Control Loop Tuning Made Easy

By Todd Harlow

Abstract

With the time pressures put on plant engineers these days, technically correct control loop tuning is quickly becoming a thing of the past. Most manual “tuning” is done by feel now, with the control loop closed or in automatic.

The result is variability within the product that can lead to poor quality and drive the end customer elsewhere. No matter what type of control system is used, tuning can be to the point and dependable. Math and procedures are easy to share. This may take some time up front to understand, but the user will always have the tools needed to correctly manually tune loops with limited amounts of time.

Introduction

There are not a lot of secrets to success in life; most of the things you must do to be successful are common sense. You work hard at keeping your priorities, well, priorities. Give your boss what he is supposed to get for his money, and keep in mind that if you can’t produce a profit within your own world, there won’t be a lot of other reasons to keep you around.

One way to produce profit is to give your customers what they need to produce their profits. Some good ways to do this are to increase production and quality or decrease cost. Ah, and you thought I would never get here: in order to increase production and quality, or decrease cost, you need to make sure your loops within your operation are not swinging all over the place causing variability. As I stated, there are not a lot of secrets to success. However, I have got one: there is a secret here that few engineers know, even though they would never admit this. The secret is you cannot tune a loop effectively while it is in automatic (closed loop) and unstable. Oh, I know some say you can, and they even have procedures for doing so, but you need to know what you are doing. If you don’t tune that often, you probably don’t know what you are doing. With open loop tuning, it’s simply math. I enjoyed math in school, and I know some of you may not have looked forward to math homework, but the reason it was created was because our world is basically mathematical. Tuning a loop is more mathematics than mystery. Whatever your method of looking at your operation, if you are seeing what appears to be a beautiful curve swinging around your desired set point, you have a problem. I understand you must pick your battles in this time demanding world, but when you get ready to do something about it, I recommend you use the methods contained in this paper. Look, if you are not in process control, don’t tell your process control department you know how to tune loops after this. If you are in the process control department, just pretend you knew all this already and get those loops tuned. That is exactly what I did.

Once you decide to tune a loop, you need to commit some time. It is easy, but it can take some time. Being rushed to tune a loop is like being rushed through a game of golf. If you don’t have the time, don’t even tee up your first ball. Documentation is also very important. Writing initial tuning parameters on that blank sheet of paper the operator gave you from the printer, or worse, on a napkin from the local café, is not recommended. Commit to buying a notebook just for tuning. Documentation today often includes screenshots, historian bookmarks, comments in DCS change logs, and tuning tag backups. These protect against unintended impacts when other systems (MES, APC, analytics) depend on loop stability data. At least write down the date and time every time you sit down to tune. You would be amazed at how many times I wished I could go back in time to see what the parameters were before I started changing them. Be very organized about this. If people start making jokes about your taking the time to do this, you are doing this just about right.

Self-Regulating Loops

There are two types of loops. We nerds like to call them non self-regulating and self-regulating. Self-regulating loops tend to work toward an equilibrium point, where non self-regulating loops do not. OK, let’s put this in English. What this really means is you are either working on a tank level or you ain’t. I did not say good English. Level loops are non self-regulating. When you increase or decrease the position of the control valve, you only change the direction the level is headed, and it does not normally settle out on its own. By the way, if your objective in tank level control is to see all of your tank levels showing “straight lines,” then you really are not using your tanks to take out variability in the process. Let the tanks take out variability in your flows, pHs, and pressure loops. Oops, sorry, I am really ahead of myself here. Let’s get back to tuning. I want to start off with the easier of the two types of loops I mentioned: the self-regulating loop. These are flows, pressures, pHs, and temperature loops, and any other loop, although I can’t think of one right now, that involves a control valve that, when moved, will change the process to another value and settle out.

Let’s use the flow loop for example. Flow loops tend to be relatively fast-responding loops with a smaller lag. When you make a control valve change, you see the change quickly. This is a good thing for loop tuners: the less lag, the easier the loop is to tune. I can explain lag with an example that occurs in your everyday life. When you get into the shower and you turn the hot water on more and more, then all at once the hot water hits. You frantically turn it off, and then the cold water hits and makes you jump out of the shower. You have just experienced the problem with lag. The hot water does not come on exactly when you turn the knob. Hopefully, over the years, you have adjusted, “tuning” yourself to understand this lag.

Now that we understand lag, let’s start with the first step to tuning: get a Diet Coke. OK, that is not really the first step, but usually I need a Coke when I sit down in front of the system. The real first step is to observe the process. Ask yourself, is it stable? Is the flow jumping around all over the place, or is the operator making, or needing to make, a lot of changes? If so, this is where the Diet Coke comes in. You will need the caffeine, because you have to just sit and wait until the process is settled. You don’t want to fall asleep. Your boss won’t believe you are tuning if you are sleeping.

