Part 3: More on derivative control

To investigate how derivative action works, let’s look at a proportional derivative or PD controller. PID controllers are far more common than PD alone, but we already have an understanding of the integral component’s effects from the first two parts of this series, so we don’t need to review it again.

For a PD controller, we add the derivative of the error into the equation. Similar to what we discussed in the previous posts, we’re not really interested in deriving a derivative of the error function. Conceptually, the derivative in this case refers to how fast the error is changing. So, if we take the change in error divided by the change in time we get the slope.

To explain how this works, let’s look at the pseudo code for this controller. The calculation of error is the same as before: setpoint minus process value. Since the derivative reduces down to the change in error, the output is now the same proportional component as before: gain times error. The current error minus last error is multiplied by the gain and divided by the derivative time constant. The current error is stored in last error for use in the next scan.

Error : = Setpoint – ProcessValue;

Output : = K * Error + K/tau_i * (Error – LastError);

LastError : = Error; 


So what does this mean?

The proportional component is affected by the error at that time, in the present. The integral component is affected by an accumulation of the error, or the past. The derivative component is a measure of how fast the error is changing, or a prediction of the future error.

How is this prediction of the future used? At first glance you might think that this term would be used to get you to your setpoint that much faster. But, that is not really the case. In practice, the derivative component is used to detect when the process variable is changing too fast, and it puts the brakes on to prevent overshooting the setpoint.

So if the derivative component acts as brakes on the momentum, how does it get you to the setpoint faster? It does this by allowing you to use a higher proportional gain to get you there quickly, but dampening the overshoot that would normally make that level of gain unstable.

The tuning constants for derivative control are typically the same units as the time constant for reset. A couple of other considerations though are important. On many controllers the derivative term is filtered independently. This prevents signal noise or spurious disturbances from being interpreted as a change in momentum, which causes the derivative action to overreact. Also, on some controllers the derivative does not actually derive from the error, but instead on the process variable signal alone. This prevents a change is set point from being seen as a change in momentum.

Part 2: Adding integral and derivative to the mix.

Last week we started with proportional. (Read Part 1) Now let’s look at the next part of the equation, the integral component:

The most striking (and scariest) part of this equation is the big integral sign in the middle. If you’ve had high school calculus, you think to yourself, “I’ve got this. Integrals don’t scare me. I just need to find the area under the curve from time zero to time t of the error function.”

But, this is the real world. What is time zero? How do I integrate an error function? The good news is that the real definition is much simpler than calculus. What the PID function does is take a portion of the error and adds it to a running total. This running total, sometimes called reset, is added to the output. Since reset increases or decreases a little at a time, it adjusts the output of the valve incrementally each scan.

For a PI controller, the two factors that we have covered so far are K_p and K_i, but if you look at the faceplate for most industrial systems, there is only one K (gain) that has no units, and a τ_i (integral time constant) designated as seconds or minutes per repeat. So, a little translation is required. Most industrial controllers don’t use the independent form of the equation shown above. Instead, they use the dependent form of the equation: 

The K is typically the same as the proportional gain, K_p.  The factor τ_i determines how much of the error is going to be applied to the accumulated reset on each scan. So in the big mathy equation, K_i can essentially be replaced by the faceplate parameters:  K⁄τ_i.

What’s important to understand from this is that the gain that affects the proportional action of a controller also affects the integral action. But, the integral time constant τ_i only affects the integral action.

In pseudo code this would look like:

Error := Setpoint - ProcessValue;
Reset := Reset + K/tau_i * Error;
Output := K * Error + Reset;
The unit’s minutes per repeat for the integral time constant τ_i  comes from the fact that if the error stays constant, that is how long would it take for the integral accumulator to repeat the proportional change in output.

Note: Another way of specifying the integral tuning parameter is in seconds, and then it is the reciprocal of seconds per repeat. If the integral time constant is in seconds, the bigger the number, then the slower the response. If the integral is in seconds per repeat, the opposite is true.

