If you increase the controller gain by the same factor that you increase reset time (e.g. double gain and reset time), how does it affect key performance indicators such as quality, yield, on-stream time, and environmental costs? If you make the measurement faster, how does it affect these same KPI? If you want to improve a KPI, what is the priority of solutions?

The equations for the peak (Ex) and integrated error (Ei) in terms of controller settings, shown on slide 1 of EffectsLoopTuning&Dynamics-KPI.pdf, provide an answer to many of these questions if you embrace your inner geekness (see the finale Control Talk Jan issue "The Future is Now")

Both equations were derived in Appendix A and B of Tuning and Control Loop Performance (scheduled to be back in print by Momentum Press, 2010). The derivation of the equation for the integrated error was included in Appendix C of New Directions in Bioprocess Measurement and Control (ISA, 2007) along with a unification of controller tuning rules. This unification, which showed how all the major tuning rules give basically the same result for a controller gain to minimize peak error, was personally satisfying but possibly not for people who are adamant about the relative merits of personal favorites.

Since the integrated error is inversely proportional to the controller gain and proportional to the reset time, doubling the controller gain and reset time cancel each other out. However, doubling the controller gain reduces the peak error since reset time doesn't appear in the equation of the peak error. Reset time has an effect on peak error but it is negligible unless the reset time is decreased to the point where it approaches the reset time. This can happen for deadtime dominant systems, but the peak error here is basically the open loop (error with the controller in manual) as evident from the equations on slide 2 of EffectsLoopTuning&Dynamics-KPI.pdf.

Nearly all the process control literature focuses on integrated absolute error (IAE) as the measure of loop performance. The IAE is a good measure of product that is off-spec that can lead to reduce yield and the raw material or recycle processing to product cost ratio (euros per kg and dollars per lb). If the off-spec cannot be recycled or the feed rate cannot not be increased to compensate, there is also a loss in production rate. If the off-spec is not recoverable, there is an additional waste treatment cost.

What we usually don't take into account is the filtering effect of back mixed volumes as indicated by the equation on slide 3 of EffectsLoopTuning&Dynamics-KPI.pdf. For pulp and paper plants, nearly all of the variability expressed by the IAE ends up in the sheet since most of the processing is done in pipes and unagitated vessels. For plastics and textiles, the IAE in the polymer lines and extruders show up as yarns and webs. However, these plants often have extensive blend tanks that smooth out the plus and minus fluctuations in product quality.

I ran into a process control improvement (PCI) study, where after an hour of discussion and investigation it became obvious a reduction in the considerable variability observed in each textile line had no value because the product coming out of the huge blend tank was always in spec and the variable speed pumps were maxed out. My decision to move on to better opportunities was not well received, so we stayed for 2 days to confirm there were no PCI opportunities (reducing the size or inventory in the existing tank or replacing the pumps were considered accounting or process design improvements).

When loops are oscillating across the split range point (common case due to valve stick-slip and installed valve characteristics), there can be a cross neutralization of acids and bases or a cross compensation of hot and cold heat transfer fluids that increases reagent and energy costs. Here the IAE is important but an integration of individual reagent and heat transfer fluids is a better indication.

If there are appreciable back mixed volumes whose residence time is much larger than the control loop period, the integrated error (Ei) where the plus and minus errors cancel out for a disturbance can be a better indication of product quality. Furthermore, this integrated error is the IAE for an over-damped or critically damped response.

This topic will roam on for 4 parts. In part 2, I discuss the effect of the peak error on onstream time and environmental costs. In part 3 I cover how measurement and valve dynamics impacts both types of errors and hence KPI. In part 4, I conclude with some rules of thumb on the priority of PCI solutions for various scenarios.

Knowledge of the flows and the accumulation of material in a unit operation are fundamental to the understanding and analysis of process and equipment performance. Flows are the primary way of affecting the process. Root cause analysis requires sensitive and repeatable flow measurements. I have seen costly expert systems fail to deliver benefits because of missing or inaccurate flows ("Drowning in Data, Starving for Information - 1").