Once your operator gives you the go-ahead, put the loop in manual. Now, this is important: you want to make changes to the flow but don’t upset the operator. Most modern DCS platforms flag manual mode transitions in alarm logs and performance analytics. Notify operations early so plant KPI dashboards don’t “alert the world” during your tuning session. Tell them you need to make significant changes in the flow, at least 5%, or you will have to come back and bug him again later with his boss in tow. He will agree to allow you to make the changes in most cases. I almost forgot your valve position needs to be as close to 50% as possible. Actually, I would take 25 to 75%. If it is not in that range, then you may want to get someone to make sure the valve is sized right or come back later when the operator will let you move the valve there.

With the loop in manual and the process steady, create a chart showing the present conditions: process flow, range of the flow meter or flow in %, your choice, valve position, and date. Have a column for time, but don’t put that down yet until you are ready to make your first bump. When you make a valve position change, a bump, do it all at once. Don’t use ramp buttons. Type the value into the system, and then just before you hit Enter or Return, note the time to the second. Then enter the value. Make sure you have a trend up so you can measure the response of the flow. When the flow settles out, you need to measure both the time it took to reach stability, usually in seconds, and the amount of flow change that occurred. By the way, make sure you calculate the flow change in % and not engineering units like GPM. So if your flow range is 0 to 400 GPM and you see a 20 GPM change, then the bump caused a 5% flow change, 20 divided by 400. Make several more bumps and chart the responses. High-resolution historian data now allows automated bump test capture and process reaction modeling. Advanced tuning software tools can calculate these values instantly, but manual math remains an essential engineering skill.

You should end up with data like this:

	Date	Time	Flow	Flow in %	Valve Position
	6/5/2025	11:00:00am	200 GPM	50.0%	35%
Settled		11:00:15am	232 GPM	58.0%	40%
		11:03:00am	232 GPM	58.0%	40%
Settled		11:03:16am	260 GPM	65.0%	45%
		11:05:00am	260 GPM	65.0%	45%
Settled		11:05:16am	230 GPM	57.5%	40%
		11:07:00am	230 GPM	57.5%	40%
Settled		11:07:17am	200 GPM	50.0%	35%

Ok, so you have gathered lots of data. At this point, you may be proud. But don’t get excited. You haven’t done anything yet. Take another sip of Diet Coke and look at the data. Notice it took 15 to 17 seconds to fully respond to your bumps. Also notice for your 5% valve change, this changes the process by about 7.5% on average. With these numbers and some constants, you can calculate tuning parameters. Before you do, make sure you note the existing tuning parameters. Tuning parameters are usually called P, I, and D, thus the name PID loop. The P is the proportional term, the I is the integral term, and the D is the derivative term. Let’s make it 33% easier. Do not use any derivative (D). You don’t have the skills yet.

Derivative is the least-used setting in industry because noise in instrumentation has increased with faster sampling rates. Unless you can prove dead time dominance and clean signals, D = Danger. Let’s talk about the proportional gain. Sometimes this is called proportional band. Don’t worry, however, if your system uses band, it is just 100 divided by Gain. So a simple calculation can keep you at ease. The I is the integral gain, usually in repeats per minute, so we may have to convert seconds to minutes. Also, some systems use minutes per repeat and call this integral time. However, it is just the reciprocal. Data historians today let you export directly into Excel or tuning tools for calculation. But keep the notebook anyway. Engineers never regret having too much documentation.

The first calculation you must make is the one associated with your process. We like to call this the process gain. Please do not confuse this with the proportional gain. I know the abbreviations would be the same, but the meanings are not. In order to calculate the process gain, you use this equation: flow change, in %, divided by the valve change, in %. So, using our example above, this would equal 7.5% divided by 5%, or a process gain of 1.5.

Next, we need to calculate how long it took our process to settle out after our bump. Our settling time average is 16 seconds. However, to calculate the proportional gain, we need to take that amount and divide it by 4. Don’t ask why. Ok, ask why. We need to come up with some constants to complete the math. We use Tau as a constant that describes a process response at 63%. This means Tau is the amount of time it took for the process to get to 63% of its final settling value. Tau turns out to be very close to the Settling Time divided by 4, thus the divide by 4. One more constant is Lambda, and we need to define it. Sorry for the Greek. Lambda is officially the closed loop time constant. By the way, this tuning procedure is based on a method called Lambda tuning and is the most suitable for industrial applications.