Derivative
Now let’s look at derivative:

Again, this is another mathy looking equation with a simple explanation. The mathy definition first, the output will be changed by the derivative (or rate of change) of the error function. What this means is that the output will be affected by the change in error from one scan to another. Adding this to our pseudocode gives us:

Error := Setpoint - ProcessValue;
Reset := Reset + K/tau_i * Error;
Output := K * Error + Reset + ((PreError – Error) * K/tau_d));

PreError := Error;  //Save the error for the next scan
What is intended is for the output to change as soon as the process variable begins to move either toward or away from the setpoint. What results can be a very quick response to a change in error from one scan to another.

The intention of derivative action is to respond to changes as they begin to occur. For example, if a temperature is starting to rise, the valve will begin to open as soon as it sees the change instead of waiting for it to cross a setpoint. This can result in a very rapid response to a small change. This rapid response can become unstable if there is noise in the process variable or on a setpoint change. So, the derivative action is often filtered separately and is sometimes calculated on PV only to ignore setpoint changes.

Summary
So now we have reviewed the three components of the PID algorithm. One way they have been described is in terms of the flow of time. P depends on the present error, I on the accumulation of past errors, and D on the prediction of future errors based on current rate of change. 

Automation’s current challenge: Finding opportunity in obsolescence

It is no secret that many of our control systems are reaching their twilight years. For some, they are already there. According to one report, there are currently $65 billion worth of obsolete control systems worldwide, and that number is increasing every day.

This is especially true in oil and gas, a sector that is quickly outgrowing the various upgrades and modifications that have been made to its aging sys­tems over the years. But the term “upgrades” is a misnomer here, as the intention is simply to main­tain—not improve—basic operational functionality. These manufacturers continue to refurbish obsolete systems with the hope of squeezing another year or two out of them. Though the goal is cost sav­ings, ultimately this approach is the least efficient and most costly. Significant downtime is inevitable when the system completely breaks down.

But breakdowns are not the only concern. Ob­solescence is. With the ever-increasing velocity of change in manufacturing, it is becoming more and more clear that the old way is no longer the only path forward. In fact, it is a dead end. To keep up with the evolving automation landscape, we have to approach obsolescence as an oppor­tunity for operational improvement and cost re­duction. An opportunity to innovate rather than replicate. An opportunity for American manufac­turers to regain their competitive edge.

Different approaches to DCS and PLC migration

When a control system begins to outlive its use-fullness, isolating failed parts and replacing them with new ones is a common approach. But begins as required maintenance quickly becomes overextension. Systems running above their design capacity reduce operational efficiency. This means the cost savings from replacing a part rather than the entire system are not just nullified; they are actually reversed. You might think you are saving money, but you are actually losing more of it than you think due to production inefficiencies.

Fully leverage and innovate

Proactive manufacturers do not wait for process downtime to force their hand. They have migra­tion strategies in place before the system begins to lag. They bring in outside vendors to demonstrate new technology and systems integrators for unbi­ased support and expertise. They conduct front-end loading (FEL) studies to identify opportunities for improvement. They do not just look to get by; they look to get ahead.

Make the most of this opportunity Perhaps you have already begun to consider mi­grating your distributed control system (DCS) or programmable logic controller (PLC) system. Or perhaps your system is on its last leg, and you are worried about downtime once it fails completely. Either way, if you want to remain competitive—or regain your competitive edge—waiting is not an option in today’s manufacturing landscape.

Conduct FEL studies to determine how efficien­cies built into your new system can help you re-coup the costs of migration sooner than you think. Take what you learn to make a case for the capital you will need to move forward. Collaborate with systems integration experts to determine the best path forward. And, above all, start today

Part 1: The basic concepts and proportional control.

Most process control engineers have been exposed to the basic equation in a form that looks something like this:

More than you want to swallow in one bite? Let’s break this down into the major components:

Output: u(t)  is the output of the controller at the end of the scan. If the output of the controller is a valve, then the output is the valve position that the controller is requesting after it has seen the inputs. In most controllers, this is actually the change in output from 50%. So if u(t) = 0 then the valve output is 50%; if u(t) = 1 then the valve output is 51%; and if u(t) = -2 then the valve output is 48%. You get the idea. But what’s important is that it’s not a change in output from the previous scan, but a new output.

