Greg, in different articles and books you will normally talk about resolution limits; I am not sure if I totally understand the concept and all it comprehends. What should we understand by such term; how will I identify I am experiencing such? What kind of control issues will I have? How can I solve a resolution limit problem?
Hector, Good question. A resolution limit is the smallest input change that will cause an output change. When the input change exceeds this limit, the output change is an integer multiple of the resolution limit. Thus, the output response is a series of steps with a size that is an integer multiple of the resolution limit . In contrast when a change in input exceeds the threshold sensitivity limit, the change in output equals the change in input. The result is a step size that matches the input change. Resolution limits come from digital devices. However, the ISA standard for valve response testing expresses stick-slip as a resolution limit when really a threshold sensitivity limit is more at play where slip is about equal to the stick.
The 1980s vintage DCS had only 12 bits in the input cards. Since one bit is for sign, there was only 11 bits for resolution. If you divide 100% by 2 to the 11th power, you get a resolution limit of 0.05% which doesn't seem bad until you consider the practice at the time was to use wide range thermocouple input cards rather than transmitters to save on field hardware costs. These cards caused a series of steps of about 0.4 degF that caused such severe bumps in the PID output from rate action that derivative could not be used on reactors where derivative is most needed to compensate for secondary time constants from thermal lags. Today's DCS has 16 bit input and output cards.
The standard signal input card for Variable Speed Drives (VSD) last time I checked (2008) has only 8 bits which if there is one sign bit translates to a resolution of 0.78% which is really lousy when you consider the resolution limit of a sliding stem valve, digital valve controller, and diaphragm actuator is close to 0.1%. Users need to specify a VSD input card with at least 12 bits. Why this is a special card shows the lack of understanding of resolution limits.
When a step change in the PV occurs the derivative mode thinks the entire change occurred in one PID execution. Exothermic liquid reactors have a slow temperature response and use a PID gain greater than 10 and a rate time greater than 120 seconds to prevent a runaway. Since the step from a resolution limit is divided by the PID execution time and multiplied by the product of the PID gain and rate time, a 0.4 degF step can cause a full scale bump in the PID output.
Resolution and threshold sensitivity limits both cause limit cycles if there is any integral action in the process or the controller. The amplitude depends upon the process gain. For pH control on the steep part of a titration curve the process gain is so large, the limit cycle can violate pH limits. Such pH processes are very sensitive to valve resolution and threshold sensitivity limits.
Most sensors and analyzers have a threshold sensitivity limit larger than the resolution limit in todays smart transmitters. The wireless default trigger level is really a threshold sensitivity limit. The default update rate helps prevent a limit cycle if the trigger level is set too large.
The best solution is to use transmitters and valves with the best resolution and threshold sensitivity. Limit cycles and bumps in the PID output from rate action can be eliminated by the use the enhanced PID with external reset feedback.
Greg
Greg is a retired Senior Fellow from Monsanto-Solutia and an ISA Fellow. Greg was inducted into the Control “Process Automation Hall of Fame” in 2001 and received the ISA Life Achievement Award in 2010.