Using your in-tune-ition

One of the reasons PID compensators are so popular is that it is easy to conceive of how each term contributes to the overall output. The D (derivative) term introduces resistance or drag, the P (proportional) term introduces a linear restoring force, and the I (integral) introduces a time-dependent windup term.

The first manual tuning method that we will discuss works directly in conjunction with this “intuitive” notion of the PID loop. Referred to as the step-response method, it measures the response of the servo system to an instantaneous (within one servo cycle) change in position. To make this method work, or for that matter any manual tuning method, we need an accurate performance trace facility to display the results of our moves. See INSET for more information. For step-response tuning we need to display desired position, actual position, and position error (the difference between these two).

Equations - form PID

Here is the basic approach used with step-response tuning: Initialize the I term to zero, and set the D term to a small nonzero value. Increase P from zero until the system substantially overshoots. Then increase D until the oscillation is “critically damped.” Figures 2A, 2B, and 2C show approximate traces of underdamped, overdamped, and critically damped step responses. Continue this process until you find values that have a high P while still being critically damped.

Although very easy to use, this method has the problem that increasing D will cause the optimum value of P to change, which in turn changes the optimum value of D, etc. This requires a number of iterations to get to stable values. In general terms this is because the D term of a PID operates at the highest frequency zone, the P term at a middle point, and the I term at the lowest frequency zone. What would be better is if we could first tune the highest frequency component, then move to the middlerange value, and finish with the low frequency part.