Proportional
K_pe(t) is the proportional component, the P in PID. If you have a controller configured as proportional only, this is it. So let’s look at how this works.

Let’s start with my own misconception of how I thought it worked. When I imagine a controller, I picture myself turning a valve while watching a gage. I look at the gage, decide if I need more or less, turn that valve a little more or a little less, and then repeat the process until the gage shows the value I want. That sounds fundamentally logical, but it is not how a proportional only controller works. It’s more like if I were to look at the gage, subtract what it reads from what I want it to read, and then take that error over to a chart to look up a new value for the valve.

e(t) usually called error, is simply the difference between the setpoint and the process variable. It is the difference between where you are and where you want to be, right now, at this instant.

K_p gain, is a factor that is multiplied by the error to give you the new output, the new valve position. It’s that simple. The error at that instant of the scan is calculated and the new output is calculated.

Let’s look at an example of pseudo code to explore how this works:

Error = Setpoint - ProcessValue;
Output = K * Error;
This control algorithm is deceptively simple, yet it gives an immediate response to a setpoint change or a disturbance in the process. And if K is set correctly, will quickly move the process toward the setpoint. But, it won’t get the process to the setpoint because there has to be some error if the output is anything other than 50%.

Note: On some systems (though not often in modern systems), gain is expressed as proportional band. Proportional band is defined as the amount of change in the controlled variable required to drive the loop output from 0 to 100%. To convert between the two, gain = 100/PB.

Tuning PID control loops for fast response

When choosing a tuning strategy for a specific control loop, it is important to match the technique to the needs of that loop and the larger process. It is also important to have more than one approach in your repertoire, and the Cohen-Coon method can be a handy addition in the right situation.

The well-known Ziegler-Nichols tuning rules work well only on processes with very long time constants relative to their dead times, and on level control loops. However, its performance is not good on flow, liquid pressure, and many other loops that require fast adjustment. In contrast, the Cohen-Coon tuning rules work well on virtually all self-regulating processes and were designed to give a very fast response.

The method's original design resulted in loops with too much oscillatory response and consequently fell into disuse. However, with some modification, Cohen-Coon tuning rules proved their value for control loops that need to respond quickly while being much less prone to oscillations.

Applicable process types

The Cohen-Coon tuning method isn't suitable for every application. For starters, it can be used only on self-regulating processes. Most control loops, e.g., flow, temperature, pressure, speed, and composition, are, at least to some extent, self-regulating processes. (On the other hand, the most common integrating process is a level control loop.)

A self-regulating process always stabilizes at some point of equilibrium, which depends on the process design and the controller output. If the controller output is set to a different value, the process will respond and stabilize at a new point of equilibrium.

Target controller algorithm

Cohen-Coon tuning rules have been designed for use on a non-interactive controller algorithm such as that provided by the Dataforth MAQ 20 industrial data acquisition and control system. There are controllers with similar characteristics available from other suppliers.

Procedure

To apply modified Cohen-Coon tuning rules, follow the steps below. The process variable and controller output must be time-trended so that measurements can be taken from them.

1. Do a controller output step test:

• Put the controller in manual and wait for the process to settle out.
• Make a step change in the CO (controller output) of a few percent and wait for the PV (process variable) to settle out. The size of this step should be large enough that the PV moves well clear of the process noise and disturbance level. A total movement of five times more than the peak-to-peak level of the noise and disturbances on the PV should be sufficient.

2. Determine the process characteristics (see Figure 1):

• If the PV is not ranged 0-100%, convert the change in PV to a percentage of the range: change in PV [in %] = change in PV [in engineering units] × 100 / (PV upper calibration limit - PV lower calibration limit).
• Calculate the process gain (g_p): g_p = total change in PV [in %] / change in CO [in %].
• Find the maximum slope of the PV response curve. This will be at the point of inflection. Draw a tangential line through the PV response curve at this point.
• Extend this line to intersect with the original level of the PV before the step in CO.
• Take note of the time value at this intersection and calculate the dead time (t_d): t_d = time difference between the change in CO and the intersection of the tangential line and the original PV level.
• If t_d was measured in seconds, divide it by 60 to convert it to minutes. (Since the Dataforth PID controller uses minutes as its time base for integral time, all measurements have to be made in minutes or converted to minutes. Many other controllers are similar.)
• Calculate the value of the PV at 63% of its total change.
• On the PV reaction curve, find the time value at which the PV reaches this level.
• Calculate the time constant (t): t = time difference between intersection at the end of dead time and the PV reaching 63% of its total change.
• If t was measured in seconds, divide it by 60 to convert it to minutes.