Back to the constant, Lambda. To make it easy, you need to think of these two constants as a ratio. The ratio will be Lambda divided by Tau. For each type of loop mentioned, we will use a different range of the Lambda to Tau ratio. For pressure loops, use 0.8 to 1.0. For temperature loops, use 1.0 to 1.5. And for flow loops, use 1.5 to 2.0. These Lambda to Tau ratios represent the foundation of IMC-based tuning methods used in advanced controllers. Many modern software tools compute these automatically, but the engineer must choose the right aggressiveness.

If you have made it this far, the rest is very easy. All you have to do now is take all of these numbers and plug them into the following equations to come up with tuning parameters.

In this example, we will assume that there is negligible dead time, the time it takes the process to move once the valve moves. This is usually the case with flow loops. So, since it took 16 seconds for our process to settle, our Tau will be 4:

Process Gain = Flow Change in %/Valve Change in %

Proportional Gain = 1/((Lambda/Tau) * Process Gain)

Integral Gain = 60 (Sec/Min) / Tau

Let’s use a Lambda/Tau ratio of 2.0 and our data from our flow example earlier:

Process Gain = 7.5%/5.0% = 1.5

Proportional Gain = 1/(2*1.5) = 0.33

Integral Gain = 60/4 = 15 repeats/min

Since integral can be in minutes per repeat for some systems, obviously you would just use the reciprocal. You would call that integral time, not gain. Some controllers now default to seconds per repeat instead of minutes per repeat. Always verify the units. Incorrect integral time units are one of the top causes of tuning disasters in today’s plants.

So, our tuning constants we should try are P = 0.33 and I = 15. For a control system where the proportional term is in band instead of gain and the integral term is in minutes per repeat, the numbers would be: Pband = 100/0.33 = 300 and I = 0.067.

You would plug these numbers into your controller and then put it in automatic, verifying closed loop performance with both setpoint tests and load disturbances. Many modern platforms include built in performance indices like IAE or variability metrics to validate improvements objectively. At this point, we could go back and try a Lambda to Tau ratio of 1.5. This would give us more gain, making the loop more aggressive if you see your loop needs it.

During some time at one of my plants, I created some trends a few years ago, not related to the example above, to show an open loop and two closed loop bumps for your viewing pleasure.

Above is a picture of an actual bump test on a pressure loop in the Moore APACS DCS. The yellow pen is the position of the control valve being “bumped.” Starting at about 5 pm one evening, I put the control loop in manual and made a small bump to get the valve to a round number, in this case 66 percent. Then, close to 5:02 pm, I made the first bump from 66% to 61%. Notice the pressure, the green pen, came up from about 55 psig to 57 psig. Then, around 5:03 pm, I made a 10% bump from 61% to 71%. Less than a minute later, I made my final open loop bump back to the original valve position of 66%, and the pressure settled out about where it started. Notice the pressure responded well to my valve position changes.

Above is a picture of a closed loop bump. The setpoint (red pen) was bumped while the loop was in automatic from 55 psig to 57 psig. Notice the reaction of the valve. It begins to decrease slowly, and the pressure comes up to setpoint. This loop took about 3 minutes to reach setpoint. The process gain of the loop should allow the loop to be tuned more aggressively. Three minutes is too long for this loop.

The final closed loop bump is performed by moving the setpoint from 57 psig to 52 psig. Again, the reaction time of the loop is too slow. Notice I did not even wait until the PV reached 52 before I captured this. At the end of these bumps, I put the setpoint back where I found it and let the operator know I was complete. Today, most DCS platforms allow live capture of tuning experiments with annotation directly on trends, enabling quicker collaboration and remote review when support engineers are offsite.

Level Loops

The previous example and equations hold true for the self-regulating type loops, such as consistency, pressure, temperature, and flow. For level loops, non self-regulating, we will use a different procedure and different equations.

Level loops can be harder to tune than the other loops. With some shortcuts, we can get to the initial tuning parameters quickly. To figure the process gain quickly, you can make a 10% valve output change and then time how long it takes in seconds to get 10% of the level. Note: this level is in %. If yours is in another unit, make sure you time a 10% change. Take the reciprocal of this time, and you have your process gain.

As stated earlier, one purpose of a tank is to take variability in the process out. However, if you let your tank overflow or run dry, you have created variability. If you burn up a pump or put product in the street, your job may become variable. The first thing you need to observe is where the operator normally runs the level of the tank. Not all tanks are run at 50%. Some operators like to run up to 80%, given the choice. This is so they have more time to react to upsets and still supply product. For our example, let’s just say our tank is a product tank that the operator does run at 80%. This means we have about 20% of the tank level that our controller can use to arrest the level when a disturbance occurs. We are saying that our operator wants his controller to react before we reach 100%. This 20% is called the allowable level variation, ALV. Don’t you just love abbreviations? We can use a shortcut here to figure our proportional gain. Gain = 100/ALV = 100/20 = 5.

