I am having trouble imaging a PID controller without a feedback loop. The reason is that P, I and D controllers each calculate their response based on the error between the target and the current state. If there is no feedback to provide the current state, then I can't imagine how they would work in principle.
UPDATE: After reading Abel's post, I realized (because I had to do some development of PID controllers) that in the early development stage of a controller, where you need to have a first feel of the behavior of the controller the most basic technique is to inject an artificial signal (e.g. a step function in the system). This is considered open loop (because there are no feedback from the output).
However, in the later stages of the development where you need to actually test the controller with simulations in a real environment, there are the following two options:
Software in the loop (SIL) where the entire plant and the interaction between the controller and the plant is software (in Simulink)
Hardware in the loop (HIL) where you can actually connect a Real time Matlab/Simulink PC to the plant and monitor/adjust the controller
Figure: Difference between SIL and HIL. Source: The CDIO model in architectural education and research by design
In both those cases, although you might not actually have feedback loop on both of them, there is still a loop connecting the plant's output to the input of the controller.