3. Repeat steps 1 and 2 three more times to obtain good average values for the process characteristics.

4. Calculate controller settings for a PI or PID controller using the modified Cohen-Coon equations below. (The modified rules calculate the controller gain as ½ of that calculated by the original rules.) 

5. Enter the values into the controller, make sure the algorithm is set to non-interactive, and put the controller in automatic mode.

6. Change the setpoint to test the new values.

Do fine tuning if necessary. The control loop's response can be slowed down and made less oscillatory, if needed, by decreasing K_C and/or increasing T_I.

Conclusion

These modified Cohen-Coon tuning rules are an excellent method for achieving fast response on virtually all control loops with self-regulating processes. They are an effective and highly reliable alternative to the Ziegler-Nichols tuning method, which does not work well when applied to many self-regulating processes.

The Future of Industrial Automation

Since the turn of the century, the global recession has affected most businesses, including industrial automation. After four years of the new millennium, here are my views on the directions in which the automation industry is moving.

The rear-view mirror

Because of the relatively small production volumes and huge varieties of applications, industrial automation typically utilizes new technologies developed in other markets. Automation companies tend to customize products for specific applications and requirements. So the innovation comes from targeted applications, rather than any hot, new technology.

Over the past few decades, some innovations have indeed given industrial automation new surges of growth: The programmable logic controller (PLC) – developed by Dick Morley and others – was designed to replace relay-logic; it generated growth in applications where custom logic was difficult to implement and change. The PLC was a lot more reliable than relay-contacts, and much easier to program and reprogram. Growth was rapid in automobile test-installations, which had to be re-programmed often for new car models. The PLC has had a long and productive life – some three decades – and (understandably) has now become a commodity.

At about the same time that the PLC was developed, another surge of innovation came through the use of computers for control systems. Mini-computers replaced large central mainframes in central control rooms, and gave rise to "distributed" control systems (DCS), pioneered by Honeywell with its TDC 2000. But, these were not really "distributed" because they were still relatively large clumps of computer hardware and cabinets filled with I/O connections.

The arrival of the PC brought low-cost PC-based hardware and software, which provided DCS functionality with significantly reduced cost and complexity. There was no fundamental technology innovation here—rather, these were innovative extensions of technology developed for other mass markets, modified and adapted for industrial automation requirements.

On the sensor side were indeed some significant innovations and developments which generated good growth for specific companies. With better specifications and good marketing, Rosemount's differential pressure flow-sensor quickly displaced lesser products. And there were a host of other smaller technology developments that caused pockets of growth for some companies. But few grew beyond a few hundred million dollars in annual revenue.

Automation software has had its day, and can't go much further. No "inflection point" here. In the future, software will embed within products and systems, with no major independent innovation on the horizon. The plethora of manufacturing software solutions and services will yield significant results, but all as part of other systems.

So, in general, innovation and technology can and will reestablish growth in industrial automation. But, there won't be any technology innovations that will generate the next Cisco or Apple or Microsoft.

We cannot figure out future trends merely by extending past trends; it’s like trying to drive by looking only at a rear-view mirror. The automation industry does NOT extrapolate to smaller and cheaper PLCs, DCSs, and supervisory control and data acquisition systems; those functions will simply be embedded in hardware and software. Instead, future growth will come from totally new directions.

New technology directions

Industrial automation can and will generate explosive growth with technology related to new inflection points: nanotechnology and nanoscale assembly systems; MEMS and nanotech sensors (tiny, low-power, low-cost sensors) which can measure everything and anything; and the pervasive Internet, machine to machine (M2M) networking.

