The question arises quite often, “What is the normal or standard form of the PID (proportional-integral-derivative) algorithm?” The answer is both simple and complex. Before we explore the answer, consider the screen displays shown below (click for a large view of example 1 or example 2):
A controller seeks to maintain the measured process variable (PV) at set point (SP) in spite of unplanned and unmeasured disturbances. Since e(t) = SP — PV, this is equivalent to saying that a controller seeks to maintain controller error, e(t), equal to zero.
Processes with streams comprised of gases, liquids, powders, slurries and melts tend to exhibit variations in behavior as operating level changes. This, in fact, is the very nature of a nonlinear process. For this reason, our recipe for controller design and tuning begins by specifying our design level of operation.