The process gains of the more important process variables (e.g. composition, pH, and temperature) are best quantified and visualized in a plot versus a ratio of flows (e.g. coolant/feed, reactant A/reactant B, reagent/feed, reflux/feed, and steam/feed). If you are still into differential equations, you can checkout my Advanced Application Note 4 to see how process gains are dependent upon the ratios of flows.

The importance of flow ratios for affecting the process is seen in the prevalence of flow ratio control as detailed in my entries "What Have I Learned? - Flow Ratio Control" on this website.

The amount of time material spends in a unit operation is critical for crystallization and reaction. For continuous operation of well mixed volumes, the amount of time is the residence that is the fluid volume divided by the total throughput flow. Conversion is maximized by increasing volume or decreasing feed flows. For batch processes, the amount of time is the cycle time. Conversion is maximized by charging the feeds as fast as possible (increasing feed flows), to leave more of the batch cycle time for conversion.

In the direct material balance control scheme where the distillate flow is manipulated for overhead receiver level control, the sensitivity of the temperature and hence the composition control requires an exceptionally sensitive level measurement, low noise, and a high controller gain. Changes in distillate flow do not affect the column until there is a corresponding change in the reflux flow that maintains the material balance.

Then of course, there is the need to minimize the amount of storage of materials in the process. Ideally, storage tanks would be almost empty with just enough raw materials and intermediates to continually meet the flow demand of downstream operations and just enough products to continually meet the flow demand of customers.

For more information on how advances in flow and level measurements can improve material balance control, residence time control, inventory control, and process analysis and modeling, checkout "Advances in Flow and Level Measurements Enhance Process Knowledge, Control"

It is well known that measurement noise reduces or eliminates the use of derivative action. Since rate is not popular (another story), the exclusion of rate is not seen as a significant disadvantage even though temperature loops could benefit from rate since it can compensate for thermowell and heat transfer surface lags and reduce overshoot. In the 1980s and 1990s many temperature loops suffered from the prevalent use of 12 bit I/O and wide range thermocouple input cards that caused a resolution error of 0.25 degrees in a signal whose true rate of change of temperature was usually much slower than 0.25 per minute. The result was a poor signal to noise ratio. We tried to filter the heck out of the signal so we could use rate but this added another lag. Fortunately, today we have 16 bit I/O systems and smart transmitters so that signal resolution is better than the sensitivity of the sensor - just one of the many reasons to get your automation system into the 21st century.

A wider consequence of measurement noise not so readily recognized is the reduction in permissible controller gain. For loops with a true integrating or "near integrating" response where the process variable ramps when the controller is put in manual, the high limit for controller gain is way above the normal range of consideration. For example, level and batch temperature loops normally have a ramp rate so slow (0.000001 %/sec), that the controller gain could be higher than 50 if there was no measurement noise and the reset time was not too small (a big "if"). Since the peak and integrated errors are inversely proportional to the controller gain, these and other loops could significantly benefit from a smoother signal and better tuning.