Let’s also assume we have run a test telling us how long it takes to see a 10% level change when we move the valve 10%. Be careful with these tests. Depending on what tank you are testing, work with operations to decide how and when these tests can be done. If you go into the control room and empty the feed tank, you may never be allowed back in. I speak from experience. For our example, say it took 12 seconds to see the 10%. We can now calculate the integral gain: I = 15 * Proportional Gain * Process Gain = 15 * 5 * 1/12 = 6.25 repeats per minute. Many modern systems now include anti-reset windup features for level loops to prevent integral saturation when pumps trip or flow is interrupted. Make sure it is enabled.

Often with level loops, most of your time tuning them is spent observing the closed loop response. If your loop appears unstable, too aggressive, you can cut the proportional and the integral in half and observe the response. If your loop is not aggressive enough, you can double the proportional and integral and observe the loop. These adjustments are due to your observation of how your controller is reacting to the process. If your loop is cycling due to tuning, then you must either cut back the integral or increase the proportional. Increasing the proportional too much will cause the valve to both wear out and disturb the flow unnecessarily. In this case, it would be better to decrease the integral. Again, this is really closed loop tuning and should only be done to fine tune this loop. Since most engineers tune by feel with the loop closed or in automatic, most loops in plants are very under tuned, or very sluggish. So avoid tuning by feel in general. Smart positioners today can monitor valve travel and wear. Aggressive tuning might improve level control short term but increase maintenance costs. Tune with mechanics in mind.

Cycling of a level loop is most often the result of what is called “stiction” in the level control valve. When a valve is “sticking,” you or the controller can send it small signal increases or decreases and the valve will not move. It is stuck. When you or the controller sends enough small changes, it finally overcomes the stiction and moves all at once. But by then it moves way too much and you continually overshoot the setpoint. No matter how much you tune the loop, you will not stop this cycling. You can only change the frequency of the cycling. Two methods are recommended to help solve this problem. Tune with a fairly high gain so the noise on the transmitter signal will cause the valve to jitter by the amount of the stiction. Then, when the valve does need to move, it will have already overcome the stiction. This, however, would not be a long-term fix because of the valve wear. Another way is to cascade the level loop with a flow loop. Let the output of the level loop, instead of going to the control valve directly, feed as a setpoint to a new flow loop, if a flow signal is available. The flow loop can be set up as a faster responding loop, creating less lag. The important thing is to assess the quality of the valve response before you start any tuning. Cascaded level-to-flow control is now considered a best practice automation standard in most industries, especially where safety or environmental containment are concerned.

Another shortcut you can use is to group tanks at your plant into three size categories: small, medium, and large. This grouping is based on the theory that the residence time is proportional to the size of the tank. The residence time of a tank is defined as the time it takes, usually in minutes, to fill or empty the tank with the valve wide open or fully closed. For economic reasons, designers do not usually provide very large valves, lines, or pumps for large tanks. Therefore, the residence time tends to increase with the increasing size of the tank. The smaller tanks should end up with an integral of about 60.0, the medium tanks about 6, and the large tanks should end up around 1 to 1.5. What is small, medium, and large? When you group your tanks, you will find out. Small tanks tend to be those 5 to 10 ft tall tanks. Small chemical tanks are an example. Medium tanks are most of the tanks with controls in your plant, such as blend chests, reactors, and large distillation columns. The large tank category is reserved for giant storage tanks and large clarifiers. Keep in mind that these are rules of thumb and, depending on the valve, line, and pump sizes, these numbers may need to be adjusted. Model-based level tuning tools now exist, but these rules of thumb remain industry-standard starting points.

Conclusions

I was thinking I ought to keep this article short. If I wrote 5000 words on “Control Loop Tuning Made Easy,” the length of the article would contradict the title. So, I will conclude. I hope you have found the information in this post helpful.

Although I think industrial production is more art than science, some plants I have been in would classify production as neither art nor science, but as a miracle. Just for the record, I think tuning should always be viewed as a science.

Even as automation evolves with predictive alarms, advanced analytics, and smart field devices, the fundamentals of good loop tuning drive everything else: reduced variability, better uptime, and operators who do not stare angrily at the screen.

Happy Tuning!!

Todd Harlow - Project Manager