Slow oscillations can be difficult to recognize especially when the period is beyond the typical time frame of the trend chart or there are intervening disturbances or recycle. Slow oscillations can be more detrimental to product quality because the large period means the amplitude is less attenuated by intervening volumes.
An oscillation is considered slow if it is greater than twice the ultimate period. The ultimate period can be considered to be about 4 times the total loop dead time. An exception is the severely dead time dominant process where the ultimate period is about twice the dead time. Some sources of slow oscillations and examples of root causes:
(1) Batch Operations (e.g. batch reactor and centrifuge)
(2) Defrosting (e.g. crystallization)
(3) Regeneration (e.g. demineralized water units and catalyst beds)
(4) Ambient conditions (e.g. day - night, sun - shade, rain - snow)
(5) Dead band (e.g. valve backlash)
(6) Resolution limit (e.g. valve stick-slip)
(7) Threshold sensitivity limit (e.g. valve stick-slip)
(8) Split range discontinuity (e.g. heating - cooling)
(9) Low valve gain (flat installed characteristic)
(10) Low PID gain or reset time (e.g. integrating or runaway process)
The oscillations for items (1) through (4) persist when the subject loop is put in manual.
A particularly disruptive batch operation is the centrifuge because the cycle times are much more frequent than many other batch operations, such as batch reactors and crystallizers. Surge tank level controllers that have batch feeds should have the level controller arrest time set to spread the upset over the maximum possible range of level. See slides 125-127 of the ISA-New-Orleans-Effective-Use-of-PID-Controllers for the equations to compute the arrest time. Note that simply decreasing the PID gain will cause the slow rolling oscillations noted in item (10).
The period of oscillation for items (1) through (3) is the time between successive end points of batch operation and start points of defrost and regeneration. The start points of defrost are rather unpredictable if done only when crystal growth excessively limits heat transfer. In any case, the oscillations should be recognizable when included on a trend chart for the subject loop with a suitable time scale. Often the effect of rail or truck shipments is overlooked. If there is no agitator or recirculation stream in the raw material storage tank, concentration differences exists as layers with only a slight degree of mixing by mass transfer from areas of high to low concentration or settling by gravity. The layering makes the upset more discontinuous.
The effects for item (4) can be quite varied. For previous generations of transmitters you could see the effect of weather and day to night in the change in controller output. Most smart transmitters have significantly reduced the effect of ambient temperature changes. Load cells and capillary systems may still be affected by sun and wind. Air compressor suction flow density and moisture will change with temperature and humidity. A rain storm can drastically lower the temperature and vapor flow in the upper part of a column and reflux condenser for a reactor or column. Adding ambient conditions to the trend chart can greatly help in spotting affected components realizing that variability in the measurement is transferred to the PID output.
Items (5), (6), (7), and (8) can cause a limit cycle (equal amplitude oscillation). The amplitude may not appear to be equal due to disturbances, noise, and changes in the backlash and stick-slip with operating point. A sure sign of these items is if the period doubles when the reset time is doubled. The oscillations associated with item (8) will traverse the split range point where the discontinuity is the greatest. The discontinuity and oscillations are larger if there is a change in phase (e.g. water to steam) or if tight shut-off control valves are used (e.g. high seating or sealing friction). Whereas a limit cycle will occur for items (6) through (8) if there is just 1 or more integrator, item (5) requires 2 or more integrators somewhere in the process (e.g. level or batch operation), controller (e.g. PI or PID), or positioner. Integral deadband in the PID or positioner can turn off integral action when the controlled variable within the deadband at setpoint to kill the limit cycle if the deadband is set to be greater than the limit cycle amplitude. External reset feedback with a fast readback of actual valve position can inherently stop the limit cycle with no adjustment required. Similarly, the enhanced PID for wireless will kill a limit cycle if a threshold sensitivity limit screens out unnecessary updates from noise.
Unnecessary excursions across the split range point that create item (8) limit cycles and decrease process efficiency (energy use and/or yield), can be reduced by the addition of a setpoint rate limit in the direction of the split range point. External reset feedback is turned on to make sure the PID has the necessary patience and does not try to out run the set point. Safety factors must be considered. For example, the transition from cooling to heating might be slowed down but not vice versa for an exothermic reactor.
Item (9) causes a wandering of the PID output from a flat characteristic most often associated with rotary valve openings larger than 50 degrees and low valve to system drop pressure ratios causing a running out of valve capacity.
Item (10) may be difficult to detect because the period of oscillation is so great. For large distillation columns, the trend chart needs to cover several shifts of operation to see the period. Feed disturbances make will change the oscillation to the point it is no longer recognizable. The column may appear to be oscillating with no particular pattern. For more information on this common problem see the 04/11/2012 Control Talk Blog "How to Avoid a Common PID Tuning Mistake" The product of the PID gain and reset time should be greater than twice the inverse of the integrating process gain. A generally conservative fix is to simply increase the reset time by one or two orders of magnitude.
To see the oscillations and recognize the period and source, it is important to set the trend chart PV and PID output scale small enough to see small oscillations but large enough to so noise does not hide the pattern. Compression must be removed for small oscillations. See the 07/26/2012 Control Talk Blog "Checklist for Trend Chart Analysis" for more details.
Intelligent filtering and velocity limiting can help screen out noise as discussed in the Control Talk 07/05/2012 Control Talk Blog "What are the Alternatives to Reduce Noise?"
The time scale must be large enough to cover several periods. The oscillations are usually more apparent in the PID output. Loops affected by the culprit loop for items (5) - (10) will show an oscillation of the same period. I was surprised at a talk at ISA Automation Week 2011 by how simply inverting the measurement of the culprit on the same chart as the affected measurement revealed the obvious time correlation.
Culprit loops are typically on the same unit operation or upstream. Recycle and heat integration can result in downstream loops either initiating or aggravating the problem. Regardless, the oscillations should stop when the culprit loop is put in manual. The most frequent source of oscillations is a level loop on a surge tank with too low of a PID gain or reset time. The solution is to compute the arrest time per slides 125-128 as previously mentioned to spread the change in flows into the surge tank over the entire level range.
A power spectrum analyzer can rapidly point you to the culprit by indicating which loops are experiencing significant peaks in the power at the same frequency. The first step is to get the data for loops in automatic into the power spectrum analyzer. The data gathering must be done quickly enough to prevent aliasing. For most chemical processes, it is sufficient to use data from a historian with no compression and an update time of 1 second. For liquid/polymer pressure and surge control and sheets (webs), you may need to store the data using a device with an exceptionally fast scan time (50 milliseconds or less) that is directly connected to the process variable or PID output terminals.
Data storage is so cheap, old rules about compression, and exception and periodic reporting should be going by the way side. Unfortunately, old practices may be hard to undo. It is important to realize that the role of Information Technology (IT) is to meet the needs of the user and not vice versa.
Statistical tools with principal component analysis (PCA) can reveal correlations. These tools are particularly valuable as the number of variables increase. A drill down into the principal components can show what inputs are most correlated with the oscillation observed. Process and automation system knowledge is then used to verify if the input output correlation is a cause and effect or a coincidence or result of output correlations.