What is measurement noise and where does it come from? In my book, measurement noise is any fluctuation in the measurement signal that should be ignored by the controller. If the controller reacts to a fluctuation it really cannot correct, the loop inflicts a disturbance upon itself. If resolution problems are behind us, the biggest sources of measurement noise are inadequate axial (back) mixing, bubbles and foam in liquids, liquid droplets in steam or gas, inconsistent profiles, lqiuid and pressure waves, and insufficient measurement rangeability. Measurement noise is amplified by high process gains (e.g. steep titration curve for pH control) and sensitive measurement ranges (e.g. - 0.25 to 0.25 inches of water column for draft pressure control). The Table in MeasurementNoiseSourcesControlBandAmplitude.pdf provides a summary of my assessment of noise sources, control bands (allowable control error), and noise amplitude (peak to peak) for common loops. The noise amplitude should be less than ¼ the allowable control band for fast disturbances. A reduction in noise amplitude is ideally achieved by eliminating the source of the problem. If the correction is not practical or is not yet implemented, a signal filter is often used to attenuate the noise. The ratio of the amplitude of the filtered signal to raw signal is roughly proportional to the ratio of the period to the filter time when the filter time is greater than the period (simplification of the Bode plot attenuation equation). The filter time becomes effectively additional deadtime in a loop when it is less than the process time constant. If the filter time is considerably greater than the process time constant, the measured process variable amplitude may look better but the real amplitude is worse because you are seeing a very attenuated version of the real world. I have seen where an ISA conference speaker said he almost did not get permission to give his presentation because the improvement was so great it was considered proprietary. He had increased the measurement filter so much he was drawing a straight line no matter what was happening in the process. I have seen where a biochemist withdrew a temperature sensor halfway in its thermowell and proudly said this was the way to run the bioreactor because the temperature reading was so much smoother. Then there were the cases of sand in thermowells and the mounting of extruder temperature sensors in massive blocks of metal giving the illusion of smooth temperature. These are all old stories but I am sure people are being fooled today especially since one can so easily add a filter via the damping setting in the transmitter, the analog input block, and the PID block. Provided the filter setting is not so large it eliminates any recognition of process variability, the key symptom of too large of a filter setting is a long control loop period or recovery time if the controller gain is not so detuned you can't see the effect of more loop dead time (see Advanced Application Note 5 for estimation of how the detuning of a controller is equivalent to additional deadtime in the loop). To prevent the loop from inflicting disturbances upon itself by reacting to noise, the filter time should be set just large enough to keep the fluctuations in the controller output smaller than the resolution (stick-slip) of the final control element (e.g. control valve). A less desirable but widely used way of keeping the fluctuations in the controller output small enough is to reduce the controller gain.

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.

For comic relief for the New Year I offer here some of my broken resolutions published in my Control Talk column plus a new number one.

(20) Listen intently to my wife's instructions. Why does my mind still jump to weighty matters like what is next for dinner?

(19) Stop making cheap control valve jokes. Could the next final element reputation I hurt be my own?

(18) Help make smart diagnostics smarter. Do I need to de-fussify my fuzzy logic?

(17) Stop lusting in my heart for more computing power. Is it the PC or me that is the constraint?

(16) Turndown the volume on my headphones. What did you say?

(15) Stop drinking cheap wine. Does good wine ever come in a size large enough?

(14) Read a college text on control theory. Can I watch Star Trek without setting up the state space equations?

(13) Stop answering a question with a question. Why should a consultant do this?

(12) Spend more time with my wife than with Control magazine. Whatever happened to my January issue?

(11) More bark than bite. Can I at least growl? Will I be forced to wear an anti-bark collar? Is this better than a muzzle?

(10) Stop making fun of seniors. Who else do I know? We certainly aren't an endangered species with the influx of baby boomers.

(9) Stop focusing on deadtime. What else is there at Sun City? Whoops, I am already breaking my last resolution.

(8) Final element resolution resolution. Why should I get unstuck when valves are stuck and it gives me a chance to repeat words?

(7) Get into hybrids. No issue here with fashion models. Can a hybrid face up to a 2 ton high lift truck with a cattle guard? Can I drive under a cow?

(6) Show my more sensitive side. Wait, will I confuse people including myself? Do I have to start watching "Brothers and Sisters?"

(5) Stop drinking cheap booze. I will give this another shot.

(4) Listen to hip-hop. What if I am not hip and can't hop?

(3) Become rich and famous. How about poor and infamous?

(2) Lean how to sell. How can I sell a product when I can't sell myself?

(1) Stop pushing the Essential Book even though the royalties are donated for wireless research at the University of Texas and the book is like a fine wine with a lush blend of technology with rich overtones, a balanced feel, and a lingering finish. What if readers like cheap wine? What if readers are not UT fans? What if they are rooting for Alabama? What if they think wireless research will be used in the BCS game?

The figures in the attached VariableSpeedDriveRangeability.pdf and the following discussion is an excerpt from the ISA book The Essentials of Modern Measurements and Final Elements - A Guide to Design, Configuration, Installation, and Maintenance.

The 4 main practical reasons that variable speed drives (VSD) drives are not used as extensively as one might think for pump control are as follows [35].

1. Drives are generally not built just for pumps. They handle conveyors, extruders, etc. There are a lot of VSD menu choices and options not pertinent to pumping applications.

