Modeling and Control

Oscillations are indicative of a controller that is tuned too fast unless the oscillations are very slow or are limit cycles caused by valve stick-slip for any type of process or valve dead band for an integrating process (e.g. level). The amplitude of fast oscillations that are not limit cycles can be reduced by decreasing the controller gain. Oscillations in the process variable may upset other loops and show up as off spec product if there are insufficient blend volumes downstream. Oscillations in the controller output may cause similar problems by affecting other process variables. Also, such oscillations make it more difficult to see patterns in process behavior either visually or by data analytics. Loops with a dead time approaching or exceeding the process time are often tuned too fast.

The integrated error for a given unmeasured disturbance is inversely proportional to the controller gain. If you double the controller gain, you halve the integrated error. However, you need to keep the controller gain below a maximum that prevents oscillations from adverse changes in the process dynamics. The maximum controller gain corresponds to Lambda equal to the loop dead time (lambda factor equal to the dead time to time constant ratio).

The dead time from valve stick-slip or valve dead band is also inversely proportional to the controller gain so if you double the controller gain, you can halve the valve dead time, which further reduces the integrated error.

The improvement is only observable when there is a disturbance. Also, if the disturbance is very slow, small, or infrequent the integrated error from upsets may be negligible. For these cases, an increase in the controller gain has little effect on the standard deviation.

However, when there are a lot of upsets or set point changes, the increase in controller gain is important. A much smaller than possible controller gain is similar to additional dead time. For example, a lambda factor of one is equivalent to a dead time that is half of the process time constant. Stated another way, if the controller is tuned too slow, reducing the loop dead time by a faster valve, process, or measurement will not show a reduction in error. Nearly all studies on improvements in process dynamics retune the controller for a faster response to show the benefits.

Tools are now available to identify the process dynamics and calculate tuning settings. The tools can indicate a relative speed (faster or slower) of the new tuning versus the old tuning. However, the new tuning settings depend upon the lambda factor or the desired speed chosen. Thus it is still up to the user or consultant to decide whether the loop should be faster or slower.

For me, the period and amplitude of the oscillations provide a clue. Oscillations with a period much less than natural period of the loop are effectively uncontrollable noise. Oscillations with a period in the neighborhood of the natural period of the loop will get amplified by control action. In either case, the loop needs to be slowed down and the source of the oscillations tracked down and reduced. The natural period for a single time constant plus dead time (first order plus dead time) approximation of a self-regulating process varies from about 2 to 4 times the dead time.

Limit cycles (constant amplitude oscillations) are generally indicative of valve problems. A slower tuning will make the oscillations slower. This may be good or bad. If the oscillations are upsetting other loops, you probably want to slow them down. If the oscillations are being attenuated out by a downstream volume, it might be better to make the oscillations faster to get more effective filtering action by the volume and reduce the dead time from the valve stick-slip and dead band by a higher controller gain.

If the oscillations are not limit cycles and are much slower than the loop, the source could be a slow oscillating disturbance upstream, in which case it is better to speed up the loop.

If the loop’s response is never really oscillatory (e.g. a predominant period 100 times larger than the natural period), then the loop should be speeded up for set point changes and those occasional upsets as long as big abrupt changes in the control valve don’t upset other loops. For reactors, columns, and large mixed volumes, big steps in the controller output disturb the operator more than the process.

A power spectrum analysis can show the frequencies (periods) with the greatest power.

So you can still see the forest and not just the trees while deep in the woods, there are a couple of concepts to remember. First, there is tradeoff between reducing fluctuations in the controlled variable (e.g. composition, level, temperature, and pressure) and increasing the fluctuations in the manipulated variable (e.g. flow) of a loop. A controller tuned for a faster response, transfers more variability from the controlled variable to the manipulated variable whose movement can upset other loops. Second, there a tradeoff between tuning speed (aggressiveness) and robustness (stability). A controller tuned for a smooth but faster response, will develop oscillations for a smaller increase in process dead time or process gain. Tuning is overly conservative because faster tuning presents a greater risk for oscillations in this loop and other loops. A loop that behaved badly is remembered more than a hundred loops that became more responsive from a change in tuning. A good loop performance monitoring and tuning tool is essential for evaluation and confidence.

If the amplitude of the oscillations and the standard deviation are small, who cares?

Who is living with the process every minute? Who changes the feed rates or charges? Who changes the modes and set points of the control system? Who starts or stops batches or unit operations? In most plants, it is the operator, yet the displays and education of the operator haven’t changed much in the last 20 years. We still have faceplates, trend charts, and digital values of process variables, and changing or flashing colors or shades. We still have minimal operator training based more on tiebacks and interface familiarization than on first principles and process understanding.

If the operator knew the yield and cost per pound of product for the last eight hours of each shift, the operator could be more recognizant and probably more competitive. This could be achieved by flows that are synchronized, shift totalized, and ratioed with dollar amounts assigned for each flow. Consider a reactor and an 8 hour shift. Here the total flow of each reactant and utility for the last 8 hours would be ratioed to the total product flow for the last 8 hours for each shift. Each flow total would be multiplied by the cost of the stream ($/lb) to provide cost to product ratios for the last eight hours. The reactant and utility flows could be delayed to match them up time wise with the product flow. The use of totals for the last 8 hours reduces the accuracy requirement of this synchronization besides decreasing noise. The use of ratios decreases the effect of production rate on metrics. Also, changes in ratios offer keys to tracking down disturbances and changes in concentrations of feeds (e.g. raw materials, intermediate, or recycle streams). Both totals and ratios for each shift could be indicated. Shift metrics could be treated similar to batch metrics where each shift is like a different piece of equipment running the same batch process. The shift metrics could be plotted similar to batch metrics.

For waste pH systems, it would simply be the total reagent flow ratioed to the total effluent flow ratio for the last eight hours. I developed a real time virtual plant in DeltaV using this concept a couple of years ago to show the value of adaptive controller tuning for pH control. If you want a copy, contact your rep.

The concept could be expanded to use totals to cover the last week or month or the last "n" number of batches for each shift and all shifts.

If the operator could plot these ratios versus changes in operating points, what insight could be gained on process nonlinearity and for process optimization? What if the operator had XY plots, worm plots, and 3-D plots built into the operator graphics for all historized variables like what engineers generate in Excel and statistical packages?

When comparing the performance of similar plants in the USA and Belgium, it was found that the Belgium plants had consistently better yields. The Belgium operators lead the design of experiments and guided the process improvements. Could better online performance metrics and process training be the key for operators to perform roles of the increasingly scarce process and process control engineers?