Question #11 - What is the difference between parallel and
series derivative?
January 23, 2004
Question:
What is the difference between series and parallel algorithms? I have also heard the this is the same choice as interacting and non-interacting.
Answer:
The terms interacting and non-interacting have several meanings. These include the interaction of gain with the other parameters and the interaction between the integral and derivative terms. Therefore I will use the terms series or parallel to discuss the relationship between the integral and derivative terms.
To repeat the beginning of last week’s Q&A, the traditional PID equation, in its simplest form, is:
Error = Set point - Input
A block diagram of this algorithm is:
The actual implementation of the PID algorithm in many industrial controllers takes the derivative of the error or input (see last week’s Q&A) and adds the derivative and error, and then integrates the sum, as shown in the following diagram:
Because error and the derivative of the error are integrated, the output changes faster than if only the error was integrated, the tuning parameters are different. For the series algorithm, the equation becomes:
R is reset rate, D is minutes. Typically, for PID controllers tuned with most common tuning methods, the product of R and D is 0.25
There is no actual advantage of the series implementation over the parallel implementation other than consistency with previous controllers. For the 80 to 90% of the PID loops that do not use derivative, there is no difference. For those that do use derivative, the series implementation requires a reduction of the gain and an increase in the reset rate and derivative by approximate 25% under typical tuning conditions.