Real-time systems will give way to complex adaptive systems and multi-processing. The future belongs to nanotech, wireless everything, and complex adaptive systems.

Major new software applications will be in wireless sensors and distributed peer-to-peer networks – tiny operating systems in wireless sensor nodes, and the software that allows nodes to communicate with each other as a larger complex adaptive system. That is the wave of the future.

The fully-automated factory

Automated factories and processes are too expensive to be rebuilt for every modification and design change – so they have to be highly configurable and flexible. To successfully reconfigure an entire production line or process requires direct access to most of its control elements – switches, valves, motors and drives – down to a fine level of detail.

The vision of fully automated factories has already existed for some time now: customers order online, with electronic transactions that negotiate batch size (in some cases as low as one), price, size and color; intelligent robots and sophisticated machines smoothly and rapidly fabricate a variety of customized products on demand.

The promise of remote-controlled automation is finally making headway in manufacturing settings and maintenance applications. The decades-old machine-based vision of automation – powerful super-robots without people to tend them – underestimated the importance of communications. But today, this is purely a matter of networked intelligence which is now well developed and widely available.

Communications support of a very high order is now available for automated processes: lots of sensors, very fast networks, quality diagnostic software and flexible interfaces – all with high levels of reliability and pervasive access to hierarchical diagnosis and error-correction advisories through centralized operations.

The large, centralized production plant is a thing of the past. The factory of the future will be small, movable (to where the resources are, and where the customers are). For example, there is really no need to transport raw materials long distances to a plant, for processing, and then transport the resulting product long distances to the consumer. In the old days, this was done because of the localized know-how and investments in equipment, technology and personnel. Today, those things are available globally.

Hard truths about globalization

The assumption has always been that the US and other industrialized nations will keep leading in knowledge-intensive industries while developing nations focus on lower skills and lower labor costs. That's now changed. The impact of the wholesale entry of 2.5 billion people (China and India) into the global economy will bring big new challenges and amazing opportunities.

Beyond just labor, many businesses (including major automation companies) are also outsourcing knowledge work such as design and engineering services. This trend has already become significant, causing joblessness not only for manufacturing labor, but also for traditionally high-paying engineering positions.

Innovation is the true source of value, and that is in danger of being dissipated – sacrificed to a short-term search for profit, the capitalistic quarterly profits syndrome. Countries like Japan and Germany will tend to benefit from their longer-term business perspectives. But, significant competition is coming from many rapidly developing countries with expanding technology prowess. So, marketing speed and business agility will be offsetting advantages.

The winning differences

In a global market, there are three keys that constitute the winning edge:

• Proprietary products: developed quickly and inexpensively (and perhaps globally), with a continuous stream of upgrade and adaptation to maintain leadership.
• High-value-added products: proprietary products and knowledge offered through effective global service providers, tailored to specific customer needs.
• Global yet local services: the special needs and custom requirements of remote customers must be handled locally, giving them the feeling of partnership and proximity.

To implementing these directions demands management and leadership abilities that are different from old, financially-driven models. In the global economy, automation companies have little choice – they must find more ways and means to expand globally. To do this they need to minimize domination of central corporate cultures, and maximize responsiveness to local customer needs. Multi-cultural countries, like the U.S., will have significant advantages in these important business aspects.

In the new and different business environment of the 21st century, the companies that can adapt, innovate and utilize global resources will generate significant growth and success.

4 Big Trends that Impact Industrial Automation and What To Do About Them, Part 1 of 2

Every decade has its big manufacturing trends and hyped-up IT issue(s). Remember Y2K? Nowadays there are several topics that have been the subject of numerous articles in manufacturing trade publications. These include:

1. The Internet of Things (IoT)
2. Big Data
3. Cloud Computing
4. Industry 4.0.

All of these trends involve a lot of devices networked together and a lot of data available to do things. They also include deciding whether data is stored and applications accessed from the computer next to you or from a server located somewhere else.

The good news is: The supporting technologies behind all the buzzwords are already available. Are they empty hype, a valid threat, or an opportunity? (the answer is yes). In this article, I’ll tackle each of these topics one by one, focusing on what you need to know to sort out reality and react to each.