2. Users don't like the complexity of the VSD. The user must address setup, maintenance, and design issues. Special practices are needed to prevent EMI in instrument signals and from getting harmonics back into the power supply.

3. Someone needs to do the right calculations on dollars saved. Typically calculations don't take into account the drop in drive efficiency at low speeds. The duty cycle (amount of time speed is really turned down) is not known in advance. If there is a high static head, the energy savings of a drive disappear.

4. It is rare to compare a VSD and valve. There are generally no decision points in the project for this comparison.

Is a Valve or VSD Faster?

Exceptionally fast loops (e.g. furnace pressure, liquid pressure, and surge control) can ramp off-scale in milliseconds. These loops have essentially a zero process deadtime and may have a high process gain due to a narrow control range (e.g. fractional inches of water column for furnace pressures). These loops require DCS scan times of 0.05 to 0.1 seconds. Special fast scan rate digital controllers or analog controllers are needed. DCS scan time requirements of 0.2 seconds or less signify a VSD opportunity. A properly designed VSD has no measureable dead time while control valves and dampers take anywhere from 0.2 to 2.0 seconds to start to move. For example, an incinerator pressure and polymer pressure loop that could get into trouble in less than 0.1 second required a VSD and analog controller to stay within the desired control band [20][23][35].

The VSD has a negligible time delay unless a deadband or dead zone is introduced in the drive electronics to reduce reaction to process measurement noise or a low resolution input card is used. A control valve or damper has a deadtime that is proportional to the resolution limit (sticktion) or deadband (backlash) divided by the rate of change of the process controller output. For large or fast changes in signal this deadtime disappears.

A pneumatic actuator has a pre-stroke deadtime that is the time it takes for the actuator pressure to change enough to move the actuator shaft. For large actuators, the pre-stroke deadtime can be several seconds unless a booster is added.

The inertial time constant of liquid flow response is inversely proportional to flow. Consequently, the process lag at low flow rates and at the initial start of flow can be quite slow (e.g. 5 seconds) compared to the process lag at normal flows (e.g. 0.5 seconds). The comparison between VSD and control valve response should be at normal flows.

In a published comparison of the dynamic response of a control valve and a pump for flow control for a system with negligible static head, the integral times were about the same for the VSD and valve loops. However, the controller gain could be increased by over a factor of 6 for the VSD loop. As a result, the set point response was faster [38]. In this test the valve deadband was about 8% and there was no static head. In unpublished lab test results of control valves with low sticktion, low backlash, and a digital positioner and a VSD with a volts/hertz PWM drive for liquid flow control, the speed of response of the valve and VSD were similar.

Variable speed drives, control valves, and dampers have a velocity limited exponential response. The velocity limiting in a drive depends upon the available motor torque and the inertia of the motor rotor, the pump shaft, and the pump impeller. The exponential term is generally much smaller for a VSD than for a control valve or damper. On the other hand, the velocity limiting is slower for a VSD unless the actuator size is large and boosters are not used. Consequently, for small changes in signal, a well designed VSD is faster. Conversely, for large changes in signal, a small control valve is faster (see section on dynamics). This leads to the conflicting statements about whether a VSD or control valve is faster. Which final element is faster often depends upon the size of the change in signal.

VSD Best Practices

To summarize, a VSD is most likely to offer energy savings or better loop performance as a final element for the following types of applications:

• Loops that require 0.2 seconds or faster scan time
• Valves and dampers with 0.5% or more sticktion or backlash
• Large utility flows
• Integrating and runaway processes without a secondary flow loop
• Low static head processes requiring frequent turndown

A tachometer or inferential speed feedback signal should be sent to the process controller in the DCS that is sending the signal to the drive. The speed feedback should be used in a similar way to the position feedback from a digital positioner to prevent the process controller output from changing faster than the final element can respond. The use of the dynamic reset limit option for the loops in the DCS can automatically prevent the process controller from outrunning the final element response (see section on dynamics).

