This is an open loop PID autotuner using a novel s-curve inflection point test method. Tuning parameters are typically determined in about ½Tau on a first-order system with time delay. Full 5Tau testing and multiple serial output options are provided.

Well, looking at just the small tangent line, the first derivative is the slope. As the tangent moves along the curve, at first the slope keeps increasing. Then, at some point, the slope begins to decrease. This is the point of inflection (POI).

In order to detect this point, we just keep taking the second derivative and are interested only in when the sign changes from positive to negative.

If this were a cooling process, the graph would be flipped (top to bottom). In this case, the POI would be when the sign of the second derivative changes from negative to positive.

The test completes at the POI. From here, there is enough information to calculate remaining results, rather than waiting to take measurements. The test duration is about an order of magnitude less than testing to pvMax.