Depends on what you mean by a PID Controller - if you mean a specific device, then probably not, they are not in general able to handle a pulsed feedback, if you are using a current measurement as a feedback element. Thay also do not typically have the frequency response needed. The feedback can be filtered - but then you are typically distorting the signal... However, a PID control scheme - implemented in a uController would work well, if properly designed. The critical design factor will be how fast do you need the control to be?
Although, I won't disagree completely with Wind, depending on the application the answer to your question is yes. PIDs often are aimed at controlling pulsed inputs/outputs. However, I think what you want, if I'm understanding correctly, is a driver. If this is a homework question then please move your post to the approiate discussion venue.
If you are using a FPGA then you are using discrete control. Discrete control systems can use PID type control, but sometimes (at least in the case of a Microchip Pic controlled line following robot buggy) we found that Bang-Bang control was the better option! In terms of knowing the transfer model of the function it can help with the control - and could prove beneficial if you want to do some PID tuning... You might be interested in reading about Kalman Filters & this PID controlled espresso machine is pretty cool! http://www.kickstarter.com/projects/zpmespresso/pid-controlled-espresso-machine