For best performance users should consider the following during the specification and implementation of variable speed drive systems:

• High resolution input cards
• Pump head well above static head
• On-off valves for isolation
• Design B TEFC motors with class F insulation and 1.15 service factor
• Larger motor frame size
• XPLE jacketed foil/braided or armored shielded cables
• Separate trays for instrumentation and VFD cables
• Inverter chokes and isolation transformers
• Ceramic bearing insulation
• Pulse width modulated inverters
• Properly set deadband and velocity limiting in the drive electronics
• Drive control strategy to meet rangeability and regulation requirements
• Dynamic reset limiting using inferential speed or tachometer feedback

VSD Response

The response of variable speed drives more closely resembles a pure ramp with no rounding or time delay provided a filter or deadband has not been added in the drive electronics to attenuate process noise in the process controller output signal. The ramp time in the VSD depends upon the size of the load compared to the available torque from the motor. In general, the ramp time of a VSD is longer than the stroking time of a control valve but is shorter than the stroking time of a large damper. Longer than necessary VSD ramp times may inadvertently be imposed in the drive electronics.

There is essentially no sticktion or backlash in variable speed drives for axial and centrifugal blowers, fans, and pumps but this does not necessarily mean there is no resolution limit or deadband in the VSD response.

Controller outputs invariably have fluctuations that originate from process or sensor noise and transmitter resolution limits. These fluctuations are not representative of the actual value of the process variable and are best ignored. These fluctuations are particularly large and fast for flow and pressure loops. A deadband is sometimes introduced in the VSD electronics to prevent changing the speed. The effect may be a true deadband where the desired speed does not change upon a change in direction until the change in signal is larger than the deadband setting. The effect here is similar to backlash in a control valve. In other cases, it may be a deadzone setting, in that the desired speed does not change until the accumulated change in signal since the last change in speed is larger than the deadzone setting. Here the effect is similar to a resolution limit.

If there is no deadzone setting, the resolution limit in a VSD is largely determined by the input card. Assuming there is no sign bit, the VSD resolution limit is simply 100% divided by 2 raised to the number of bits (n) of the input card. Unfortunately, VSD manufacturers did not understand the limit cycle that would result from the resolution limit and offered an 8 bit input card (0.4%) as the standard card. Higher resolution input cards (e.g. 12 bit and 16 bit) should be specified to make the VSD I/O resolution comparable to the DCS I/O resolution.

VSD Installed Gain

In a variable speed drive for liquid flow, the pump characteristic curve shifts with pump speed. Since there is no control valve, there is no valve drop and the flow is at the intersection of the pump curve and the system frictional loss curve.

For a negligible static head and an idealized pump, motor, and VSD, the change in flow with speed is linear. If the static head is negligible, the loss in pump efficiency and the increase in slip at low speed, cause a decrease in gain (sensitivity) at low speed. This loss of sensitivity is seen as a flattening at low speed in the plot of flow versus speed.

If we ignore the loss in pump efficiency and increase in slip, a pump curve that approaches the static head will show a sharp bend downward to zero flow at low speed. The plummet of the speed at low speed causes a significant increase in gain and a nosier flow at low speeds [46].

A flat pump curve will cause almost a quick open type of flow characteristic. The high gain (sensitivity) at low speed can cause cycling [46]. Operation on a relatively flat pump curve can occur from improper pump selection or over-sizing.

VSD Rangeability

For variable speed drives, estimating rangeability gets tricky. The decrease in process gain from speed slip offsets the increase in process gain as the pump discharge head approaches the static head. If there are no overheating or cogging problems as suggested is the case for a pump and valve system with a well designed open loop (volts/hertz) PWM drive, high resolution input card, and negligible static head, the rangeability is normally 40:1. When the pump head is operating near the static head, the minimum controllable flow is set by rapid changes in the static head and frictional loss. These rapid changes could be due to noise and sudden or large disturbances. The speed can not be turned down below the amplitude of these fast fluctuations.

The rangeability of a VSD could drop to 4:1 for the following systems:

(1) Older VSD technologies such as 6-step voltage (excessive slip at low speed)

(2) Systems with a high static head (flow plummets to zero at a low speed)

(3) Operation on the flat portion of the prime mover curve (cycling at low speed)

(4) Hot gases (motor overheats at a low speed)

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."