How to interpret negative D term from PID tuner?

Question

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Hello:

I have been using the Simulink PID tuner to tune a controller (both continuous time and discrete time) and I noticed that the D term ends up being negative. The plant that is being controlled is a linear system and it is 3rd order (servo motor for a hard disk read/write head).

From my understanding the purpose of the derivative action in PID is to predict the error of the control system ahead by time Td (Td should be proportional to the D term in the PID tuner), which improves the stability of the control system. Therefore I was wondering how would you go about and interpret how a negative Td predicts the error? Any help is always much appreciated.

Thanks!