth because you can change them to any value between 0 and 1 whereas a change in structure makes a discrete switch between 0 and 1.

Dinner is waiting on me so we will have to wait till next week for more about weights.

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.

After watching a PI controller take an incredibly long time to cycle through a very small resolution limit, I figured it would be helpful to develop an equation that would provide an estimate of the period of the limit cycle (sustained equal amplitude oscillation) from a valve resolution limit (e.g. stick-slip). The attached equation shows that while dead band in itself does not cause a limit cycle in a single self-regulating loop, dead band can have a profound effect on the period of the oscillation. Since on-off rotary valves disguised as throttling valves can have dead bands more than 10 times the resolution limit, drawn out limit cycles is not an uncommon phenomenon. The following file tells the story.

Valve Limit Cycle Period

Last week we discussed how a resolution limit (stick-slip) in a control valve can cause a saw tooth oscillation in the controller output for a self-regulating (steady state) process. For a flow or liquid pressure loop where the process time constant is small, the oscillation in the process variable (PV) is a square wave. For a gas pressure loop where the process time constant is significant, the oscillation in the PV is rounded. Note that if the resolution limit was zero, dead band in itself would not cause this oscillation for a self-regulating process. In real systems, the resolution limit is never zero, so oscillations exist but may be so small that they are lost in the noise or upsets.

For integrating processes such as level, a dead band will create a limit cycle independent of whether a resolution limit exists. In an integrating process, there is no steady state. The PV ramps unless the controller output exactly balances the load, which only occurs for a perfect valve and no disturbances or noise. The lost motion of the control valve from dead band (backlash) causes the PV to ramp until it has worked through the dead band. The result is a saw tooth in the PV whereas for self-regulating processes the saw tooth was in the controller output. While the dead band is never zero, the amplitude of the saw tooth of the PV can be so small it is lost in the noise or upsets.

Whether a valve limit cycle affects the product quality depends whether there is a back mixed volume down stream that filters (attenuates) the oscillation. The analogy in circuit theory works well here where the filtered amplitude for large filter times is proportional to the period of the oscillation and inversely proportional to the filter time.

For a well agitated vessel, the filter time is the vessel residence time (volume divided by throughput flow). Even if the vessel does not have agitation, turbulence of boiling mixtures, the entrance and recirculation of flows, and the migration of compounds from low to high concentrations results in significant smoothing of the oscillation. Thus, for chemical processes involving blend tanks, columns, evaporators, and reactors, the limit cycles typically have little economic impact for reasonably good valves (e.g. resolutions and dead bands less than 0.5%). The exception of course is pH, where the process gain and thus the amplification of a resolution limit can be extremely large for strong acids and bases. In fact, a reagent valve with exceptional resolution combined with advanced control techniques can eliminate a stage of neutralization and the associated equipment, piping, and instrumentation costs.

For pipeline composition control or sheet thickness control, limit cycles are not attenuated because there is essentially no back mixed volume. Oscillations readily appear in the final product and the impact of the valve response plays a more important role. Consequently, the pulp and paper industry is much more sensitive to valve problems.

For split ranged valves, the topic for next week, all bets are off.

Any process with split ranged valves is prone to limit cycling for many reasons. The periods are unpredictable. Some are process related. For example, the transition between steam and coolant creates a severe discontinuity. There is a change of phase and disruptive change in magnitude and sign of the effect. There is no happy medium for a small cooling or heating requirement. When the steam replaces the coolant in the jacket or coils or vice versa, by the time the controller sees that the consequence of its action is too large, it is too late.

The real behavior of control valves also make the transition at the split range point less than smooth. The resolution (stick-slip) at the seat at process conditions is often an order of magnitude larger than the stated resolution of the valve. Tight shutoff specifications and designs, high temperatures, solids, and fouling increases the friction and stick-slip as the valve trim, ball, or disk tries to break free of the seat or seal. Tests done by the manufacturer are usually done far away from shutoff (e.g. 50%). There are exceptions as noted in the blog “Control Valves on the Skids” on May 10 in the Plant Design category.

The slope of an installed characteristic of a control valve is also typically largest near shutoff and smallest near the wide open position. So besides the difference in valve gain due to valve capacity, there is also a change in valve gain due to the installed characteristic.

