Question #10 - What is the advantage of derivative on
process rather than on error?
January 16, 2004
Question:
Some controllers offer the option of derivative on the error or on the input only. What is the difference and why should I use one or the other?
Answer:
The traditional PID equation, in its simplest form, is:
Error = Set point - Input
In this equation the derivative applies to the error. The problem is that a change in set point is treated the same as a change in the process measurement. However, it is likely that the operator will make a set change in the set point. This is particularly likely with digital control systems when the operator types in a new set point and hits enter. Suddenly there is a step change in set point and error.
The derivative of a step change is a spike that goes to infinity. The controller can’t take the output to infinity, but it will drive the output to its limit momentarily, likely causing an upset in the rest of the process. To eliminate this problem, many controllers offer the option of derivative on input rather than derivative on error. The equation is changed to:
The derivative will apply to changes in process input and to the feedback loop. It will have all the advantages of derivative, including allowing the use of a higher gain with the same stability. However, it will not spike the output when the operator makes a set point change.
There are times that derivative on error is appropriate. If the secondary loop of a cascade pair has derivative (e.g. jacket temperature on reactor temperature control) and the set point is only going to be adjusted by the primary controller, then the step change is not a problem and the derivative on the set point changes can provide an advantage.