In applying various tuning rules or optimization methods for optimizing P, I and D gain parameters for PID control systems, one must usually estimate the system gain, the dead time, and the time constant. Graphical methods for estimating them from a step input response curve are most popular.
However, it’s possible to estimate a negative dead time. Of course, the underlying concept of a negative dead time isn’t reasonable, but in a time constant dominated system the dead time can be neglible, and various subtleties can lead to the estimate for the dead time becoming negative, or for example having zero within the likely error.
Often the tuning rules will create negative values for some of the P, I, D values. Maybe this is nutty. Or, who knows, maybe some of these are sensible, at least for systems whose driving output isn’t clamped. The overall trend should produce negative feedback (ie positive parameters), but that doesn’t mean all the terms would always necessarily be negative feedback or positive sign.
What’s the Straight Dope on signs in estimating dead time and the control parameters?