ExperTune Library

Properly tuned and optimized PID loops increase product quality, plant uptime and throughput

John Gerry, President, ExperTune Inc.,
Hubertus, Wisconsin

Reprinted with permission from Plant Services. This article appeared in the September 1999 issue of Plant Services

One of the most common approaches to controlling a field device is the proportional-integral-derivative (PID) controller. PID loops are everywhere in plants, controlling the critical flows, pressures, temperatures and compositions that make or break plant uptime and product quality. Use of the latest software tools helps get these loops tuned and optimized. To optimize the loop, the individual components of the loop must be working properly. This includes a valve (or drive) sizing with minimal stiction and hysteresis. Then, linearize the entire loop, not just the valve. Next, identify and eliminate interactions or cyclic upsets. Finally, tune the PID controller and set the optimum process variable filter. Improving any of these steps can have a significant impact on improving functionality in your plant.

PID loops are everywhere
in plants, controlling the critical flows,
pressures, temperatures and compositions
that make or break plant
uptime and product quality.

Get connected

There are a variety of ways to connect analysis software to your PID loops. Most analysis software supports DDE (Windows Dynamic Data Exchange) or imported plant data from plain ASCII files. Other software supports OPC (OLE for Process Control). OPC will eventually replace DDE as a standard way to connect your controller to a variety of Windows software. Some software includes wizards, which simplify the connecting process. There are also connections via direct drivers through a PC's serial port. The brute force approach is to use a small industrially hardened data acquisition system that reads voltage signals and includes jacks to clip in parallel across your control system's I/O.

Valve working?

Often overlooked, making sure your control valve works properly is key to getting the loop optimized. Hysteresis is unwanted slop or dead zone in the valve. If hysteresis suffering, and possibly cycling.

To check the hysteresis, follow these steps:

• With the controller in manual mode, move the controller output 10 percent and let the process variable (PV) settle.
• Move the output another 10 percent in the same direction. Wait for the PV to settle. Record how much it changed. Call this PV₂
• Move the controller output back 10 percent. Let the PV settle. Record how much it changed from the last step as PV₃.
• The hysteresis is 10 (1 - PV₃/PV₂) percent.
  **Post-publication authors note: the 10% changes above result in a simple calculation, but are probably too large of a change to make in your plant. (ExperTune software includes a hysteresis checker that lets you make any size bumps)

If your hysteresis is more than one percent for valves with positioners or three percent for valves without positioners, consider repairing or changing equipment to reduce hysteresis and improve control. Often, the addition of a valve positioner will correct the problem. Caution: Use of valve positioners in flow loops is usually not recommended.

Analysis software can automatically find the hysteresis for you from less rigid test data. It will also check the sizing and transmitter spans. By adding the correct process variable filter, you can increase the life of your valve or drive without affecting loop performance.

Increase uptime and throughput: linearize that loop

Most loops are not linear; process gain changes as the measurement or controller output changes. Non-linear loops respond quickly, even to the point of oscillation, at one end of the range (or at one production rate) and are sluggish at others. A classic example is pH loops, but most loops are non-linear to some degree and can benefit by linearization.

The simplest approach to these loops is to tune the controller for the condition when the process gain is the highest. The result is sluggish tuning everywhere else. A more optimal strategy is adding a characterizer or linearizer to the loop. The combination of the characterizer with the non-linear process yields a linearized loop. With characterization, you tune the loop for great response across the entire range. This will provide better product quality, increase your uptime, and in many cases, allow you to increase your production rate without changing your equipment.

There are two type of characterizers: input and output.

Most loops need the output characterizer. If the linearity changes with load or production rate, use an output characterizer. Examples are: flow, pressure and temperature loops; jacket temperature in split-range chemical reactors; slave loops in cascades or any loop in which the setpoint will change. Use an input characterizer with pH, pIon, oxidation reduction and some temperature control loops on distillation columns.

To design the characterizer, you need data from your process. Output characterizers use plant data from the range of output you want to linearize. Input characterizers use lab titration data. The latest cutting edge software includes wizards that take you through the entire characterizer design process. The software does everything from collecting data to writing the characterizer XY points or equations and finally optimally tuning the controller.