1. Connected Industrial Devices aka the Internet of Things (IoT)

The IoT is about a lot of industrial devices networked together. For example, I’ve encountered automotive plants with 8,000 devices on a single network and consumer products plants with 12,000.

The benefits of networking these devices include:

• Managing everything from anywhere.
• Reducing complexity and hardware costs with one network technology.
• Moving control and information at will.
• Expanding it all easily.
  

The Internet of Things (IoT) is about connecting industrial devices together and taking advantage of the connectivity for business improvement.

The IoT ChallengeThe challenge is in learning the new technology and understanding how to carefully design for systems that dwarf even the largest fieldbuses.

As the IoT concept continues to develop, vendors and standards groups will take care of the hard stuff. The technology will evolve to accommodate the growth—more wireless will be added, everything will be made more secure, higher levels of network traffic will get managed, and more IP addresses will be created.

When all is said and done, you’ll be able to continue as before, just with a few more zeroes in the number of devices on your network.

The IoT OpportunityUltimately, however, it will be up to you to decide how your company can operate differently when virtually anything can be on your network.

2. The Next Frontier of Manufacturing IT: Big Data

Big Data is about having a ton of information to use. Ten years ago, manufacturers recognized they could and should store production data and, in response, they added storage space at an alarmingly fast rate.

The Big Data ChallengeNow that all this data is at hand, more than one manufacturer has been known to say: “We’re collecting everything, but we aren’t really using any of it; and we aren’t sure what we should do with it all.”

This trend continues today, but with software that knows how to analyze and help you use that data. Some of the best technology is derived from search engine and web companies, like Google and Amazon that measure, interpret and record every twitch their users make. Vendors will continue to make data transport and storage bigger and faster, and will keep creating software to help you use the data.

The challenge with Big Data is how to use it to gain efficiencies, insight speed and competitive advantage.

The Big Data OpportunityYour decision is how to connect the information “gold” in your hands to your company’s business challenges to see new opportunities to gain efficiencies, insight, speed and competitive advantage.

3. Cloud Computing

Cloud computing is about storing your information and computing power somewhere other than the computer next to you. Today, most see cloud computing as an opportunity to gain more computing power and storage space, while reducing the overall cost of maintaining and managing IT equipment and software. They also see new ways to collaborate with others.

While the computing aspect of cloud computing has a ways to go to become truly viable for the industrial space, storage is coming on strong as an easy way to back up and share data.

The Cloud Computing ChallengeLike the IoT and Big Data, vendors will handle the technology issues here as well. Your job is to assess the benefits and risks of having your critical data available and secure when it is located and managed by someone else, somewhere else.

In the industrial world, we define “real-time” and “mission-critical” different than the IT group, so our comfort level with what and how the cloud can work for us may vary dramatically. Proceed here with caution.

The Cloud Computing OpportunityOnce satisfied, however, you can determine how your company might benefit by having virtually unlimited computing power, storage and, eventually, new avenues of collaboration.

4. Industry 4.0

Industry 4.0/Manufacturing 4.0, which originated in Germany, is about the strategic use of smart devices. As a frame of reference, consider this:

• In the 1990s, a photo eye was available that held more than 30 pieces of information when networked on DeviceNet.
• About the same time, variable frequency drives (VFDs) and motor starters went from having only a few analog and digital signals tied in with their power to sharing hundreds of pieces of information when networked.

The point here is that the technology behind Industry 4.0 isn’t new.

The Industry 4.0 Opportunity and ChallengeThe new opportunity with Industry 4.0 is using the wealth of information available from smart, networked devices to revolutionize industrial processes.

The challenge is to think big and drive the change necessary within your organization to capitalize on information available today to for success tomorrow.

Poised to Take AdvantageGiven that the supporting technologies behind all these futuristic industry concepts are available today, the question is: Are you ready to take advantage of them?

In part 2 of this series I will address the steps you need to take to take advantage of these 4 big trends. I will also present some ideas of how these trends might be used by forward thinking organizations.

What do you think of Big Data or the Internet of Things? Is your organization examining how to use them for competitive advantages? I look forward to hearing your thoughts.