When a small control valve is split ranged with a large control valve, there may be an improvement in rangeability when you are throttling just the small valve but there is the increase in stick-slip in the transition to the big valve and a loss of sensitivity when throttling the big valve. Model predictive control can eliminate the need for this split ranging by simultaneously manipulating both valves as described in Advanced Application Note 2 available at http://www.easydeltav.com/controlinsights/

When the split ranged valves are for different streams that have opposite effects, the limit cycle across the split range point poses a significant loss in process efficiency. The cycling between coolant and steam wastes energy and the cycling between acids and bases waste reagent. Here not only is there difference in the valve gain, but also in the process gain, dead time, time constant, and sign. Adding a dead band in the split ranged point adds dead time in all processes and creates a limit cycle for integrating processes.

A controller with just the right tuning is a rare bird but knowing when tuning is important is the real game. While it is nice to say that all loops should be tuned better, what are the benefits and issues? New software can identify the process dynamics but the user is still left with the question - how fast or slow should I tune the controller? This choice comes up as a relative specification (fast or slow) as a menu choice or slider bar or a numerical specification, such as Lambda (closed loop time constant), or a Lambda factor (ratio of the closed loop time constant to the process time constant).

Controller tuning that is too slow (controller gain too low and/or too reset time high) may transfer insufficient variability from the controlled variable (primary process variable) to the manipulated variable (e.g. final element or secondary loop set point). Slower tuning results in larger standard deviations of the controlled variable during upsetting times, startups, grade changes, and batch operation. During quiet operation of continuous self-regulating processes with good control valves (minimal stick-slip) the standard deviation may be negligible so slower tuning does not always mean a problem. Furthermore, the value of reducing the standard deviation depends upon the economic importance of the process variable, blending, and control in downstream equipment. Column, crystallizer, evaporator, extruder, dryer, kiln, and reactor temperatures are indicators of composition and thus generally important. However, if the oscillation period is much faster than the downstream blend time of surge or storage tanks or is much slower than the Lambda of concentration control loops downstream, the effect may be negligible. For example, an opportunity assessment of continuous polymerization line with plug flow reactors showed there was an opportunity for better polymer temperature and pressure control both of which was important for product quality. However, the process engineers placed no economic value on a reduction of the standard deviation because fluctuations from an individual polymer production line were averaged out by the huge storage tank downstream. A similar state of affairs occurred for the temperature of a purification column train. A fair question is why not take out the storage or run at a lower level? Well in this case many lines or trains dumped into the same tank so the tank had to be large enough to accommodate a dynamic unbalance between supply and demand. Less inventory translates to more changes in production rate to match changes in customer and distribution requirements, which means transferring more variability from sales and transportation to production.

My general experience is that temperature loops on large agitated or boiling volumes (e.g. columns, evaporators, fermenters, and stirred reactors) are tuned too slow because the appropriate Lamdda factor is in the range of 0.05 to 0.5 whereas users are comfortable with Lambda factors of 1 to 10 that are suitable for volumes without much back mixing (e.g. extruders, heat exchangers, kilns, pipelines, plug flow reactors, sheet lines, and static mixers) and for flow loops. Similarly, gas pressure control requires lambda factors an order of magnitude lower than liquid pressure control loops. Thus, reactor gas pressure controllers are often tuned too slow. An important point to remember is that variability in a manipulated variable, such as steam, coolant, or vent flow, is usually not as important as decreasing a variability in the controlled variable that is an inference of product composition.

Stay tuned for Part 2 on the signs and consequences of a loop tuned too fast, Part 3 on the quantitative assessment of slow tuning, and finally Part 4 on suggested tools.

Oscillations are indicative of a controller that is tuned too fast unless the oscillations are very slow or are limit cycles caused by valve stick-slip for any type of process or valve dead band for an integrating process (e.g. level). The amplitude of fast oscillations that are not limit cycles can be reduced by decreasing the controller gain. Oscillations in the process variable may upset other loops and show up as off spec product if there are insufficient blend volumes downstream. Oscillations in the controller output may cause similar problems by affecting other process variables. Also, such oscillations make it more difficult to see patterns in process behavior either visually or by data analytics. Loops with a dead time approaching or exceeding the process time are often tuned too fast.