Figure 1. Titration points for a pH loop and the corresponding characterizer to linearize it

Figure 1 shows titration points for a pH loop (crosses on the graph) and the characterizer (redboxes) to linearize it. In this case, the characterizer output is a set of equations, but the user can also select XY points or other languages.

Implement an output characterizer by appending it to the controller output. An input characterizer is slightly more complex. With the input characterizer, characterize both the setpoint and the process variable. However, for display purposes, use the actual pH and setpoint before they are characterized. Also be sure that the setpoint entry is finished before the characterizer.

Product quality cycling

If a loop is cycling, the cause may be from interactions with other loops or from an upstream cyclic loop. State-of-the-art software tools help uncover these mysterious and hard-to-trace process cycling problems.

There are several tools available. One is cross-correlation analysis, which examines if a loop is affecting others. If it is, you can use a tool called "relative response time," a relative indicator of the speed of the control loop, to separate and decouple the loops. The smaller the relative response, the faster the loop. The higher the relative response value, the slower the loop.

To prevent interaction, adjust the tunings in the interacting loops so that the relative response time is different by a factor of five. The loops will then be responding at different times, reducing their interactions.

Another useful tool for pinpointing cycling is "power spectral density." It uncovers hidden cycles in the signal. Analogous to a prism that separates out the colors of white light, power spectral density mathematically separates normal operating data into its spectral or frequency components. A peak in the power spectral density indicates a cycling problem. Once you find a suspicious frequency, keep searching upstream until the peak is lower. The prior loop exhibiting the peak will be the problem.

PID tuning—the icing on the cake

Once your loop has only small hysteresis and is fairly linear, it's time to tune. The latest software tunes the PID controller and provides additional analysis—all from one loop test.

From the same test data used for tuning, some analysis software includes modeling, simulation and robustness plots. These let you see how the loop will respond offline before you use the tuning parameters in the plant. Robustness is an important consideration since there is always a tradeoff between fast response and sensitivity to the process changing.

Robustness plots graphically show how robust or sensitive the control loop is to process changes.

They also show how changing dead time or gain affect the stability of the loop.

The robustness plot has a region of stability and a region of instability. In Figure 2, the green area indicates instability (higher gain and dead time). The yellow area is stable. The line between indicates the verge of instability or continuous oscillations. For example, looking at the robustness plot, if the dead time were approximately 20 with a process gain of about 2.2, the loop would be on the verge of instability. In general, tune the loop to stay out of the red area in the plot.

The red and blue lines compare different tunings or uses of filtering. In our case, the red line is for a controller with a filter and the blue line for one without. Without the filter, the loop is slightly more stable.

How to make valves last (almost) forever

By simply filtering the PV, you might extend your valve's life by as much as a factor of three to five. Adding a correctly sized filter to the PV reduces the controller output jitters without degrading the loop's performance.

There is a fine line in choosing the correct size filter. If too small, it does nothing. Too large and the filter becomes slow enough to degrade the performance of the loop. State-of-the-art analysis software automatically finds the largest filter time possible without hurting your loop.

Figure 2. State-of-the-art analysis software automatically finds the largest filter time possible without hurting your loop

In Figure 2, the red lines show responses and robustness with the filter. Blue lines are without thefilter. In the lower graph (measured noise response), using the filter (red line) greatly decreases how much the valve will move. The "valve travel index" just above the lower graph assigns a numerical value to how much less the valve will move-in this case about 600 percent less. It also reverses 60 percent less. Adding the filter greatly reduces valve movement and reversals in this system. There is always a trade-off in process control and the robustness plot shows what we give up to get the increased valve life. In this case, not much. Looking at the robustness plot, the difference between the two systems is very small. Addition of the filter made the loop slightly less stable. Had we added a larger filter, the stability would decrease further.

Conclusions

By using state-of-the-art analysis software, you can derive the most efficient use of your equipment, and, therefore, reap the greatest efficiency benefits in your plant. Once optimized, your plant operations will improve more than you thought possible with higher quality than ever before. Find more information on the OPC Foundation at www.opcfoundation.org and on ExperTune at www.expertune.com. Figures courtesy of ExperTune, Inc.