Effect of Controller Dynamics on Loop Performance Tips

Tuning has a profound effect on the practical limit to control loop performance. While the effect of execution time and filter time is often much less in comparison, these time settings can get the user into trouble depending on tuning and loop dynamics.  Here is a perspective, overview, and recommendations.

Perspective

The integrated error for unmeasured load disturbances is proportional to the PID reset time plus the execution time and filter time as shown in the equation on slide 95 in the short course ISA-New-Orleans-Effective-Use-of-PID-Controllers.

These PID execution time and filter time settings can potentially further decrease performance by creating additional dead time. Conclusions depend upon the "before" and "after" of loop dynamics and PID tuning. However, the consequences are not well recognized leading to misconceptions.

Test cases using simulations are often misleading because they do not have the spectrum of dynamics and timing randomness. An open loop test on the effect of PID execution time may not show an increase in dead time if the introduced change arrives before instead of after a PID execution. An open test of an increase in filter time will not show an increase in dead time if there are no other time constants in the loop.  

The results for closed loop tests depend upon the tuning. If the controller is sufficiently detuned, no deterioration is observable beyond what is predicted by the equation for the integrated error. Equations for the implied dead time from tuning are developed to help guide the practitioner. The implied dead time minus the original dead time is the margin of dead time available for execution time and filter time without degrading the performance and requiring retuning to prevent an oscillatory response.

The implied dead time is a back calculation of dead time from the actual tuning settings as shown on slide 96 in the short course ISA-New-Orleans-Effective-Use-of-PID-Controllers. Note that most PID controllers are not tuned as aggressively as permitted by the actual loop dead time. Consequently the implied dead time is almost always greater than the actual dead time. The major insight is that a sluggishly PID tuned will perform as badly as a loop with an actual dead time equal to the implied dead time.

A transmitter damping setting has the same effect as a signal filter. For wireless devices, it is desirable to use the transmitter damping rather than a signal filter in the DCS to reduce noise. The transmitter damping can be set to keep measurement noise less than the wireless trigger level to prevent unnecessary updates prolonging battery life.

A large signal filter time can have a particularly devious effect. If the signal filter becomes the largest time constant in the loop, the filter time is the open loop time constant in the tuning equations. An increase in the signal filter time will enable an increase in the controller gain. Oscillations that already existed may have smaller amplitude from the attenuation of the actual oscillations per the equation on slide 12 in the short course ISA-New-Orleans-Effective-Use-of-Measurements-Valves-and-VSD. Operations may think the performance is actually better as the signal filter is increased smoothing out the picture. The saving grace is that the signal before the filtering can be displayed and trended. Also, if there are other time constants in the loop, a greater fraction is converted to dead time leading to an increase in the period of oscillation.

An increase in execution time and signal filter time will increase the ultimate period, which is the best indicator of adverse results of increased dead time. Since the ultimate oscillation method of tuning is not practical, most practitioners are unaware of changes in the ultimate period. The relay oscillation method of auto tuning computes the ultimate period and gain. This auto tuner will show the effect. The effect of execution time may not be noticeable if a change in module execution time alters auto tuner evaluation of results and is less than other variations in real world applications.

While it is great being able to compute probable effects, in actual applications the unexpected should be expected. Plant operations have a great way of humbling the most knowledgeable process control engineer. There are no experts in the control room.

To help deal with the unknowns and unrealized consequences, simple diagnostic techniques such as noting the effect of a dramatic increase in the reset time or putting a PID momentarily in manual can help determine if there is a tuning problem and what is the mostly likely correction.

Life is a balance. Proper tuning also involves a balance, in terms of the contribution of the proportional, integral, and derivative modes. Each mode has relative advantages and disadvantages. Problems develop when one mode dominates to the detriment of the overall objective. Diagnostic techniques and smart reset logic can maintain a balance.

Overview

The equation for the integrated error shows the effect of PID execution time and signal filter time for a given set of tuning settings. If an increase in the dead time from the execution time and filter time causes the total dead time to exceed the implied dead time from the tuning settings, the controller needs to be re-tuned to prevent the start of an oscillatory behavior.

The dead time from the PID controller is ½ the execution time and plus a fraction of the signal filter time assuming the calculation in the module with the PID does not cause a latency in terms of the PID output availability. The fraction approaches 1 as the filter time becomes small compared to the largest time constant in the loop. Hopefully the largest time constant is in the process to slow down the actual process excursion from fast disturbances. If the signal filter becomes the largest time constant, the PID is no longer seeing the response of the actual process variable and an illusion of better control may occur leading to further detrimental increases in the filter time.

The increase in loop dead time from an increase in the PID execution time or signal filter time will show up as an increase in the ultimate period. If the signal filter time is large enough to be considered the secondary time constant the effect is even greater for integrating and runaway processes as revealed by the equations for the ultimate period in Chapter 4. Whereas the rate time can be set equal to the secondary time constant to compensate the detrimental effect, the best practice is not to create the secondary time constant in the first place by avoiding an excessive signal filter.

The pattern of a PID's response to a disturbance or a setpoint change can be used to diagnose what tuning setting is too large or small causing an unbalance in the contribution of the proportional, integral, and derivative modes. Rules of thumb are developed to point to the setting and direction of change needed.

The rules can be automated. Since the integral setting is the most frequent culprit, smart reset action logic is outlined to take advantage of pattern recognition. The user can choose to only allow the logic to increase the reset time, which is the most common correction needed and always leads to greater stability.

Equations can also be developed to detail the calculations needed for saturated PID outputs to get the output off of the output limit at the best time to minimize rise time but prevent overshoot. A deadband can be increased to provide more protection against overshoot.

Recommendations

•1.      The PID execution time should be large enough to minimize resolution or threshold sensitivity errors in slow loops.

•2.      The PID execution time should be small enough not to appreciably increase the peak or integrated error.

•3.      Use the equation for the integrated error to determine if the PID execution time and signal filter time are too large.

•4.      Estimate the increase in peak error as the PID execution time or filter time multiplied by the maximum rate of change of the process variable.

•5.      Minimize the use of signal filters particularly on processes with a fast integrating response (e.g. gas pressure) or a runaway response (exothermic reactor).

•6.      If the filter time becomes the largest time constant in the loop, use chapter 6 equation to compute actual process variable amplitude from measured amplitude.

•7.      For wireless devices, set the transmitter damping setting to keep measurement noise less than the trigger level to prolong battery life.  

•8.      Set the signal filter just large enough so fluctuations in the controller output from noise do not cause a change in valve position or prime mover speed.

•9.      Use the pattern recognition techniques to determine if one of the PID settings is considerably out of balance with the other tuning settings.

•10.  If the output is saturated, determine if the reset time is too small or large causing the output to come off of the output limit too late or soon, respectively.

The execution time must be less than ½ the oscillation period to prevent aliasing. Making sure the execution time is significantly less than the reset time and total loop dead time, is generally a more stringent requirement on the maximum execution time.

For more details see the Control Talk Blogs "What is the best Transmitter Damping and Signal Filter Setting" and "What is the Best PID Execution Time"

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